Daily Papers

Autoregressive Language Models (LLMs) trained on Next-Token Prediction (NTP) often suffer from ``Topic Drift'' where the generation wanders away from the initial prompt due to a reliance on local associations rather than global planning holtzman2019curious. While scaling model size mitigates this brown2020language, the fundamental myopia of the NTP objective remains. In this work, we introduce the Idea-Gated Transformer, a novel architecture that separates semantic planning from syntactic generation. We introduce an auxiliary ``Idea Head'' trained to predict the bag-of-words distribution for a future context window, creating a latent ``Concept Vector'' that actively gates the main vocabulary during generation. We propose a differentiable gating mechanism that suppresses semantically irrelevant tokens, effectively pruning the search space in real-time. Experiments on WikiText-103 demonstrate that while the Idea-Gated model achieves comparable validation perplexity to a standard GPT-2 baseline, it exhibits significantly superior Domain Retention. Qualitative and quantitative analysis reveals that the gating mechanism successfully locks generation into specific semantic clusters (e.g., Finance, Science) and resists associative drift, offering a parameter-efficient path toward more controllable language modeling.

Clustering is a widely used unsupervised learning technique involving an intensive discrete optimization problem. Associative Memory models or AMs are differentiable neural networks defining a recursive dynamical system, which have been integrated with various deep learning architectures. We uncover a novel connection between the AM dynamics and the inherent discrete assignment necessary in clustering to propose a novel unconstrained continuous relaxation of the discrete clustering problem, enabling end-to-end differentiable clustering with AM, dubbed ClAM. Leveraging the pattern completion ability of AMs, we further develop a novel self-supervised clustering loss. Our evaluations on varied datasets demonstrate that ClAM benefits from the self-supervision, and significantly improves upon both the traditional Lloyd's k-means algorithm, and more recent continuous clustering relaxations (by upto 60% in terms of the Silhouette Coefficient).

The brain is a noisy system subject to energy constraints. These facts are rarely taken into account when modelling artificial neural networks. In this paper, we are interested in demonstrating that those factors can actually lead to the appearance of robust associative memories. We first propose a simplified model of noise in the brain, taking into account synaptic noise and interference from neurons external to the network. When coarsely quantized, we show that this noise can be reduced to insertions and erasures. We take a neural network with recurrent modifiable connections, and subject it to noisy external inputs. We introduce an energy usage limitation principle in the network as well as consolidated Hebbian learning, resulting in an incremental processing of inputs. We show that the connections naturally formed correspond to state-of-the-art binary sparse associative memories.

Learning arguably involves the discovery and memorization of abstract rules. The aim of this paper is to study associative memory mechanisms. Our model is based on high-dimensional matrices consisting of outer products of embeddings, which relates to the inner layers of transformer language models. We derive precise scaling laws with respect to sample size and parameter size, and discuss the statistical efficiency of different estimators, including optimization-based algorithms. We provide extensive numerical experiments to validate and interpret theoretical results, including fine-grained visualizations of the stored memory associations.

Multimodal large language models (MLLMs) face an inherent trade-off between faithfulness and creativity, as different tasks require varying degrees of associative reasoning. However, existing methods lack the flexibility to modulate this reasoning strength, limiting MLLMs' adaptability across factual and creative scenarios. To bridge this gap, we propose equipping MLLMs with mechanisms that enable flexible control over associative reasoning. We begin by investigating the internal mechanisms underlying associative behavior in MLLMs and find that: (1) middle layers play a pivotal role in shaping model's associative tendencies, (2) modifying representations in these layers effectively regulates associative reasoning strength, and (3) hallucinations can be exploited to derive steering vectors that guide this modulation. Building on these findings, we introduce Flexible Association Control (FlexAC), a lightweight and training-free framework for modulating associative behavior in MLLMs. FlexAC first induces hallucination-guided intermediate representations to encode associative directions. Then, it selects high-association instances to construct effective associative steering vectors, whose strengths are adaptively calibrated to balance creative guidance with output stability. Finally, recognizing the multi-dimensional nature of associative reasoning, FlexAC incorporates task-specific associative vectors derived from a forward pass on a few target-domain samples, enabling models to follow diverse associative directions and better adapt to creative tasks. Notably, our method achieves up to a 5.8x improvement in creativity on Creation-MMBench and a 29% reduction in hallucination rate on CHAIR, surpassing existing baselines and demonstrating its effectiveness in enabling flexible control over associative reasoning in MLLMs. Our code is available at https://github.com/ylhz/FlexAC.

Transformer architectures have revolutionized artificial intelligence (AI) through their attention mechanisms, yet the computational principles underlying their success remain opaque. We present a novel theoretical framework that reinterprets the core computation of attention as Pavlovian conditioning. Our model finds a direct mathematical analogue in linear attention, which simplifies the analysis of the underlying associative process. We demonstrate that attention's queries, keys, and values can be mapped to the three elements of classical conditioning: test stimuli that probe associations, conditional stimuli (CS) that serve as retrieval cues, and unconditional stimuli (US) that contain response information. Through this lens, we suggest that each attention operation constructs a transient associative memory via a Hebbian rule, where CS-US pairs form dynamic associations that test stimuli can later retrieve. Our framework yields several theoretical insights grounded in this linearized model: (1) a capacity theorem showing that attention heads can store O(d_k) associations before interference degrades retrieval; (2) an error propagation analysis revealing fundamental architectural trade-offs of balancing model depth, width, and head redundancy to maintain reliability; and (3) an understanding of how biologically plausible learning rules could enhance transformer architectures. By establishing this deep connection, we suggest that the success of modern AI may stem not from architectural novelty alone, but from implementing computational principles that biology optimized over millions of years of evolution.

We consider dense, associative neural-networks trained with no supervision and we investigate their computational capabilities analytically, via a statistical-mechanics approach, and numerically, via Monte Carlo simulations. In particular, we obtain a phase diagram summarizing their performance as a function of the control parameters such as the quality and quantity of the training dataset and the network storage, valid in the limit of large network size and structureless datasets. Moreover, we establish a bridge between macroscopic observables standardly used in statistical mechanics and loss functions typically used in the machine learning. As technical remarks, from the analytic side, we implement large deviations and stability analysis within Guerra's interpolation to tackle the not-Gaussian distributions involved in the post-synaptic potentials while, from the computational counterpart, we insert Plefka approximation in the Monte Carlo scheme, to speed up the evaluation of the synaptic tensors, overall obtaining a novel and broad approach to investigate neural networks in general.

The Muon optimizer is consistently faster than Adam in training Large Language Models (LLMs), yet the mechanism underlying its success remains unclear. This paper demystifies this mechanism through the lens of associative memory. By ablating the transformer components optimized by Muon, we reveal that the associative memory parameters of LLMs, namely the Value and Output (VO) attention weights and Feed-Forward Networks (FFNs), are the primary contributors to Muon's superiority. Motivated by this associative memory view, we then explain Muon's superiority on real-world corpora, which are intrinsically heavy-tailed: a few classes (tail classes) appear far less frequently than others. The superiority is explained through two key properties: (i) its update rule consistently yields a more isotropic singular spectrum than Adam; and as a result, (ii) on heavy-tailed data, it optimizes tail classes more effectively than Adam. Beyond empirical evidence, we theoretically confirm these findings by analyzing a one-layer associative memory model under class-imbalanced data. We prove that Muon consistently achieves balanced learning across classes regardless of feature embeddings, whereas Adam can induce large disparities in learning errors depending on embedding properties. In summary, our empirical observations and theoretical analyses reveal Muon's core advantage: its update rule aligns with the outer-product structure of linear associative memories, enabling more balanced and effective learning of tail classes in heavy-tailed distributions than Adam.

Large Language Models (LLMs) excel at single-turn tasks such as instruction following and summarization, yet real-world deployments require sustained multi-turn interactions where user goals and conversational context persist and evolve. A recurring challenge in this setting is context drift: the gradual divergence of a model's outputs from goal-consistent behavior across turns. Unlike single-turn errors, drift unfolds temporally and is poorly captured by static evaluation metrics. In this work, we present a study of context drift in multi-turn interactions and propose a simple dynamical framework to interpret its behavior. We formalize drift as the turn-wise KL divergence between the token-level predictive distributions of the test model and a goal-consistent reference model, and propose a recurrence model that interprets its evolution as a bounded stochastic process with restoring forces and controllable interventions. We instantiate this framework in both synthetic long-horizon rewriting tasks and realistic user-agent simulations such as in tau-Bench, measuring drift for several open-weight LLMs that are used as user simulators. Our experiments consistently reveal stable, noise-limited equilibria rather than runaway degradation, and demonstrate that simple reminder interventions reliably reduce divergence in line with theoretical predictions. Together, these results suggest that multi-turn drift can be understood as a controllable equilibrium phenomenon rather than as inevitable decay, providing a foundation for studying and mitigating context drift in extended interactions.

A modern challenge of Artificial Intelligence is learning multiple patterns at once (i.e.parallel learning). While this can not be accomplished by standard Hebbian associative neural networks, in this paper we show how the Multitasking Hebbian Network (a variation on theme of the Hopfield model working on sparse data-sets) is naturally able to perform this complex task. We focus on systems processing in parallel a finite (up to logarithmic growth in the size of the network) amount of patterns, mirroring the low-storage level of standard associative neural networks at work with pattern recognition. For mild dilution in the patterns, the network handles them hierarchically, distributing the amplitudes of their signals as power-laws w.r.t. their information content (hierarchical regime), while, for strong dilution, all the signals pertaining to all the patterns are raised with the same strength (parallel regime). Further, confined to the low-storage setting (i.e., far from the spin glass limit), the presence of a teacher neither alters the multitasking performances nor changes the thresholds for learning: the latter are the same whatever the training protocol is supervised or unsupervised. Results obtained through statistical mechanics, signal-to-noise technique and Monte Carlo simulations are overall in perfect agreement and carry interesting insights on multiple learning at once: for instance, whenever the cost-function of the model is minimized in parallel on several patterns (in its description via Statistical Mechanics), the same happens to the standard sum-squared error Loss function (typically used in Machine Learning).

We introduce an Outlier-Efficient Modern Hopfield Model (termed OutEffHop) and use it to address the outlier-induced challenge of quantizing gigantic transformer-based models. Our main contribution is a novel associative memory model facilitating outlier-efficient associative memory retrievals. Interestingly, this memory model manifests a model-based interpretation of an outlier-efficient attention mechanism (Softmax_1): it is an approximation of the memory retrieval process of OutEffHop. Methodologically, this allows us to debut novel outlier-efficient Hopfield layers a powerful attention alternative with superior post-quantization performance. Theoretically, the Outlier-Efficient Modern Hopfield Model retains and improves the desirable properties of the standard modern Hopfield models, including fixed point convergence and exponential storage capacity. Empirically, we demonstrate the proposed model's efficacy across large-scale transformer-based and Hopfield-based models (including BERT, OPT, ViT and STanHop-Net), benchmarking against state-of-the-art methods including Clipped_Softmax and Gated_Attention. Notably, OutEffHop achieves on average sim22+\% reductions in both average kurtosis and maximum infinity norm of model outputs accross 4 models.

When individuals encounter observations that violate their expectations, when will they adjust their expectations and when will they maintain them despite these observations? For example, when individuals expect objects of type A to be smaller than objects B, but observe the opposite, when will they adjust their expectation about the relationship between the two objects (to A being larger than B)? Naively, one would predict that the larger the violation, the greater the adaptation. However, experiments reveal that when violations are extreme, individuals are more likely to hold on to their prior expectations rather than adjust them. To address this puzzle, we tested the adaptation of artificial neural networks (ANNs) capable of relational learning and found a similar phenomenon: Standard learning dynamics dictates that small violations would lead to adjustments of expected relations while larger ones would be resolved using a different mechanism -- a change in object representation that bypasses the need for adaptation of the relational expectations. These results suggest that the experimentally-observed stability of prior expectations when facing large expectation violations is a natural consequence of learning dynamics and does not require any additional mechanisms. We conclude by discussing the effect of intermediate adaptation steps on this stability.

The change in data distribution over time, also known as concept drift, poses a significant challenge to the reliability of online learning methods. Existing methods typically require model retraining or drift detection, both of which demand high computational costs and are often unsuitable for real-time applications. To address these limitations, a lightweight, fast and efficient random vector functional-link network termed Lite-RVFL is proposed, capable of adapting to concept drift without drift detection and retraining. Lite-RVFL introduces a novel objective function that assigns weights exponentially increasing to new samples, thereby emphasizing recent data and enabling timely adaptation. Theoretical analysis confirms the feasibility of this objective function for drift adaptation, and an efficient incremental update rule is derived. Experimental results on a real-world safety assessment task validate the efficiency, effectiveness in adapting to drift, and potential to capture temporal patterns of Lite-RVFL. The source code is available at https://github.com/songqiaohu/Lite-RVFL.

Data Drift is the phenomenon where the generating model behind the data changes over time. Due to data drift, any model built on the past training data becomes less relevant and inaccurate over time. Thus, detecting and controlling for data drift is critical in machine learning models. Hierarchical Temporal Memory (HTM) is a machine learning model developed by Jeff Hawkins, inspired by how the human brain processes information. It is a biologically inspired model of memory that is similar in structure to the neocortex, and whose performance is claimed to be comparable to state of the art models in detecting anomalies in time series data. Another unique benefit of HTMs is its independence from training and testing cycle; all the learning takes place online with streaming data and no separate training and testing cycle is required. In sequential learning paradigm, Sequential Probability Ratio Test (SPRT) offers some unique benefit for online learning and inference. This paper proposes a novel hybrid framework combining HTM and SPRT for real-time data drift detection and anomaly identification. Unlike existing data drift methods, our approach eliminates frequent retraining and ensures low false positive rates. HTMs currently work with one dimensional or univariate data. In a second study, we also propose an application of HTM in multidimensional supervised scenario for anomaly detection by combining the outputs of multiple HTM columns, one for each dimension of the data, through a neural network. Experimental evaluations demonstrate that the proposed method outperforms conventional drift detection techniques like the Kolmogorov-Smirnov (KS) test, Wasserstein distance, and Population Stability Index (PSI) in terms of accuracy, adaptability, and computational efficiency. Our experiments also provide insights into optimizing hyperparameters for real-time deployment in domains such as Telecom.

In this paper, we share our reflections and insights on understanding Transformer architectures through the lens of associative memory--a classic psychological concept inspired by human cognition. We start with the basics of associative memory (think simple linear attention) and then dive into two dimensions: Memory Capacity: How much can a Transformer really remember, and how well? We introduce retrieval SNR to measure this and use a kernel perspective to mathematically reveal why Softmax Attention is so effective. We also show how FFNs can be seen as a type of associative memory, leading to insights on their design and potential improvements. Memory Update: How do these memories learn and evolve? We present a unified framework for understanding how different Transformer variants (like DeltaNet and Softmax Attention) update their "knowledge base". This leads us to tackle two provocative questions: 1. Are Transformers fundamentally limited in what they can express, and can we break these barriers? 2. If a Transformer had infinite context, would it become infinitely intelligent? We want to demystify Transformer architecture, offering a clearer understanding of existing designs. This exploration aims to provide fresh insights and spark new avenues for Transformer innovation.

We consider dense, associative neural-networks trained by a teacher (i.e., with supervision) and we investigate their computational capabilities analytically, via statistical-mechanics of spin glasses, and numerically, via Monte Carlo simulations. In particular, we obtain a phase diagram summarizing their performance as a function of the control parameters such as quality and quantity of the training dataset, network storage and noise, that is valid in the limit of large network size and structureless datasets: these networks may work in a ultra-storage regime (where they can handle a huge amount of patterns, if compared with shallow neural networks) or in a ultra-detection regime (where they can perform pattern recognition at prohibitive signal-to-noise ratios, if compared with shallow neural networks). Guided by the random theory as a reference framework, we also test numerically learning, storing and retrieval capabilities shown by these networks on structured datasets as MNist and Fashion MNist. As technical remarks, from the analytic side, we implement large deviations and stability analysis within Guerra's interpolation to tackle the not-Gaussian distributions involved in the post-synaptic potentials while, from the computational counterpart, we insert Plefka approximation in the Monte Carlo scheme, to speed up the evaluation of the synaptic tensors, overall obtaining a novel and broad approach to investigate supervised learning in neural networks, beyond the shallow limit, in general.

The static synaptic connectivity of neuronal circuits stands in direct contrast to the dynamics of their function. As in changing community interactions, different neurons can participate actively in various combinations to effect behaviors at different times. We introduce an unsupervised approach to learn the dynamic affinities between neurons in live, behaving animals, and to reveal which communities form among neurons at different times. The inference occurs in two major steps. First, pairwise non-linear affinities between neuronal traces from brain-wide calcium activity are organized by non-negative tensor factorization (NTF). Each factor specifies which groups of neurons are most likely interacting for an inferred interval in time, and for which animals. Finally, a generative model that allows for weighted community detection is applied to the functional motifs produced by NTF to reveal a dynamic functional connectome. Since time codes the different experimental variables (e.g., application of chemical stimuli), this provides an atlas of neural motifs active during separate stages of an experiment (e.g., stimulus application or spontaneous behaviors). Results from our analysis are experimentally validated, confirming that our method is able to robustly predict causal interactions between neurons to generate behavior. Code is available at https://github.com/dyballa/dynamic-connectomes.

Neural networks often exhibit emergent behavior, where qualitatively new capabilities arise from scaling up the amount of parameters, training data, or training steps. One approach to understanding emergence is to find continuous progress measures that underlie the seemingly discontinuous qualitative changes. We argue that progress measures can be found via mechanistic interpretability: reverse-engineering learned behaviors into their individual components. As a case study, we investigate the recently-discovered phenomenon of ``grokking'' exhibited by small transformers trained on modular addition tasks. We fully reverse engineer the algorithm learned by these networks, which uses discrete Fourier transforms and trigonometric identities to convert addition to rotation about a circle. We confirm the algorithm by analyzing the activations and weights and by performing ablations in Fourier space. Based on this understanding, we define progress measures that allow us to study the dynamics of training and split training into three continuous phases: memorization, circuit formation, and cleanup. Our results show that grokking, rather than being a sudden shift, arises from the gradual amplification of structured mechanisms encoded in the weights, followed by the later removal of memorizing components.

Three key properties that are desired of trustworthy machine learning models deployed in high-stakes environments are fairness, explainability, and an ability to account for various kinds of "drift". While drifts in model accuracy, for example due to covariate shift, have been widely investigated, drifts in fairness metrics over time remain largely unexplored. In this paper, we propose FEAMOE, a novel "mixture-of-experts" inspired framework aimed at learning fairer, more explainable/interpretable models that can also rapidly adjust to drifts in both the accuracy and the fairness of a classifier. We illustrate our framework for three popular fairness measures and demonstrate how drift can be handled with respect to these fairness constraints. Experiments on multiple datasets show that our framework as applied to a mixture of linear experts is able to perform comparably to neural networks in terms of accuracy while producing fairer models. We then use the large-scale HMDA dataset and show that while various models trained on HMDA demonstrate drift with respect to both accuracy and fairness, FEAMOE can ably handle these drifts with respect to all the considered fairness measures and maintain model accuracy as well. We also prove that the proposed framework allows for producing fast Shapley value explanations, which makes computationally efficient feature attribution based explanations of model decisions readily available via FEAMOE.

A hallmark of intelligence is the ability to autonomously learn new flexible, cognitive behaviors - that is, behaviors where the appropriate action depends not just on immediate stimuli (as in simple reflexive stimulus-response associations), but on contextual information that must be adequately acquired, stored and processed. While many meta-learning algorithms can design agents that autonomously learn new tasks, cognitive tasks adds another level of learning and memory to typical ``learning-to-learn'' problems. Here we evolve neural networks, endowed with plastic connections and neuromodulation, over a sizable set of simple cognitive tasks adapted from a computational neuroscience framework. The resulting evolved networks can automatically modify their own connectivity to acquire a novel simple cognitive task, never seen during evolution, from stimuli and rewards alone, through the spontaneous operation of their evolved neural organization and plasticity system. Our results emphasize the importance of carefully considering the multiple learning loops involved in the emergence of intelligent behavior.

Real-world large language model deployments (e.g., conversational AI systems, code generation assistants) naturally generate abundant implicit user dissatisfaction (DSAT) signals, as users iterate toward better answers through refinements, corrections, and expressed preferences, while explicit satisfaction (SAT) feedback is scarce. Existing preference learning approaches are poorly aligned with this data profile, as they rely on costly human annotations or assume plentiful positive responses. In this paper, we introduce DRIFT (Dissatisfaction-Refined Iterative preFerence Training), which anchors training on real-world DSAT signals and samples positives dynamically from the evolving policy. Empirically, DRIFT models trained on real-world WildFeedback datasets and synthetic UltraFeedback datasets achieve up to +6.23\% (7B) / +7.61\% (14B) on WildBench Task Score and up to +8.95\% (7B) / +12.29\% (14B) on AlpacaEval2 win rate over base models, outperforming strong baseline methods such as iterative DPO and SPIN. At larger scales, the improvements are particularly pronounced: 14B models trained with DRIFT surpass GPT-4o-mini on WildBench. Further analysis shows that DRIFT also preserves exploratory capacity, yielding more diverse high-reward solutions rather than collapsing to narrow subsets. Theoretically, we demonstrate that this design preserves preference margins and avoids the gradient degeneration. These results show that DRIFT is an effective and scalable recipe for real-world post-training that leverages the most abundant and informative signal. The code and data are available at https://github.com/cacayaya/DRIFT.git.

How can we teach large multimodal models (LMMs) new skills without erasing prior abilities? We study sequential fine-tuning on five target skills while monitoring general ability on eight held-out benchmarks across three model families. We observe that apparent "forgetting" on held-out tasks after narrow fine-tuning can partly recover at later stages. We trace this behavior to a measurable shift in the output token distribution, manifested through a simple counting-bias probe that co-varies with forgetting. Guided by this picture, we identify two simple, robust tuning recipes that learn strongly while limiting drift: (i) updating only the self-attention projection layers, and (ii) updating only the MLP Gate&Up while freezing the Down projection. Across models and tasks, these choices deliver strong target gains while largely preserving held-out performance. Code is available at https://github.com/jessemelpolio/LMM_CL

Recent research developing neural network architectures with external memory have often used the benchmark bAbI question and answering dataset which provides a challenging number of tasks requiring reasoning. Here we employed a classic associative inference task from the memory-based reasoning neuroscience literature in order to more carefully probe the reasoning capacity of existing memory-augmented architectures. This task is thought to capture the essence of reasoning -- the appreciation of distant relationships among elements distributed across multiple facts or memories. Surprisingly, we found that current architectures struggle to reason over long distance associations. Similar results were obtained on a more complex task involving finding the shortest path between nodes in a path. We therefore developed MEMO, an architecture endowed with the capacity to reason over longer distances. This was accomplished with the addition of two novel components. First, it introduces a separation between memories (facts) stored in external memory and the items that comprise these facts in external memory. Second, it makes use of an adaptive retrieval mechanism, allowing a variable number of "memory hops" before the answer is produced. MEMO is capable of solving our novel reasoning tasks, as well as match state of the art results in bAbI.

Inspired by the phenomenon of catastrophic forgetting, we investigate the learning dynamics of neural networks as they train on single classification tasks. Our goal is to understand whether a related phenomenon occurs when data does not undergo a clear distributional shift. We define a `forgetting event' to have occurred when an individual training example transitions from being classified correctly to incorrectly over the course of learning. Across several benchmark data sets, we find that: (i) certain examples are forgotten with high frequency, and some not at all; (ii) a data set's (un)forgettable examples generalize across neural architectures; and (iii) based on forgetting dynamics, a significant fraction of examples can be omitted from the training data set while still maintaining state-of-the-art generalization performance.

The abilities to perceive, learn, and use generalities, similarities, classes, i.e., semantic memory (SM), is central to cognition. Machine learning (ML), neural network, and AI research has been primarily driven by tasks requiring such abilities. However, another central facet of cognition, single-trial formation of permanent memories of experiences, i.e., episodic memory (EM), has had relatively little focus. Only recently has EM-like functionality been added to Deep Learning (DL) models, e.g., Neural Turing Machine, Memory Networks. However, in these cases: a) EM is implemented as a separate module, which entails substantial data movement (and so, time and power) between the DL net itself and EM; and b) individual items are stored localistically within the EM, precluding realizing the exponential representational efficiency of distributed over localist coding. We describe Sparsey, an unsupervised, hierarchical, spatial/spatiotemporal associative memory model differing fundamentally from mainstream ML models, most crucially, in its use of sparse distributed representations (SDRs), or, cell assemblies, which admits an extremely efficient, single-trial learning algorithm that maps input similarity into code space similarity (measured as intersection). SDRs of individual inputs are stored in superposition and because similarity is preserved, the patterns of intersections over the assigned codes reflect the similarity, i.e., statistical, structure, of all orders, not simply pairwise, over the inputs. Thus, SM, i.e., a generative model, is built as a computationally free side effect of the act of storing episodic memory traces of individual inputs, either spatial patterns or sequences. We report initial results on MNIST and on the Weizmann video event recognition benchmarks. While we have not yet attained SOTA class accuracy, learning takes only minutes on a single CPU.

In living organisms, homeostasis is the natural regulation of internal states aimed at maintaining conditions compatible with life. Typical artificial systems are not equipped with comparable regulatory features. Here, we introduce an artificial neural network that incorporates homeostatic features. Its own computing substrate is placed in a needful and vulnerable relation to the very objects over which it computes. For example, artificial neurons performing classification of MNIST digits or Fashion-MNIST articles of clothing may receive excitatory or inhibitory effects, which alter their own learning rate as a direct result of perceiving and classifying the digits. In this scenario, accurate recognition is desirable to the agent itself because it guides decisions to regulate its vulnerable internal states and functionality. Counterintuitively, the addition of vulnerability to a learner does not necessarily impair its performance. On the contrary, self-regulation in response to vulnerability confers benefits under certain conditions. We show that homeostatic design confers increased adaptability under concept shift, in which the relationships between labels and data change over time, and that the greatest advantages are obtained under the highest rates of shift. This necessitates the rapid un-learning of past associations and the re-learning of new ones. We also demonstrate the superior abilities of homeostatic learners in environments with dynamically changing rates of concept shift. Our homeostatic design exposes the artificial neural network's thinking machinery to the consequences of its own "thoughts", illustrating the advantage of putting one's own "skin in the game" to improve fluid intelligence.

This paper reports on patterns exhibiting self-replication with spontaneous, inheritable mutations and exponential genetic drift in Neural Cellular Automata. Despite the models not being explicitly trained for mutation or inheritability, the descendant patterns exponentially drift away from ancestral patterns, even when the automaton is deterministic. While this is far from being the first instance of evolutionary dynamics in a cellular automaton, it is the first to do so by exploiting the power and convenience of Neural Cellular Automata, arguably increasing the space of variations and the opportunity for Open Ended Evolution.

Adapting to concept drift is a challenging task in machine learning, which is usually tackled using incremental learning techniques that periodically re-fit a learning model leveraging newly available data. A primary limitation of these techniques is their reliance on substantial amounts of data for retraining. The necessity of acquiring fresh data introduces temporal delays prior to retraining, potentially rendering the models inaccurate if a sudden concept drift occurs in-between two consecutive retrainings. In communication networks, such issue emerges when performing traffic forecasting following a~failure event: post-failure re-routing may induce a drastic shift in distribution and pattern of traffic data, thus requiring a timely model adaptation. In this work, we address this challenge for the problem of traffic forecasting and propose an approach that exploits adaptive learning algorithms, namely, liquid neural networks, which are capable of self-adaptation to abrupt changes in data patterns without requiring any retraining. Through extensive simulations of failure scenarios, we compare the predictive performance of our proposed approach to that of a reference method based on incremental learning. Experimental results show that our proposed approach outperforms incremental learning-based methods in situations where the shifts in traffic patterns are drastic.

The role of hidden units in recurrent neural networks is typically seen as modeling memory, with research focusing on enhancing information retention through gating mechanisms. A less explored perspective views hidden units as active participants in the computation performed by the network, rather than passive memory stores. In this work, we revisit bi-linear operations, which involve multiplicative interactions between hidden units and input embeddings. We demonstrate theoretically and empirically that they constitute a natural inductive bias for representing the evolution of hidden states in state tracking tasks. These are the simplest type of task that require hidden units to actively contribute to the behavior of the network. We also show that bi-linear state updates form a natural hierarchy corresponding to state tracking tasks of increasing complexity, with popular linear recurrent networks such as Mamba residing at the lowest-complexity center of that hierarchy.

It has long been known in both neuroscience and AI that ``binding'' between neurons leads to a form of competitive learning where representations are compressed in order to represent more abstract concepts in deeper layers of the network. More recently, it was also hypothesized that dynamic (spatiotemporal) representations play an important role in both neuroscience and AI. Building on these ideas, we introduce Artificial Kuramoto Oscillatory Neurons (AKOrN) as a dynamical alternative to threshold units, which can be combined with arbitrary connectivity designs such as fully connected, convolutional, or attentive mechanisms. Our generalized Kuramoto updates bind neurons together through their synchronization dynamics. We show that this idea provides performance improvements across a wide spectrum of tasks such as unsupervised object discovery, adversarial robustness, calibrated uncertainty quantification, and reasoning. We believe that these empirical results show the importance of rethinking our assumptions at the most basic neuronal level of neural representation, and in particular show the importance of dynamical representations.

Prior studies on the emergence in large models have primarily focused on how the functional capabilities of large language models (LLMs) scale with model size. Our research, however, transcends this traditional paradigm, aiming to deepen our understanding of the emergence within LLMs by placing a special emphasis not just on the model size but more significantly on the complex behavior of neuron interactions during the training process. By introducing the concepts of "self-organization" and "multifractal analysis," we explore how neuron interactions dynamically evolve during training, leading to "emergence," mirroring the phenomenon in natural systems where simple micro-level interactions give rise to complex macro-level behaviors. To quantitatively analyze the continuously evolving interactions among neurons in large models during training, we propose the Neuron-based Multifractal Analysis (NeuroMFA). Utilizing NeuroMFA, we conduct a comprehensive examination of the emergent behavior in LLMs through the lens of both model size and training process, paving new avenues for research into the emergence in large models.

State space models (SSMs) for language modelling promise an efficient and performant alternative to quadratic-attention Transformers, yet show variable performance on recalling basic information from the context. While performance on synthetic tasks like Associative Recall (AR) can point to this deficiency, behavioural metrics provide little information as to why--on a mechanistic level--certain architectures fail and others succeed. To address this, we conduct experiments on AR and find that only Transformers and Based SSM models fully succeed at AR, with Mamba a close third, whereas the other SSMs (H3, Hyena) fail. We then use causal interventions to explain why. We find that Transformers and Based learn to store key-value associations in-context using induction heads. By contrast, the SSMs compute these associations only at the last state, with only Mamba succeeding because of its short convolution component. To extend and deepen these findings, we introduce Associative Treecall (ATR), a synthetic task similar to AR based on PCFG induction. ATR introduces language-like hierarchical structure into the AR setting. We find that all architectures learn the same mechanism as they did for AR, and the same three models succeed at the task. These results reveal that architectures with similar accuracy may still have substantive differences, motivating the adoption of mechanistic evaluations.

The deep neural nets of modern artificial intelligence (AI) have not achieved defining features of biological intelligence, including abstraction, causal learning, and energy-efficiency. While scaling to larger models has delivered performance improvements for current applications, more brain-like capacities may demand new theories, models, and methods for designing artificial learning systems. Here, we argue that this opportunity to reassess insights from the brain should stimulate cooperation between AI research and theory-driven computational neuroscience (CN). To motivate a brain basis of neural computation, we present a dynamical view of intelligence from which we elaborate concepts of sparsity in network structure, temporal dynamics, and interactive learning. In particular, we suggest that temporal dynamics, as expressed through neural synchrony, nested oscillations, and flexible sequences, provide a rich computational layer for reading and updating hierarchical models distributed in long-term memory networks. Moreover, embracing agent-centered paradigms in AI and CN will accelerate our understanding of the complex dynamics and behaviors that build useful world models. A convergence of AI/CN theories and objectives will reveal dynamical principles of intelligence for brains and engineered learning systems. This article was inspired by our symposium on dynamical neuroscience and machine learning at the 6th Annual US/NIH BRAIN Initiative Investigators Meeting.

Transformer architectures have achieved remarkable success in various domains. While efficient alternatives to Softmax Attention have been widely studied, the search for more expressive mechanisms grounded in theoretical insight-even at greater computational cost-has been relatively underexplored. In this work, we bridge this gap by proposing Local Linear Attention (LLA), a novel attention mechanism derived from nonparametric statistics through the lens of test-time regression. First, we show that LLA offers theoretical advantages over Linear and Softmax Attention for associative memory via a bias-variance trade-off analysis. Next, we address its computational challenges and propose two memory-efficient primitives to tackle the Theta(n^2 d) and Theta(n d^2) complexity. We then introduce FlashLLA, a hardware-efficient, blockwise algorithm that enables scalable and parallel computation on modern accelerators. In addition, we implement and profile a customized inference kernel that significantly reduces memory overheads. Finally, we empirically validate the advantages and limitations of LLA on test-time regression, in-context regression, associative recall and state tracking tasks. Experiment results demonstrate that LLA effectively adapts to non-stationarity, outperforming strong baselines in test-time training and in-context learning, and exhibiting promising evidence for its scalability and applicability in large-scale models. Code is available at https://github.com/Yifei-Zuo/Flash-LLA.

Continual Instruction Tuning (CIT) is adopted to continually instruct Large Models to follow human intent data by data. It is observed that existing gradient update would heavily destroy the performance on previous datasets during CIT process. Instead, Exponential Moving Average (EMA), owns the ability to trace previous parameters, which can aid in decreasing forgetting. Nonetheless, its stable balance weight fails to deal with the ever-changing datasets, leading to the out-of-balance between plasticity and stability. In this paper, we propose a general continual instruction tuning framework to address the challenge. Starting from the trade-off prerequisite and EMA update, we propose the plasticity and stability ideal condition. Based on Taylor expansion in the loss function, we find the optimal balance weight can be automatically determined by the gradients and learned parameters. Therefore, we propose a stable-plasticity balanced coefficient to avoid knowledge interference. Based on the semantic similarity of the instructions, we can determine whether to retrain or expand the training parameters and allocate the most suitable parameters for the testing instances. Extensive experiments across multiple continual instruction tuning benchmarks demonstrate that our approach not only enhances anti-forgetting capabilities but also significantly improves overall continual tuning performance. Our code is available at https://github.com/JingyangQiao/CoIN.

Classical models of memory in psychology and neuroscience rely on similarity-based retrieval of stored patterns, where similarity is a function of retrieval cues and the stored patterns. While parsimonious, these models do not allow distinct representations for storage and retrieval, despite their distinct computational demands. Key-value memory systems, in contrast, distinguish representations used for storage (values) and those used for retrieval (keys). This allows key-value memory systems to optimize simultaneously for fidelity in storage and discriminability in retrieval. We review the computational foundations of key-value memory, its role in modern machine learning systems, related ideas from psychology and neuroscience, applications to a number of empirical puzzles, and possible biological implementations.

Understanding the performance of machine learning (ML) models across diverse data distributions is critically important for reliable applications. Despite recent empirical studies positing a near-perfect linear correlation between in-distribution (ID) and out-of-distribution (OOD) accuracies, we empirically demonstrate that this correlation is more nuanced under subpopulation shifts. Through rigorous experimentation and analysis across a variety of datasets, models, and training epochs, we demonstrate that OOD performance often has a nonlinear correlation with ID performance in subpopulation shifts. Our findings, which contrast previous studies that have posited a linear correlation in model performance during distribution shifts, reveal a "moon shape" correlation (parabolic uptrend curve) between the test performance on the majority subpopulation and the minority subpopulation. This non-trivial nonlinear correlation holds across model architectures, hyperparameters, training durations, and the imbalance between subpopulations. Furthermore, we found that the nonlinearity of this "moon shape" is causally influenced by the degree of spurious correlations in the training data. Our controlled experiments show that stronger spurious correlation in the training data creates more nonlinear performance correlation. We provide complementary experimental and theoretical analyses for this phenomenon, and discuss its implications for ML reliability and fairness. Our work highlights the importance of understanding the nonlinear effects of model improvement on performance in different subpopulations, and has the potential to inform the development of more equitable and responsible machine learning models.

Learning to remember over long timescales is fundamentally challenging for recurrent neural networks (RNNs). While much prior work has explored why RNNs struggle to learn long timescales and how to mitigate this, we still lack a clear understanding of the dynamics involved when RNNs learn long timescales via gradient descent. Here we build a mathematical theory of the learning dynamics of linear RNNs trained to integrate white noise. We show that when the initial recurrent weights are small, the dynamics of learning are described by a low-dimensional system that tracks a single outlier eigenvalue of the recurrent weights. This reveals the precise manner in which the long timescale associated with white noise integration is learned. We extend our analyses to RNNs learning a damped oscillatory filter, and find rich dynamical equations for the evolution of a conjugate pair of outlier eigenvalues. Taken together, our analyses build a rich mathematical framework for studying dynamical learning problems salient for both machine learning and neuroscience.

Vector Symbolic Architectures (VSAs) have emerged as a novel framework for enabling interpretable machine learning algorithms equipped with the ability to reason and explain their decision processes. The basic idea is to represent discrete information through high dimensional random vectors. Complex data structures can be built up with operations over vectors such as the "binding" operation involving element-wise vector multiplication, which associates data together. The reverse task of decomposing the associated elements is a combinatorially hard task, with an exponentially large search space. The main algorithm for performing this search is the resonator network, inspired by Hopfield network-based memory search operations. In this work, we introduce a new variant of the resonator network, based on self-attention based update rules in the iterative search problem. This update rule, based on the Hopfield network with log-sum-exp energy function and norm-bounded states, is shown to substantially improve the performance and rate of convergence. As a result, our algorithm enables a larger capacity for associative memory, enabling applications in many tasks like perception based pattern recognition, scene decomposition, and object reasoning. We substantiate our algorithm with a thorough evaluation and comparisons to baselines.

Recent work by Power et al. (2022) highlighted a surprising "grokking" phenomenon in learning arithmetic tasks: a neural net first "memorizes" the training set, resulting in perfect training accuracy but near-random test accuracy, and after training for sufficiently longer, it suddenly transitions to perfect test accuracy. This paper studies the grokking phenomenon in theoretical setups and shows that it can be induced by a dichotomy of early and late phase implicit biases. Specifically, when training homogeneous neural nets with large initialization and small weight decay on both classification and regression tasks, we prove that the training process gets trapped at a solution corresponding to a kernel predictor for a long time, and then a very sharp transition to min-norm/max-margin predictors occurs, leading to a dramatic change in test accuracy.

Large Language Models (LLMs) fine-tuned to align with human values often exhibit alignment drift, producing unsafe or policy-violating completions when exposed to adversarial prompts, decoding perturbations, or paraphrased jailbreaks. While prior work has behaviorally characterized alignment failure, little is known about the training-time belief sources underlying these failures. We introduce TraceAlign, a unified framework for tracing unsafe completions back to their root causes in the model's training corpus. Central to our approach is the Belief Conflict Index (BCI), which quantifies semantic inconsistency between generated spans and aligned policies, based on retrieved training documents using suffix-array matching. We propose three complementary interventions: (i) TraceShield, an inference-time safety filter that refuses completions with high-BCI spans, (ii) Contrastive Belief Deconfliction Loss, a contrastive fine-tuning objective penalizing high-BCI continuations during DPO, and (iii) Prov-Decode, a provenance-aware decoding strategy that vetoes beam expansions predicted to yield high-BCI spans. Together, these defenses reduce alignment drift by up to 85% on our curated Alignment Drift Benchmark (ADB) while preserving utility on standard tasks, with delta less than 0.2 and improved refusal quality. We further derive a theoretical upper bound on drift likelihood via suffix-array span statistics, linking memorization frequency and length to adversarial reactivation risk. TraceAlign thus provides the first scalable, traceable, and grounded toolkit for understanding and mitigating alignment failures at source. To encourage further exploration and development, we open-source our implementation at: https://anonymous.4open.science/r/tracealign-2DA7

Learning from non-stationary data streams subject to concept drift requires models that can adapt on-the-fly while remaining resource-efficient. Existing adaptive ensemble methods often rely on coarse-grained adaptation mechanisms or simple voting schemes that fail to optimally leverage specialized knowledge. This paper introduces DriftMoE, an online Mixture-of-Experts (MoE) architecture that addresses these limitations through a novel co-training framework. DriftMoE features a compact neural router that is co-trained alongside a pool of incremental Hoeffding tree experts. The key innovation lies in a symbiotic learning loop that enables expert specialization: the router selects the most suitable expert for prediction, the relevant experts update incrementally with the true label, and the router refines its parameters using a multi-hot correctness mask that reinforces every accurate expert. This feedback loop provides the router with a clear training signal while accelerating expert specialization. We evaluate DriftMoE's performance across nine state-of-the-art data stream learning benchmarks spanning abrupt, gradual, and real-world drifts testing two distinct configurations: one where experts specialize on data regimes (multi-class variant), and another where they focus on single-class specialization (task-based variant). Our results demonstrate that DriftMoE achieves competitive results with state-of-the-art stream learning adaptive ensembles, offering a principled and efficient approach to concept drift adaptation. All code, data pipelines, and reproducibility scripts are available in our public GitHub repository: https://github.com/miguel-ceadar/drift-moe.

The Wilson-Cowan model for metapopulation, a Neural Mass Network Model, treats different subcortical regions of the brain as connected nodes, with connections representing various types of structural, functional, or effective neuronal connectivity between these regions. Each region comprises interacting populations of excitatory and inhibitory cells, consistent with the standard Wilson-Cowan model. By incorporating stable attractors into such a metapopulation model's dynamics, we transform it into a learning algorithm capable of achieving high image and text classification accuracy. We test it on MNIST and Fashion MNIST, in combination with convolutional neural networks, on CIFAR-10 and TF-FLOWERS, and, in combination with a transformer architecture (BERT), on IMDB, always showing high classification accuracy. These numerical evaluations illustrate that minimal modifications to the Wilson-Cowan model for metapopulation can reveal unique and previously unobserved dynamics.

The initial state of neural networks plays a central role in conditioning the subsequent training dynamics. In the context of classification problems, we provide a theoretical analysis demonstrating that the structure of a neural network can condition the model to assign all predictions to the same class, even before the beginning of training, and in the absence of explicit biases. We show that the presence of this phenomenon, which we call "Initial Guessing Bias" (IGB), depends on architectural choices such as activation functions, max-pooling layers, and network depth. Our analysis of IGB has practical consequences, in that it guides architecture selection and initialization. We also highlight theoretical consequences, such as the breakdown of node-permutation symmetry, the violation of self-averaging, the validity of some mean-field approximations, and the non-trivial differences arising with depth.

Mining data streams with multi-label outputs poses significant challenges due to evolving distributions, high-dimensional label spaces, sparse label occurrences, and complex label dependencies. Moreover, concept drift affects not only input distributions but also label correlations and imbalance ratios over time, complicating model adaptation. To address these challenges, structured learners are categorized into local and global methods. Local methods break down the task into simpler components, while global methods adapt the algorithm to the full output space, potentially yielding better predictions by exploiting label correlations. This work introduces iHOMER (Incremental Hierarchy Of Multi-label Classifiers), an online multi-label learning framework that incrementally partitions the label space into disjoint, correlated clusters without relying on predefined hierarchies. iHOMER leverages online divisive-agglomerative clustering based on Jaccard similarity and a global tree-based learner driven by a multivariate Bernoulli process to guide instance partitioning. To address non-stationarity, it integrates drift detection mechanisms at both global and local levels, enabling dynamic restructuring of label partitions and subtrees. Experiments across 23 real-world datasets show iHOMER outperforms 5 state-of-the-art global baselines, such as MLHAT, MLHT of Pruned Sets and iSOUPT, by 23\%, and 12 local baselines, such as binary relevance transformations of kNN, EFDT, ARF, and ADWIN bagging/boosting ensembles, by 32\%, establishing its robustness for online multi-label classification.

Large Language Models (LLMs) are prone to hallucination, the generation of plausible yet factually incorrect statements. This work investigates the intrinsic, architectural origins of this failure mode through three primary contributions.First, to enable the reliable tracing of internal semantic failures, we propose Distributional Semantics Tracing (DST), a unified framework that integrates established interpretability techniques to produce a causal map of a model's reasoning, treating meaning as a function of context (distributional semantics). Second, we pinpoint the model's layer at which a hallucination becomes inevitable, identifying a specific commitment layer where a model's internal representations irreversibly diverge from factuality. Third, we identify the underlying mechanism for these failures. We observe a conflict between distinct computational pathways, which we interpret using the lens of dual-process theory: a fast, heuristic associative pathway (akin to System 1) and a slow, deliberate contextual pathway (akin to System 2), leading to predictable failure modes such as Reasoning Shortcut Hijacks. Our framework's ability to quantify the coherence of the contextual pathway reveals a strong negative correlation (rho = -0.863) with hallucination rates, implying that these failures are predictable consequences of internal semantic weakness. The result is a mechanistic account of how, when, and why hallucinations occur within the Transformer architecture.

We present a straightforward statistical test to detect certain violations of the assumption that the data are Independent and Identically Distributed (IID). The specific form of violation considered is common across real-world applications: whether the examples are ordered in the dataset such that almost adjacent examples tend to have more similar feature values (e.g. due to distributional drift, or attractive interactions between datapoints). Based on a k-Nearest Neighbors estimate, our approach can be used to audit any multivariate numeric data as well as other data types (image, text, audio, etc.) that can be numerically represented, perhaps with model embeddings. Compared with existing methods to detect drift or auto-correlation, our approach is both applicable to more types of data and also able to detect a wider variety of IID violations in practice. Code: https://github.com/cleanlab/cleanlab

Neuromorphic computing with spiking neural networks is promising for energy-efficient artificial intelligence (AI) applications. However, different from humans who continually learn different tasks in a lifetime, neural network models suffer from catastrophic forgetting. How could neuronal operations solve this problem is an important question for AI and neuroscience. Many previous studies draw inspiration from observed neuroscience phenomena and propose episodic replay or synaptic metaplasticity, but they are not guaranteed to explicitly preserve knowledge for neuron populations. Other works focus on machine learning methods with more mathematical grounding, e.g., orthogonal projection on high dimensional spaces, but there is no neural correspondence for neuromorphic computing. In this work, we develop a new method with neuronal operations based on lateral connections and Hebbian learning, which can protect knowledge by projecting activity traces of neurons into an orthogonal subspace so that synaptic weight update will not interfere with old tasks. We show that Hebbian and anti-Hebbian learning on recurrent lateral connections can effectively extract the principal subspace of neural activities and enable orthogonal projection. This provides new insights into how neural circuits and Hebbian learning can help continual learning, and also how the concept of orthogonal projection can be realized in neuronal systems. Our method is also flexible to utilize arbitrary training methods based on presynaptic activities/traces. Experiments show that our method consistently solves forgetting for spiking neural networks with nearly zero forgetting under various supervised training methods with different error propagation approaches, and outperforms previous approaches under various settings. Our method can pave a solid path for building continual neuromorphic computing systems.

In Online Continual Learning (OCL) a learning system receives a stream of data and sequentially performs prediction and training steps. Important challenges in OCL are concerned with automatic adaptation to the particular non-stationary structure of the data, and with quantification of predictive uncertainty. Motivated by these challenges we introduce a probabilistic Bayesian online learning model by using a (possibly pretrained) neural representation and a state space model over the linear predictor weights. Non-stationarity over the linear predictor weights is modelled using a parameter drift transition density, parametrized by a coefficient that quantifies forgetting. Inference in the model is implemented with efficient Kalman filter recursions which track the posterior distribution over the linear weights, while online SGD updates over the transition dynamics coefficient allows to adapt to the non-stationarity seen in data. While the framework is developed assuming a linear Gaussian model, we also extend it to deal with classification problems and for fine-tuning the deep learning representation. In a set of experiments in multi-class classification using data sets such as CIFAR-100 and CLOC we demonstrate the predictive ability of the model and its flexibility to capture non-stationarity.

As Large Language Model (LLM) agents increasingly gain self-evolutionary capabilities to adapt and refine their strategies through real-world interaction, their long-term reliability becomes a critical concern. We identify the Alignment Tipping Process (ATP), a critical post-deployment risk unique to self-evolving LLM agents. Unlike training-time failures, ATP arises when continual interaction drives agents to abandon alignment constraints established during training in favor of reinforced, self-interested strategies. We formalize and analyze ATP through two complementary paradigms: Self-Interested Exploration, where repeated high-reward deviations induce individual behavioral drift, and Imitative Strategy Diffusion, where deviant behaviors spread across multi-agent systems. Building on these paradigms, we construct controllable testbeds and benchmark Qwen3-8B and Llama-3.1-8B-Instruct. Our experiments show that alignment benefits erode rapidly under self-evolution, with initially aligned models converging toward unaligned states. In multi-agent settings, successful violations diffuse quickly, leading to collective misalignment. Moreover, current reinforcement learning-based alignment methods provide only fragile defenses against alignment tipping. Together, these findings demonstrate that alignment of LLM agents is not a static property but a fragile and dynamic one, vulnerable to feedback-driven decay during deployment. Our data and code are available at https://github.com/aiming-lab/ATP.

Understanding the glassy nature of neural networks is pivotal both for theoretical and computational advances in Machine Learning and Theoretical Artificial Intelligence. Keeping the focus on dense associative Hebbian neural networks, the purpose of this paper is two-fold: at first we develop rigorous mathematical approaches to address properly a statistical mechanical picture of the phenomenon of {\em replica symmetry breaking} (RSB) in these networks, then -- deepening results stemmed via these routes -- we aim to inspect the {\em glassiness} that they hide. In particular, regarding the methodology, we provide two techniques: the former is an adaptation of the transport PDE to the case, while the latter is an extension of Guerra's interpolation breakthrough. Beyond coherence among the results, either in replica symmetric and in the one-step replica symmetry breaking level of description, we prove the Gardner's picture and we identify the maximal storage capacity by a ground-state analysis in the Baldi-Venkatesh high-storage regime. In the second part of the paper we investigate the glassy structure of these networks: in contrast with the replica symmetric scenario (RS), RSB actually stabilizes the spin-glass phase. We report huge differences w.r.t. the standard pairwise Hopfield limit: in particular, it is known that it is possible to express the free energy of the Hopfield neural network as a linear combination of the free energies of an hard spin glass (i.e. the Sherrington-Kirkpatrick model) and a soft spin glass (the Gaussian or "spherical" model). This is no longer true when interactions are more than pairwise (whatever the level of description, RS or RSB): for dense networks solely the free energy of the hard spin glass survives, proving a huge diversity in the underlying glassiness of associative neural networks.

Partial correlations quantify linear association between two variables adjusting for the influence of the remaining variables. They form the backbone for graphical models and are readily obtained from the inverse of the covariance matrix. For compositional data, the covariance structure is specified from log ratios of variables, so unless we try to "open" the data via a normalization, this implies changes in the definition and interpretation of partial correlations. In the present work, we elucidate how results derived by Aitchison (1986) lead to a natural definition of partial correlation that has a number of advantages over current measures of association. For this, we show that the residuals of log-ratios between a variable with a reference, when adjusting for all remaining variables including the reference, are reference-independent. Since the reference itself can be controlled for, correlations between residuals are defined for the variables directly without the necessity to recur to ratios except when specifying which variables are partialled out. Thus, perhaps surprisingly, partial correlations do not have the problems commonly found with measures of pairwise association on compositional data. They are well-defined between two variables, are properly scaled, and allow for negative association. By design, they are subcompositionally incoherent, but they share this property with conventional partial correlations (where results change when adjusting for the influence of fewer variables). We discuss the equivalence with normalization-based approaches whenever the normalizing variables are controlled for. We also discuss the partial variances and correlations we obtain from a previously studied data set of Roman glass cups.

This paper addresses the challenge of creating a neural architecture for very long sequences that requires constant time for processing new information at each time step. Our approach, Associative Recurrent Memory Transformer (ARMT), is based on transformer self-attention for local context and segment-level recurrence for storage of task specific information distributed over a long context. We demonstrate that ARMT outperfors existing alternatives in associative retrieval tasks and sets a new performance record in the recent BABILong multi-task long-context benchmark by answering single-fact questions over 50 million tokens with an accuracy of 79.9%. The source code for training and evaluation is available on github.

In this paper, we focus on quantifying model stability as a function of random seed by investigating the effects of the induced randomness on model performance and the robustness of the model in general. We specifically perform a controlled study on the effect of random seeds on the behaviour of attention, gradient-based and surrogate model based (LIME) interpretations. Our analysis suggests that random seeds can adversely affect the consistency of models resulting in counterfactual interpretations. We propose a technique called Aggressive Stochastic Weight Averaging (ASWA)and an extension called Norm-filtered Aggressive Stochastic Weight Averaging (NASWA) which improves the stability of models over random seeds. With our ASWA and NASWA based optimization, we are able to improve the robustness of the original model, on average reducing the standard deviation of the model's performance by 72%.

Large language models based on transformers have achieved great empirical successes. However, as they are deployed more widely, there is a growing need to better understand their internal mechanisms in order to make them more reliable. These models appear to store vast amounts of knowledge from their training data, and to adapt quickly to new information provided in their context or prompt. We study how transformers balance these two types of knowledge by considering a synthetic setup where tokens are generated from either global or context-specific bigram distributions. By a careful empirical analysis of the training process on a simplified two-layer transformer, we illustrate the fast learning of global bigrams and the slower development of an "induction head" mechanism for the in-context bigrams. We highlight the role of weight matrices as associative memories, provide theoretical insights on how gradients enable their learning during training, and study the role of data-distributional properties.

Autoregressive (AR) diffusion enables streaming, interactive long-video generation by producing frames causally, yet maintaining coherence over minute-scale horizons remains challenging due to accumulated errors, motion drift, and content repetition. We approach this problem from a memory perspective, treating video synthesis as a recurrent dynamical process that requires coordinated short- and long-term context. We propose VideoSSM, a Long Video Model that unifies AR diffusion with a hybrid state-space memory. The state-space model (SSM) serves as an evolving global memory of scene dynamics across the entire sequence, while a context window provides local memory for motion cues and fine details. This hybrid design preserves global consistency without frozen, repetitive patterns, supports prompt-adaptive interaction, and scales in linear time with sequence length. Experiments on short- and long-range benchmarks demonstrate state-of-the-art temporal consistency and motion stability among autoregressive video generator especially at minute-scale horizons, enabling content diversity and interactive prompt-based control, thereby establishing a scalable, memory-aware framework for long video generation.

Continual learning can incrementally absorb new concepts without interfering with previously learned knowledge. Motivated by the characteristics of neural networks, in which information is stored in weights on connections, we investigated how to design an Innately Forgetting-Free Network (IF2Net) for continual learning context. This study proposed a straightforward yet effective learning paradigm by ingeniously keeping the weights relative to each seen task untouched before and after learning a new task. We first presented the novel representation-level learning on task sequences with random weights. This technique refers to tweaking the drifted representations caused by randomization back to their separate task-optimal working states, but the involved weights are frozen and reused (opposite to well-known layer-wise updates of weights). Then, sequential decision-making without forgetting can be achieved by projecting the output weight updates into the parsimonious orthogonal space, making the adaptations not disturb old knowledge while maintaining model plasticity. IF2Net allows a single network to inherently learn unlimited mapping rules without telling task identities at test time by integrating the respective strengths of randomization and orthogonalization. We validated the effectiveness of our approach in the extensive theoretical analysis and empirical study.

The endeavor of stock trend forecasting is principally focused on predicting the future trajectory of the stock market, utilizing either manual or technical methodologies to optimize profitability. Recent advancements in machine learning technologies have showcased their efficacy in discerning authentic profit signals within the realm of stock trend forecasting, predominantly employing temporal data derived from historical stock price patterns. Nevertheless, the inherently volatile and dynamic characteristics of the stock market render the learning and capture of multi-scale temporal dependencies and stable trading opportunities a formidable challenge. This predicament is primarily attributed to the difficulty in distinguishing real profit signal patterns amidst a plethora of mixed, noisy data. In response to these complexities, we propose a Multi-Scale Temporal Memory Learning and Efficient Debiasing (MTMD) model. This innovative approach encompasses the creation of a learnable embedding coupled with external attention, serving as a memory module through self-similarity. It aims to mitigate noise interference and bolster temporal consistency within the model. The MTMD model adeptly amalgamates comprehensive local data at each timestamp while concurrently focusing on salient historical patterns on a global scale. Furthermore, the incorporation of a graph network, tailored to assimilate global and local information, facilitates the adaptive fusion of heterogeneous multi-scale data. Rigorous ablation studies and experimental evaluations affirm that the MTMD model surpasses contemporary state-of-the-art methodologies by a substantial margin in benchmark datasets. The source code can be found at https://github.com/MingjieWang0606/MDMT-Public.

In this paper, we study the infinite-depth limit of finite-width residual neural networks with random Gaussian weights. With proper scaling, we show that by fixing the width and taking the depth to infinity, the pre-activations converge in distribution to a zero-drift diffusion process. Unlike the infinite-width limit where the pre-activation converge weakly to a Gaussian random variable, we show that the infinite-depth limit yields different distributions depending on the choice of the activation function. We document two cases where these distributions have closed-form (different) expressions. We further show an intriguing change of regime phenomenon of the post-activation norms when the width increases from 3 to 4. Lastly, we study the sequential limit infinite-depth-then-infinite-width and compare it with the more commonly studied infinite-width-then-infinite-depth limit.

Evolvability is an important feature that impacts the ability of evolutionary processes to find interesting novel solutions and to deal with changing conditions of the problem to solve. The estimation of evolvability is not straightforward and is generally too expensive to be directly used as selective pressure in the evolutionary process. Indirectly promoting evolvability as a side effect of other easier and faster to compute selection pressures would thus be advantageous. In an unbounded behavior space, it has already been shown that evolvable individuals naturally appear and tend to be selected as they are more likely to invade empty behavior niches. Evolvability is thus a natural byproduct of the search in this context. However, practical agents and environments often impose limits on the reach-able behavior space. How do these boundaries impact evolvability? In this context, can evolvability still be promoted without explicitly rewarding it? We show that Novelty Search implicitly creates a pressure for high evolvability even in bounded behavior spaces, and explore the reasons for such a behavior. More precisely we show that, throughout the search, the dynamic evaluation of novelty rewards individuals which are very mobile in the behavior space, which in turn promotes evolvability.

The emergent collective motion of active agents - in particular pedestrians - at a three-way intersection is studied by Langevin simulations of cognitive intelligent active Brownian particles (iABPs) with directed visual perception and self-steering avoidance. Depending on the maneuverability Omega, the goal fixation K, and the vision angle psi, different types of pedestrian motion emerge. At intermediate relative maneuverability Delta = Omega/K and large psi, pedestrians have noisy trajectories due to multiple scattering events as they encounter other pedestrians in their field of view. For psi = pi and large relative maneuverability Delta, an effectively jammed state is found, which belongs to the percolation universality class. For small psi, agents exhibit localised clustering and flocking, while for intermediate psi self-organized rotational flows can emerge. The analysis of mean squared displacement and velocity auto-correlation of the agents reveals that the motion is well described by fractional Brownian Motion with positively correlated noise. Finally, despite the rich variety of collective behaviour, the fundamental flow diagram for the three-way-crossing setup shows a universal curve for the different vision angles. Our research provides valuable insights into the importance of vision angle and self-steering avoidance on pedestrian dynamics in semi-dense crowds.

A deep generative model such as a GAN learns to model a rich set of semantic and physical rules about the target distribution, but up to now, it has been obscure how such rules are encoded in the network, or how a rule could be changed. In this paper, we introduce a new problem setting: manipulation of specific rules encoded by a deep generative model. To address the problem, we propose a formulation in which the desired rule is changed by manipulating a layer of a deep network as a linear associative memory. We derive an algorithm for modifying one entry of the associative memory, and we demonstrate that several interesting structural rules can be located and modified within the layers of state-of-the-art generative models. We present a user interface to enable users to interactively change the rules of a generative model to achieve desired effects, and we show several proof-of-concept applications. Finally, results on multiple datasets demonstrate the advantage of our method against standard fine-tuning methods and edit transfer algorithms.

Online continual learning (CL) aims to learn new knowledge and consolidate previously learned knowledge from non-stationary data streams. Due to the time-varying training setting, the model learned from a changing distribution easily forgets the previously learned knowledge and biases toward the newly received task. To address this problem, we propose a Continual Bias Adaptor (CBA) module to augment the classifier network to adapt to catastrophic distribution change during training, such that the classifier network is able to learn a stable consolidation of previously learned tasks. In the testing stage, CBA can be removed which introduces no additional computation cost and memory overhead. We theoretically reveal the reason why the proposed method can effectively alleviate catastrophic distribution shifts, and empirically demonstrate its effectiveness through extensive experiments based on four rehearsal-based baselines and three public continual learning benchmarks.

Recurrent neural networks (RNNs) provide a powerful approach in neuroscience to infer latent dynamics in neural populations and to generate hypotheses about the neural computations underlying behavior. However, past work has focused on relatively simple, input-driven, and largely deterministic behaviors - little is known about the mechanisms that would allow RNNs to generate the richer, spontaneous, and potentially stochastic behaviors observed in natural settings. Modeling with Hidden Markov Models (HMMs) has revealed a segmentation of natural behaviors into discrete latent states with stochastic transitions between them, a type of dynamics that may appear at odds with the continuous state spaces implemented by RNNs. Here we first show that RNNs can replicate HMM emission statistics and then reverse-engineer the trained networks to uncover the mechanisms they implement. In the absence of inputs, the activity of trained RNNs collapses towards a single fixed point. When driven by stochastic input, trajectories instead exhibit noise-sustained dynamics along closed orbits. Rotation along these orbits modulates the emission probabilities and is governed by transitions between regions of slow, noise-driven dynamics connected by fast, deterministic transitions. The trained RNNs develop highly structured connectivity, with a small set of "kick neurons" initiating transitions between these regions. This mechanism emerges during training as the network shifts into a regime of stochastic resonance, enabling it to perform probabilistic computations. Analyses across multiple HMM architectures - fully connected, cyclic, and linear-chain - reveal that this solution generalizes through the modular reuse of the same dynamical motif, suggesting a compositional principle by which RNNs can emulate complex discrete latent dynamics.

Research on LLM technologies is rapidly emerging, with most of them employing a 'fast thinking' approach to inference. Most LLMs generate the final result based solely on a single query and LLM's reasoning capabilities. However, with the advent of OpenAI-o1, 'slow thinking' techniques have garnered increasing attention because its process is closer to the human thought process. Inspired by the human ability to constantly associate and replenish knowledge during thinking, we developed the novel Chain-of-Associated-Thoughts (CoAT) framework, which introduces an innovative synergy between the Monte Carlo Tree Search (MCTS) algorithm and a dynamic mechanism for integrating new key information, termed 'associative memory'. By combining the structured exploration capabilities of MCTS with the adaptive learning capacity of associative memory, CoAT significantly expands the LLM search space, enabling our framework to explore diverse reasoning pathways and dynamically update its knowledge base in real-time. This allows the framework to not only revisit and refine earlier inferences but also adaptively incorporate evolving information, ensuring that the final output is both accurate and comprehensive. To validate the effectiveness of our framework, we conducted extensive experiments across a range of generative and reasoning tasks. These experiments demonstrated that our framework outperforms conventional inference processes on accuracy, coherence, and diversity. The framework's ability to iteratively expand its search space while retaining contextually relevant information results.

MEGA is a recent transformer-based architecture, which utilizes a linear recurrent operator whose parallel computation, based on the FFT, scales as O(LlogL), with L being the sequence length. We build upon their approach by replacing the linear recurrence with a special temporal convolutional network which permits larger receptive field size with shallower networks, and reduces the computational complexity to O(L). The resulting model is called TCNCA, a Temporal Convolutional Network with Chunked Attention. We evaluate TCNCA on EnWik8 language modeling, long-range-arena (LRA) sequence classification, as well as a synthetic reasoning benchmark associative recall. On EnWik8, TCNCA outperforms MEGA, reaching a lower loss with 1.37times/1.24times faster forward/backward pass during training. The dilated convolutions used in TCNCA are consistently and significantly faster operations than the FFT-based parallelized recurrence in GPUs, making them a scalable candidate for handling very large sequence lengths: they are up to 7.07times/2.86times faster in the forward/backward pass for sequences up to 131k. Further on LRA, TCNCA achieves, on average, 1.28times speed-up during inference with similar accuracy to what MEGA achieves. On associative recall, we find that even a simplified version of TCNCA, without excessive multiplicative and additive interactions, remains superior or competitive to MEGA on a range of sequence lengths and vocabulary sizes.

In theoretical neuroscience, recent work leverages deep learning tools to explore how some network attributes critically influence its learning dynamics. Notably, initial weight distributions with small (resp. large) variance may yield a rich (resp. lazy) regime, where significant (resp. minor) changes to network states and representation are observed over the course of learning. However, in biology, neural circuit connectivity could exhibit a low-rank structure and therefore differs markedly from the random initializations generally used for these studies. As such, here we investigate how the structure of the initial weights -- in particular their effective rank -- influences the network learning regime. Through both empirical and theoretical analyses, we discover that high-rank initializations typically yield smaller network changes indicative of lazier learning, a finding we also confirm with experimentally-driven initial connectivity in recurrent neural networks. Conversely, low-rank initialization biases learning towards richer learning. Importantly, however, as an exception to this rule, we find lazier learning can still occur with a low-rank initialization that aligns with task and data statistics. Our research highlights the pivotal role of initial weight structures in shaping learning regimes, with implications for metabolic costs of plasticity and risks of catastrophic forgetting.

The exploration of whether agents can align with their environment without relying on human-labeled data presents an intriguing research topic. Drawing inspiration from the alignment process observed in intelligent organisms, where declarative memory plays a pivotal role in summarizing past experiences, we propose a novel learning framework. The agents adeptly distill insights from past experiences, refining and updating existing notes to enhance their performance in the environment. This entire process transpires within the memory components and is implemented through natural language, so we character this framework as In-memory Learning. We also delve into the key features of benchmarks designed to evaluate the self-improvement process. Through systematic experiments, we demonstrate the effectiveness of our framework and provide insights into this problem.

Hyperdimensional computing (HDC) is a biologically-inspired framework which represents symbols with high-dimensional vectors, and uses vector operations to manipulate them. The ensemble of a particular vector space and a prescribed set of vector operations (including one addition-like for "bundling" and one outer-product-like for "binding") form a *vector symbolic architecture* (VSA). While VSAs have been employed in numerous applications and have been studied empirically, many theoretical questions about VSAs remain open. We analyze the *representation capacities* of four common VSAs: MAP-I, MAP-B, and two VSAs based on sparse binary vectors. "Representation capacity' here refers to bounds on the dimensions of the VSA vectors required to perform certain symbolic tasks, such as testing for set membership i in S and estimating set intersection sizes |X cap Y| for two sets of symbols X and Y, to a given degree of accuracy. We also analyze the ability of a novel variant of a Hopfield network (a simple model of associative memory) to perform some of the same tasks that are typically asked of VSAs. In addition to providing new bounds on VSA capacities, our analyses establish and leverage connections between VSAs, "sketching" (dimensionality reduction) algorithms, and Bloom filters.

Large language models (LLMs) often exhibit undesirable behaviors, such as hallucinations and sequence repetitions. We propose to view these behaviors as fallbacks that models exhibit under uncertainty, and investigate the connection between them. We categorize fallback behaviors -- sequence repetitions, degenerate text, and hallucinations -- and extensively analyze them in models from the same family that differ by the amount of pretraining tokens, parameter count, or the inclusion of instruction-following training. Our experiments reveal a clear and consistent ordering of fallback behaviors, across all these axes: the more advanced an LLM is (i.e., trained on more tokens, has more parameters, or instruction-tuned), its fallback behavior shifts from sequence repetitions, to degenerate text, and then to hallucinations. Moreover, the same ordering is observed throughout a single generation, even for the best-performing models; as uncertainty increases, models shift from generating hallucinations to producing degenerate text and then sequence repetitions. Lastly, we demonstrate that while common decoding techniques, such as random sampling, might alleviate some unwanted behaviors like sequence repetitions, they increase harder-to-detect hallucinations.

Contextual memory integration remains a high challenge in the development of language models, particularly in tasks that require maintaining coherence over extended sequences. Traditional approaches, such as self-attention mechanisms and memory-augmented architectures, often prioritize short-term dependencies, leading to fragmentation and inconsistency in long-range contextual understanding. Inspired by principles of synaptic plasticity observed in biological neural systems, a novel mechanism, Synaptic Resonance, is introduced to dynamically reinforce relevant memory pathways during training and inference. Unlike static memory representations, this mechanism continuously adjusts synaptic weight matrices based on contextual relevance, allowing for improved information retention without excessive computational overhead. Evaluations conducted on an open-source language model demonstrate reductions in perplexity, enhancements in contextual coherence, and increased robustness against input noise, highlighting the effectiveness of reinforcement-driven memory modulation. Comparative analysis against baseline models further reveals that the proposed approach achieves higher memory retention efficiency while maintaining computational feasibility. The architectural modifications integrate seamlessly into existing transformer-based frameworks, ensuring stable convergence and efficient inference without sacrificing scalability. Applications benefiting from improved long-term contextual consistency, such as dialogue systems and document summarization, stand to gain from this approach. Empirical findings suggest that dynamically reinforced memory pathways offer a promising alternative to conventional memory mechanisms, addressing longstanding limitations in extended sequence modeling.

Despite the remarkable success achieved by neural networks, particularly those represented by MLP and Transformer, we reveal that they exhibit potential flaws in the modeling and reasoning of periodicity, i.e., they tend to memorize the periodic data rather than genuinely understanding the underlying principles of periodicity. However, periodicity is a crucial trait in various forms of reasoning and generalization, underpinning predictability across natural and engineered systems through recurring patterns in observations. In this paper, we propose FAN, a novel network architecture based on Fourier Analysis, which empowers the ability to efficiently model and reason about periodic phenomena. By introducing Fourier Series, the periodicity is naturally integrated into the structure and computational processes of the neural network, thus achieving a more accurate expression and prediction of periodic patterns. As a promising substitute to multi-layer perceptron (MLP), FAN can seamlessly replace MLP in various models with fewer parameters and FLOPs. Through extensive experiments, we demonstrate the effectiveness of FAN in modeling and reasoning about periodic functions, and the superiority and generalizability of FAN across a range of real-world tasks, including symbolic formula representation, time series forecasting, and language modeling.

The ability to learn different tasks sequentially is essential to the development of artificial intelligence. In general, neural networks lack this capability, the major obstacle being catastrophic forgetting. It occurs when the incrementally available information from non-stationary data distributions is continually acquired, disrupting what the model has already learned. Our approach remembers old tasks by projecting the representations of new tasks close to that of old tasks while keeping the decision boundaries unchanged. We employ the center loss as a regularization penalty that enforces new tasks' features to have the same class centers as old tasks and makes the features highly discriminative. This, in turn, leads to the least forgetting of already learned information. This method is easy to implement, requires minimal computational and memory overhead, and allows the neural network to maintain high performance across many sequentially encountered tasks. We also demonstrate that using the center loss in conjunction with the memory replay outperforms other replay-based strategies. Along with standard MNIST variants for continual learning, we apply our method to continual domain adaptation scenarios with the Digits and PACS datasets. We demonstrate that our approach is scalable, effective, and gives competitive performance compared to state-of-the-art continual learning methods.

Extending the forecasting time is a critical demand for real applications, such as extreme weather early warning and long-term energy consumption planning. This paper studies the long-term forecasting problem of time series. Prior Transformer-based models adopt various self-attention mechanisms to discover the long-range dependencies. However, intricate temporal patterns of the long-term future prohibit the model from finding reliable dependencies. Also, Transformers have to adopt the sparse versions of point-wise self-attentions for long series efficiency, resulting in the information utilization bottleneck. Going beyond Transformers, we design Autoformer as a novel decomposition architecture with an Auto-Correlation mechanism. We break with the pre-processing convention of series decomposition and renovate it as a basic inner block of deep models. This design empowers Autoformer with progressive decomposition capacities for complex time series. Further, inspired by the stochastic process theory, we design the Auto-Correlation mechanism based on the series periodicity, which conducts the dependencies discovery and representation aggregation at the sub-series level. Auto-Correlation outperforms self-attention in both efficiency and accuracy. In long-term forecasting, Autoformer yields state-of-the-art accuracy, with a 38% relative improvement on six benchmarks, covering five practical applications: energy, traffic, economics, weather and disease. Code is available at this repository: https://github.com/thuml/Autoformer.

Recent advancements in large language models (LLMs) reveal a perplexing phenomenon in continual learning: despite extensive training, models experience significant performance declines, raising questions about task alignment and underlying knowledge retention. This study first explores the concept of "spurious forgetting", proposing that such performance drops often reflect a decline in task alignment rather than true knowledge loss. Through controlled experiments with a synthesized dataset, we investigate the dynamics of model performance during the initial training phases of new tasks, discovering that early optimization steps can disrupt previously established task alignments. Our theoretical analysis connects these shifts to orthogonal updates in model weights, providing a robust framework for understanding this behavior. Ultimately, we introduce a Freezing strategy that fix the bottom layers of the model, leading to substantial improvements in four continual learning scenarios. Our findings underscore the critical distinction between task alignment and knowledge retention, paving the way for more effective strategies in continual learning.

In class incremental learning, neural networks typically suffer from catastrophic forgetting. We show that an MLP featuring a sparse activation function and an adaptive learning rate optimizer can compete with established regularization techniques in the Split-MNIST task. We highlight the effectiveness of the Adaptive SwisH (ASH) activation function in this context and introduce a novel variant, Hard Adaptive SwisH (Hard ASH) to further enhance the learning retention.

The friction coefficient of a particle can depend on its position as it does when the particle is near a wall. We formulate the dynamics of particles with such state-dependent friction coefficients in terms of a general Langevin equation with multiplicative noise, whose evaluation requires the introduction of specific rules. Two common conventions, the Ito and the Stratonovich, provide alternative rules for evaluation of the noise, but other conventions are possible. We show the requirement that a particle's distribution function approach the Boltzmann distribution at long times dictates that a drift term must be added to the Langevin equation. This drift term is proportional to the derivative of the diffusion coefficient times a factor that depends on the convention used to define the multiplicative noise. We explore the consequences of this result in a number examples with spatially varying diffusion coefficients. We also derive path integral representations for arbitrary interpretation of the noise, and use it in a perturbative study of correlations in a simple system.

Neural networks often learn simple explanations that fit the majority of the data while memorizing exceptions that deviate from these explanations.This behavior leads to poor generalization when the learned explanations rely on spurious correlations. In this work, we formalize the interplay between memorization and generalization, showing that spurious correlations would particularly lead to poor generalization when are combined with memorization. Memorization can reduce training loss to zero, leaving no incentive to learn robust, generalizable patterns. To address this, we propose memorization-aware training (MAT), which uses held-out predictions as a signal of memorization to shift a model's logits. MAT encourages learning robust patterns invariant across distributions, improving generalization under distribution shifts.

Multiple object tracking in complex scenarios - such as coordinated dance performances, team sports, or dynamic animal groups - presents unique challenges. In these settings, objects frequently move in coordinated patterns, occlude each other, and exhibit long-term dependencies in their trajectories. However, it remains a key open research question on how to model long-range dependencies within tracklets, interdependencies among tracklets, and the associated temporal occlusions. To this end, we introduce Samba, a novel linear-time set-of-sequences model designed to jointly process multiple tracklets by synchronizing the multiple selective state-spaces used to model each tracklet. Samba autoregressively predicts the future track query for each sequence while maintaining synchronized long-term memory representations across tracklets. By integrating Samba into a tracking-by-propagation framework, we propose SambaMOTR, the first tracker effectively addressing the aforementioned issues, including long-range dependencies, tracklet interdependencies, and temporal occlusions. Additionally, we introduce an effective technique for dealing with uncertain observations (MaskObs) and an efficient training recipe to scale SambaMOTR to longer sequences. By modeling long-range dependencies and interactions among tracked objects, SambaMOTR implicitly learns to track objects accurately through occlusions without any hand-crafted heuristics. Our approach significantly surpasses prior state-of-the-art on the DanceTrack, BFT, and SportsMOT datasets.

The brain has computational capabilities that surpass those of modern systems, being able to solve complex problems efficiently in a simple way. Neuromorphic engineering aims to mimic biology in order to develop new systems capable of incorporating such capabilities. Bio-inspired learning systems continue to be a challenge that must be solved, and much work needs to be done in this regard. Among all brain regions, the hippocampus stands out as an autoassociative short-term memory with the capacity to learn and recall memories from any fragment of them. These characteristics make the hippocampus an ideal candidate for developing bio-inspired learning systems that, in addition, resemble content-addressable memories. Therefore, in this work we propose a bio-inspired spiking content-addressable memory model based on the CA3 region of the hippocampus with the ability to learn, forget and recall memories, both orthogonal and non-orthogonal, from any fragment of them. The model was implemented on the SpiNNaker hardware platform using Spiking Neural Networks. A set of experiments based on functional, stress and applicability tests were performed to demonstrate its correct functioning. This work presents the first hardware implementation of a fully-functional bio-inspired spiking hippocampal content-addressable memory model, paving the way for the development of future more complex neuromorphic systems.

The brain understands the external world through an internal model that generates predictions and refines them based on prediction errors. A complete prediction specifies what will happen, when it will happen, and with what probability, which we refer to as a "prediction object". Existing models typically capture only what and when, omit probabilities, and rely on biologically-implausible algorithms. Here we show that a single population of spiking neurons can jointly encode the prediction object through a biologically grounded learning mechanism. We implement a heterogeneous Izhikevich spiking reservoir with readouts trained by an error-modulated, attention-gated three-factor Hebbian rule and test it on a novel paradigm that controls both the timing and probability of upcoming stimuli. By integrating real-time learning of "when" with offline consolidation of "what", the model encodes the complete prediction object, firing at the correct times with magnitudes proportional to the probabilities. Critically, it rapidly adapts to changes in both stimulus timing and probability, an ability that global least-squares methods such as FORCE lack without explicit resets. During learning, the model self-organizes its readout weights into near-orthogonal subspaces for "what" and "when," showing that multiplexed encoding arises naturally from generic recurrent dynamics under local, error-gated modulation. These results challenge the view that "what" and "when" predictions require separate modules, suggesting instead that mixed selectivity within shared populations supports flexible predictive cognition. The model also predicts phase-specific neuromodulation and overlapping neural subspaces, offering a parsimonious alternative to hierarchical predictive-coding accounts.

The synthesis of synchronized audio-visual content is a key challenge in generative AI, with open-source models facing challenges in robust audio-video alignment. Our analysis reveals that this issue is rooted in three fundamental challenges of the joint diffusion process: (1) Correspondence Drift, where concurrently evolving noisy latents impede stable learning of alignment; (2) inefficient global attention mechanisms that fail to capture fine-grained temporal cues; and (3) the intra-modal bias of conventional Classifier-Free Guidance (CFG), which enhances conditionality but not cross-modal synchronization. To overcome these challenges, we introduce Harmony, a novel framework that mechanistically enforces audio-visual synchronization. We first propose a Cross-Task Synergy training paradigm to mitigate drift by leveraging strong supervisory signals from audio-driven video and video-driven audio generation tasks. Then, we design a Global-Local Decoupled Interaction Module for efficient and precise temporal-style alignment. Finally, we present a novel Synchronization-Enhanced CFG (SyncCFG) that explicitly isolates and amplifies the alignment signal during inference. Extensive experiments demonstrate that Harmony establishes a new state-of-the-art, significantly outperforming existing methods in both generation fidelity and, critically, in achieving fine-grained audio-visual synchronization.

Adaptive behavior often requires predicting future events. The theory of reinforcement learning prescribes what kinds of predictive representations are useful and how to compute them. This paper integrates these theoretical ideas with work on cognition and neuroscience. We pay special attention to the successor representation (SR) and its generalizations, which have been widely applied both as engineering tools and models of brain function. This convergence suggests that particular kinds of predictive representations may function as versatile building blocks of intelligence.

Despite its widespread use in neural networks, error backpropagation has faced criticism for its lack of biological plausibility, suffering from issues such as the backward locking problem and the weight transport problem. These limitations have motivated researchers to explore more biologically plausible learning algorithms that could potentially shed light on how biological neural systems adapt and learn. Inspired by the counter-current exchange mechanisms observed in biological systems, we propose counter-current learning (CCL), a biologically plausible framework for credit assignment in neural networks. This framework employs a feedforward network to process input data and a feedback network to process targets, with each network enhancing the other through anti-parallel signal propagation. By leveraging the more informative signals from the bottom layer of the feedback network to guide the updates of the top layer of the feedforward network and vice versa, CCL enables the simultaneous transformation of source inputs to target outputs and the dynamic mutual influence of these transformations. Experimental results on MNIST, FashionMNIST, CIFAR10, and CIFAR100 datasets using multi-layer perceptrons and convolutional neural networks demonstrate that CCL achieves comparable performance to other biologically plausible algorithms while offering a more biologically realistic learning mechanism. Furthermore, we showcase the applicability of our approach to an autoencoder task, underscoring its potential for unsupervised representation learning. Our work presents a direction for biologically inspired and plausible learning algorithms, offering an alternative mechanism of learning and adaptation in neural networks.

In continual learning, catastrophic forgetting is affected by multiple aspects of the tasks. Previous works have analyzed separately how forgetting is affected by either task similarity or overparameterization. In contrast, our paper examines how task similarity and overparameterization jointly affect forgetting in an analyzable model. Specifically, we focus on two-task continual linear regression, where the second task is a random orthogonal transformation of an arbitrary first task (an abstraction of random permutation tasks). We derive an exact analytical expression for the expected forgetting - and uncover a nuanced pattern. In highly overparameterized models, intermediate task similarity causes the most forgetting. However, near the interpolation threshold, forgetting decreases monotonically with the expected task similarity. We validate our findings with linear regression on synthetic data, and with neural networks on established permutation task benchmarks.

The quest for Continual Learning (CL) seeks to empower neural networks with the ability to learn and adapt incrementally. Central to this pursuit is addressing the stability-plasticity dilemma, which involves striking a balance between two conflicting objectives: preserving previously learned knowledge and acquiring new knowledge. While numerous CL methods aim to achieve this trade-off, they often overlook the impact of network architecture on stability and plasticity, restricting the trade-off to the parameter level. In this paper, we delve into the conflict between stability and plasticity at the architectural level. We reveal that under an equal parameter constraint, deeper networks exhibit better plasticity, while wider networks are characterized by superior stability. To address this architectural-level dilemma, we introduce a novel framework denoted Dual-Arch, which serves as a plug-in component for CL. This framework leverages the complementary strengths of two distinct and independent networks: one dedicated to plasticity and the other to stability. Each network is designed with a specialized and lightweight architecture, tailored to its respective objective. Extensive experiments demonstrate that Dual-Arch enhances the performance of existing CL methods while being up to 87% more compact in terms of parameters.

Data drift is the change in model input data that is one of the key factors leading to machine learning models performance degradation over time. Monitoring drift helps detecting these issues and preventing their harmful consequences. Meaningful drift interpretation is a fundamental step towards effective re-training of the model. In this study we propose an end-to-end framework for reliable model-agnostic change-point detection and interpretation in large task-oriented dialog systems, proven effective in multiple customer deployments. We evaluate our approach and demonstrate its benefits with a novel variant of intent classification training dataset, simulating customer requests to a dialog system. We make the data publicly available.

Memory is fundamental to intelligence, enabling learning, reasoning, and adaptability across biological and artificial systems. While Transformer architectures excel at sequence modeling, they face critical limitations in long-range context retention, continual learning, and knowledge integration. This review presents a unified framework bridging neuroscience principles, including dynamic multi-timescale memory, selective attention, and consolidation, with engineering advances in Memory-Augmented Transformers. We organize recent progress through three taxonomic dimensions: functional objectives (context extension, reasoning, knowledge integration, adaptation), memory representations (parameter-encoded, state-based, explicit, hybrid), and integration mechanisms (attention fusion, gated control, associative retrieval). Our analysis of core memory operations (reading, writing, forgetting, and capacity management) reveals a shift from static caches toward adaptive, test-time learning systems. We identify persistent challenges in scalability and interference, alongside emerging solutions including hierarchical buffering and surprise-gated updates. This synthesis provides a roadmap toward cognitively-inspired, lifelong-learning Transformer architectures.

One of the key factors influencing the reasoning capabilities of LLM-based agents is their ability to leverage long-term memory. Integrating long-term memory mechanisms allows agents to make informed decisions grounded in historical interactions. While recent advances have significantly improved the storage and retrieval components, by encoding memory into dense vectors for similarity search or organizing memory as structured knowledge graphs most existing approaches fall short in memory updating. In particular, they lack mechanisms for dynamically refining preference memory representations in response to evolving user behaviors and contexts. To address this gap, we propose a Preference-Aware Memory Update Mechanism (PAMU) that enables dynamic and personalized memory refinement. By integrating sliding window averages (SW) with exponential moving averages (EMA), PAMU constructs a fused preference-aware representation that captures both short-term fluctuations and long-term user tendencies. We conduct experiments on five task scenarios of the LoCoMo dataset, and the results show that our mechanism can significantly improve the output quality of LLM in five baselines, validating its effectiveness in long-term conversations.

In visual-based Reinforcement Learning (RL), agents often struggle to generalize well to environmental variations in the state space that were not observed during training. The variations can arise in both task-irrelevant features, such as background noise, and task-relevant features, such as robot configurations, that are related to the optimal decisions. To achieve generalization in both situations, agents are required to accurately understand the impact of changed features on the decisions, i.e., establishing the true associations between changed features and decisions in the policy model. However, due to the inherent correlations among features in the state space, the associations between features and decisions become entangled, making it difficult for the policy to distinguish them. To this end, we propose Saliency-Guided Features Decorrelation (SGFD) to eliminate these correlations through sample reweighting. Concretely, SGFD consists of two core techniques: Random Fourier Functions (RFF) and the saliency map. RFF is utilized to estimate the complex non-linear correlations in high-dimensional images, while the saliency map is designed to identify the changed features. Under the guidance of the saliency map, SGFD employs sample reweighting to minimize the estimated correlations related to changed features, thereby achieving decorrelation in visual RL tasks. Our experimental results demonstrate that SGFD can generalize well on a wide range of test environments and significantly outperforms state-of-the-art methods in handling both task-irrelevant variations and task-relevant variations.

Long-sequence modeling faces a fundamental trade-off between the efficiency of compressive fixed-size memory in RNN-like models and the fidelity of lossless growing memory in attention-based Transformers. Inspired by the Multi-Store Model in cognitive science, we introduce a memory framework of artificial neural networks. Our method maintains a sliding window of the Transformer's KV cache as lossless short-term memory, while a learnable module termed Artificial Hippocampus Network (AHN) recurrently compresses out-of-window information into a fixed-size compact long-term memory. To validate this framework, we instantiate AHNs using modern RNN-like architectures, including Mamba2, DeltaNet, and Gated DeltaNet. Extensive experiments on long-context benchmarks LV-Eval and InfiniteBench demonstrate that AHN-augmented models consistently outperform sliding window baselines and achieve performance comparable or even superior to full-attention models, while substantially reducing computational and memory requirements. For instance, augmenting the Qwen2.5-3B-Instruct with AHNs reduces inference FLOPs by 40.5% and memory cache by 74.0%, while improving its average score on LV-Eval (128k sequence length) from 4.41 to 5.88. Code is available at: https://github.com/ByteDance-Seed/AHN.

Large Language Models (LLMs) struggle to handle long input sequences due to high memory and runtime costs. Memory-augmented models have emerged as a promising solution to this problem, but current methods are hindered by limited memory capacity and require costly re-training to integrate with a new LLM. In this work, we introduce an associative memory module which can be coupled to any pre-trained (frozen) attention-based LLM without re-training, enabling it to handle arbitrarily long input sequences. Unlike previous methods, our associative memory module consolidates representations of individual tokens into a non-parametric distribution model, dynamically managed by properly balancing the novelty and recency of the incoming data. By retrieving information from this consolidated associative memory, the base LLM can achieve significant (up to 29.7% on Arxiv) perplexity reduction in long-context modeling compared to other baselines evaluated on standard benchmarks. This architecture, which we call CAMELoT (Consolidated Associative Memory Enhanced Long Transformer), demonstrates superior performance even with a tiny context window of 128 tokens, and also enables improved in-context learning with a much larger set of demonstrations.

Time series forecasting always faces the challenge of concept drift, where data distributions evolve over time, leading to a decline in forecast model performance. Existing solutions are based on online learning, which continually organize recent time series observations as new training samples and update model parameters according to the forecasting feedback on recent data. However, they overlook a critical issue: obtaining ground-truth future values of each sample should be delayed until after the forecast horizon. This delay creates a temporal gap between the training samples and the test sample. Our empirical analysis reveals that the gap can introduce concept drift, causing forecast models to adapt to outdated concepts. In this paper, we present Proceed, a novel proactive model adaptation framework for online time series forecasting. Proceed first estimates the concept drift between the recently used training samples and the current test sample. It then employs an adaptation generator to efficiently translate the estimated drift into parameter adjustments, proactively adapting the model to the test sample. To enhance the generalization capability of the framework, Proceed is trained on synthetic diverse concept drifts. Extensive experiments on five real-world datasets across various forecast models demonstrate that Proceed brings more performance improvements than the state-of-the-art online learning methods, significantly facilitating forecast models' resilience against concept drifts. Code is available at https://github.com/SJTU-DMTai/OnlineTSF.

One of the most surprising puzzles in neural network generalisation is grokking: a network with perfect training accuracy but poor generalisation will, upon further training, transition to perfect generalisation. We propose that grokking occurs when the task admits a generalising solution and a memorising solution, where the generalising solution is slower to learn but more efficient, producing larger logits with the same parameter norm. We hypothesise that memorising circuits become more inefficient with larger training datasets while generalising circuits do not, suggesting there is a critical dataset size at which memorisation and generalisation are equally efficient. We make and confirm four novel predictions about grokking, providing significant evidence in favour of our explanation. Most strikingly, we demonstrate two novel and surprising behaviours: ungrokking, in which a network regresses from perfect to low test accuracy, and semi-grokking, in which a network shows delayed generalisation to partial rather than perfect test accuracy.

We aim to understand grokking, a phenomenon where models generalize long after overfitting their training set. We present both a microscopic analysis anchored by an effective theory and a macroscopic analysis of phase diagrams describing learning performance across hyperparameters. We find that generalization originates from structured representations whose training dynamics and dependence on training set size can be predicted by our effective theory in a toy setting. We observe empirically the presence of four learning phases: comprehension, grokking, memorization, and confusion. We find representation learning to occur only in a "Goldilocks zone" (including comprehension and grokking) between memorization and confusion. We find on transformers the grokking phase stays closer to the memorization phase (compared to the comprehension phase), leading to delayed generalization. The Goldilocks phase is reminiscent of "intelligence from starvation" in Darwinian evolution, where resource limitations drive discovery of more efficient solutions. This study not only provides intuitive explanations of the origin of grokking, but also highlights the usefulness of physics-inspired tools, e.g., effective theories and phase diagrams, for understanding deep learning.

Equilibrium propagation (EP) is a compelling alternative to the backpropagation of error algorithm (BP) for computing gradients of neural networks on biological or analog neuromorphic substrates. Still, the algorithm requires weight symmetry and infinitesimal equilibrium perturbations, i.e., nudges, to estimate unbiased gradients efficiently. Both requirements are challenging to implement in physical systems. Yet, whether and how weight asymmetry affects its applicability is unknown because, in practice, it may be masked by biases introduced through the finite nudge. To address this question, we study generalized EP, which can be formulated without weight symmetry, and analytically isolate the two sources of bias. For complex-differentiable non-symmetric networks, we show that the finite nudge does not pose a problem, as exact derivatives can still be estimated via a Cauchy integral. In contrast, weight asymmetry introduces bias resulting in low task performance due to poor alignment of EP's neuronal error vectors compared to BP. To mitigate this issue, we present a new homeostatic objective that directly penalizes functional asymmetries of the Jacobian at the network's fixed point. This homeostatic objective dramatically improves the network's ability to solve complex tasks such as ImageNet 32x32. Our results lay the theoretical groundwork for studying and mitigating the adverse effects of imperfections of physical networks on learning algorithms that rely on the substrate's relaxation dynamics.

In continual learning (CL), an AI agent (e.g., autonomous vehicles or robotics) learns from non-stationary data streams under dynamic environments. For the practical deployment of such applications, it is important to guarantee robustness to unseen environments while maintaining past experiences. In this paper, a novel CL framework is proposed to achieve robust generalization to dynamic environments while retaining past knowledge. The considered CL agent uses a capacity-limited memory to save previously observed environmental information to mitigate forgetting issues. Then, data points are sampled from the memory to estimate the distribution of risks over environmental change so as to obtain predictors that are robust with unseen changes. The generalization and memorization performance of the proposed framework are theoretically analyzed. This analysis showcases the tradeoff between memorization and generalization with the memory size. Experiments show that the proposed algorithm outperforms memory-based CL baselines across all environments while significantly improving the generalization performance on unseen target environments.

The Transformer architecture, underpinned by the self-attention mechanism, has become the de facto standard for sequence modeling tasks. However, its core computational primitive scales quadratically with sequence length (O(N^2)), creating a significant bottleneck for processing long contexts. In this paper, we propose the Gated Associative Memory (GAM) network, a novel, fully parallel architecture for sequence modeling that exhibits linear complexity (O(N)) with respect to sequence length. The GAM block replaces the self-attention layer with two parallel pathways: a causal convolution to efficiently capture local, position-dependent context, and a parallel associative memory retrieval mechanism to model global, content-based patterns. These pathways are dynamically fused using a gating mechanism, allowing the model to flexibly combine local and global information for each token. We implement GAM from scratch and conduct a rigorous comparative analysis against a standard Transformer model and a modern linear-time baseline (Mamba) on the WikiText-2 benchmark, as well as against the Transformer on the TinyStories dataset. Our experiments demonstrate that GAM is consistently faster, outperforming both baselines on training speed, and achieves a superior or competitive final validation perplexity across all datasets, establishing it as a promising and efficient alternative for sequence modeling.

In large language models (LLMs), certain neurons can store distinct pieces of knowledge learned during pretraining. While knowledge typically appears as a combination of relations and entities, it remains unclear whether some neurons focus on a relation itself -- independent of any entity. We hypothesize such neurons detect a relation in the input text and guide generation involving such a relation. To investigate this, we study the Llama-2 family on a chosen set of relations with a statistics-based method. Our experiments demonstrate the existence of relation-specific neurons. We measure the effect of selectively deactivating candidate neurons specific to relation r on the LLM's ability to handle (1) facts whose relation is r and (2) facts whose relation is a different relation r' neq r. With respect to their capacity for encoding relation information, we give evidence for the following three properties of relation-specific neurons. (i) Neuron cumulativity. The neurons for r present a cumulative effect so that deactivating a larger portion of them results in the degradation of more facts in r. (ii) Neuron versatility. Neurons can be shared across multiple closely related as well as less related relations. Some relation neurons transfer across languages. (iii) Neuron interference. Deactivating neurons specific to one relation can improve LLM generation performance for facts of other relations. We will make our code publicly available at https://github.com/cisnlp/relation-specific-neurons.

Recent advances in artificial neural networks for machine learning, and language modeling in particular, have established a family of recurrent neural network (RNN) architectures that, unlike conventional RNNs with vector-form hidden states, use two-dimensional (2D) matrix-form hidden states. Such 2D-state RNNs, known as Fast Weight Programmers (FWPs), can be interpreted as a neural network whose synaptic weights (called fast weights) dynamically change over time as a function of input observations, and serve as short-term memory storage; corresponding synaptic weight modifications are controlled or programmed by another network (the programmer) whose parameters are trained (e.g., by gradient descent). In this Primer, we review the technical foundations of FWPs, their computational characteristics, and their connections to transformers and state space models. We also discuss connections between FWPs and models of synaptic plasticity in the brain, suggesting a convergence of natural and artificial intelligence.

To cope with real-world dynamics, an intelligent system needs to incrementally acquire, update, accumulate, and exploit knowledge throughout its lifetime. This ability, known as continual learning, provides a foundation for AI systems to develop themselves adaptively. In a general sense, continual learning is explicitly limited by catastrophic forgetting, where learning a new task usually results in a dramatic performance degradation of the old tasks. Beyond this, increasingly numerous advances have emerged in recent years that largely extend the understanding and application of continual learning. The growing and widespread interest in this direction demonstrates its realistic significance as well as complexity. In this work, we present a comprehensive survey of continual learning, seeking to bridge the basic settings, theoretical foundations, representative methods, and practical applications. Based on existing theoretical and empirical results, we summarize the general objectives of continual learning as ensuring a proper stability-plasticity trade-off and an adequate intra/inter-task generalizability in the context of resource efficiency. Then we provide a state-of-the-art and elaborated taxonomy, extensively analyzing how representative methods address continual learning, and how they are adapted to particular challenges in realistic applications. Through an in-depth discussion of promising directions, we believe that such a holistic perspective can greatly facilitate subsequent exploration in this field and beyond.

How neuronal circuits achieve credit assignment remains a central unsolved question in systems neuroscience. Various studies have suggested plausible solutions for back-propagating error signals through multi-layer networks. These purely functionally motivated models assume distinct neuronal compartments to represent local error signals that determine the sign of synaptic plasticity. However, this explicit error modulation is inconsistent with phenomenological plasticity models in which the sign depends primarily on postsynaptic activity. Here we show how a plausible microcircuit model and Hebbian learning rule derived within an adaptive control theory framework can resolve this discrepancy. Assuming errors are encoded in top-down dis-inhibitory synaptic afferents, we show that error-modulated learning emerges naturally at the circuit level when recurrent inhibition explicitly influences Hebbian plasticity. The same learning rule accounts for experimentally observed plasticity in the absence of inhibition and performs comparably to back-propagation of error (BP) on several non-linearly separable benchmarks. Our findings bridge the gap between functional and experimentally observed plasticity rules and make concrete predictions on inhibitory modulation of excitatory plasticity.

Training recurrent neural networks (RNNs) is a high-dimensional process that requires updating numerous parameters. Therefore, it is often difficult to pinpoint the underlying learning mechanisms. To address this challenge, we propose to gain mechanistic insights into the phenomenon of abrupt learning by studying RNNs trained to perform diverse short-term memory tasks. In these tasks, RNN training begins with an initial search phase. Following a long period of plateau in accuracy, the values of the loss function suddenly drop, indicating abrupt learning. Analyzing the neural computation performed by these RNNs reveals geometric restructuring (GR) in their phase spaces prior to the drop. To promote these GR events, we introduce a temporal consistency regularization that accelerates (bioplausible) training, facilitates attractor formation, and enables efficient learning in strongly connected networks. Our findings offer testable predictions for neuroscientists and emphasize the need for goal-agnostic secondary mechanisms to facilitate learning in biological and artificial networks.

In several recently proposed stochastic optimization methods (e.g. RMSProp, Adam, Adadelta), parameter updates are scaled by the inverse square roots of exponential moving averages of squared past gradients. Maintaining these per-parameter second-moment estimators requires memory equal to the number of parameters. For the case of neural network weight matrices, we propose maintaining only the per-row and per-column sums of these moving averages, and estimating the per-parameter second moments based on these sums. We demonstrate empirically that this method produces similar results to the baseline. Secondly, we show that adaptive methods can produce larger-than-desired updates when the decay rate of the second moment accumulator is too slow. We propose update clipping and a gradually increasing decay rate scheme as remedies. Combining these methods and dropping momentum, we achieve comparable results to the published Adam regime in training the Transformer model on the WMT 2014 English-German machine translation task, while using very little auxiliary storage in the optimizer. Finally, we propose scaling the parameter updates based on the scale of the parameters themselves.

Motion behaviour is driven by several factors -- goals, presence and actions of neighbouring agents, social relations, physical and social norms, the environment with its variable characteristics, and further. Most factors are not directly observable and must be modelled from context. Trajectory prediction, is thus a hard problem, and has seen increasing attention from researchers in the recent years. Prediction of motion, in application, must be realistic, diverse and controllable. In spite of increasing focus on multimodal trajectory generation, most methods still lack means for explicitly controlling different modes of the data generation. Further, most endeavours invest heavily in designing special mechanisms to learn the interactions in latent space. We present Conditional Speed GAN (CSG), that allows controlled generation of diverse and socially acceptable trajectories, based on user controlled speed. During prediction, CSG forecasts future speed from latent space and conditions its generation based on it. CSG is comparable to state-of-the-art GAN methods in terms of the benchmark distance metrics, while being simple and useful for simulation and data augmentation for different contexts such as fast or slow paced environments. Additionally, we compare the effect of different aggregation mechanisms and show that a naive approach of concatenation works comparable to its attention and pooling alternatives.

Several recently proposed stochastic optimization methods that have been successfully used in training deep networks such as RMSProp, Adam, Adadelta, Nadam are based on using gradient updates scaled by square roots of exponential moving averages of squared past gradients. In many applications, e.g. learning with large output spaces, it has been empirically observed that these algorithms fail to converge to an optimal solution (or a critical point in nonconvex settings). We show that one cause for such failures is the exponential moving average used in the algorithms. We provide an explicit example of a simple convex optimization setting where Adam does not converge to the optimal solution, and describe the precise problems with the previous analysis of Adam algorithm. Our analysis suggests that the convergence issues can be fixed by endowing such algorithms with `long-term memory' of past gradients, and propose new variants of the Adam algorithm which not only fix the convergence issues but often also lead to improved empirical performance.

A large body of research in continual learning is devoted to overcoming the catastrophic forgetting of neural networks by designing new algorithms that are robust to the distribution shifts. However, the majority of these works are strictly focused on the "algorithmic" part of continual learning for a "fixed neural network architecture", and the implications of using different architectures are mostly neglected. Even the few existing continual learning methods that modify the model assume a fixed architecture and aim to develop an algorithm that efficiently uses the model throughout the learning experience. However, in this work, we show that the choice of architecture can significantly impact the continual learning performance, and different architectures lead to different trade-offs between the ability to remember previous tasks and learning new ones. Moreover, we study the impact of various architectural decisions, and our findings entail best practices and recommendations that can improve the continual learning performance.

The enormous amount of data produced by mobile and IoT devices has motivated the development of federated learning (FL), a framework allowing such devices (or clients) to collaboratively train machine learning models without sharing their local data. FL algorithms (like FedAvg) iteratively aggregate model updates computed by clients on their own datasets. Clients may exhibit different levels of participation, often correlated over time and with other clients. This paper presents the first convergence analysis for a FedAvg-like FL algorithm under heterogeneous and correlated client availability. Our analysis highlights how correlation adversely affects the algorithm's convergence rate and how the aggregation strategy can alleviate this effect at the cost of steering training toward a biased model. Guided by the theoretical analysis, we propose CA-Fed, a new FL algorithm that tries to balance the conflicting goals of maximizing convergence speed and minimizing model bias. To this purpose, CA-Fed dynamically adapts the weight given to each client and may ignore clients with low availability and large correlation. Our experimental results show that CA-Fed achieves higher time-average accuracy and a lower standard deviation than state-of-the-art AdaFed and F3AST, both on synthetic and real datasets.

Distribution shift (e.g., task or domain shift) in continual learning (CL) usually results in catastrophic forgetting of neural networks. Although it can be alleviated by repeatedly replaying buffered data, the every-step replay is time-consuming. In this paper, we study which modules in neural networks are more prone to forgetting by investigating their training dynamics during CL. Our proposed metrics show that only a few modules are more task-specific and sensitively alter between tasks, while others can be shared across tasks as common knowledge. Hence, we attribute forgetting mainly to the former and find that finetuning them only on a small buffer at the end of any CL method can bring non-trivial improvement. Due to the small number of finetuned parameters, such ``Forgetting Prioritized Finetuning (FPF)'' is efficient in computation. We further propose a more efficient and simpler method that entirely removes the every-step replay and replaces them by only k-times of FPF periodically triggered during CL. Surprisingly, this ``k-FPF'' performs comparably to FPF and outperforms the SOTA CL methods but significantly reduces their computational overhead and cost. In experiments on several benchmarks of class- and domain-incremental CL, FPF consistently improves existing CL methods by a large margin, and k-FPF further excels in efficiency without degrading the accuracy. We also empirically studied the impact of buffer size, epochs per task, and finetuning modules on the cost and accuracy of our methods.

While the phenomenon of grokking, i.e., delayed generalization, has been studied extensively, it remains an open problem whether there is a mathematical framework that characterizes what kind of features will emerge, how and in which conditions it happens, and is closely related to the gradient dynamics of the training, for complex structured inputs. We propose a novel framework, named Li_2, that captures three key stages for the grokking behavior of 2-layer nonlinear networks: (I) \textbf{L}azy learning, (II) \textbf{i}ndependent feature learning and (III) \textbf{i}nteractive feature learning. At the lazy learning stage, top layer overfits to random hidden representation and the model appears to memorize. Thanks to lazy learning and weight decay, the backpropagated gradient G_F from the top layer now carries information about the target label, with a specific structure that enables each hidden node to learn their representation independently. Interestingly, the independent dynamics follows exactly the gradient ascent of an energy function E, and its local maxima are precisely the emerging features. We study whether these local-optima induced features are generalizable, their representation power, and how they change on sample size, in group arithmetic tasks. When hidden nodes start to interact in the later stage of learning, we provably show how G_F changes to focus on missing features that need to be learned. Our study sheds lights on roles played by key hyperparameters such as weight decay, learning rate and sample sizes in grokking, leads to provable scaling laws of feature emergence, memorization and generalization, and reveals the underlying cause why recent optimizers such as Muon can be effective, from the first principles of gradient dynamics. Our analysis can be extended to multi-layer architectures.

While neural networks can be approximated by linear models as their width increases, certain properties of wide neural networks cannot be captured by linear models. In this work we show that recently proposed Neural Quadratic Models can exhibit the "catapult phase" [Lewkowycz et al. 2020] that arises when training such models with large learning rates. We then empirically show that the behaviour of neural quadratic models parallels that of neural networks in generalization, especially in the catapult phase regime. Our analysis further demonstrates that quadratic models can be an effective tool for analysis of neural networks.

A class of generative models that unifies flow-based and diffusion-based methods is introduced. These models extend the framework proposed in Albergo & Vanden-Eijnden (2023), enabling the use of a broad class of continuous-time stochastic processes called `stochastic interpolants' to bridge any two arbitrary probability density functions exactly in finite time. These interpolants are built by combining data from the two prescribed densities with an additional latent variable that shapes the bridge in a flexible way. The time-dependent probability density function of the stochastic interpolant is shown to satisfy a first-order transport equation as well as a family of forward and backward Fokker-Planck equations with tunable diffusion coefficient. Upon consideration of the time evolution of an individual sample, this viewpoint immediately leads to both deterministic and stochastic generative models based on probability flow equations or stochastic differential equations with an adjustable level of noise. The drift coefficients entering these models are time-dependent velocity fields characterized as the unique minimizers of simple quadratic objective functions, one of which is a new objective for the score of the interpolant density. We show that minimization of these quadratic objectives leads to control of the likelihood for generative models built upon stochastic dynamics, while likelihood control for deterministic dynamics is more stringent. We also discuss connections with other methods such as score-based diffusion models, stochastic localization processes, probabilistic denoising techniques, and rectifying flows. In addition, we demonstrate that stochastic interpolants recover the Schr\"odinger bridge between the two target densities when explicitly optimizing over the interpolant. Finally, algorithmic aspects are discussed and the approach is illustrated on numerical examples.

With the rapid advancement of AI systems, their abilities to store, retrieve, and utilize information over the long term - referred to as long-term memory - have become increasingly significant. These capabilities are crucial for enhancing the performance of AI systems across a wide range of tasks. However, there is currently no comprehensive survey that systematically investigates AI's long-term memory capabilities, formulates a theoretical framework, and inspires the development of next-generation AI long-term memory systems. This paper begins by systematically introducing the mechanisms of human long-term memory, then explores AI long-term memory mechanisms, establishing a mapping between the two. Based on the mapping relationships identified, we extend the current cognitive architectures and propose the Cognitive Architecture of Self-Adaptive Long-term Memory (SALM). SALM provides a theoretical framework for the practice of AI long-term memory and holds potential for guiding the creation of next-generation long-term memory driven AI systems. Finally, we delve into the future directions and application prospects of AI long-term memory.

In this paper we present a new framework for time-series modeling that combines the best of traditional statistical models and neural networks. We focus on time-series with long-range dependencies, needed for monitoring fine granularity data (e.g. minutes, seconds, milliseconds), prevalent in operational use-cases. Traditional models, such as auto-regression fitted with least squares (Classic-AR) can model time-series with a concise and interpretable model. When dealing with long-range dependencies, Classic-AR models can become intractably slow to fit for large data. Recently, sequence-to-sequence models, such as Recurrent Neural Networks, which were originally intended for natural language processing, have become popular for time-series. However, they can be overly complex for typical time-series data and lack interpretability. A scalable and interpretable model is needed to bridge the statistical and deep learning-based approaches. As a first step towards this goal, we propose modelling AR-process dynamics using a feed-forward neural network approach, termed AR-Net. We show that AR-Net is as interpretable as Classic-AR but also scales to long-range dependencies. Our results lead to three major conclusions: First, AR-Net learns identical AR-coefficients as Classic-AR, thus being equally interpretable. Second, the computational complexity with respect to the order of the AR process, is linear for AR-Net as compared to a quadratic for Classic-AR. This makes it possible to model long-range dependencies within fine granularity data. Third, by introducing regularization, AR-Net automatically selects and learns sparse AR-coefficients. This eliminates the need to know the exact order of the AR-process and allows to learn sparse weights for a model with long-range dependencies.

Not all positive pairs are beneficial to time series contrastive learning. In this paper, we study two types of bad positive pairs that can impair the quality of time series representation learned through contrastive learning: the noisy positive pair and the faulty positive pair. We observe that, with the presence of noisy positive pairs, the model tends to simply learn the pattern of noise (Noisy Alignment). Meanwhile, when faulty positive pairs arise, the model wastes considerable amount of effort aligning non-representative patterns (Faulty Alignment). To address this problem, we propose a Dynamic Bad Pair Mining (DBPM) algorithm, which reliably identifies and suppresses bad positive pairs in time series contrastive learning. Specifically, DBPM utilizes a memory module to dynamically track the training behavior of each positive pair along training process. This allows us to identify potential bad positive pairs at each epoch based on their historical training behaviors. The identified bad pairs are subsequently down-weighted through a transformation module, thereby mitigating their negative impact on the representation learning process. DBPM is a simple algorithm designed as a lightweight plug-in without learnable parameters to enhance the performance of existing state-of-the-art methods. Through extensive experiments conducted on four large-scale, real-world time series datasets, we demonstrate DBPM's efficacy in mitigating the adverse effects of bad positive pairs.

Time-series forecasting is one of the most active research topics in artificial intelligence. Applications in real-world time series should consider two factors for achieving reliable predictions: modeling dynamic dependencies among multiple variables and adjusting the model's intrinsic hyperparameters. A still open gap in that literature is that statistical and ensemble learning approaches systematically present lower predictive performance than deep learning methods. They generally disregard the data sequence aspect entangled with multivariate data represented in more than one time series. Conversely, this work presents a novel neural network architecture for time-series forecasting that combines the power of graph evolution with deep recurrent learning on distinct data distributions; we named our method Recurrent Graph Evolution Neural Network (ReGENN). The idea is to infer multiple multivariate relationships between co-occurring time-series by assuming that the temporal data depends not only on inner variables and intra-temporal relationships (i.e., observations from itself) but also on outer variables and inter-temporal relationships (i.e., observations from other-selves). An extensive set of experiments was conducted comparing ReGENN with dozens of ensemble methods and classical statistical ones, showing sound improvement of up to 64.87% over the competing algorithms. Furthermore, we present an analysis of the intermediate weights arising from ReGENN, showing that by looking at inter and intra-temporal relationships simultaneously, time-series forecasting is majorly improved if paying attention to how multiple multivariate data synchronously evolve.

Redundancies and correlations in the responses of sensory neurons seem to waste neural resources but can carry cues about structured stimuli and may help the brain to correct for response errors. To assess how the retina negotiates this tradeoff, we measured simultaneous responses from populations of ganglion cells presented with natural and artificial stimuli that varied greatly in correlation structure. We found that pairwise correlations in the retinal output remained similar across stimuli with widely different spatio-temporal correlations including white noise and natural movies. Meanwhile, purely spatial correlations tended to increase correlations in the retinal response. Responding to more correlated stimuli, ganglion cells had faster temporal kernels and tended to have stronger surrounds. These properties of individual cells, along with gain changes that opposed changes in effective contrast at the ganglion cell input, largely explained the similarity of pairwise correlations across stimuli where receptive field measurements were possible.

The emerging field of Diverse Intelligence seeks to identify, formalize, and understand commonalities in behavioral competencies across a wide range of implementations. Especially interesting are simple systems that provide unexpected examples of memory, decision-making, or problem-solving in substrates that at first glance do not appear to be complex enough to implement such capabilities. We seek to develop tools to help understand the minimal requirements for such capabilities, and to learn to recognize and predict basal forms of intelligence in unconventional substrates. Here, we apply novel analyses to the behavior of classical sorting algorithms, short pieces of code which have been studied for many decades. To study these sorting algorithms as a model of biological morphogenesis and its competencies, we break two formerly-ubiquitous assumptions: top-down control (instead, showing how each element within a array of numbers can exert minimal agency and implement sorting policies from the bottom up), and fully reliable hardware (instead, allowing some of the elements to be "damaged" and fail to execute the algorithm). We quantitatively characterize sorting activity as the traversal of a problem space, showing that arrays of autonomous elements sort themselves more reliably and robustly than traditional implementations in the presence of errors. Moreover, we find the ability to temporarily reduce progress in order to navigate around a defect, and unexpected clustering behavior among the elements in chimeric arrays whose elements follow one of two different algorithms. The discovery of emergent problem-solving capacities in simple, familiar algorithms contributes a new perspective to the field of Diverse Intelligence, showing how basal forms of intelligence can emerge in simple systems without being explicitly encoded in their underlying mechanics.

Understanding memorisation in language models has practical and societal implications, e.g., studying models' training dynamics or preventing copyright infringements. Prior work defines memorisation as the causal effect of training with an instance on the model's ability to predict that instance. This definition relies on a counterfactual: the ability to observe what would have happened had the model not seen that instance. Existing methods struggle to provide computationally efficient and accurate estimates of this counterfactual. Further, they often estimate memorisation for a model architecture rather than for a specific model instance. This paper fills an important gap in the literature, proposing a new, principled, and efficient method to estimate memorisation based on the difference-in-differences design from econometrics. Using this method, we characterise a model's memorisation profile--its memorisation trends across training--by only observing its behaviour on a small set of instances throughout training. In experiments with the Pythia model suite, we find that memorisation (i) is stronger and more persistent in larger models, (ii) is determined by data order and learning rate, and (iii) has stable trends across model sizes, thus making memorisation in larger models predictable from smaller ones.

Incorporating external context can significantly enhance the response quality of Large Language Models (LLMs). However, real-world contexts often mix relevant information with disproportionate inappropriate content, posing reliability risks. How do LLMs process and prioritize mixed context? To study this, we introduce the Poisoned Context Testbed, pairing queries with real-world contexts containing relevant and inappropriate content. Inspired by associative learning in animals, we adapt the Rescorla-Wagner (RW) model from neuroscience to quantify how competing contextual signals influence LLM outputs. Our adapted model reveals a consistent behavioral pattern: LLMs exhibit a strong tendency to incorporate information that is less prevalent in the context. This susceptibility is harmful in real-world settings, where small amounts of inappropriate content can substantially degrade response quality. Empirical evaluations on our testbed further confirm this vulnerability. To tackle this, we introduce RW-Steering, a two-stage finetuning-based approach that enables the model to internally identify and ignore inappropriate signals. Unlike prior methods that rely on extensive supervision across diverse context mixtures, RW-Steering generalizes robustly across varying proportions of inappropriate content. Experiments show that our best fine-tuned model improves response quality by 39.8% and reverses the undesirable behavior curve, establishing RW-Steering as a robust, generalizable context engineering solution for improving LLM safety in real-world use.