Daily Papers

Post-hoc gradient-based interpretability methods [Simonyan et al., 2013, Smilkov et al., 2017] that provide instance-specific explanations of model predictions are often based on assumption (A): magnitude of input gradients -- gradients of logits with respect to input -- noisily highlight discriminative task-relevant features. In this work, we test the validity of assumption (A) using a three-pronged approach. First, we develop an evaluation framework, DiffROAR, to test assumption (A) on four image classification benchmarks. Our results suggest that (i) input gradients of standard models (i.e., trained on original data) may grossly violate (A), whereas (ii) input gradients of adversarially robust models satisfy (A). Second, we introduce BlockMNIST, an MNIST-based semi-real dataset, that by design encodes a priori knowledge of discriminative features. Our analysis on BlockMNIST leverages this information to validate as well as characterize differences between input gradient attributions of standard and robust models. Finally, we theoretically prove that our empirical findings hold on a simplified version of the BlockMNIST dataset. Specifically, we prove that input gradients of standard one-hidden-layer MLPs trained on this dataset do not highlight instance-specific signal coordinates, thus grossly violating assumption (A). Our findings motivate the need to formalize and test common assumptions in interpretability in a falsifiable manner [Leavitt and Morcos, 2020]. We believe that the DiffROAR evaluation framework and BlockMNIST-based datasets can serve as sanity checks to audit instance-specific interpretability methods; code and data available at https://github.com/harshays/inputgradients.

In this work we revisit the most fundamental building block in deep learning, the multi-layer perceptron (MLP), and study the limits of its performance on vision tasks. Empirical insights into MLPs are important for multiple reasons. (1) Given the recent narrative "less inductive bias is better", popularized due to transformers eclipsing convolutional models, it is natural to explore the limits of this hypothesis. To that end, MLPs offer an ideal test bed, being completely free of any inductive bias. (2) MLPs have almost exclusively been the main protagonist in the deep learning theory literature due to their mathematical simplicity, serving as a proxy to explain empirical phenomena observed for more complex architectures. Surprisingly, experimental datapoints for MLPs are very difficult to find in the literature, especially when coupled with large pre-training protocols. This discrepancy between practice and theory is worrying: Do MLPs reflect the empirical advances exhibited by practical models? Or do theorists need to rethink the role of MLPs as a proxy? We provide insights into both these aspects. We show that the performance of MLPs drastically improves with scale (93% on CIFAR10, 79% on CIFAR100, 69% on TinyImageNet), highlighting that lack of inductive bias can indeed be compensated. We observe that MLPs mimic the behaviour of their modern counterparts faithfully, with some components in the learning setting however surprisingly exhibiting stronger or unexpected behaviours. Due to their inherent computational efficiency, large pre-training experiments become more accessible for academic researchers. All of our experiments were run on a single GPU.

A mechanistic understanding of how MLPs do computation in deep neural networks remains elusive. Current interpretability work can extract features from hidden activations over an input dataset but generally cannot explain how MLP weights construct features. One challenge is that element-wise nonlinearities introduce higher-order interactions and make it difficult to trace computations through the MLP layer. In this paper, we analyze bilinear MLPs, a type of Gated Linear Unit (GLU) without any element-wise nonlinearity that nevertheless achieves competitive performance. Bilinear MLPs can be fully expressed in terms of linear operations using a third-order tensor, allowing flexible analysis of the weights. Analyzing the spectra of bilinear MLP weights using eigendecomposition reveals interpretable low-rank structure across toy tasks, image classification, and language modeling. We use this understanding to craft adversarial examples, uncover overfitting, and identify small language model circuits directly from the weights alone. Our results demonstrate that bilinear layers serve as an interpretable drop-in replacement for current activation functions and that weight-based interpretability is viable for understanding deep-learning models.

Multi-layer perceptron (MLP) is a fundamental component of deep learning that has been extensively employed for various problems. However, recent empirical successes in MLP-based architectures, particularly the progress of the MLP-Mixer, have revealed that there is still hidden potential in improving MLPs to achieve better performance. In this study, we reveal that the MLP-Mixer works effectively as a wide MLP with certain sparse weights. Initially, we clarify that the mixing layer of the Mixer has an effective expression as a wider MLP whose weights are sparse and represented by the Kronecker product. This expression naturally defines a permuted-Kronecker (PK) family, which can be regarded as a general class of mixing layers and is also regarded as an approximation of Monarch matrices. Subsequently, because the PK family effectively constitutes a wide MLP with sparse weights, one can apply the hypothesis proposed by Golubeva, Neyshabur and Gur-Ari (2021) that the prediction performance improves as the width (sparsity) increases when the number of weights is fixed. We empirically verify this hypothesis by maximizing the effective width of the MLP-Mixer, which enables us to determine the appropriate size of the mixing layers quantitatively.

The ability of neural networks to represent more features than neurons makes interpreting them challenging. This phenomenon, known as superposition, has spurred efforts to find architectures that are more interpretable than standard multilayer perceptrons (MLPs) with elementwise activation functions. In this note, I examine bilinear layers, which are a type of MLP layer that are mathematically much easier to analyze while simultaneously performing better than standard MLPs. Although they are nonlinear functions of their input, I demonstrate that bilinear layers can be expressed using only linear operations and third order tensors. We can integrate this expression for bilinear layers into a mathematical framework for transformer circuits, which was previously limited to attention-only transformers. These results suggest that bilinear layers are easier to analyze mathematically than current architectures and thus may lend themselves to deeper safety insights by allowing us to talk more formally about circuits in neural networks. Additionally, bilinear layers may offer an alternative path for mechanistic interpretability through understanding the mechanisms of feature construction instead of enumerating a (potentially exponentially) large number of features in large models.

Machine unlearning methods seek to revise pretrained models such that effects of certain training samples can be removed. In addition to effective erasure, low computational cost and general utility retention are also highly desirable. Existing unlearning methods usually involve iterative updates over the model parameters, which incurs a high computational cost. In this work, we propose an efficient method that only requires a one-time gradient computation, with which we modify only a single layer of model parameters. Specifically, we first identify a small number of model layers that lie on the Pareto front of high forget importance and low retain influence as critical layers. Then we search for a suitable step size and take a step along the gradient direction of a single critical layer while keeping other layers frozen. This method is highly modular and can be used to unlearn multiple concepts simultaneously in a controllable manner. We demonstrate the effectiveness and efficiency of this method on various models including CLIP, stable diffusion, and VLMs, surpassing other state-of-the-art methods.

Inspired by the Kolmogorov-Arnold representation theorem, we propose Kolmogorov-Arnold Networks (KANs) as promising alternatives to Multi-Layer Perceptrons (MLPs). While MLPs have fixed activation functions on nodes ("neurons"), KANs have learnable activation functions on edges ("weights"). KANs have no linear weights at all -- every weight parameter is replaced by a univariate function parametrized as a spline. We show that this seemingly simple change makes KANs outperform MLPs in terms of accuracy and interpretability. For accuracy, much smaller KANs can achieve comparable or better accuracy than much larger MLPs in data fitting and PDE solving. Theoretically and empirically, KANs possess faster neural scaling laws than MLPs. For interpretability, KANs can be intuitively visualized and can easily interact with human users. Through two examples in mathematics and physics, KANs are shown to be useful collaborators helping scientists (re)discover mathematical and physical laws. In summary, KANs are promising alternatives for MLPs, opening opportunities for further improving today's deep learning models which rely heavily on MLPs.

In recent years, significant efforts have been directed toward adapting modern neural network architectures for tabular data. However, despite their larger number of parameters and longer training and inference times, these models often fail to consistently outperform vanilla multilayer perceptron (MLP) neural networks. Moreover, MLP-based ensembles have recently demonstrated superior performance and efficiency compared to advanced deep learning methods. Therefore, rather than focusing on building deeper and more complex deep learning models, we propose investigating whether MLP neural networks can be replaced with more efficient architectures without sacrificing performance. In this paper, we first introduce GG MoE, a mixture-of-experts (MoE) model with a Gumbel-Softmax gating function. We then demonstrate that GG MoE with an embedding layer achieves the highest performance across 38 datasets compared to standard MoE and MLP models. Finally, we show that both MoE and GG MoE utilize significantly fewer parameters than MLPs, making them a promising alternative for scaling and ensemble methods.

Recent advancements in both representation learning and function learning have demonstrated substantial promise across diverse domains of artificial intelligence. However, the effective integration of these paradigms poses a significant challenge, particularly in cases where users must manually decide whether to apply a representation learning or function learning model based on dataset characteristics. To address this issue, we introduce MLP-KAN, a unified method designed to eliminate the need for manual model selection. By integrating Multi-Layer Perceptrons (MLPs) for representation learning and Kolmogorov-Arnold Networks (KANs) for function learning within a Mixture-of-Experts (MoE) architecture, MLP-KAN dynamically adapts to the specific characteristics of the task at hand, ensuring optimal performance. Embedded within a transformer-based framework, our work achieves remarkable results on four widely-used datasets across diverse domains. Extensive experimental evaluation demonstrates its superior versatility, delivering competitive performance across both deep representation and function learning tasks. These findings highlight the potential of MLP-KAN to simplify the model selection process, offering a comprehensive, adaptable solution across various domains. Our code and weights are available at https://github.com/DLYuanGod/MLP-KAN.

For the past ten years, CNN has reigned supreme in the world of computer vision, but recently, Transformer has been on the rise. However, the quadratic computational cost of self-attention has become a serious problem in practice applications. There has been much research on architectures without CNN and self-attention in this context. In particular, MLP-Mixer is a simple architecture designed using MLPs and hit an accuracy comparable to the Vision Transformer. However, the only inductive bias in this architecture is the embedding of tokens. This leaves open the possibility of incorporating a non-convolutional (or non-local) inductive bias into the architecture, so we used two simple ideas to incorporate inductive bias into the MLP-Mixer while taking advantage of its ability to capture global correlations. A way is to divide the token-mixing block vertically and horizontally. Another way is to make spatial correlations denser among some channels of token-mixing. With this approach, we were able to improve the accuracy of the MLP-Mixer while reducing its parameters and computational complexity. The small model that is RaftMLP-S is comparable to the state-of-the-art global MLP-based model in terms of parameters and efficiency per calculation. In addition, we tackled the problem of fixed input image resolution for global MLP-based models by utilizing bicubic interpolation. We demonstrated that these models could be applied as the backbone of architectures for downstream tasks such as object detection. However, it did not have significant performance and mentioned the need for MLP-specific architectures for downstream tasks for global MLP-based models. The source code in PyTorch version is available at https://github.com/okojoalg/raft-mlp.

All-MLP architectures have attracted increasing interest as an alternative to attention-based models. In NLP, recent work like gMLP shows that all-MLPs can match Transformers in language modeling, but still lag behind in downstream tasks. In this work, we analyze the limitations of MLPs in expressiveness, and propose sparsely activated MLPs with mixture-of-experts (MoEs) in both feature and input (token) dimensions. Such sparse all-MLPs significantly increase model capacity and expressiveness while keeping the compute constant. We address critical challenges in incorporating conditional computation with two routing strategies. The proposed sparse all-MLP improves language modeling perplexity and obtains up to 2times improvement in training efficiency compared to both Transformer-based MoEs (GShard, Switch Transformer, Base Layers and HASH Layers) as well as dense Transformers and all-MLPs. Finally, we evaluate its zero-shot in-context learning performance on six downstream tasks, and find that it surpasses Transformer-based MoEs and dense Transformers.

Multi-layer perceptrons (MLPs) conventionally follow a narrow-wide-narrow design where skip connections operate at the input/output dimensions while processing occurs in expanded hidden spaces. We challenge this convention by proposing wide-narrow-wide (Hourglass) MLP blocks where skip connections operate at expanded dimensions while residual computation flows through narrow bottlenecks. This inversion leverages higher-dimensional spaces for incremental refinement while maintaining computational efficiency through parameter-matched designs. Implementing Hourglass MLPs requires an initial projection to lift input signals to expanded dimensions. We propose that this projection can remain fixed at random initialization throughout training, enabling efficient training and inference implementations. We evaluate both architectures on generative tasks over popular image datasets, characterizing performance-parameter Pareto frontiers through systematic architectural search. Results show that Hourglass architectures consistently achieve superior Pareto frontiers compared to conventional designs. As parameter budgets increase, optimal Hourglass configurations favor deeper networks with wider skip connections and narrower bottlenecks-a scaling pattern distinct from conventional MLPs. Our findings suggest reconsidering skip connection placement in modern architectures, with potential applications extending to Transformers and other residual networks.

Convolutional Neural Networks (CNNs) are the go-to model for computer vision. Recently, attention-based networks, such as the Vision Transformer, have also become popular. In this paper we show that while convolutions and attention are both sufficient for good performance, neither of them are necessary. We present MLP-Mixer, an architecture based exclusively on multi-layer perceptrons (MLPs). MLP-Mixer contains two types of layers: one with MLPs applied independently to image patches (i.e. "mixing" the per-location features), and one with MLPs applied across patches (i.e. "mixing" spatial information). When trained on large datasets, or with modern regularization schemes, MLP-Mixer attains competitive scores on image classification benchmarks, with pre-training and inference cost comparable to state-of-the-art models. We hope that these results spark further research beyond the realms of well established CNNs and Transformers.

Printed Electronics (PE) feature distinct and remarkable characteristics that make them a prominent technology for achieving true ubiquitous computing. This is particularly relevant in application domains that require conformal and ultra-low cost solutions, which have experienced limited penetration of computing until now. Unlike silicon-based technologies, PE offer unparalleled features such as non-recurring engineering costs, ultra-low manufacturing cost, and on-demand fabrication of conformal, flexible, non-toxic, and stretchable hardware. However, PE face certain limitations due to their large feature sizes, that impede the realization of complex circuits, such as machine learning classifiers. In this work, we address these limitations by leveraging the principles of Approximate Computing and Bespoke (fully-customized) design. We propose an automated framework for designing ultra-low power Multilayer Perceptron (MLP) classifiers which employs, for the first time, a holistic approach to approximate all functions of the MLP's neurons: multiplication, accumulation, and activation. Through comprehensive evaluation across various MLPs of varying size, our framework demonstrates the ability to enable battery-powered operation of even the most intricate MLP architecture examined, significantly surpassing the current state of the art.

Token interaction operation is one of the core modules in MLP-based models to exchange and aggregate information between different spatial locations. However, the power of token interaction on the spatial dimension is highly dependent on the spatial resolution of the feature maps, which limits the model's expressive ability, especially in deep layers where the feature are down-sampled to a small spatial size. To address this issue, we present a novel method called Strip-MLP to enrich the token interaction power in three ways. Firstly, we introduce a new MLP paradigm called Strip MLP layer that allows the token to interact with other tokens in a cross-strip manner, enabling the tokens in a row (or column) to contribute to the information aggregations in adjacent but different strips of rows (or columns). Secondly, a Cascade Group Strip Mixing Module (CGSMM) is proposed to overcome the performance degradation caused by small spatial feature size. The module allows tokens to interact more effectively in the manners of within-patch and cross-patch, which is independent to the feature spatial size. Finally, based on the Strip MLP layer, we propose a novel Local Strip Mixing Module (LSMM) to boost the token interaction power in the local region. Extensive experiments demonstrate that Strip-MLP significantly improves the performance of MLP-based models on small datasets and obtains comparable or even better results on ImageNet. In particular, Strip-MLP models achieve higher average Top-1 accuracy than existing MLP-based models by +2.44\% on Caltech-101 and +2.16\% on CIFAR-100. The source codes will be available at~https://github.com/Med-Process/Strip_MLP{https://github.com/Med-Process/Strip\_MLP.

Token-mixing multi-layer perceptron (MLP) models have shown competitive performance in computer vision tasks with a simple architecture and relatively small computational cost. Their success in maintaining computation efficiency is mainly attributed to avoiding the use of self-attention that is often computationally heavy, yet this is at the expense of not being able to mix tokens both globally and locally. In this paper, to exploit both global and local dependencies without self-attention, we present Mix-Shift-MLP (MS-MLP) which makes the size of the local receptive field used for mixing increase with respect to the amount of spatial shifting. In addition to conventional mixing and shifting techniques, MS-MLP mixes both neighboring and distant tokens from fine- to coarse-grained levels and then gathers them via a shifting operation. This directly contributes to the interactions between global and local tokens. Being simple to implement, MS-MLP achieves competitive performance in multiple vision benchmarks. For example, an MS-MLP with 85 million parameters achieves 83.8% top-1 classification accuracy on ImageNet-1K. Moreover, by combining MS-MLP with state-of-the-art Vision Transformers such as the Swin Transformer, we show MS-MLP achieves further improvements on three different model scales, e.g., by 0.5% on ImageNet-1K classification with Swin-B. The code is available at: https://github.com/JegZheng/MS-MLP.

The multilayer perceptron (MLP), a fundamental paradigm in current artificial intelligence, is widely applied in fields such as computer vision and natural language processing. However, the recently proposed Kolmogorov-Arnold Network (KAN), based on nonlinear additive connections, has been proven to achieve performance comparable to MLPs with significantly fewer parameters. Despite this potential, the use of a single activation function space results in reduced performance of KAN and related works across different tasks. To address this issue, we propose an activation space Selectable KAN (S-KAN). S-KAN employs an adaptive strategy to choose the possible activation mode for data at each feedforward KAN node. Our approach outperforms baseline methods in seven representative function fitting tasks and significantly surpasses MLP methods with the same level of parameters. Furthermore, we extend the structure of S-KAN and propose an activation space selectable Convolutional KAN (S-ConvKAN), which achieves leading results on four general image classification datasets. Our method mitigates the performance variability of the original KAN across different tasks and demonstrates through extensive experiments that feedforward KANs with selectable activations can achieve or even exceed the performance of MLP-based methods. This work contributes to the understanding of the data-centric design of new AI paradigms and provides a foundational reference for innovations in KAN-based network architectures.

Transformer layers, which use an alternating pattern of multi-head attention and multi-layer perceptron (MLP) layers, provide an effective tool for a variety of machine learning problems. As the transformer layers use residual connections to avoid the problem of vanishing gradients, they can be viewed as the numerical integration of a differential equation. In this extended abstract, we build upon this connection and propose a modification of the internal architecture of a transformer layer. The proposed model places the multi-head attention sublayer and the MLP sublayer parallel to each other. Our experiments show that this simple modification improves the performance of transformer networks in multiple tasks. Moreover, for the image classification task, we show that using neural ODE solvers with a sophisticated integration scheme further improves performance.

In this paper, we focus on a typical two-phase phenomenon in the learning of multi-layer perceptrons (MLPs), and we aim to explain the reason for the decrease of feature diversity in the first phase. Specifically, people find that, in the training of MLPs, the training loss does not decrease significantly until the second phase. To this end, we further explore the reason why the diversity of features over different samples keeps decreasing in the first phase, which hurts the optimization of MLPs. We explain such a phenomenon in terms of the learning dynamics of MLPs. Furthermore, we theoretically explain why four typical operations can alleviate the decrease of the feature diversity.

Fine-tuning a pre-trained language model (PLM) emerges as the predominant strategy in many natural language processing applications. However, even fine-tuning the PLMs and doing inference are expensive, especially on edge devices with low computing power. Some general approaches (e.g. quantization and distillation) have been widely studied to reduce the compute/memory of PLM fine-tuning, while very few one-shot compression techniques are explored. In this paper, we investigate the neural tangent kernel (NTK)--which reveals the gradient descent dynamics of neural networks--of the multilayer perceptrons (MLP) modules in a PLM and propose to coin a lightweight PLM through NTK-approximating MLP fusion. To achieve this, we reconsider the MLP as a bundle of sub-MLPs, and cluster them into a given number of centroids, which can then be restored as a compressed MLP and surprisingly shown to well approximate the NTK of the original PLM. Extensive experiments of PLM fine-tuning on both natural language understanding (NLU) and generation (NLG) tasks are provided to verify the effectiveness of the proposed method MLP fusion. Our code is available at https://github.com/weitianxin/MLP_Fusion.

Recent progress on Transformers and multi-layer perceptron (MLP) models provide new network architectural designs for computer vision tasks. Although these models proved to be effective in many vision tasks such as image recognition, there remain challenges in adapting them for low-level vision. The inflexibility to support high-resolution images and limitations of local attention are perhaps the main bottlenecks. In this work, we present a multi-axis MLP based architecture called MAXIM, that can serve as an efficient and flexible general-purpose vision backbone for image processing tasks. MAXIM uses a UNet-shaped hierarchical structure and supports long-range interactions enabled by spatially-gated MLPs. Specifically, MAXIM contains two MLP-based building blocks: a multi-axis gated MLP that allows for efficient and scalable spatial mixing of local and global visual cues, and a cross-gating block, an alternative to cross-attention, which accounts for cross-feature conditioning. Both these modules are exclusively based on MLPs, but also benefit from being both global and `fully-convolutional', two properties that are desirable for image processing. Our extensive experimental results show that the proposed MAXIM model achieves state-of-the-art performance on more than ten benchmarks across a range of image processing tasks, including denoising, deblurring, deraining, dehazing, and enhancement while requiring fewer or comparable numbers of parameters and FLOPs than competitive models. The source code and trained models will be available at https://github.com/google-research/maxim.

This paper presents a novel technique based on gradient boosting to train the final layers of a neural network (NN). Gradient boosting is an additive expansion algorithm in which a series of models are trained sequentially to approximate a given function. A neural network can also be seen as an additive expansion where the scalar product of the responses of the last hidden layer and its weights provide the final output of the network. Instead of training the network as a whole, the proposed algorithm trains the network sequentially in T steps. First, the bias term of the network is initialized with a constant approximation that minimizes the average loss of the data. Then, at each step, a portion of the network, composed of J neurons, is trained to approximate the pseudo-residuals on the training data computed from the previous iterations. Finally, the T partial models and bias are integrated as a single NN with T times J neurons in the hidden layer. Extensive experiments in classification and regression tasks, as well as in combination with deep neural networks, are carried out showing a competitive generalization performance with respect to neural networks trained with different standard solvers, such as Adam, L-BFGS, SGD and deep models. Furthermore, we show that the proposed method design permits to switch off a number of hidden units during test (the units that were last trained) without a significant reduction of its generalization ability. This permits the adaptation of the model to different classification speed requirements on the fly.

Mixture-of-Experts (MoE), a conditional computation architecture, achieved promising performance by scaling local module (i.e. feed-forward network) of transformer. However, scaling the cross-token module (i.e. self-attention) is challenging due to the unstable training. This work proposes Sparse-MLP, an all-MLP model which applies sparsely-activated MLPs to cross-token modeling. Specifically, in each Sparse block of our all-MLP model, we apply two stages of MoE layers: one with MLP experts mixing information within channels along image patch dimension, the other with MLP experts mixing information within patches along the channel dimension. In addition, by proposing importance-score routing strategy for MoE and redesigning the image representation shape, we further improve our model's computational efficiency. Experimentally, we are more computation-efficient than Vision Transformers with comparable accuracy. Also, our models can outperform MLP-Mixer by 2.5\% on ImageNet Top-1 accuracy with fewer parameters and computational cost. On downstream tasks, i.e. Cifar10 and Cifar100, our models can still achieve better performance than baselines.

Our understanding of the generalization capabilities of neural networks (NNs) is still incomplete. Prevailing explanations are based on implicit biases of gradient descent (GD) but they cannot account for the capabilities of models from gradient-free methods nor the simplicity bias recently observed in untrained networks. This paper seeks other sources of generalization in NNs. Findings. To understand the inductive biases provided by architectures independently from GD, we examine untrained, random-weight networks. Even simple MLPs show strong inductive biases: uniform sampling in weight space yields a very biased distribution of functions in terms of complexity. But unlike common wisdom, NNs do not have an inherent "simplicity bias". This property depends on components such as ReLUs, residual connections, and layer normalizations. Alternative architectures can be built with a bias for any level of complexity. Transformers also inherit all these properties from their building blocks. Implications. We provide a fresh explanation for the success of deep learning independent from gradient-based training. It points at promising avenues for controlling the solutions implemented by trained models.

This paper demonstrates that a single-layer neural network using Parametric Rectified Linear Unit (PReLU) activation can solve the XOR problem, a simple fact that has been overlooked so far. We compare this solution to the multi-layer perceptron (MLP) and the Growing Cosine Unit (GCU) activation function and explain why PReLU enables this capability. Our results show that the single-layer PReLU network can achieve 100\% success rate in a wider range of learning rates while using only three learnable parameters.

Self-attention mechanism is the key of the Transformer but often criticized for its computation demands. Previous token pruning works motivate their methods from the view of computation redundancy but still need to load the full network and require same memory costs. This paper introduces a novel strategy that simplifies vision transformers and reduces computational load through the selective removal of non-essential attention layers, guided by entropy considerations. We identify that regarding the attention layer in bottom blocks, their subsequent MLP layers, i.e. two feed-forward layers, can elicit the same entropy quantity. Meanwhile, the accompanied MLPs are under-exploited since they exhibit smaller feature entropy compared to those MLPs in the top blocks. Therefore, we propose to integrate the uninformative attention layers into their subsequent counterparts by degenerating them into identical mapping, yielding only MLP in certain transformer blocks. Experimental results on ImageNet-1k show that the proposed method can remove 40% attention layer of DeiT-B, improving throughput and memory bound without performance compromise. Code is available at https://github.com/sihaoevery/lambda_vit.

Transformer-based architectures are the model of choice for natural language understanding, but they come at a significant cost, as they have quadratic complexity in the input length, require a lot of training data, and can be difficult to tune. In the pursuit of lower costs, we investigate simple MLP-based architectures. We find that existing architectures such as MLPMixer, which achieves token mixing through a static MLP applied to each feature independently, are too detached from the inductive biases required for natural language understanding. In this paper, we propose a simple variant, HyperMixer, which forms the token mixing MLP dynamically using hypernetworks. Empirically, we demonstrate that our model performs better than alternative MLP-based models, and on par with Transformers. In contrast to Transformers, HyperMixer achieves these results at substantially lower costs in terms of processing time, training data, and hyperparameter tuning.

We study subliminal learning, a surprising phenomenon where language models transmit behavioral traits via semantically unrelated data. In our main experiments, a "teacher" model with some trait T (such as liking owls or being misaligned) generates a dataset consisting solely of number sequences. Remarkably, a "student" model trained on this dataset learns T. This occurs even when the data is filtered to remove references to T. We observe the same effect when training on code or reasoning traces generated by the same teacher model. However, we do not observe the effect when the teacher and student have different base models. To help explain our findings, we prove a theoretical result showing that subliminal learning occurs in all neural networks under certain conditions, and demonstrate subliminal learning in a simple MLP classifier. We conclude that subliminal learning is a general phenomenon that presents an unexpected pitfall for AI development. Distillation could propagate unintended traits, even when developers try to prevent this via data filtering.

In this note (work in progress towards a full-length paper) we show that a family of sequence models based on recurrent linear layers~(including S4, S5, and the LRU) interleaved with position-wise multi-layer perceptrons~(MLPs) can approximate arbitrarily well any sufficiently regular non-linear sequence-to-sequence map. The main idea behind our result is to see recurrent layers as compression algorithms that can faithfully store information about the input sequence into an inner state, before it is processed by the highly expressive MLP.

We investigate the learning of implicit neural representation (INR) using an overparameterized multilayer perceptron (MLP) via a novel nonparametric teaching perspective. The latter offers an efficient example selection framework for teaching nonparametrically defined (viz. non-closed-form) target functions, such as image functions defined by 2D grids of pixels. To address the costly training of INRs, we propose a paradigm called Implicit Neural Teaching (INT) that treats INR learning as a nonparametric teaching problem, where the given signal being fitted serves as the target function. The teacher then selects signal fragments for iterative training of the MLP to achieve fast convergence. By establishing a connection between MLP evolution through parameter-based gradient descent and that of function evolution through functional gradient descent in nonparametric teaching, we show for the first time that teaching an overparameterized MLP is consistent with teaching a nonparametric learner. This new discovery readily permits a convenient drop-in of nonparametric teaching algorithms to broadly enhance INR training efficiency, demonstrating 30%+ training time savings across various input modalities.

Multilayer-perceptrons (MLP) are known to struggle with learning functions of high-frequencies, and in particular cases with wide frequency bands. We present a spatially adaptive progressive encoding (SAPE) scheme for input signals of MLP networks, which enables them to better fit a wide range of frequencies without sacrificing training stability or requiring any domain specific preprocessing. SAPE gradually unmasks signal components with increasing frequencies as a function of time and space. The progressive exposure of frequencies is monitored by a feedback loop throughout the neural optimization process, allowing changes to propagate at different rates among local spatial portions of the signal space. We demonstrate the advantage of SAPE on a variety of domains and applications, including regression of low dimensional signals and images, representation learning of occupancy networks, and a geometric task of mesh transfer between 3D shapes.

Recent works have empirically analyzed in-context learning and shown that transformers trained on synthetic linear regression tasks can learn to implement ridge regression, which is the Bayes-optimal predictor, given sufficient capacity [Aky\"urek et al., 2023], while one-layer transformers with linear self-attention and no MLP layer will learn to implement one step of gradient descent (GD) on a least-squares linear regression objective [von Oswald et al., 2022]. However, the theory behind these observations remains poorly understood. We theoretically study transformers with a single layer of linear self-attention, trained on synthetic noisy linear regression data. First, we mathematically show that when the covariates are drawn from a standard Gaussian distribution, the one-layer transformer which minimizes the pre-training loss will implement a single step of GD on the least-squares linear regression objective. Then, we find that changing the distribution of the covariates and weight vector to a non-isotropic Gaussian distribution has a strong impact on the learned algorithm: the global minimizer of the pre-training loss now implements a single step of pre-conditioned GD. However, if only the distribution of the responses is changed, then this does not have a large effect on the learned algorithm: even when the response comes from a more general family of nonlinear functions, the global minimizer of the pre-training loss still implements a single step of GD on a least-squares linear regression objective.

We study the problem of learning a single neuron with respect to the L_2^2-loss in the presence of adversarial label noise. We give an efficient algorithm that, for a broad family of activations including ReLUs, approximates the optimal L_2^2-error within a constant factor. Our algorithm applies under much milder distributional assumptions compared to prior work. The key ingredient enabling our results is a novel connection to local error bounds from optimization theory.

This paper studies the curious phenomenon for machine learning models with Transformer architectures that their activation maps are sparse. By activation map we refer to the intermediate output of the multi-layer perceptrons (MLPs) after a ReLU activation function, and by sparse we mean that on average very few entries (e.g., 3.0% for T5-Base and 6.3% for ViT-B16) are nonzero for each input to MLP. Moreover, larger Transformers with more layers and wider MLP hidden dimensions are sparser as measured by the percentage of nonzero entries. Through extensive experiments we demonstrate that the emergence of sparsity is a prevalent phenomenon that occurs for both natural language processing and vision tasks, on both training and evaluation data, for Transformers of various configurations, at layers of all depth levels, as well as for other architectures including MLP-mixers and 2-layer MLPs. We show that sparsity also emerges using training datasets with random labels, or with random inputs, or with infinite amount of data, demonstrating that sparsity is not a result of a specific family of datasets. We discuss how sparsity immediately implies a way to significantly reduce the FLOP count and improve efficiency for Transformers. Moreover, we demonstrate perhaps surprisingly that enforcing an even sparser activation via Top-k thresholding with a small value of k brings a collection of desired but missing properties for Transformers, namely less sensitivity to noisy training data, more robustness to input corruptions, and better calibration for their prediction confidence.

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.

In-context learning (ICL), the remarkable ability to solve a task from only input exemplars, is often assumed to be a unique hallmark of Transformer models. By examining commonly employed synthetic ICL tasks, we demonstrate that multi-layer perceptrons (MLPs) can also learn in-context. Moreover, MLPs, and the closely related MLP-Mixer models, learn in-context competitively with Transformers given the same compute budget in this setting. We further show that MLPs outperform Transformers on a series of classical tasks from psychology designed to test relational reasoning, which are closely related to in-context classification. These results underscore a need for studying in-context learning beyond attention-based architectures, while also challenging strong prior arguments about MLPs' limited ability to solve relational tasks. Altogether, our results highlight the unexpected competence of MLPs, and support the growing interest in all-MLP alternatives to task-specific architectures.

Our work presents extensive empirical evidence that layer rotation, i.e. the evolution across training of the cosine distance between each layer's weight vector and its initialization, constitutes an impressively consistent indicator of generalization performance. In particular, larger cosine distances between final and initial weights of each layer consistently translate into better generalization performance of the final model. Interestingly, this relation admits a network independent optimum: training procedures during which all layers' weights reach a cosine distance of 1 from their initialization consistently outperform other configurations -by up to 30% test accuracy. Moreover, we show that layer rotations are easily monitored and controlled (helpful for hyperparameter tuning) and potentially provide a unified framework to explain the impact of learning rate tuning, weight decay, learning rate warmups and adaptive gradient methods on generalization and training speed. In an attempt to explain the surprising properties of layer rotation, we show on a 1-layer MLP trained on MNIST that layer rotation correlates with the degree to which features of intermediate layers have been trained.

Neural Radiance Field (NeRF) has achieved superior performance for novel view synthesis by modeling the scene with a Multi-Layer Perception (MLP) and a volume rendering procedure, however, when fewer known views are given (i.e., few-shot view synthesis), the model is prone to overfit the given views. To handle this issue, previous efforts have been made towards leveraging learned priors or introducing additional regularizations. In contrast, in this paper, we for the first time provide an orthogonal method from the perspective of network structure. Given the observation that trivially reducing the number of model parameters alleviates the overfitting issue, but at the cost of missing details, we propose the multi-input MLP (mi-MLP) that incorporates the inputs (i.e., location and viewing direction) of the vanilla MLP into each layer to prevent the overfitting issue without harming detailed synthesis. To further reduce the artifacts, we propose to model colors and volume density separately and present two regularization terms. Extensive experiments on multiple datasets demonstrate that: 1) although the proposed mi-MLP is easy to implement, it is surprisingly effective as it boosts the PSNR of the baseline from 14.73 to 24.23. 2) the overall framework achieves state-of-the-art results on a wide range of benchmarks. We will release the code upon publication.

The canonical deep learning approach for learning requires computing a gradient term at each layer by back-propagating the error signal from the output towards each learnable parameter. Given the stacked structure of neural networks, where each layer builds on the representation of the layer below, this approach leads to hierarchical representations. More abstract features live on the top layers of the model, while features on lower layers are expected to be less abstract. In contrast to this, we introduce a new learning method named NoProp, which does not rely on either forward or backwards propagation. Instead, NoProp takes inspiration from diffusion and flow matching methods, where each layer independently learns to denoise a noisy target. We believe this work takes a first step towards introducing a new family of gradient-free learning methods, that does not learn hierarchical representations -- at least not in the usual sense. NoProp needs to fix the representation at each layer beforehand to a noised version of the target, learning a local denoising process that can then be exploited at inference. We demonstrate the effectiveness of our method on MNIST, CIFAR-10, and CIFAR-100 image classification benchmarks. Our results show that NoProp is a viable learning algorithm which achieves superior accuracy, is easier to use and computationally more efficient compared to other existing back-propagation-free methods. By departing from the traditional gradient based learning paradigm, NoProp alters how credit assignment is done within the network, enabling more efficient distributed learning as well as potentially impacting other characteristics of the learning process.

Neural fields, mapping low-dimensional input coordinates to corresponding signals, have shown promising results in representing various signals. Numerous methodologies have been proposed, and techniques employing MLPs and grid representations have achieved substantial success. MLPs allow compact and high expressibility, yet often suffer from spectral bias and slow convergence speed. On the other hand, methods using grids are free from spectral bias and achieve fast training speed, however, at the expense of high spatial complexity. In this work, we propose a novel way for exploiting both MLPs and grid representations in neural fields. Unlike the prevalent methods that combine them sequentially (extract features from the grids first and feed them to the MLP), we inject spectral bias-free grid representations into the intermediate features in the MLP. More specifically, we suggest a Coordinate-Aware Modulation (CAM), which modulates the intermediate features using scale and shift parameters extracted from the grid representations. This can maintain the strengths of MLPs while mitigating any remaining potential biases, facilitating the rapid learning of high-frequency components. In addition, we empirically found that the feature normalizations, which have not been successful in neural filed literature, proved to be effective when applied in conjunction with the proposed CAM. Experimental results demonstrate that CAM enhances the performance of neural representation and improves learning stability across a range of signals. Especially in the novel view synthesis task, we achieved state-of-the-art performance with the least number of parameters and fast training speed for dynamic scenes and the best performance under 1MB memory for static scenes. CAM also outperforms the best-performing video compression methods using neural fields by a large margin.

The success of large language models (LLMs) can be attributed in part to their ability to efficiently store factual knowledge as key-value mappings within their MLP parameters. Recent work has proposed explicit weight constructions to build such fact-storing MLPs, providing an improved understanding of LLM fact storage mechanisms. In this paper, we introduce an MLP construction framework that improves over previous constructions in three areas: it 1) works for all but a measure-zero set of feasible input-output pairs, 2) achieves asymptotically optimal parameter efficiency matching information-theoretic bounds for some embeddings, and 3) maintains usability within Transformers for factual recall. Through our improvements, we 1) discover a metric on value embeddings that characterizes facts-per-parameter scaling for both constructed and gradient-descent-trained MLPs, 2) identify a simple encoder-decoder mechanism that empirically matches gradient-descent MLP facts-per-parameter asymptotics across all the inputs and outputs we test, and 3) uncover a fundamental tradeoff between an MLP's fact-storage capacity and its usability within Transformers. Finally, we demonstrate a proof-of-concept application of fact-storing MLPs: modular fact editing on one-layer Transformers by replacing entire MLPs at once.

Click-through rate (CTR) prediction is one of the fundamental tasks for online advertising and recommendation. While multi-layer perceptron (MLP) serves as a core component in many deep CTR prediction models, it has been widely recognized that applying a vanilla MLP network alone is inefficient in learning multiplicative feature interactions. As such, many two-stream interaction models (e.g., DeepFM and DCN) have been proposed by integrating an MLP network with another dedicated network for enhanced CTR prediction. As the MLP stream learns feature interactions implicitly, existing research focuses mainly on enhancing explicit feature interactions in the complementary stream. In contrast, our empirical study shows that a well-tuned two-stream MLP model that simply combines two MLPs can even achieve surprisingly good performance, which has never been reported before by existing work. Based on this observation, we further propose feature gating and interaction aggregation layers that can be easily plugged to make an enhanced two-stream MLP model, FinalMLP. In this way, it not only enables differentiated feature inputs but also effectively fuses stream-level interactions across two streams. Our evaluation results on four open benchmark datasets as well as an online A/B test in our industrial system show that FinalMLP achieves better performance than many sophisticated two-stream CTR models. Our source code will be available at MindSpore/models.

It is not fully understood why adversarial examples can deceive neural networks and transfer between different networks. To elucidate this, several studies have hypothesized that adversarial perturbations, while appearing as noises, contain class features. This is supported by empirical evidence showing that networks trained on mislabeled adversarial examples can still generalize well to correctly labeled test samples. However, a theoretical understanding of how perturbations include class features and contribute to generalization is limited. In this study, we provide a theoretical framework for understanding learning from perturbations using a one-hidden-layer network trained on mutually orthogonal samples. Our results highlight that various adversarial perturbations, even perturbations of a few pixels, contain sufficient class features for generalization. Moreover, we reveal that the decision boundary when learning from perturbations matches that from standard samples except for specific regions under mild conditions. The code is available at https://github.com/s-kumano/learning-from-adversarial-perturbations.

Self-attention performs well in long context but has quadratic complexity. Existing RNN layers have linear complexity, but their performance in long context is limited by the expressive power of their hidden state. We propose a new class of sequence modeling layers with linear complexity and an expressive hidden state. The key idea is to make the hidden state a machine learning model itself, and the update rule a step of self-supervised learning. Since the hidden state is updated by training even on test sequences, our layers are called Test-Time Training (TTT) layers. We consider two instantiations: TTT-Linear and TTT-MLP, whose hidden state is a linear model and a two-layer MLP respectively. We evaluate our instantiations at the scale of 125M to 1.3B parameters, comparing with a strong Transformer and Mamba, a modern RNN. Both TTT-Linear and TTT-MLP match or exceed the baselines. Similar to Transformer, they can keep reducing perplexity by conditioning on more tokens, while Mamba cannot after 16k context. With preliminary systems optimization, TTT-Linear is already faster than Transformer at 8k context and matches Mamba in wall-clock time. TTT-MLP still faces challenges in memory I/O, but shows larger potential in long context, pointing to a promising direction for future research.

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.

A key goal in mechanistic interpretability is circuit analysis: finding sparse subgraphs of models corresponding to specific behaviors or capabilities. However, MLP sublayers make fine-grained circuit analysis on transformer-based language models difficult. In particular, interpretable features -- such as those found by sparse autoencoders (SAEs) -- are typically linear combinations of extremely many neurons, each with its own nonlinearity to account for. Circuit analysis in this setting thus either yields intractably large circuits or fails to disentangle local and global behavior. To address this we explore transcoders, which seek to faithfully approximate a densely activating MLP layer with a wider, sparsely-activating MLP layer. We successfully train transcoders on language models with 120M, 410M, and 1.4B parameters, and find them to perform at least on par with SAEs in terms of sparsity, faithfulness, and human-interpretability. We then introduce a novel method for using transcoders to perform weights-based circuit analysis through MLP sublayers. The resulting circuits neatly factorize into input-dependent and input-invariant terms. Finally, we apply transcoders to reverse-engineer unknown circuits in the model, and we obtain novel insights regarding the greater-than circuit in GPT2-small. Our results suggest that transcoders can prove effective in decomposing model computations involving MLPs into interpretable circuits. Code is available at https://github.com/jacobdunefsky/transcoder_circuits.

This paper does not introduce a novel method. Instead, it offers a fairer and more comprehensive comparison of KAN and MLP models across various tasks, including machine learning, computer vision, audio processing, natural language processing, and symbolic formula representation. Specifically, we control the number of parameters and FLOPs to compare the performance of KAN and MLP. Our main observation is that, except for symbolic formula representation tasks, MLP generally outperforms KAN. We also conduct ablation studies on KAN and find that its advantage in symbolic formula representation mainly stems from its B-spline activation function. When B-spline is applied to MLP, performance in symbolic formula representation significantly improves, surpassing or matching that of KAN. However, in other tasks where MLP already excels over KAN, B-spline does not substantially enhance MLP's performance. Furthermore, we find that KAN's forgetting issue is more severe than that of MLP in a standard class-incremental continual learning setting, which differs from the findings reported in the KAN paper. We hope these results provide insights for future research on KAN and other MLP alternatives. Project link: https://github.com/yu-rp/KANbeFair

Robust generalization is a major challenge in deep learning, particularly when the number of trainable parameters is very large. In general, it is very difficult to know if the network has memorized a particular set of examples or understood the underlying rule (or both). Motivated by this challenge, we study an interpretable model where generalizing representations are understood analytically, and are easily distinguishable from the memorizing ones. Namely, we consider multi-layer perceptron (MLP) and Transformer architectures trained on modular arithmetic tasks, where (xi cdot 100%) of labels are corrupted (i.e. some results of the modular operations in the training set are incorrect). We show that (i) it is possible for the network to memorize the corrupted labels and achieve 100% generalization at the same time; (ii) the memorizing neurons can be identified and pruned, lowering the accuracy on corrupted data and improving the accuracy on uncorrupted data; (iii) regularization methods such as weight decay, dropout and BatchNorm force the network to ignore the corrupted data during optimization, and achieve 100% accuracy on the uncorrupted dataset; and (iv) the effect of these regularization methods is (``mechanistically'') interpretable: weight decay and dropout force all the neurons to learn generalizing representations, while BatchNorm de-amplifies the output of memorizing neurons and amplifies the output of the generalizing ones. Finally, we show that in the presence of regularization, the training dynamics involves two consecutive stages: first, the network undergoes grokking dynamics reaching high train and test accuracy; second, it unlearns the memorizing representations, where the train accuracy suddenly jumps from 100% to 100 (1-xi)%.

Developing Intelligent Systems involves artificial intelligence approaches including artificial neural networks. Here, we present a tutorial of Deep Neural Networks (DNNs), and some insights about the origin of the term "deep"; references to deep learning are also given. Restricted Boltzmann Machines, which are the core of DNNs, are discussed in detail. An example of a simple two-layer network, performing unsupervised learning for unlabeled data, is shown. Deep Belief Networks (DBNs), which are used to build networks with more than two layers, are also described. Moreover, examples for supervised learning with DNNs performing simple prediction and classification tasks, are presented and explained. This tutorial includes two intelligent pattern recognition applications: hand- written digits (benchmark known as MNIST) and speech recognition.

Designing machine learning architectures for processing neural networks in their raw weight matrix form is a newly introduced research direction. Unfortunately, the unique symmetry structure of deep weight spaces makes this design very challenging. If successful, such architectures would be capable of performing a wide range of intriguing tasks, from adapting a pre-trained network to a new domain to editing objects represented as functions (INRs or NeRFs). As a first step towards this goal, we present here a novel network architecture for learning in deep weight spaces. It takes as input a concatenation of weights and biases of a pre-trained MLP and processes it using a composition of layers that are equivariant to the natural permutation symmetry of the MLP's weights: Changing the order of neurons in intermediate layers of the MLP does not affect the function it represents. We provide a full characterization of all affine equivariant and invariant layers for these symmetries and show how these layers can be implemented using three basic operations: pooling, broadcasting, and fully connected layers applied to the input in an appropriate manner. We demonstrate the effectiveness of our architecture and its advantages over natural baselines in a variety of learning tasks.

We revisit the one-shot Neural Architecture Search (NAS) paradigm and analyze its advantages over existing NAS approaches. Existing one-shot method, however, is hard to train and not yet effective on large scale datasets like ImageNet. This work propose a Single Path One-Shot model to address the challenge in the training. Our central idea is to construct a simplified supernet, where all architectures are single paths so that weight co-adaption problem is alleviated. Training is performed by uniform path sampling. All architectures (and their weights) are trained fully and equally. Comprehensive experiments verify that our approach is flexible and effective. It is easy to train and fast to search. It effortlessly supports complex search spaces (e.g., building blocks, channel, mixed-precision quantization) and different search constraints (e.g., FLOPs, latency). It is thus convenient to use for various needs. It achieves start-of-the-art performance on the large dataset ImageNet.

One of the most striking features of Large Language Models (LLM) is their ability to learn in context. Namely at inference time an LLM is able to learn new patterns without any additional weight update when these patterns are presented in the form of examples in the prompt, even if these patterns were not seen during training. The mechanisms through which this can happen are still largely unknown. In this work, we show that the stacking of a self-attention layer with an MLP, allows the transformer block to implicitly modify the weights of the MLP layer according to the context. We argue through theory and experimentation that this simple mechanism may be the reason why LLMs can learn in context and not only during training. Specifically, we show under mild simplifying assumptions how a transformer block implicitly transforms a context into a low-rank weight-update of the MLP layer.

In this paper, we delve into several mechanisms employed by Transformer-based language models (LLMs) for factual recall tasks. We outline a pipeline consisting of three major steps: (1) Given a prompt ``The capital of France is,'' task-specific attention heads extract the topic token, such as ``France,'' from the context and pass it to subsequent MLPs. (2) As attention heads' outputs are aggregated with equal weight and added to the residual stream, the subsequent MLP acts as an ``activation,'' which either erases or amplifies the information originating from individual heads. As a result, the topic token ``France'' stands out in the residual stream. (3) A deep MLP takes ``France'' and generates a component that redirects the residual stream towards the direction of the correct answer, i.e., ``Paris.'' This procedure is akin to applying an implicit function such as ``get\_capital(X),'' and the argument X is the topic token information passed by attention heads. To achieve the above quantitative and qualitative analysis for MLPs, we proposed a novel analytic method aimed at decomposing the outputs of the MLP into components understandable by humans. Additionally, we observed a universal anti-overconfidence mechanism in the final layer of models, which suppresses correct predictions. We mitigate this suppression by leveraging our interpretation to improve factual recall confidence. The above interpretations are evaluated across diverse tasks spanning various domains of factual knowledge, using various language models from the GPT-2 families, 1.3B OPT, up to 7B Llama-2, and in both zero- and few-shot setups.

The self-attention mechanism utilizes large implicit weight matrices, programmed through dot product-based activations with very few trainable parameters, to enable long sequence modeling. In this paper, we investigate the possibility of discarding residual learning by employing large implicit kernels to achieve full context interaction at each layer of the network. To accomplish it, we introduce coordinate-based implicit MLPs as a slow network to generate hyper-kernels for another fast convolutional network. To get context-varying weights for fast dynamic encoding, we propose a HyperZ{cdotZ{cdot}W} operator that connects hyper-kernels (W) and hidden activations (Z) through simple elementwise multiplication, followed by convolution of Z using the context-dependent W. Based on this design, we present a novel Terminator architecture that integrates hyper-kernels of different sizes to produce multi-branch hidden representations for enhancing the feature extraction capability of each layer. Additionally, a bottleneck layer is employed to compress the concatenated channels, allowing only valuable information to propagate to the subsequent layers. Notably, our model incorporates several innovative components and exhibits excellent properties, such as introducing local feedback error for updating the slow network, stable zero-mean features, faster training convergence, and fewer model parameters. Extensive experimental results on pixel-level 1D and 2D image classification benchmarks demonstrate the superior performance of our architecture.

Transformers, with their attention mechanisms, have emerged as the state-of-the-art architectures of sequential modeling and empirically outperform feed-forward neural networks (FFNNs) across many fields, such as natural language processing and computer vision. However, their generalization ability, particularly for low-sensitivity functions, remains less studied. We bridge this gap by analyzing transformers on the k-parity problem. Daniely and Malach (NeurIPS 2020) show that FFNNs with one hidden layer and O(nk^7 log k) parameters can learn k-parity, where the input length n is typically much larger than k. In this paper, we prove that FFNNs require at least Omega(n) parameters to learn k-parity, while transformers require only O(k) parameters, surpassing the theoretical lower bound needed by FFNNs. We further prove that this parameter efficiency cannot be achieved with fixed attention heads. Our work establishes transformers as theoretically superior to FFNNs in learning parity function, showing how their attention mechanisms enable parameter-efficient generalization in functions with low sensitivity.

Convolutional Neural Networks (CNNs) have revolutionized image classification by extracting spatial features and enabling state-of-the-art accuracy in vision-based tasks. The squeeze and excitation network proposed module gathers channelwise representations of the input. Multilayer perceptrons (MLP) learn global representation from the data and in most image classification models used to learn extracted features of the image. In this paper, we introduce a novel aggregated multilayer perceptron, a multi-branch dense layer, within the Squeeze excitation residual module designed to surpass the performance of existing architectures. Our approach leverages a combination of squeeze excitation network module with dense layers. This fusion enhances the network's ability to capture channel-wise patterns and have global knowledge, leading to a better feature representation. This proposed model has a negligible increase in parameters when compared to SENet. We conduct extensive experiments on benchmark datasets to validate the model and compare them with established architectures. Experimental results demonstrate a remarkable increase in the classification accuracy of the proposed model.

Voice anti-spoofing systems are crucial auxiliaries for automatic speaker verification (ASV) systems. A major challenge is caused by unseen attacks empowered by advanced speech synthesis technologies. Our previous research on one-class learning has improved the generalization ability to unseen attacks by compacting the bona fide speech in the embedding space. However, such compactness lacks consideration of the diversity of speakers. In this work, we propose speaker attractor multi-center one-class learning (SAMO), which clusters bona fide speech around a number of speaker attractors and pushes away spoofing attacks from all the attractors in a high-dimensional embedding space. For training, we propose an algorithm for the co-optimization of bona fide speech clustering and bona fide/spoof classification. For inference, we propose strategies to enable anti-spoofing for speakers without enrollment. Our proposed system outperforms existing state-of-the-art single systems with a relative improvement of 38% on equal error rate (EER) on the ASVspoof2019 LA evaluation set.

In recent years, NLP practitioners have converged on the following practice: (i) import an off-the-shelf pretrained (masked) language model; (ii) append a multilayer perceptron atop the CLS token's hidden representation (with randomly initialized weights); and (iii) fine-tune the entire model on a downstream task (MLP-FT). This procedure has produced massive gains on standard NLP benchmarks, but these models remain brittle, even to mild adversarial perturbations. In this work, we demonstrate surprising gains in adversarial robustness enjoyed by Model-tuning Via Prompts (MVP), an alternative method of adapting to downstream tasks. Rather than appending an MLP head to make output prediction, MVP appends a prompt template to the input, and makes prediction via text infilling/completion. Across 5 NLP datasets, 4 adversarial attacks, and 3 different models, MVP improves performance against adversarial substitutions by an average of 8% over standard methods and even outperforms adversarial training-based state-of-art defenses by 3.5%. By combining MVP with adversarial training, we achieve further improvements in adversarial robustness while maintaining performance on unperturbed examples. Finally, we conduct ablations to investigate the mechanism underlying these gains. Notably, we find that the main causes of vulnerability of MLP-FT can be attributed to the misalignment between pre-training and fine-tuning tasks, and the randomly initialized MLP parameters.

Transformer architecture currently represents the main driver behind many successes in a variety of tasks addressed by deep learning, especially the recent advances in natural language processing (NLP) culminating with large language models (LLM). In addition, transformer architecture has found a wide spread of interest from computer vision (CV) researchers and practitioners, allowing for many advancements in vision-related tasks and opening the door for multi-task and multi-modal deep learning architectures that share the same principle of operation. One drawback to these architectures is their reliance on the scaled dot product attention mechanism with the softmax activation function, which is computationally expensive and requires large compute capabilities both for training and inference. This paper investigates substituting the attention mechanism usually adopted for transformer architecture with an architecture incorporating gated linear unit (GLU) activation within a multi-layer perceptron (MLP) structure in conjunction with the default MLP incorporated in the traditional transformer design. Another step forward taken by this paper is to eliminate the second non-gated MLP to further reduce the computational cost. Experimental assessments conducted by this research show that both proposed modifications and reductions offer competitive performance in relation to baseline architectures, in support of the aims of this work in establishing a more efficient yet capable alternative to the traditional attention mechanism as the core component in designing transformer architectures.

Modern large language models excel in knowledge-intensive tasks, yet how transformers acquire (store) knowledge during pre-training and extract (retrieve) it during post-fine-tuning inference remains theoretically opaque. While prior theoretical work has begun to investigate these questions through the analysis of training dynamics, such studies are limited to single-layer, attention-only architectures. However, most existing studies suggest that MLPs are the most contributing components for storing knowledge in transformer-based language models. Meanwhile, our empirical investigations reveal that such simplified models, when trained using standard next-token prediction objectives, may be incapable of acquiring or extracting factual knowledge. To overcome this limitation, we introduce a tractable one-layer transformer framework that crucially incorporates both self-attention and MLP modules. By tracking its gradient dynamics, we establish convergence and generalization guarantees that illuminate the ability of knowledge acquisition and extraction. We prove that 1) Transformers can achieve near-optimal training loss during pre-training, signifying effective knowledge acquisition; 2) With a large fine-tuning dataset and specific data multiplicity conditions met, transformers can achieve low generalization error when tested on factual knowledge learned during pre-training but not reinforced during the fine-tuning, indicating successful knowledge extraction; 3) When the conditions are not satisfied, transformers exhibit high generalization loss, resulting in hallucinations. Our analysis includes both full fine-tuning and low-rank fine-tuning. Furthermore, our analysis offers theoretical insights into several pertinent empirical phenomena, such as the role of learning rate schedules. Experiments on synthetic and real-world PopQA datasets with GPT-2 and Llama-3.2-1B validate our results.

The inference demand for LLMs has skyrocketed in recent months, and serving models with low latencies remains challenging due to the quadratic input length complexity of the attention layers. In this work, we investigate the effect of dropping MLP and attention layers at inference time on the performance of Llama-v2 models. We find that dropping dreeper attention layers only marginally decreases performance but leads to the best speedups alongside dropping entire layers. For example, removing 33\% of attention layers in a 13B Llama2 model results in a 1.8\% drop in average performance over the OpenLLM benchmark. We also observe that skipping layers except the latter layers reduces performances for more layers skipped, except for skipping the attention layers.

Recent years have witnessed the great success of Graph Neural Networks (GNNs) in handling graph-related tasks. However, MLPs remain the primary workhorse for practical industrial applications due to their desirable inference efficiency and scalability. To reduce their gaps, one can directly distill knowledge from a well-designed teacher GNN to a student MLP, which is termed as GNN-to-MLP distillation. However, the process of distillation usually entails a loss of information, and ``which knowledge patterns of GNNs are more likely to be left and distilled into MLPs?" becomes an important question. In this paper, we first factorize the knowledge learned by GNNs into low- and high-frequency components in the spectral domain and then derive their correspondence in the spatial domain. Furthermore, we identified a potential information drowning problem for existing GNN-to-MLP distillation, i.e., the high-frequency knowledge of the pre-trained GNNs may be overwhelmed by the low-frequency knowledge during distillation; we have described in detail what it represents, how it arises, what impact it has, and how to deal with it. In this paper, we propose an efficient Full-Frequency GNN-to-MLP (FF-G2M) distillation framework, which extracts both low-frequency and high-frequency knowledge from GNNs and injects it into MLPs. Extensive experiments show that FF-G2M improves over the vanilla MLPs by 12.6% and outperforms its corresponding teacher GNNs by 2.6% averaged over six graph datasets and three common GNN architectures.

Printed Electronics (PE) stands out as a promisingtechnology for widespread computing due to its distinct attributes, such as low costs and flexible manufacturing. Unlike traditional silicon-based technologies, PE enables stretchable, conformal,and non-toxic hardware. However, PE are constrained by larger feature sizes, making it challenging to implement complex circuits such as machine learning (ML) classifiers. Approximate computing has been proven to reduce the hardware cost of ML circuits such as Multilayer Perceptrons (MLPs). In this paper, we maximize the benefits of approximate computing by integrating hardware approximation into the MLP training process. Due to the discrete nature of hardware approximation, we propose and implement a genetic-based, approximate, hardware-aware training approach specifically designed for printed MLPs. For a 5% accuracy loss, our MLPs achieve over 5x area and power reduction compared to the baseline while outperforming state of-the-art approximate and stochastic printed MLPs.

The non-convexity of the artificial neural network (ANN) training landscape brings inherent optimization difficulties. While the traditional back-propagation stochastic gradient descent (SGD) algorithm and its variants are effective in certain cases, they can become stuck at spurious local minima and are sensitive to initializations and hyperparameters. Recent work has shown that the training of an ANN with ReLU activations can be reformulated as a convex program, bringing hope to globally optimizing interpretable ANNs. However, naively solving the convex training formulation has an exponential complexity, and even an approximation heuristic requires cubic time. In this work, we characterize the quality of this approximation and develop two efficient algorithms that train ANNs with global convergence guarantees. The first algorithm is based on the alternating direction method of multiplier (ADMM). It solves both the exact convex formulation and the approximate counterpart. Linear global convergence is achieved, and the initial several iterations often yield a solution with high prediction accuracy. When solving the approximate formulation, the per-iteration time complexity is quadratic. The second algorithm, based on the "sampled convex programs" theory, is simpler to implement. It solves unconstrained convex formulations and converges to an approximately globally optimal classifier. The non-convexity of the ANN training landscape exacerbates when adversarial training is considered. We apply the robust convex optimization theory to convex training and develop convex formulations that train ANNs robust to adversarial inputs. Our analysis explicitly focuses on one-hidden-layer fully connected ANNs, but can extend to more sophisticated architectures.

Understanding the inner workings of machine learning models like Transformers is vital for their safe and ethical use. This paper provides a comprehensive analysis of a one-layer Transformer model trained to perform n-digit integer addition. Our findings suggest that the model dissects the task into parallel streams dedicated to individual digits, employing varied algorithms tailored to different positions within the digits. Furthermore, we identify a rare scenario characterized by high loss, which we explain. By thoroughly elucidating the model's algorithm, we provide new insights into its functioning. These findings are validated through rigorous testing and mathematical modeling, thereby contributing to the broader fields of model understanding and interpretability. Our approach opens the door for analyzing more complex tasks and multi-layer Transformer models.

Machine unlearning seeks to remove the influence of particular data or class from trained models to meet privacy, legal, or ethical requirements. Existing unlearning methods tend to forget shallowly: phenomenon of an unlearned model pretend to forget by adjusting only the model response, while its internal representations retain information sufficiently to restore the forgotten data or behavior. We empirically confirm the widespread shallowness by reverting the forgetting effect of various unlearning methods via training-free performance recovery attack and gradient-inversion-based data reconstruction attack. To address this vulnerability fundamentally, we define a theoretical criterion of ``deep forgetting'' based on one-point-contraction of feature representations of data to forget. We also propose an efficient approximation algorithm, and use it to construct a novel general-purpose unlearning algorithm: One-Point-Contraction (OPC). Empirical evaluations on image classification unlearning benchmarks show that OPC achieves not only effective unlearning performance but also superior resilience against both performance recovery attack and gradient-inversion attack. The distinctive unlearning performance of OPC arises from the deep feature forgetting enforced by its theoretical foundation, and recaps the need for improved robustness of machine unlearning methods.

To efficiently deploy strong, often pre-trained feature extractors, recent Industrial Anomaly Detection and Segmentation (IADS) methods process low-resolution images, e.g., 224x224 pixels, obtained by downsampling the original input images. However, while numerous industrial applications demand the identification of both large and small defects, downsampling the input image to a low resolution may hinder a method's ability to pinpoint tiny anomalies. We propose a novel Teacher--Student paradigm to leverage strong pre-trained features while processing high-resolution input images very efficiently. The core idea concerns training two shallow MLPs (the Students) by nominal images so as to mimic the mappings between the patch embeddings induced by the self-attention layers of a frozen vision Transformer (the Teacher). Indeed, learning these mappings sets forth a challenging pretext task that small-capacity models are unlikely to accomplish on out-of-distribution data such as anomalous images. Our method can spot anomalies from high-resolution images and runs way faster than competitors, achieving state-of-the-art performance on MVTec AD and the best segmentation results on VisA. We also propose novel evaluation metrics to capture robustness to defect size, i.e., the ability to preserve good localisation from large anomalies to tiny ones. Evaluating our method also by these metrics reveals its neatly superior performance.

Attention-based architectures have become ubiquitous in machine learning, yet our understanding of the reasons for their effectiveness remains limited. This work proposes a new way to understand self-attention networks: we show that their output can be decomposed into a sum of smaller terms, each involving the operation of a sequence of attention heads across layers. Using this decomposition, we prove that self-attention possesses a strong inductive bias towards "token uniformity". Specifically, without skip connections or multi-layer perceptrons (MLPs), the output converges doubly exponentially to a rank-1 matrix. On the other hand, skip connections and MLPs stop the output from degeneration. Our experiments verify the identified convergence phenomena on different variants of standard transformer architectures.

It is well noted that coordinate based MLPs benefit -- in terms of preserving high-frequency information -- through the encoding of coordinate positions as an array of Fourier features. Hitherto, the rationale for the effectiveness of these positional encodings has been solely studied through a Fourier lens. In this paper, we strive to broaden this understanding by showing that alternative non-Fourier embedding functions can indeed be used for positional encoding. Moreover, we show that their performance is entirely determined by a trade-off between the stable rank of the embedded matrix and the distance preservation between embedded coordinates. We further establish that the now ubiquitous Fourier feature mapping of position is a special case that fulfills these conditions. Consequently, we present a more general theory to analyze positional encoding in terms of shifted basis functions. To this end, we develop the necessary theoretical formulae and empirically verify that our theoretical claims hold in practice. Codes available at https://github.com/osiriszjq/Rethinking-positional-encoding.

The costly self-attention layers in modern Transformers require memory and compute quadratic in sequence length. Existing approximation methods usually underperform and fail to obtain significant speedups in practice. Here we present SwitchHead - a novel method that reduces both compute and memory requirements and achieves wall-clock speedup, while matching the language modeling performance of baseline Transformers with the same parameter budget. SwitchHead uses Mixture-of-Experts (MoE) layers for the value and output projections and requires 4 to 8 times fewer attention matrices than standard Transformers. Our novel attention can also be combined with MoE MLP layers, resulting in an efficient fully-MoE "SwitchAll" Transformer model. Our code is public.

In this work, we demonstrate that a simple two-layer neural network with standard activation functions can learn an arbitrary word operation in any finite group, provided sufficient width is available and exhibits grokking while doing so. To explain the mechanism by which this is achieved, we reframe the problem as that of learning a particular 3-tensor, which we show is typically of low rank. A key insight is that low-rank implementations of this tensor can be obtained by decomposing it along triplets of basic self-conjugate representations of the group and leveraging the fusion structure to rule out many components. Focusing on a phenomenologically similar but more tractable surrogate model, we show that the network is able to find such low-rank implementations (or approximations thereof), thereby using limited width to approximate the word-tensor in a generalizable way. In the case of the simple multiplication word, we further elucidate the form of these low-rank implementations, showing that the network effectively implements efficient matrix multiplication in the sense of Strassen. Our work also sheds light on the mechanism by which a network reaches such a solution under gradient descent.

Recent approximations to backpropagation (BP) have mitigated many of BP's computational inefficiencies and incompatibilities with biology, but important limitations still remain. Moreover, the approximations significantly decrease accuracy in benchmarks, suggesting that an entirely different approach may be more fruitful. Here, grounded on recent theory for Hebbian learning in soft winner-take-all networks, we present multilayer SoftHebb, i.e. an algorithm that trains deep neural networks, without any feedback, target, or error signals. As a result, it achieves efficiency by avoiding weight transport, non-local plasticity, time-locking of layer updates, iterative equilibria, and (self-) supervisory or other feedback signals -- which were necessary in other approaches. Its increased efficiency and biological compatibility do not trade off accuracy compared to state-of-the-art bio-plausible learning, but rather improve it. With up to five hidden layers and an added linear classifier, accuracies on MNIST, CIFAR-10, STL-10, and ImageNet, respectively reach 99.4%, 80.3%, 76.2%, and 27.3%. In conclusion, SoftHebb shows with a radically different approach from BP that Deep Learning over few layers may be plausible in the brain and increases the accuracy of bio-plausible machine learning. Code is available at https://github.com/NeuromorphicComputing/SoftHebb.

Federated learning alleviates the privacy risk in distributed learning by transmitting only the local model updates to the central server. However, it faces challenges including statistical heterogeneity of clients' datasets and resource constraints of client devices, which severely impact the training performance and user experience. Prior works have tackled these challenges by combining personalization with model compression schemes including quantization and pruning. However, the pruning is data-dependent and thus must be done on the client side which requires considerable computation cost. Moreover, the pruning normally trains a binary supermask in {0, 1} which significantly limits the model capacity yet with no computation benefit. Consequently, the training requires high computation cost and a long time to converge while the model performance does not pay off. In this work, we propose HideNseek which employs one-shot data-agnostic pruning at initialization to get a subnetwork based on weights' synaptic saliency. Each client then optimizes a sign supermask in {-1, +1} multiplied by the unpruned weights to allow faster convergence with the same compression rates as state-of-the-art. Empirical results from three datasets demonstrate that compared to state-of-the-art, HideNseek improves inferences accuracies by up to 40.6\% while reducing the communication cost and training time by up to 39.7\% and 46.8\% respectively.

Large language models (LLMs) continue to face challenges in reliably solving reasoning tasks, particularly those that require precise rule following, as often found in mathematical reasoning. This paper introduces a novel neurosymbolic method that improves LLM reasoning by encoding hidden states into neurosymbolic vectors, enabling problem-solving within a neurosymbolic vector space. The results are decoded and merged with the original hidden state, significantly boosting the model's performance on numerical reasoning tasks. By offloading computation through neurosymbolic representations, this method enhances efficiency, reliability, and interpretability. Experimental results demonstrate an average of 88.6% lower cross-entropy loss and 15.4 times more problems correctly solved on a suite of mathematical reasoning tasks compared to chain-of-thought prompting and supervised fine-tuning (LoRA), without degrading performance on other tasks. We make our code available at: https://github.com/vdhanraj/Neurosymbolic-LLM.

Contextual hallucinations -- statements unsupported by given context -- remain a significant challenge in AI. We demonstrate a practical interpretability insight: a generator-agnostic observer model detects hallucinations via a single forward pass and a linear probe on its residual stream. This probe isolates a single, transferable linear direction separating hallucinated from faithful text, outperforming baselines by 5-27 points and showing robust mid-layer performance across Gemma-2 models (2B to 27B). Gradient-times-activation localises this signal to sparse, late-layer MLP activity. Critically, manipulating this direction causally steers generator hallucination rates, proving its actionability. Our results offer novel evidence of internal, low-dimensional hallucination tracking linked to specific MLP sub-circuits, exploitable for detection and mitigation. We release the 2000-example ContraTales benchmark for realistic assessment of such solutions.

Implicit Neural Representations (INRs) have recently gained attention as a powerful approach for continuously representing signals such as images, videos, and 3D shapes using multilayer perceptrons (MLPs). However, MLPs are known to exhibit a low-frequency bias, limiting their ability to capture high-frequency details accurately. This limitation is typically addressed by incorporating high-frequency input embeddings or specialized activation layers. In this work, we demonstrate that these embeddings and activations are often configured with hyperparameters that perform well on average but are suboptimal for specific input signals under consideration, necessitating a costly grid search to identify optimal settings. Our key observation is that the initial frequency spectrum of an untrained model's output correlates strongly with the model's eventual performance on a given target signal. Leveraging this insight, we propose frequency shifting (or FreSh), a method that selects embedding hyperparameters to align the frequency spectrum of the model's initial output with that of the target signal. We show that this simple initialization technique improves performance across various neural representation methods and tasks, achieving results comparable to extensive hyperparameter sweeps but with only marginal computational overhead compared to training a single model with default hyperparameters.

We present SpiralMLP, a novel architecture that introduces a Spiral FC layer as a replacement for the conventional Token Mixing approach. Differing from several existing MLP-based models that primarily emphasize axes, our Spiral FC layer is designed as a deformable convolution layer with spiral-like offsets. We further adapt Spiral FC into two variants: Self-Spiral FC and Cross-Spiral FC, which enable both local and global feature integration seamlessly, eliminating the need for additional processing steps. To thoroughly investigate the effectiveness of the spiral-like offsets and validate our design, we conduct ablation studies and explore optimal configurations. In empirical tests, SpiralMLP reaches state-of-the-art performance, similar to Transformers, CNNs, and other MLPs, benchmarking on ImageNet-1k, COCO and ADE20K. SpiralMLP still maintains linear computational complexity O(HW) and is compatible with varying input image resolutions. Our study reveals that targeting the full receptive field is not essential for achieving high performance, instead, adopting a refined approach offers better results.

Recent work has shown that the training of a one-hidden-layer, scalar-output fully-connected ReLU neural network can be reformulated as a finite-dimensional convex program. Unfortunately, the scale of such a convex program grows exponentially in data size. In this work, we prove that a stochastic procedure with a linear complexity well approximates the exact formulation. Moreover, we derive a convex optimization approach to efficiently solve the "adversarial training" problem, which trains neural networks that are robust to adversarial input perturbations. Our method can be applied to binary classification and regression, and provides an alternative to the current adversarial training methods, such as Fast Gradient Sign Method (FGSM) and Projected Gradient Descent (PGD). We demonstrate in experiments that the proposed method achieves a noticeably better adversarial robustness and performance than the existing methods.

We introduce GateSkip, a simple residual-stream gating mechanism that enables token-wise layer skipping in decoder-only LMs. Each Attention/MLP branch is equipped with a sigmoid-linear gate that condenses the branch's output before it re-enters the residual stream. During inference we rank tokens by the gate values and skip low-importance ones using a per-layer budget. While early-exit or router-based Mixture-of-Depths models are known to be unstable and need extensive retraining, our smooth, differentiable gates fine-tune stably on top of pretrained models. On long-form reasoning, we save up to 15\% compute while retaining over 90\% of baseline accuracy. On instruction-tuned models we see accuracy gains at full compute and match baseline quality near 50\% savings. The learned gates give insight into transformer information flow (e.g., BOS tokens act as anchors), and the method combines easily with quantization, pruning, and self-speculative decoding.

This thesis provides methods and analysis of models which make progress on this goal. The techniques outlined are task agnostic, and should provide benefit when used with nearly any transformer LM. We introduce two new finetuning methods which add new capabilities to the models they are used on. The first adds a recurrence mechanism, which removes the fixed-window sized constraint and improves the efficiency of a transformer decoder. The second allows masked language models (MLMs) to be used for initialization of both the encoder and decoder of a non-autoregressive sequence-to-sequence transformer, opening up generative applications of models which were previously only used for natural language understanding tasks. We also introduce two new techniques for improving the quality of predictions of any transformer decoder without additional finetuning. One, hidden state optimization, can be applied to any transformer decoder to improve the quality of predictions at inference time, especially for few-shot classification. The other, conditional beam search, allows practitioners to search for natural language generation (NLG) model outputs with high likelihood while conditioning on the event that the output is not degenerate (e.g. empty, repetitive, etc.). Finally, we provide theoretical and empirical insights on the divergence of model-likelihood and output quality which has widely been observed in prior work. These insights apply to any model which represents a distribution over text, and apply to language models which are not transformers or even autoregressive. We argue that the NLP community has, to some extent, misunderstood the implications of these findings, and encourage a point of view which has more nuance.

Federated Learning (FL) has gained popularity for fine-tuning large language models (LLMs) across multiple nodes, each with its own private data. While LoRA has been widely adopted for parameter efficient federated fine-tuning, recent theoretical and empirical studies highlight its suboptimal performance in the federated learning context. In response, we propose a novel, simple, and more effective parameter-efficient fine-tuning method that does not rely on LoRA. Our approach introduces a small multi-layer perceptron (MLP) layer between two existing MLP layers the up proj (the FFN projection layer following the self-attention module) and down proj within the feed forward network of the transformer block. This solution addresses the bottlenecks associated with LoRA in federated fine tuning and outperforms recent LoRA-based approaches, demonstrating superior performance for both language models and vision encoders.

This paper presents a deep machine learning architecture, the "polyharmonic cascade" -- a sequence of packages of polyharmonic splines, where each layer is rigorously derived from the theory of random functions and the principles of indifference. This makes it possible to approximate nonlinear functions of arbitrary complexity while preserving global smoothness and a probabilistic interpretation. For the polyharmonic cascade, a training method alternative to gradient descent is proposed: instead of directly optimizing the coefficients, one solves a single global linear system on each batch with respect to the function values at fixed "constellations" of nodes. This yields synchronized updates of all layers, preserves the probabilistic interpretation of individual layers and theoretical consistency with the original model, and scales well: all computations reduce to 2D matrix operations efficiently executed on a GPU. Fast learning without overfitting on MNIST is demonstrated.

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.

This paper introduces the Point Cloud Network (PCN) architecture, a novel implementation of linear layers in deep learning networks, and provides empirical evidence to advocate for its preference over the Multilayer Perceptron (MLP) in linear layers. We train several models, including the original AlexNet, using both MLP and PCN architectures for direct comparison of linear layers (Krizhevsky et al., 2012). The key results collected are model parameter count and top-1 test accuracy over the CIFAR-10 and CIFAR-100 datasets (Krizhevsky, 2009). AlexNet-PCN16, our PCN equivalent to AlexNet, achieves comparable efficacy (test accuracy) to the original architecture with a 99.5% reduction of parameters in its linear layers. All training is done on cloud RTX 4090 GPUs, leveraging pytorch for model construction and training. Code is provided for anyone to reproduce the trials from this paper.

We conjecture that hidden state vectors corresponding to individual input tokens encode information sufficient to accurately predict several tokens ahead. More concretely, in this paper we ask: Given a hidden (internal) representation of a single token at position t in an input, can we reliably anticipate the tokens that will appear at positions geq t + 2? To test this, we measure linear approximation and causal intervention methods in GPT-J-6B to evaluate the degree to which individual hidden states in the network contain signal rich enough to predict future hidden states and, ultimately, token outputs. We find that, at some layers, we can approximate a model's output with more than 48% accuracy with respect to its prediction of subsequent tokens through a single hidden state. Finally we present a "Future Lens" visualization that uses these methods to create a new view of transformer states.

Instruction finetuning on a variety of image-text instruction data is the key to obtaining a versatile Multimodal Large Language Model (MLLM), and different configurations of the instruction data can lead to finetuned models with different capabilities. However, we have discovered that data conflicts are inevitable when mixing instruction data from distinct domains, which can result in performance drops for tasks of a specific domain. To address this issue, we propose to apply an efficient Mixture of Experts (MoE) design, which is a sparse Mixture of LoRA Experts (MoLE) for instruction finetuning MLLMs. Within the Transformer layers, we extend the popular Low-Rank Adaption (LoRA) method by creating a set of LoRA experts specifically for the MLP layer, and route each token to the top-1 expert based on a routing function, allowing adaptive choices for tokens from different domains. Since the LoRA experts are sparsely activated, the training and inference cost are kept roughly constant compared to the original LoRA method. By replacing the plain-LoRA of LLaVA-1.5 with our MoE design, our final model is named LLaVA-MoLE. Extensive experiments proved that LLaVA-MoLE effectively mitigates the data conflict issue when mixing multiple distinct instruction datasets with various configurations, and achieves consistent performance gains over the strong plain-LoRA baselines. Most importantly, on the mixed datasets, LLaVA-MoLE can even outperform the plain-LoRA baseline trained with twice the samples.

Transformers are a widespread and successful model architecture, particularly in Natural Language Processing (NLP) and Computer Vision (CV). The essential innovation of this architecture is the Attention Mechanism, which solves the problem of extracting relevant context information from long sequences in NLP and realistic scenes in CV. A classical neural network component, a Multi-Layer Perceptron (MLP), complements the attention mechanism. Its necessity is frequently justified by its capability of modeling nonlinear relationships. However, the attention mechanism itself is nonlinear through its internal use of similarity measures. A possible hypothesis is that this nonlinearity is sufficient for modeling typical application problems. As the MLPs usually contain the most trainable parameters of the whole model, their omission would substantially reduce the parameter set size. Further components can also be reorganized to reduce the number of parameters. Under some conditions, query and key matrices can be collapsed into a single matrix of the same size. The same is true about value and projection matrices, which can also be omitted without eliminating the substance of the attention mechanism. Initially, the similarity measure was defined asymmetrically, with peculiar properties such as that a token is possibly dissimilar to itself. A possible symmetric definition requires only half of the parameters. We have laid the groundwork by testing widespread CV benchmarks: MNIST and CIFAR-10. The tests have shown that simplified transformer architectures (a) without MLP, (b) with collapsed matrices, and (c) symmetric similarity matrices exhibit similar performance as the original architecture, saving up to 90% of parameters without hurting the classification performance.

Transformers have become one of the most important architectural innovations in deep learning and have enabled many breakthroughs over the past few years. Here we propose a simple network architecture, gMLP, based on MLPs with gating, and show that it can perform as well as Transformers in key language and vision applications. Our comparisons show that self-attention is not critical for Vision Transformers, as gMLP can achieve the same accuracy. For BERT, our model achieves parity with Transformers on pretraining perplexity and is better on some downstream NLP tasks. On finetuning tasks where gMLP performs worse, making the gMLP model substantially larger can close the gap with Transformers. In general, our experiments show that gMLP can scale as well as Transformers over increased data and compute.

We present a neural network architecture designed to naturally learn a positional embedding and overcome the spectral bias towards lower frequencies faced by conventional implicit neural representation networks. Our proposed architecture, SPDER, is a simple MLP that uses an activation function composed of a sinusoidal multiplied by a sublinear function, called the damping function. The sinusoidal enables the network to automatically learn the positional embedding of an input coordinate while the damping passes on the actual coordinate value by preventing it from being projected down to within a finite range of values. Our results indicate that SPDERs speed up training by 10x and converge to losses 1,500-50,000x lower than that of the state-of-the-art for image representation. SPDER is also state-of-the-art in audio representation. The superior representation capability allows SPDER to also excel on multiple downstream tasks such as image super-resolution and video frame interpolation. We provide intuition as to why SPDER significantly improves fitting compared to that of other INR methods while requiring no hyperparameter tuning or preprocessing.

According to the considerable growth in the avail of chest X-ray images in diagnosing various diseases, as well as gathering extensive datasets, having an automated diagnosis procedure using deep neural networks has occupied the minds of experts. Most of the available methods in computer vision use a CNN backbone to acquire high accuracy on the classification problems. Nevertheless, recent researches show that transformers, established as the de facto method in NLP, can also outperform many CNN-based models in vision. This paper proposes a multi-label classification deep model based on the Swin Transformer as the backbone to achieve state-of-the-art diagnosis classification. It leverages Multi-Layer Perceptron, also known as MLP, for the head architecture. We evaluate our model on one of the most widely-used and largest x-ray datasets called "Chest X-ray14," which comprises more than 100,000 frontal/back-view images from over 30,000 patients with 14 famous chest diseases. Our model has been tested with several number of MLP layers for the head setting, each achieves a competitive AUC score on all classes. Comprehensive experiments on Chest X-ray14 have shown that a 3-layer head attains state-of-the-art performance with an average AUC score of 0.810, compared to the former SOTA average AUC of 0.799. We propose an experimental setup for the fair benchmarking of existing methods, which could be used as a basis for the future studies. Finally, we followed up our results by confirming that the proposed method attends to the pathologically relevant areas of the chest.

We present SegFormer, a simple, efficient yet powerful semantic segmentation framework which unifies Transformers with lightweight multilayer perception (MLP) decoders. SegFormer has two appealing features: 1) SegFormer comprises a novel hierarchically structured Transformer encoder which outputs multiscale features. It does not need positional encoding, thereby avoiding the interpolation of positional codes which leads to decreased performance when the testing resolution differs from training. 2) SegFormer avoids complex decoders. The proposed MLP decoder aggregates information from different layers, and thus combining both local attention and global attention to render powerful representations. We show that this simple and lightweight design is the key to efficient segmentation on Transformers. We scale our approach up to obtain a series of models from SegFormer-B0 to SegFormer-B5, reaching significantly better performance and efficiency than previous counterparts. For example, SegFormer-B4 achieves 50.3% mIoU on ADE20K with 64M parameters, being 5x smaller and 2.2% better than the previous best method. Our best model, SegFormer-B5, achieves 84.0% mIoU on Cityscapes validation set and shows excellent zero-shot robustness on Cityscapes-C. Code will be released at: github.com/NVlabs/SegFormer.

Adversarial training has been widely used to enhance the robustness of neural network models against adversarial attacks. Despite the popularity of neural network models, a significant gap exists between the natural and robust accuracy of these models. In this paper, we identify one of the primary reasons for this gap is the common use of one-hot vectors as labels, which hinders the learning process for image recognition. Representing ambiguous images with one-hot vectors is imprecise and may lead the model to suboptimal solutions. To overcome this issue, we propose a novel method called Low Temperature Distillation (LTD) that generates soft labels using the modified knowledge distillation framework. Unlike previous approaches, LTD uses a relatively low temperature in the teacher model and fixed, but different temperatures for the teacher and student models. This modification boosts the model's robustness without encountering the gradient masking problem that has been addressed in defensive distillation. The experimental results demonstrate the effectiveness of the proposed LTD method combined with previous techniques, achieving robust accuracy rates of 58.19%, 31.13%, and 42.08% on CIFAR-10, CIFAR-100, and ImageNet data sets, respectively, without additional unlabeled data.

Augmenting a language model (LM) with k-nearest neighbors (kNN) retrieval on its training data alone can decrease its perplexity, though the underlying reasons for this remains elusive. In this work, we first rule out one previously posited possibility -- the "softmax bottleneck." We further identify the MLP hurdle phenomenon, where the final MLP layer in LMs may impede LM optimization early on. We explore memorization and generalization in language models with two new datasets, where advanced model like GPT-3.5-turbo find generalizing to irrelevant information in the training data challenging. However, incorporating kNN retrieval to vanilla GPT-2 117M can consistently improve performance in this setting.

Time series forecasting has played the key role in different industrial, including finance, traffic, energy, and healthcare domains. While existing literatures have designed many sophisticated architectures based on RNNs, GNNs, or Transformers, another kind of approaches based on multi-layer perceptrons (MLPs) are proposed with simple structure, low complexity, and {superior performance}. However, most MLP-based forecasting methods suffer from the point-wise mappings and information bottleneck, which largely hinders the forecasting performance. To overcome this problem, we explore a novel direction of applying MLPs in the frequency domain for time series forecasting. We investigate the learned patterns of frequency-domain MLPs and discover their two inherent characteristic benefiting forecasting, (i) global view: frequency spectrum makes MLPs own a complete view for signals and learn global dependencies more easily, and (ii) energy compaction: frequency-domain MLPs concentrate on smaller key part of frequency components with compact signal energy. Then, we propose FreTS, a simple yet effective architecture built upon Frequency-domain MLPs for Time Series forecasting. FreTS mainly involves two stages, (i) Domain Conversion, that transforms time-domain signals into complex numbers of frequency domain; (ii) Frequency Learning, that performs our redesigned MLPs for the learning of real and imaginary part of frequency components. The above stages operated on both inter-series and intra-series scales further contribute to channel-wise and time-wise dependency learning. Extensive experiments on 13 real-world benchmarks (including 7 benchmarks for short-term forecasting and 6 benchmarks for long-term forecasting) demonstrate our consistent superiority over state-of-the-art methods.

Continuous convolution has recently gained prominence due to its ability to handle irregularly sampled data and model long-term dependency. Also, the promising experimental results of using large convolutional kernels have catalyzed the development of continuous convolution since they can construct large kernels very efficiently. Leveraging neural networks, more specifically multilayer perceptrons (MLPs), is by far the most prevalent approach to implementing continuous convolution. However, there are a few drawbacks, such as high computational costs, complex hyperparameter tuning, and limited descriptive power of filters. This paper suggests an alternative approach to building a continuous convolution without neural networks, resulting in more computationally efficient and improved performance. We present self-moving point representations where weight parameters freely move, and interpolation schemes are used to implement continuous functions. When applied to construct convolutional kernels, the experimental results have shown improved performance with drop-in replacement in the existing frameworks. Due to its lightweight structure, we are first to demonstrate the effectiveness of continuous convolution in a large-scale setting, e.g., ImageNet, presenting the improvements over the prior arts. Our code is available on https://github.com/sangnekim/SMPConv

This paper presents a comparison of six machine learning (ML) algorithms: GRU-SVM (Agarap, 2017), Linear Regression, Multilayer Perceptron (MLP), Nearest Neighbor (NN) search, Softmax Regression, and Support Vector Machine (SVM) on the Wisconsin Diagnostic Breast Cancer (WDBC) dataset (Wolberg, Street, & Mangasarian, 1992) by measuring their classification test accuracy and their sensitivity and specificity values. The said dataset consists of features which were computed from digitized images of FNA tests on a breast mass (Wolberg, Street, & Mangasarian, 1992). For the implementation of the ML algorithms, the dataset was partitioned in the following fashion: 70% for training phase, and 30% for the testing phase. The hyper-parameters used for all the classifiers were manually assigned. Results show that all the presented ML algorithms performed well (all exceeded 90% test accuracy) on the classification task. The MLP algorithm stands out among the implemented algorithms with a test accuracy of ~99.04%.

The success of deep learning is due in large part to our ability to solve certain massive non-convex optimization problems with relative ease. Though non-convex optimization is NP-hard, simple algorithms -- often variants of stochastic gradient descent -- exhibit surprising effectiveness in fitting large neural networks in practice. We argue that neural network loss landscapes often contain (nearly) a single basin after accounting for all possible permutation symmetries of hidden units a la Entezari et al. 2021. We introduce three algorithms to permute the units of one model to bring them into alignment with a reference model in order to merge the two models in weight space. This transformation produces a functionally equivalent set of weights that lie in an approximately convex basin near the reference model. Experimentally, we demonstrate the single basin phenomenon across a variety of model architectures and datasets, including the first (to our knowledge) demonstration of zero-barrier linear mode connectivity between independently trained ResNet models on CIFAR-10. Additionally, we identify intriguing phenomena relating model width and training time to mode connectivity. Finally, we discuss shortcomings of the linear mode connectivity hypothesis, including a counterexample to the single basin theory.

Neural fields such as DeepSDF and Neural Radiance Fields have recently revolutionized novel-view synthesis and 3D reconstruction from RGB images and videos. However, achieving high-quality representation, reconstruction, and rendering requires deep neural networks, which are slow to train and evaluate. Although several acceleration techniques have been proposed, they often trade off speed for memory. Gaussian splatting-based methods, on the other hand, accelerate the rendering time but remain costly in terms of training speed and memory needed to store the parameters of a large number of Gaussians. In this paper, we introduce a novel neural representation that is fast, both at training and inference times, and lightweight. Our key observation is that the neurons used in traditional MLPs perform simple computations (a dot product followed by ReLU activation) and thus one needs to use either wide and deep MLPs or high-resolution and high-dimensional feature grids to parameterize complex nonlinear functions. We show in this paper that by replacing traditional neurons with Radial Basis Function (RBF) kernels, one can achieve highly accurate representation of 2D (RGB images), 3D (geometry), and 5D (radiance fields) signals with just a single layer of such neurons. The representation is highly parallelizable, operates on low-resolution feature grids, and is compact and memory-efficient. We demonstrate that the proposed novel representation can be trained for 3D geometry representation in less than 15 seconds and for novel view synthesis in less than 15 mins. At runtime, it can synthesize novel views at more than 60 fps without sacrificing quality.

Adversarial training is a widely used strategy for making neural networks resistant to adversarial perturbations. For a neural network of width m, n input training data in d dimension, it takes Omega(mnd) time cost per training iteration for the forward and backward computation. In this paper we analyze the convergence guarantee of adversarial training procedure on a two-layer neural network with shifted ReLU activation, and shows that only o(m) neurons will be activated for each input data per iteration. Furthermore, we develop an algorithm for adversarial training with time cost o(m n d) per iteration by applying half-space reporting data structure.

While neural networks are used for classification tasks across domains, a long-standing open problem in machine learning is determining whether neural networks trained using standard procedures are optimal for classification, i.e., whether such models minimize the probability of misclassification for arbitrary data distributions. In this work, we identify and construct an explicit set of neural network classifiers that achieve optimality. Since effective neural networks in practice are typically both wide and deep, we analyze infinitely wide networks that are also infinitely deep. In particular, using the recent connection between infinitely wide neural networks and Neural Tangent Kernels, we provide explicit activation functions that can be used to construct networks that achieve optimality. Interestingly, these activation functions are simple and easy to implement, yet differ from commonly used activations such as ReLU or sigmoid. More generally, we create a taxonomy of infinitely wide and deep networks and show that these models implement one of three well-known classifiers depending on the activation function used: (1) 1-nearest neighbor (model predictions are given by the label of the nearest training example); (2) majority vote (model predictions are given by the label of the class with greatest representation in the training set); or (3) singular kernel classifiers (a set of classifiers containing those that achieve optimality). Our results highlight the benefit of using deep networks for classification tasks, in contrast to regression tasks, where excessive depth is harmful.

Model editing techniques modify a minor proportion of knowledge in Large Language Models (LLMs) at a relatively low cost, which have demonstrated notable success. Existing methods assume Transformer Layer (TL) hidden states are values of key-value memories of the Feed-Forward Network (FFN). They usually optimize the TL hidden states to memorize target knowledge and use it to update the weights of the FFN in LLMs. However, the information flow of TL hidden states comes from three parts: Multi-Head Self-Attention (MHSA), FFN, and residual connections. Existing methods neglect the fact that the TL hidden states contains information not specifically required for FFN. Consequently, the performance of model editing decreases. To achieve more precise model editing, we analyze hidden states of MHSA and FFN, finding that MHSA encodes certain general knowledge extraction patterns. This implies that MHSA weights do not require updating when new knowledge is introduced. Based on above findings, we introduce PMET, which simultaneously optimizes Transformer Component (TC, namely MHSA and FFN) hidden states, while only using the optimized TC hidden states of FFN to precisely update FFN weights. Our experiments demonstrate that PMET exhibits state-of-the-art performance on both the COUNTERFACT and zsRE datasets. Our ablation experiments substantiate the effectiveness of our enhancements, further reinforcing the finding that the MHSA encodes certain general knowledge extraction patterns and indicating its storage of a small amount of factual knowledge. Our code is available at https://github.com/xpq-tech/PMET.

While modern decoder-only LLMs achieve superior performance across various domains, hallucinations have risen to be a common problem in their generated text, hindering their application in knowledge-intensive tasks. Retriever-augmented generation (RAG) offers a solution, but the non-parametric nature of the retriever hinders its deep interaction with LLM. In this work, we propose to decouple memorization from the LLM decoder using a pretrained, differentiable external memory. The external memory is an MLP pretrained by imitating the behavior of a retriever on the entire pretraining dataset. Our resulting architecture, which comprises a transformer decoder and an external MLP memory pretrained on language modeling and retriever imitation respectively, demonstrates strong perplexity and performance on downstream tasks. Experiments show our architecture exhibits steeper power-law scaling with model size, achieving 17.5% and 24.1% improvement on WikiText-103 and Web datasets compared to decoder-only models while benefiting from added training without overfitting. We demonstrate superior performance on three hallucination benchmarks and nine memory-intensive tasks. Additionally, our approach delivers 80times speedup over kNN-LM (500M tokens) and 1.3times faster inference than decoder-only models. Unlike kNN-LM, which impairs reasoning, our MLP memory improves StrategyQA performance. We will open-source our code and models in the future.

We propose Joint MLP/Attention (JoMA) dynamics, a novel mathematical framework to understand the training procedure of multilayer Transformer architectures. This is achieved by integrating out the self-attention layer in Transformers, producing a modified dynamics of MLP layers only. JoMA removes unrealistic assumptions in previous analysis (e.g., lack of residual connection) and predicts that the attention first becomes sparse (to learn salient tokens), then dense (to learn less salient tokens) in the presence of nonlinear activations, while in the linear case, it is consistent with existing works that show attention becomes sparse over time. We leverage JoMA to qualitatively explains how tokens are combined to form hierarchies in multilayer Transformers, when the input tokens are generated by a latent hierarchical generative model. Experiments on models trained from real-world dataset (Wikitext2/Wikitext103) and various pre-trained models (OPT, Pythia) verify our theoretical findings.

Recently, deep neural networks such as RNN, CNN and Transformer have been applied in the task of sequential recommendation, which aims to capture the dynamic preference characteristics from logged user behavior data for accurate recommendation. However, in online platforms, logged user behavior data is inevitable to contain noise, and deep recommendation models are easy to overfit on these logged data. To tackle this problem, we borrow the idea of filtering algorithms from signal processing that attenuates the noise in the frequency domain. In our empirical experiments, we find that filtering algorithms can substantially improve representative sequential recommendation models, and integrating simple filtering algorithms (eg Band-Stop Filter) with an all-MLP architecture can even outperform competitive Transformer-based models. Motivated by it, we propose FMLP-Rec, an all-MLP model with learnable filters for sequential recommendation task. The all-MLP architecture endows our model with lower time complexity, and the learnable filters can adaptively attenuate the noise information in the frequency domain. Extensive experiments conducted on eight real-world datasets demonstrate the superiority of our proposed method over competitive RNN, CNN, GNN and Transformer-based methods. Our code and data are publicly available at the link: blue{https://github.com/RUCAIBox/FMLP-Rec}.

Our proposed deeply-supervised nets (DSN) method simultaneously minimizes classification error while making the learning process of hidden layers direct and transparent. We make an attempt to boost the classification performance by studying a new formulation in deep networks. Three aspects in convolutional neural networks (CNN) style architectures are being looked at: (1) transparency of the intermediate layers to the overall classification; (2) discriminativeness and robustness of learned features, especially in the early layers; (3) effectiveness in training due to the presence of the exploding and vanishing gradients. We introduce "companion objective" to the individual hidden layers, in addition to the overall objective at the output layer (a different strategy to layer-wise pre-training). We extend techniques from stochastic gradient methods to analyze our algorithm. The advantage of our method is evident and our experimental result on benchmark datasets shows significant performance gain over existing methods (e.g. all state-of-the-art results on MNIST, CIFAR-10, CIFAR-100, and SVHN).

Normalization layers are one of the key building blocks for deep neural networks. Several theoretical studies have shown that batch normalization improves the signal propagation, by avoiding the representations from becoming collinear across the layers. However, results on mean-field theory of batch normalization also conclude that this benefit comes at the expense of exploding gradients in depth. Motivated by these two aspects of batch normalization, in this study we pose the following question: "Can a batch-normalized network keep the optimal signal propagation properties, but avoid exploding gradients?" We answer this question in the affirmative by giving a particular construction of an Multi-Layer Perceptron (MLP) with linear activations and batch-normalization that provably has bounded gradients at any depth. Based on Weingarten calculus, we develop a rigorous and non-asymptotic theory for this constructed MLP that gives a precise characterization of forward signal propagation, while proving that gradients remain bounded for linearly independent input samples, which holds in most practical settings. Inspired by our theory, we also design an activation shaping scheme that empirically achieves the same properties for certain non-linear activations.

These handouts are designed for people who is just starting involved with the topic artificial neural networks. We show how it works a single artificial neuron (McCulloch & Pitt model), mathematically and graphically. We do explain the delta rule, a learning algorithm to find the neuron weights. We also present some examples in MATLAB/Octave. There are examples for classification task for lineal and non-lineal problems. At the end, we present an artificial neural network, a feed-forward neural network along its learning algorithm backpropagation. ----- Estos apuntes est\'an dise\~nados para personas que por primera vez se introducen en el tema de las redes neuronales artificiales. Se muestra el funcionamiento b\'asico de una neurona, matem\'aticamente y gr\'aficamente. Se explica la Regla Delta, algoritmo deaprendizaje para encontrar los pesos de una neurona. Tambi\'en se muestran ejemplos en MATLAB/Octave. Hay ejemplos para problemas de clasificaci\'on, para problemas lineales y no-lineales. En la parte final se muestra la arquitectura de red neuronal artificial conocida como backpropagation.

While it is widely known that neural networks are universal approximators of continuous functions, a less known and perhaps more powerful result is that a neural network with a single hidden layer can approximate accurately any nonlinear continuous operator. This universal approximation theorem is suggestive of the potential application of neural networks in learning nonlinear operators from data. However, the theorem guarantees only a small approximation error for a sufficient large network, and does not consider the important optimization and generalization errors. To realize this theorem in practice, we propose deep operator networks (DeepONets) to learn operators accurately and efficiently from a relatively small dataset. A DeepONet consists of two sub-networks, one for encoding the input function at a fixed number of sensors x_i, i=1,dots,m (branch net), and another for encoding the locations for the output functions (trunk net). We perform systematic simulations for identifying two types of operators, i.e., dynamic systems and partial differential equations, and demonstrate that DeepONet significantly reduces the generalization error compared to the fully-connected networks. We also derive theoretically the dependence of the approximation error in terms of the number of sensors (where the input function is defined) as well as the input function type, and we verify the theorem with computational results. More importantly, we observe high-order error convergence in our computational tests, namely polynomial rates (from half order to fourth order) and even exponential convergence with respect to the training dataset size.

While depth tends to improve network performances, it also makes gradient-based training more difficult since deeper networks tend to be more non-linear. The recently proposed knowledge distillation approach is aimed at obtaining small and fast-to-execute models, and it has shown that a student network could imitate the soft output of a larger teacher network or ensemble of networks. In this paper, we extend this idea to allow the training of a student that is deeper and thinner than the teacher, using not only the outputs but also the intermediate representations learned by the teacher as hints to improve the training process and final performance of the student. Because the student intermediate hidden layer will generally be smaller than the teacher's intermediate hidden layer, additional parameters are introduced to map the student hidden layer to the prediction of the teacher hidden layer. This allows one to train deeper students that can generalize better or run faster, a trade-off that is controlled by the chosen student capacity. For example, on CIFAR-10, a deep student network with almost 10.4 times less parameters outperforms a larger, state-of-the-art teacher network.

Machine unlearning empowers individuals with the `right to be forgotten' by removing their private or sensitive information encoded in machine learning models. However, it remains uncertain whether MU can be effectively applied to Multimodal Large Language Models (MLLMs), particularly in scenarios of forgetting the leaked visual data of concepts. To overcome the challenge, we propose an efficient method, Single Image Unlearning (SIU), to unlearn the visual recognition of a concept by fine-tuning a single associated image for few steps. SIU consists of two key aspects: (i) Constructing Multifaceted fine-tuning data. We introduce four targets, based on which we construct fine-tuning data for the concepts to be forgotten; (ii) Jointly training loss. To synchronously forget the visual recognition of concepts and preserve the utility of MLLMs, we fine-tune MLLMs through a novel Dual Masked KL-divergence Loss combined with Cross Entropy loss. Alongside our method, we establish MMUBench, a new benchmark for MU in MLLMs and introduce a collection of metrics for its evaluation. Experimental results on MMUBench show that SIU completely surpasses the performance of existing methods. Furthermore, we surprisingly find that SIU can avoid invasive membership inference attacks and jailbreak attacks. To the best of our knowledge, we are the first to explore MU in MLLMs. We will release the code and benchmark in the near future.

Pre-trained large language models (LLMs) exhibit impressive mathematical reasoning capabilities, yet how they compute basic arithmetic, such as addition, remains unclear. This paper shows that pre-trained LLMs add numbers using Fourier features -- dimensions in the hidden state that represent numbers via a set of features sparse in the frequency domain. Within the model, MLP and attention layers use Fourier features in complementary ways: MLP layers primarily approximate the magnitude of the answer using low-frequency features, while attention layers primarily perform modular addition (e.g., computing whether the answer is even or odd) using high-frequency features. Pre-training is crucial for this mechanism: models trained from scratch to add numbers only exploit low-frequency features, leading to lower accuracy. Introducing pre-trained token embeddings to a randomly initialized model rescues its performance. Overall, our analysis demonstrates that appropriate pre-trained representations (e.g., Fourier features) can unlock the ability of Transformers to learn precise mechanisms for algorithmic tasks.

Large language models (LLMs) contain substantial factual knowledge which is commonly elicited by multiple-choice question-answering prompts. Internally, such models process the prompt through multiple transformer layers, building varying representations of the problem within its hidden states. Ultimately, however, only the hidden state corresponding to the final layer and token position are used to predict the answer label. In this work, we propose instead to learn a small separate neural network predictor module on a collection of training questions, that take the hidden states from all the layers at the last temporal position as input and outputs predictions. In effect, such a framework disentangles the representational abilities of LLMs from their predictive abilities. On a collection of hard benchmarks, our method achieves considerable improvements in performance, sometimes comparable to supervised fine-tuning procedures, but at a fraction of the computational cost.

Deep learning models have revolutionized various domains, with Multi-Layer Perceptrons (MLPs) being a cornerstone for tasks like data regression and image classification. However, a recent study has introduced Kolmogorov-Arnold Networks (KANs) as promising alternatives to MLPs, leveraging activation functions placed on edges rather than nodes. This structural shift aligns KANs closely with the Kolmogorov-Arnold representation theorem, potentially enhancing both model accuracy and interpretability. In this study, we explore the efficacy of KANs in the context of data representation via autoencoders, comparing their performance with traditional Convolutional Neural Networks (CNNs) on the MNIST, SVHN, and CIFAR-10 datasets. Our results demonstrate that KAN-based autoencoders achieve competitive performance in terms of reconstruction accuracy, thereby suggesting their viability as effective tools in data analysis tasks.

While Large Language Models (LLMs) have demonstrated impressive performance in various domains and tasks, concerns about their safety are becoming increasingly severe. In particular, since models may store unsafe knowledge internally, machine unlearning has emerged as a representative paradigm to ensure model safety. Existing approaches employ various training techniques, such as gradient ascent and negative preference optimization, in attempts to eliminate the influence of undesired data on target models. However, these methods merely suppress the activation of undesired data through parametric training without completely eradicating its informational traces within the model. This fundamental limitation makes it difficult to achieve effective continuous unlearning, rendering these methods vulnerable to relearning attacks. To overcome these challenges, we propose a Metamorphosis Representation Projection (MRP) approach that pioneers the application of irreversible projection properties to machine unlearning. By implementing projective transformations in the hidden state space of specific network layers, our method effectively eliminates harmful information while preserving useful knowledge. Experimental results demonstrate that our approach enables effective continuous unlearning and successfully defends against relearning attacks, achieving state-of-the-art performance in unlearning effectiveness while preserving natural performance. Our code is available in https://github.com/ChengcanWu/MRP.

In unsupervised anomaly detection (UAD) research, while state-of-the-art models have reached a saturation point with extensive studies on public benchmark datasets, they adopt large-scale tailor-made neural networks (NN) for detection performance or pursued unified models for various tasks. Towards edge computing, it is necessary to develop a computationally efficient and scalable solution that avoids large-scale complex NNs. Motivated by this, we aim to optimize the UAD performance with minimal changes to NN settings. Thus, we revisit the reconstruction-by-inpainting approach and rethink to improve it by analyzing strengths and weaknesses. The strength of the SOTA methods is a single deterministic masking approach that addresses the challenges of random multiple masking that is inference latency and output inconsistency. Nevertheless, the issue of failure to provide a mask to completely cover anomalous regions is a remaining weakness. To mitigate this issue, we propose Feature Attenuation of Defective Representation (FADeR) that only employs two MLP layers which attenuates feature information of anomaly reconstruction during decoding. By leveraging FADeR, features of unseen anomaly patterns are reconstructed into seen normal patterns, reducing false alarms. Experimental results demonstrate that FADeR achieves enhanced performance compared to similar-scale NNs. Furthermore, our approach exhibits scalability in performance enhancement when integrated with other single deterministic masking methods in a plug-and-play manner.

We present FOLD-SE, an efficient, explainable machine learning algorithm for classification tasks given tabular data containing numerical and categorical values. FOLD-SE generates a set of default rules-essentially a stratified normal logic program-as an (explainable) trained model. Explainability provided by FOLD-SE is scalable, meaning that regardless of the size of the dataset, the number of learned rules and learned literals stay quite small while good accuracy in classification is maintained. A model with smaller number of rules and literals is easier to understand for human beings. FOLD-SE is competitive with state-of-the-art machine learning algorithms such as XGBoost and Multi-Layer Perceptrons (MLP) wrt accuracy of prediction. However, unlike XGBoost and MLP, the FOLD-SE algorithm is explainable. The FOLD-SE algorithm builds upon our earlier work on developing the explainable FOLD-R++ machine learning algorithm for binary classification and inherits all of its positive features. Thus, pre-processing of the dataset, using techniques such as one-hot encoding, is not needed. Like FOLD-R++, FOLD-SE uses prefix sum to speed up computations resulting in FOLD-SE being an order of magnitude faster than XGBoost and MLP in execution speed. The FOLD-SE algorithm outperforms FOLD-R++ as well as other rule-learning algorithms such as RIPPER in efficiency, performance and scalability, especially for large datasets. A major reason for scalable explainability of FOLD-SE is the use of a literal selection heuristics based on Gini Impurity, as opposed to Information Gain used in FOLD-R++. A multi-category classification version of FOLD-SE is also presented.

In order to understand the in-context learning phenomenon, recent works have adopted a stylized experimental framework and demonstrated that Transformers can learn gradient-based learning algorithms for various classes of real-valued functions. However, the limitations of Transformers in implementing learning algorithms, and their ability to learn other forms of algorithms are not well understood. Additionally, the degree to which these capabilities are confined to attention-based models is unclear. Furthermore, it remains to be seen whether the insights derived from these stylized settings can be extrapolated to pretrained Large Language Models (LLMs). In this work, we take a step towards answering these questions by demonstrating the following: (a) On a test-bed with a variety of Boolean function classes, we find that Transformers can nearly match the optimal learning algorithm for 'simpler' tasks, while their performance deteriorates on more 'complex' tasks. Additionally, we find that certain attention-free models perform (almost) identically to Transformers on a range of tasks. (b) When provided a teaching sequence, i.e. a set of examples that uniquely identifies a function in a class, we show that Transformers learn more sample-efficiently. Interestingly, our results show that Transformers can learn to implement two distinct algorithms to solve a single task, and can adaptively select the more sample-efficient algorithm depending on the sequence of in-context examples. (c) Lastly, we show that extant LLMs, e.g. LLaMA-2, GPT-4, can compete with nearest-neighbor baselines on prediction tasks that are guaranteed to not be in their training set.

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.

NeRF synthesizes novel views of a scene with unprecedented quality by fitting a neural radiance field to RGB images. However, NeRF requires querying a deep Multi-Layer Perceptron (MLP) millions of times, leading to slow rendering times, even on modern GPUs. In this paper, we demonstrate that real-time rendering is possible by utilizing thousands of tiny MLPs instead of one single large MLP. In our setting, each individual MLP only needs to represent parts of the scene, thus smaller and faster-to-evaluate MLPs can be used. By combining this divide-and-conquer strategy with further optimizations, rendering is accelerated by three orders of magnitude compared to the original NeRF model without incurring high storage costs. Further, using teacher-student distillation for training, we show that this speed-up can be achieved without sacrificing visual quality.

Existing analyses of the expressive capacity of Transformer models have required excessively deep layers for data memorization, leading to a discrepancy with the Transformers actually used in practice. This is primarily due to the interpretation of the softmax function as an approximation of the hardmax function. By clarifying the connection between the softmax function and the Boltzmann operator, we prove that a single layer of self-attention with low-rank weight matrices possesses the capability to perfectly capture the context of an entire input sequence. As a consequence, we show that one-layer and single-head Transformers have a memorization capacity for finite samples, and that Transformers consisting of one self-attention layer with two feed-forward neural networks are universal approximators for continuous permutation equivariant functions on a compact domain.