Daily Papers

The new paradigm of finetuning-as-a-service introduces a new attack surface for Large Language Models (LLMs): a few harmful data uploaded by users can easily trick the finetuning to produce an alignment-broken model. We conduct an empirical analysis and uncover a harmful embedding drift phenomenon, showing a probable cause of the alignment-broken effect. Inspired by our findings, we propose Vaccine, a perturbation-aware alignment technique to mitigate the security risk of users finetuning. The core idea of Vaccine is to produce invariant hidden embeddings by progressively adding crafted perturbation to them in the alignment phase. This enables the embeddings to withstand harmful perturbation from un-sanitized user data in the finetuning phase. Our results on open source mainstream LLMs (e.g., Llama2, Opt, Vicuna) demonstrate that Vaccine can boost the robustness of alignment against harmful prompts induced embedding drift while reserving reasoning ability towards benign prompts. Our code is available at https://github.com/git-disl/Vaccine.

Machine learning models will often fail when deployed in an environment with a data distribution that is different than the training distribution. When multiple environments are available during training, many methods exist that learn representations which are invariant across the different distributions, with the hope that these representations will be transportable to unseen domains. In this work, we present a nonparametric strategy for learning invariant representations based on the recently-proposed Nadaraya-Watson (NW) head. The NW head makes a prediction by comparing the learned representations of the query to the elements of a support set that consists of labeled data. We demonstrate that by manipulating the support set, one can encode different causal assumptions. In particular, restricting the support set to a single environment encourages the model to learn invariant features that do not depend on the environment. We present a causally-motivated setup for our modeling and training strategy and validate on three challenging real-world domain generalization tasks in computer vision.

Learning representations that capture the underlying data generating process is a key problem for data efficient and robust use of neural networks. One key property for robustness which the learned representation should capture and which recently received a lot of attention is described by the notion of invariance. In this work we provide a causal perspective and new algorithm for learning invariant representations. Empirically we show that this algorithm works well on a diverse set of tasks and in particular we observe state-of-the-art performance on domain generalization, where we are able to significantly boost the score of existing models.

We introduce the first method for translating text embeddings from one vector space to another without any paired data, encoders, or predefined sets of matches. Our unsupervised approach translates any embedding to and from a universal latent representation (i.e., a universal semantic structure conjectured by the Platonic Representation Hypothesis). Our translations achieve high cosine similarity across model pairs with different architectures, parameter counts, and training datasets. The ability to translate unknown embeddings into a different space while preserving their geometry has serious implications for the security of vector databases. An adversary with access only to embedding vectors can extract sensitive information about the underlying documents, sufficient for classification and attribute inference.

Image representations are often evaluated through disjointed, task-specific protocols, leading to a fragmented understanding of model capabilities. For instance, it is unclear whether an image embedding model adept at clustering images is equally good at retrieving relevant images given a piece of text. We introduce the Massive Image Embedding Benchmark (MIEB) to evaluate the performance of image and image-text embedding models across the broadest spectrum to date. MIEB spans 38 languages across 130 individual tasks, which we group into 8 high-level categories. We benchmark 50 models across our benchmark, finding that no single method dominates across all task categories. We reveal hidden capabilities in advanced vision models such as their accurate visual representation of texts, and their yet limited capabilities in interleaved encodings and matching images and texts in the presence of confounders. We also show that the performance of vision encoders on MIEB correlates highly with their performance when used in multimodal large language models. Our code, dataset, and leaderboard are publicly available at https://github.com/embeddings-benchmark/mteb.

Recent empirical works have successfully used unlabeled data to learn feature representations that are broadly useful in downstream classification tasks. Several of these methods are reminiscent of the well-known word2vec embedding algorithm: leveraging availability of pairs of semantically "similar" data points and "negative samples," the learner forces the inner product of representations of similar pairs with each other to be higher on average than with negative samples. The current paper uses the term contrastive learning for such algorithms and presents a theoretical framework for analyzing them by introducing latent classes and hypothesizing that semantically similar points are sampled from the same latent class. This framework allows us to show provable guarantees on the performance of the learned representations on the average classification task that is comprised of a subset of the same set of latent classes. Our generalization bound also shows that learned representations can reduce (labeled) sample complexity on downstream tasks. We conduct controlled experiments in both the text and image domains to support the theory.

The goal of self-supervised learning from images is to construct image representations that are semantically meaningful via pretext tasks that do not require semantic annotations for a large training set of images. Many pretext tasks lead to representations that are covariant with image transformations. We argue that, instead, semantic representations ought to be invariant under such transformations. Specifically, we develop Pretext-Invariant Representation Learning (PIRL, pronounced as "pearl") that learns invariant representations based on pretext tasks. We use PIRL with a commonly used pretext task that involves solving jigsaw puzzles. We find that PIRL substantially improves the semantic quality of the learned image representations. Our approach sets a new state-of-the-art in self-supervised learning from images on several popular benchmarks for self-supervised learning. Despite being unsupervised, PIRL outperforms supervised pre-training in learning image representations for object detection. Altogether, our results demonstrate the potential of self-supervised learning of image representations with good invariance properties.

It has been observed that representations learned by distinct neural networks conceal structural similarities when the models are trained under similar inductive biases. From a geometric perspective, identifying the classes of transformations and the related invariances that connect these representations is fundamental to unlocking applications, such as merging, stitching, and reusing different neural modules. However, estimating task-specific transformations a priori can be challenging and expensive due to several factors (e.g., weights initialization, training hyperparameters, or data modality). To this end, we introduce a versatile method to directly incorporate a set of invariances into the representations, constructing a product space of invariant components on top of the latent representations without requiring prior knowledge about the optimal invariance to infuse. We validate our solution on classification and reconstruction tasks, observing consistent latent similarity and downstream performance improvements in a zero-shot stitching setting. The experimental analysis comprises three modalities (vision, text, and graphs), twelve pretrained foundational models, nine benchmarks, and several architectures trained from scratch.

Representation learning has become an invaluable approach for learning from symbolic data such as text and graphs. However, while complex symbolic datasets often exhibit a latent hierarchical structure, state-of-the-art methods typically learn embeddings in Euclidean vector spaces, which do not account for this property. For this purpose, we introduce a new approach for learning hierarchical representations of symbolic data by embedding them into hyperbolic space -- or more precisely into an n-dimensional Poincar\'e ball. Due to the underlying hyperbolic geometry, this allows us to learn parsimonious representations of symbolic data by simultaneously capturing hierarchy and similarity. We introduce an efficient algorithm to learn the embeddings based on Riemannian optimization and show experimentally that Poincar\'e embeddings outperform Euclidean embeddings significantly on data with latent hierarchies, both in terms of representation capacity and in terms of generalization ability.

Large scale vision and language models can achieve impressive zero-shot recognition performance by mapping class specific text queries to image content. Two distinct challenges that remain however, are high sensitivity to the choice of handcrafted class names that define queries, and the difficulty of adaptation to new, smaller datasets. Towards addressing these problems, we propose to leverage available data to learn, for each class, an optimal word embedding as a function of the visual content. By learning new word embeddings on an otherwise frozen model, we are able to retain zero-shot capabilities for new classes, easily adapt models to new datasets, and adjust potentially erroneous, non-descriptive or ambiguous class names. We show that our solution can easily be integrated in image classification and object detection pipelines, yields significant performance gains in multiple scenarios and provides insights into model biases and labelling errors.

Unsupervised learning methods based on contrastive learning have drawn increasing attention and achieved promising results. Most of them aim to learn representations invariant to instance-level variations, which are provided by different views of the same instance. In this paper, we propose Invariance Propagation to focus on learning representations invariant to category-level variations, which are provided by different instances from the same category. Our method recursively discovers semantically consistent samples residing in the same high-density regions in representation space. We demonstrate a hard sampling strategy to concentrate on maximizing the agreement between the anchor sample and its hard positive samples, which provide more intra-class variations to help capture more abstract invariance. As a result, with a ResNet-50 as the backbone, our method achieves 71.3% top-1 accuracy on ImageNet linear classification and 78.2% top-5 accuracy fine-tuning on only 1% labels, surpassing previous results. We also achieve state-of-the-art performance on other downstream tasks, including linear classification on Places205 and Pascal VOC, and transfer learning on small scale datasets.

From extracting features to generating text, the outputs of large language models (LLMs) typically rely on their final layers, following the conventional wisdom that earlier layers capture only low-level cues. However, our analysis shows that intermediate layers can encode even richer representations, often improving performance on a wide range of downstream tasks. To explain and quantify these hidden-layer properties, we propose a unified framework of representation quality metrics based on information theory, geometry, and invariance to input perturbations. Our framework highlights how each model layer balances information compression and signal preservation, revealing why mid-depth embeddings can exceed the last layer's performance. Through extensive experiments on 32 text-embedding tasks and comparisons across model architectures (transformers, state-space models) and domains (language, vision), we demonstrate that intermediate layers consistently provide stronger features. These findings challenge the standard focus on final-layer embeddings and open new directions for model analysis and optimization, including strategic use of mid-layer representations for more robust and accurate AI systems.

We adapt previous research on category theory and topological unsupervised learning to develop a functorial perspective on manifold learning, also known as nonlinear dimensionality reduction. We first characterize manifold learning algorithms as functors that map pseudometric spaces to optimization objectives and that factor through hierarchical clustering functors. We then use this characterization to prove refinement bounds on manifold learning loss functions and construct a hierarchy of manifold learning algorithms based on their equivariants. We express several popular manifold learning algorithms as functors at different levels of this hierarchy, including Metric Multidimensional Scaling, IsoMap, and UMAP. Next, we use interleaving distance to study the stability of a broad class of manifold learning algorithms. We present bounds on how closely the embeddings these algorithms produce from noisy data approximate the embeddings they would learn from noiseless data. Finally, we use our framework to derive a set of novel manifold learning algorithms, which we experimentally demonstrate are competitive with the state of the art.

We investigate compositional structures in data embeddings from pre-trained vision-language models (VLMs). Traditionally, compositionality has been associated with algebraic operations on embeddings of words from a pre-existing vocabulary. In contrast, we seek to approximate representations from an encoder as combinations of a smaller set of vectors in the embedding space. These vectors can be seen as "ideal words" for generating concepts directly within the embedding space of the model. We first present a framework for understanding compositional structures from a geometric perspective. We then explain what these compositional structures entail probabilistically in the case of VLM embeddings, providing intuitions for why they arise in practice. Finally, we empirically explore these structures in CLIP's embeddings and we evaluate their usefulness for solving different vision-language tasks such as classification, debiasing, and retrieval. Our results show that simple linear algebraic operations on embedding vectors can be used as compositional and interpretable methods for regulating the behavior of VLMs.

Many real-world tasks require models to compare images along multiple similarity conditions (e.g. similarity in color, category or shape). Existing methods often reason about these complex similarity relationships by learning condition-aware embeddings. While such embeddings aid models in learning different notions of similarity, they also limit their capability to generalize to unseen categories since they require explicit labels at test time. To address this deficiency, we propose an approach that jointly learns representations for the different similarity conditions and their contributions as a latent variable without explicit supervision. Comprehensive experiments across three datasets, Polyvore-Outfits, Maryland-Polyvore and UT-Zappos50k, demonstrate the effectiveness of our approach: our model outperforms the state-of-the-art methods, even those that are strongly supervised with pre-defined similarity conditions, on fill-in-the-blank, outfit compatibility prediction and triplet prediction tasks. Finally, we show that our model learns different visually-relevant semantic sub-spaces that allow it to generalize well to unseen categories.

The inability of deep learning models to handle data drawn from unseen distributions has sparked much interest in unsupervised out-of-distribution (U-OOD) detection, as it is crucial for reliable deep learning models. Despite considerable attention, theoretically-motivated approaches are few and far between, with most methods building on top of some form of heuristic. Recently, U-OOD was formalized in the context of data invariants, allowing a clearer understanding of how to characterize U-OOD, and methods leveraging affine invariants have attained state-of-the-art results on large-scale benchmarks. Nevertheless, the restriction to affine invariants hinders the expressiveness of the approach. In this work, we broaden the affine invariants formulation to a more general case and propose a framework consisting of a normalizing flow-like architecture capable of learning non-linear invariants. Our novel approach achieves state-of-the-art results on an extensive U-OOD benchmark, and we demonstrate its further applicability to tabular data. Finally, we show our method has the same desirable properties as those based on affine invariants.

Interpretability methods are valuable only if their explanations faithfully describe the explained model. In this work, we consider neural networks whose predictions are invariant under a specific symmetry group. This includes popular architectures, ranging from convolutional to graph neural networks. Any explanation that faithfully explains this type of model needs to be in agreement with this invariance property. We formalize this intuition through the notion of explanation invariance and equivariance by leveraging the formalism from geometric deep learning. Through this rigorous formalism, we derive (1) two metrics to measure the robustness of any interpretability method with respect to the model symmetry group; (2) theoretical robustness guarantees for some popular interpretability methods and (3) a systematic approach to increase the invariance of any interpretability method with respect to a symmetry group. By empirically measuring our metrics for explanations of models associated with various modalities and symmetry groups, we derive a set of 5 guidelines to allow users and developers of interpretability methods to produce robust explanations.

Visualizing features in deep neural networks (DNNs) can help understanding their computations. Many previous studies aimed to visualize the selectivity of individual units by finding meaningful images that maximize their activation. However, comparably little attention has been paid to visualizing to what image transformations units in DNNs are invariant. Here we propose a method to discover invariances in the responses of hidden layer units of deep neural networks. Our approach is based on simultaneously searching for a batch of images that strongly activate a unit while at the same time being as distinct from each other as possible. We find that even early convolutional layers in VGG-19 exhibit various forms of response invariance: near-perfect phase invariance in some units and invariance to local diffeomorphic transformations in others. At the same time, we uncover representational differences with ResNet-50 in its corresponding layers. We conclude that invariance transformations are a major computational component learned by DNNs and we provide a systematic method to study them.

We investigate the relationship between the geometry of token embeddings and their role in the next token prediction within transformer models. An important aspect of this connection uses the notion of empirical measure, which encodes the distribution of token point clouds across transformer layers and drives the evolution of token representations in the mean-field interacting picture. We use metrics such as intrinsic dimension, neighborhood overlap, and cosine similarity to observationally probe these empirical measures across layers. To validate our approach, we compare these metrics to a dataset where the tokens are shuffled, which disrupts the syntactic and semantic structure. Our findings reveal a correlation between the geometric properties of token embeddings and the cross-entropy loss of next token predictions, implying that prompts with higher loss values have tokens represented in higher-dimensional spaces.

Instance embeddings are an efficient and versatile image representation that facilitates applications like recognition, verification, retrieval, and clustering. Many metric learning methods represent the input as a single point in the embedding space. Often the distance between points is used as a proxy for match confidence. However, this can fail to represent uncertainty arising when the input is ambiguous, e.g., due to occlusion or blurriness. This work addresses this issue and explicitly models the uncertainty by hedging the location of each input in the embedding space. We introduce the hedged instance embedding (HIB) in which embeddings are modeled as random variables and the model is trained under the variational information bottleneck principle. Empirical results on our new N-digit MNIST dataset show that our method leads to the desired behavior of hedging its bets across the embedding space upon encountering ambiguous inputs. This results in improved performance for image matching and classification tasks, more structure in the learned embedding space, and an ability to compute a per-exemplar uncertainty measure that is correlated with downstream performance.

Neural networks embed the geometric structure of a data manifold lying in a high-dimensional space into latent representations. Ideally, the distribution of the data points in the latent space should depend only on the task, the data, the loss, and other architecture-specific constraints. However, factors such as the random weights initialization, training hyperparameters, or other sources of randomness in the training phase may induce incoherent latent spaces that hinder any form of reuse. Nevertheless, we empirically observe that, under the same data and modeling choices, the angles between the encodings within distinct latent spaces do not change. In this work, we propose the latent similarity between each sample and a fixed set of anchors as an alternative data representation, demonstrating that it can enforce the desired invariances without any additional training. We show how neural architectures can leverage these relative representations to guarantee, in practice, invariance to latent isometries and rescalings, effectively enabling latent space communication: from zero-shot model stitching to latent space comparison between diverse settings. We extensively validate the generalization capability of our approach on different datasets, spanning various modalities (images, text, graphs), tasks (e.g., classification, reconstruction) and architectures (e.g., CNNs, GCNs, transformers).

We study whether visual embedding models capture continuous, ordinal attributes along linear directions, which we term _rank axes_. We define a model as _rankable_ for an attribute if projecting embeddings onto such an axis preserves the attribute's order. Across 7 popular encoders and 9 datasets with attributes like age, crowd count, head pose, aesthetics, and recency, we find that many embeddings are inherently rankable. Surprisingly, a small number of samples, or even just two extreme examples, often suffice to recover meaningful rank axes, without full-scale supervision. These findings open up new use cases for image ranking in vector databases and motivate further study into the structure and learning of rankable embeddings. Our code is available at https://github.com/aktsonthalia/rankable-vision-embeddings.

Recent progress has been made towards learning invariant or equivariant representations with self-supervised learning. While invariant methods are evaluated on large scale datasets, equivariant ones are evaluated in smaller, more controlled, settings. We aim at bridging the gap between the two in order to learn more diverse representations that are suitable for a wide range of tasks. We start by introducing a dataset called 3DIEBench, consisting of renderings from 3D models over 55 classes and more than 2.5 million images where we have full control on the transformations applied to the objects. We further introduce a predictor architecture based on hypernetworks to learn equivariant representations with no possible collapse to invariance. We introduce SIE (Split Invariant-Equivariant) which combines the hypernetwork-based predictor with representations split in two parts, one invariant, the other equivariant, to learn richer representations. We demonstrate significant performance gains over existing methods on equivariance related tasks from both a qualitative and quantitative point of view. We further analyze our introduced predictor and show how it steers the learned latent space. We hope that both our introduced dataset and approach will enable learning richer representations without supervision in more complex scenarios. Code and data are available at https://github.com/facebookresearch/SIE.

Contrastive Language-Image Pre-Training (CLIP) is highly instrumental in machine learning applications within a large variety of domains. We investigate the geometry of this embedding, which is still not well understood. We examine the raw unnormalized embedding and show that text and image reside on linearly separable ellipsoid shells, not centered at the origin. We explain the benefits of having this structure, allowing to better embed instances according to their uncertainty during contrastive training. Frequent concepts in the dataset yield more false negatives, inducing greater uncertainty. A new notion of conformity is introduced, which measures the average cosine similarity of an instance to any other instance within a representative data set. We show this measure can be accurately estimated by simply computing the cosine similarity to the modality mean vector. Furthermore, we find that CLIP's modality gap optimizes the matching of the conformity distributions of image and text.

We consider the problem of zero-shot recognition: learning a visual classifier for a category with zero training examples, just using the word embedding of the category and its relationship to other categories, which visual data are provided. The key to dealing with the unfamiliar or novel category is to transfer knowledge obtained from familiar classes to describe the unfamiliar class. In this paper, we build upon the recently introduced Graph Convolutional Network (GCN) and propose an approach that uses both semantic embeddings and the categorical relationships to predict the classifiers. Given a learned knowledge graph (KG), our approach takes as input semantic embeddings for each node (representing visual category). After a series of graph convolutions, we predict the visual classifier for each category. During training, the visual classifiers for a few categories are given to learn the GCN parameters. At test time, these filters are used to predict the visual classifiers of unseen categories. We show that our approach is robust to noise in the KG. More importantly, our approach provides significant improvement in performance compared to the current state-of-the-art results (from 2 ~ 3% on some metrics to whopping 20% on a few).

We study the topmost weight matrix of neural network language models. We show that this matrix constitutes a valid word embedding. When training language models, we recommend tying the input embedding and this output embedding. We analyze the resulting update rules and show that the tied embedding evolves in a more similar way to the output embedding than to the input embedding in the untied model. We also offer a new method of regularizing the output embedding. Our methods lead to a significant reduction in perplexity, as we are able to show on a variety of neural network language models. Finally, we show that weight tying can reduce the size of neural translation models to less than half of their original size without harming their performance.

As the field of representation learning grows, there has been a proliferation of different loss functions to solve different classes of problems. We introduce a single information-theoretic equation that generalizes a large collection of modern loss functions in machine learning. In particular, we introduce a framework that shows that several broad classes of machine learning methods are precisely minimizing an integrated KL divergence between two conditional distributions: the supervisory and learned representations. This viewpoint exposes a hidden information geometry underlying clustering, spectral methods, dimensionality reduction, contrastive learning, and supervised learning. This framework enables the development of new loss functions by combining successful techniques from across the literature. We not only present a wide array of proofs, connecting over 23 different approaches, but we also leverage these theoretical results to create state-of-the-art unsupervised image classifiers that achieve a +8% improvement over the prior state-of-the-art on unsupervised classification on ImageNet-1K. We also demonstrate that I-Con can be used to derive principled debiasing methods which improve contrastive representation learners.

Equivariant neural networks have shown improved performance, expressiveness and sample complexity on symmetrical domains. But for some specific symmetries, representations, and choice of coordinates, the most common point-wise activations, such as ReLU, are not equivariant, hence they cannot be employed in the design of equivariant neural networks. The theorem we present in this paper describes all possible combinations of finite-dimensional representations, choice of coordinates and point-wise activations to obtain an exactly equivariant layer, generalizing and strengthening existing characterizations. Notable cases of practical relevance are discussed as corollaries. Indeed, we prove that rotation-equivariant networks can only be invariant, as it happens for any network which is equivariant with respect to connected compact groups. Then, we discuss implications of our findings when applied to important instances of exactly equivariant networks. First, we completely characterize permutation equivariant networks such as Invariant Graph Networks with point-wise nonlinearities and their geometric counterparts, highlighting a plethora of models whose expressive power and performance are still unknown. Second, we show that feature spaces of disentangled steerable convolutional neural networks are trivial representations.

Masked image modeling (MIM) has attracted much research attention due to its promising potential for learning scalable visual representations. In typical approaches, models usually focus on predicting specific contents of masked patches, and their performances are highly related to pre-defined mask strategies. Intuitively, this procedure can be considered as training a student (the model) on solving given problems (predict masked patches). However, we argue that the model should not only focus on solving given problems, but also stand in the shoes of a teacher to produce a more challenging problem by itself. To this end, we propose Hard Patches Mining (HPM), a brand-new framework for MIM pre-training. We observe that the reconstruction loss can naturally be the metric of the difficulty of the pre-training task. Therefore, we introduce an auxiliary loss predictor, predicting patch-wise losses first and deciding where to mask next. It adopts a relative relationship learning strategy to prevent overfitting to exact reconstruction loss values. Experiments under various settings demonstrate the effectiveness of HPM in constructing masked images. Furthermore, we empirically find that solely introducing the loss prediction objective leads to powerful representations, verifying the efficacy of the ability to be aware of where is hard to reconstruct.

One method for obtaining generalizable solutions to machine learning tasks when presented with diverse training environments is to find invariant representations of the data. These are representations of the covariates such that the best model on top of the representation is invariant across training environments. In the context of linear Structural Equation Models (SEMs), invariant representations might allow us to learn models with out-of-distribution guarantees, i.e., models that are robust to interventions in the SEM. To address the invariant representation problem in a {\em finite sample} setting, we consider the notion of epsilon-approximate invariance. We study the following question: If a representation is approximately invariant with respect to a given number of training interventions, will it continue to be approximately invariant on a larger collection of unseen SEMs? This larger collection of SEMs is generated through a parameterized family of interventions. Inspired by PAC learning, we obtain finite-sample out-of-distribution generalization guarantees for approximate invariance that holds probabilistically over a family of linear SEMs without faithfulness assumptions. Our results show bounds that do not scale in ambient dimension when intervention sites are restricted to lie in a constant size subset of in-degree bounded nodes. We also show how to extend our results to a linear indirect observation model that incorporates latent variables.

Conventional zero-shot learning (ZSL) methods generally learn an embedding, e.g., visual-semantic mapping, to handle the unseen visual samples via an indirect manner. In this paper, we take the advantage of generative adversarial networks (GANs) and propose a novel method, named leveraging invariant side GAN (LisGAN), which can directly generate the unseen features from random noises which are conditioned by the semantic descriptions. Specifically, we train a conditional Wasserstein GANs in which the generator synthesizes fake unseen features from noises and the discriminator distinguishes the fake from real via a minimax game. Considering that one semantic description can correspond to various synthesized visual samples, and the semantic description, figuratively, is the soul of the generated features, we introduce soul samples as the invariant side of generative zero-shot learning in this paper. A soul sample is the meta-representation of one class. It visualizes the most semantically-meaningful aspects of each sample in the same category. We regularize that each generated sample (the varying side of generative ZSL) should be close to at least one soul sample (the invariant side) which has the same class label with it. At the zero-shot recognition stage, we propose to use two classifiers, which are deployed in a cascade way, to achieve a coarse-to-fine result. Experiments on five popular benchmarks verify that our proposed approach can outperform state-of-the-art methods with significant improvements.

Vector embeddings have been tasked with an ever-increasing set of retrieval tasks over the years, with a nascent rise in using them for reasoning, instruction-following, coding, and more. These new benchmarks push embeddings to work for any query and any notion of relevance that could be given. While prior works have pointed out theoretical limitations of vector embeddings, there is a common assumption that these difficulties are exclusively due to unrealistic queries, and those that are not can be overcome with better training data and larger models. In this work, we demonstrate that we may encounter these theoretical limitations in realistic settings with extremely simple queries. We connect known results in learning theory, showing that the number of top-k subsets of documents capable of being returned as the result of some query is limited by the dimension of the embedding. We empirically show that this holds true even if we restrict to k=2, and directly optimize on the test set with free parameterized embeddings. We then create a realistic dataset called LIMIT that stress tests models based on these theoretical results, and observe that even state-of-the-art models fail on this dataset despite the simple nature of the task. Our work shows the limits of embedding models under the existing single vector paradigm and calls for future research to develop methods that can resolve this fundamental limitation.

We introduce Invariant Risk Minimization (IRM), a learning paradigm to estimate invariant correlations across multiple training distributions. To achieve this goal, IRM learns a data representation such that the optimal classifier, on top of that data representation, matches for all training distributions. Through theory and experiments, we show how the invariances learned by IRM relate to the causal structures governing the data and enable out-of-distribution generalization.

Transformers are widely used to extract semantic meanings from input tokens, yet they usually operate as black-box models. In this paper, we present a simple yet informative decomposition of hidden states (or embeddings) of trained transformers into interpretable components. For any layer, embedding vectors of input sequence samples are represented by a tensor h in R^{C times T times d}. Given embedding vector h_{c,t} in R^d at sequence position t le T in a sequence (or context) c le C, extracting the mean effects yields the decomposition \[ h_{c,t} = \mu + pos_t + ctx_c + resid_{c,t} \] where mu is the global mean vector, pos_t and ctx_c are the mean vectors across contexts and across positions respectively, and resid_{c,t} is the residual vector. For popular transformer architectures and diverse text datasets, empirically we find pervasive mathematical structure: (1) (pos_t)_{t} forms a low-dimensional, continuous, and often spiral shape across layers, (2) (ctx_c)_c shows clear cluster structure that falls into context topics, and (3) (pos_t)_{t} and (ctx_c)_c are mutually nearly orthogonal. We argue that smoothness is pervasive and beneficial to transformers trained on languages, and our decomposition leads to improved model interpretability.

For convolutional neural network models that optimize an image embedding, we propose a method to highlight the regions of images that contribute most to pairwise similarity. This work is a corollary to the visualization tools developed for classification networks, but applicable to the problem domains better suited to similarity learning. The visualization shows how similarity networks that are fine-tuned learn to focus on different features. We also generalize our approach to embedding networks that use different pooling strategies and provide a simple mechanism to support image similarity searches on objects or sub-regions in the query image.

The recent tremendous success of unsupervised word embeddings in a multitude of applications raises the obvious question if similar methods could be derived to improve embeddings (i.e. semantic representations) of word sequences as well. We present a simple but efficient unsupervised objective to train distributed representations of sentences. Our method outperforms the state-of-the-art unsupervised models on most benchmark tasks, highlighting the robustness of the produced general-purpose sentence embeddings.

The use of relative representations for latent embeddings has shown potential in enabling latent space communication and zero-shot model stitching across a wide range of applications. Nevertheless, relative representations rely on a certain amount of parallel anchors to be given as input, which can be impractical to obtain in certain scenarios. To overcome this limitation, we propose an optimization-based method to discover new parallel anchors from a limited known set (seed). Our approach can be used to find semantic correspondence between different domains, align their relative spaces, and achieve competitive results in several tasks.

We propose Equivariance by Contrast (EbC) to learn equivariant embeddings from observation pairs (y, g cdot y), where g is drawn from a finite group acting on the data. Our method jointly learns a latent space and a group representation in which group actions correspond to invertible linear maps -- without relying on group-specific inductive biases. We validate our approach on the infinite dSprites dataset with structured transformations defined by the finite group G:= (R_m times Z_n times Z_n), combining discrete rotations and periodic translations. The resulting embeddings exhibit high-fidelity equivariance, with group operations faithfully reproduced in latent space. On synthetic data, we further validate the approach on the non-abelian orthogonal group O(n) and the general linear group GL(n). We also provide a theoretical proof for identifiability. While broad evaluation across diverse group types on real-world data remains future work, our results constitute the first successful demonstration of general-purpose encoder-only equivariant learning from group action observations alone, including non-trivial non-abelian groups and a product group motivated by modeling affine equivariances in computer vision.

Learning representations that transfer well to diverse downstream tasks remains a central challenge in representation learning. Existing paradigms -- contrastive learning, self-supervised masking, and denoising auto-encoders -- balance this challenge with different trade-offs. We introduce the {contrastive Mutual Information Machine} (cMIM), a probabilistic framework that extends the Mutual Information Machine (MIM) with a contrastive objective. While MIM maximizes mutual information between inputs and latents and promotes clustering of codes, it falls short on discriminative tasks. cMIM addresses this gap by imposing global discriminative structure while retaining MIM's generative fidelity. Our contributions are threefold. First, we propose cMIM, a contrastive extension of MIM that removes the need for positive data augmentation and is substantially less sensitive to batch size than InfoNCE. Second, we introduce {informative embeddings}, a general technique for extracting enriched features from encoder-decoder models that boosts discriminative performance without additional training and applies broadly beyond MIM. Third, we provide empirical evidence across vision and molecular benchmarks showing that cMIM outperforms MIM and InfoNCE on classification and regression tasks while preserving competitive reconstruction quality. These results position cMIM as a unified framework for representation learning, advancing the goal of models that serve both discriminative and generative applications effectively.

Masked Language Modeling (MLM) has been one of the most prominent approaches for pretraining bidirectional text encoders due to its simplicity and effectiveness. One notable concern about MLM is that the special [MASK] symbol causes a discrepancy between pretraining data and downstream data as it is present only in pretraining but not in fine-tuning. In this work, we offer a new perspective on the consequence of such a discrepancy: We demonstrate empirically and theoretically that MLM pretraining allocates some model dimensions exclusively for representing [MASK] tokens, resulting in a representation deficiency for real tokens and limiting the pretrained model's expressiveness when it is adapted to downstream data without [MASK] tokens. Motivated by the identified issue, we propose MAE-LM, which pretrains the Masked Autoencoder architecture with MLM where [MASK] tokens are excluded from the encoder. Empirically, we show that MAE-LM improves the utilization of model dimensions for real token representations, and MAE-LM consistently outperforms MLM-pretrained models across different pretraining settings and model sizes when fine-tuned on the GLUE and SQuAD benchmarks.

Geometric deep learning, i.e., designing neural networks to handle the ubiquitous geometric data such as point clouds and graphs, have achieved great successes in the last decade. One critical inductive bias is that the model can maintain invariance towards various transformations such as translation, rotation, and scaling. The existing graph neural network (GNN) approaches can only maintain permutation-invariance, failing to guarantee invariance with respect to other transformations. Besides GNNs, other works design sophisticated transformation-invariant layers, which are computationally expensive and difficult to be extended. To solve this problem, we revisit why the existing neural networks cannot maintain transformation invariance when handling geometric data. Our findings show that transformation-invariant and distance-preserving initial representations are sufficient to achieve transformation invariance rather than needing sophisticated neural layer designs. Motivated by these findings, we propose Transformation Invariant Neural Networks (TinvNN), a straightforward and general framework for geometric data. Specifically, we realize transformation-invariant and distance-preserving initial point representations by modifying multi-dimensional scaling before feeding the representations into neural networks. We prove that TinvNN can strictly guarantee transformation invariance, being general and flexible enough to be combined with the existing neural networks. Extensive experimental results on point cloud analysis and combinatorial optimization demonstrate the effectiveness and general applicability of our proposed method. Based on the experimental results, we advocate that TinvNN should be considered a new starting point and an essential baseline for further studies of transformation-invariant geometric deep learning.

Compatible features enable the direct comparison of old and new learned features allowing to use them interchangeably over time. In visual search systems, this eliminates the need to extract new features from the gallery-set when the representation model is upgraded with novel data. This has a big value in real applications as re-indexing the gallery-set can be computationally expensive when the gallery-set is large, or even infeasible due to privacy or other concerns of the application. In this paper, we propose CoReS, a new training procedure to learn representations that are compatible with those previously learned, grounding on the stationarity of the features as provided by fixed classifiers based on polytopes. With this solution, classes are maximally separated in the representation space and maintain their spatial configuration stationary as new classes are added, so that there is no need to learn any mappings between representations nor to impose pairwise training with the previously learned model. We demonstrate that our training procedure largely outperforms the current state of the art and is particularly effective in the case of multiple upgrades of the training-set, which is the typical case in real applications.

This book develops an effective theory approach to understanding deep neural networks of practical relevance. Beginning from a first-principles component-level picture of networks, we explain how to determine an accurate description of the output of trained networks by solving layer-to-layer iteration equations and nonlinear learning dynamics. A main result is that the predictions of networks are described by nearly-Gaussian distributions, with the depth-to-width aspect ratio of the network controlling the deviations from the infinite-width Gaussian description. We explain how these effectively-deep networks learn nontrivial representations from training and more broadly analyze the mechanism of representation learning for nonlinear models. From a nearly-kernel-methods perspective, we find that the dependence of such models' predictions on the underlying learning algorithm can be expressed in a simple and universal way. To obtain these results, we develop the notion of representation group flow (RG flow) to characterize the propagation of signals through the network. By tuning networks to criticality, we give a practical solution to the exploding and vanishing gradient problem. We further explain how RG flow leads to near-universal behavior and lets us categorize networks built from different activation functions into universality classes. Altogether, we show that the depth-to-width ratio governs the effective model complexity of the ensemble of trained networks. By using information-theoretic techniques, we estimate the optimal aspect ratio at which we expect the network to be practically most useful and show how residual connections can be used to push this scale to arbitrary depths. With these tools, we can learn in detail about the inductive bias of architectures, hyperparameters, and optimizers.

We are born with the ability to learn concepts by comparing diverse observations. This helps us to understand the new world in a compositional manner and facilitates extrapolation, as objects naturally consist of multiple concepts. In this work, we argue that the cognitive mechanism of comparison, fundamental to human learning, is also vital for machines to recover true concepts underlying the data. This offers correctness guarantees for the field of concept learning, which, despite its impressive empirical successes, still lacks general theoretical support. Specifically, we aim to develop a theoretical framework for the identifiability of concepts with multiple classes of observations. We show that with sufficient diversity across classes, hidden concepts can be identified without assuming specific concept types, functional relations, or parametric generative models. Interestingly, even when conditions are not globally satisfied, we can still provide alternative guarantees for as many concepts as possible based on local comparisons, thereby extending the applicability of our theory to more flexible scenarios. Moreover, the hidden structure between classes and concepts can also be identified nonparametrically. We validate our theoretical results in both synthetic and real-world settings.

Masked visual modeling has attracted much attention due to its promising potential in learning generalizable representations. Typical approaches urge models to predict specific contents of masked tokens, which can be intuitively considered as teaching a student (the model) to solve given problems (predicting masked contents). Under such settings, the performance is highly correlated with mask strategies (the difficulty of provided problems). We argue that it is equally important for the model to stand in the shoes of a teacher to produce challenging problems by itself. Intuitively, patches with high values of reconstruction loss can be regarded as hard samples, and masking those hard patches naturally becomes a demanding reconstruction task. To empower the model as a teacher, we propose Hard Patches Mining (HPM), predicting patch-wise losses and subsequently determining where to mask. Technically, we introduce an auxiliary loss predictor, which is trained with a relative objective to prevent overfitting to exact loss values. Also, to gradually guide the training procedure, we propose an easy-to-hard mask strategy. Empirically, HPM brings significant improvements under both image and video benchmarks. Interestingly, solely incorporating the extra loss prediction objective leads to better representations, verifying the efficacy of determining where is hard to reconstruct. The code is available at https://github.com/Haochen-Wang409/HPM.

We propose a novel approach for preserving topological structures of the input space in latent representations of autoencoders. Using persistent homology, a technique from topological data analysis, we calculate topological signatures of both the input and latent space to derive a topological loss term. Under weak theoretical assumptions, we construct this loss in a differentiable manner, such that the encoding learns to retain multi-scale connectivity information. We show that our approach is theoretically well-founded and that it exhibits favourable latent representations on a synthetic manifold as well as on real-world image data sets, while preserving low reconstruction errors.

Zero-shot learning has gained popularity due to its potential to scale recognition models without requiring additional training data. This is usually achieved by associating categories with their semantic information like attributes. However, we believe that the potential offered by this paradigm is not yet fully exploited. In this work, we propose to utilize the structure of the space spanned by the attributes using a set of relations. We devise objective functions to preserve these relations in the embedding space, thereby inducing semanticity to the embedding space. Through extensive experimental evaluation on five benchmark datasets, we demonstrate that inducing semanticity to the embedding space is beneficial for zero-shot learning. The proposed approach outperforms the state-of-the-art on the standard zero-shot setting as well as the more realistic generalized zero-shot setting. We also demonstrate how the proposed approach can be useful for making approximate semantic inferences about an image belonging to a category for which attribute information is not available.

With hundreds of thousands of language models available on Huggingface today, efficiently evaluating and utilizing these models across various downstream, tasks has become increasingly critical. Many existing methods repeatedly learn task-specific representations of Large Language Models (LLMs), which leads to inefficiencies in both time and computational resources. To address this, we propose EmbedLLM, a framework designed to learn compact vector representations, of LLMs that facilitate downstream applications involving many models, such as model routing. We introduce an encoder-decoder approach for learning such embeddings, along with a systematic framework to evaluate their effectiveness. Empirical results show that EmbedLLM outperforms prior methods in model routing both in accuracy and latency. Additionally, we demonstrate that our method can forecast a model's performance on multiple benchmarks, without incurring additional inference cost. Extensive probing experiments validate that the learned embeddings capture key model characteristics, e.g. whether the model is specialized for coding tasks, even without being explicitly trained on them. We open source our dataset, code and embedder to facilitate further research and application.

Self-supervised representation learning approaches have recently surpassed their supervised learning counterparts on downstream tasks like object detection and image classification. Somewhat mysteriously the recent gains in performance come from training instance classification models, treating each image and it's augmented versions as samples of a single class. In this work, we first present quantitative experiments to demystify these gains. We demonstrate that approaches like MOCO and PIRL learn occlusion-invariant representations. However, they fail to capture viewpoint and category instance invariance which are crucial components for object recognition. Second, we demonstrate that these approaches obtain further gains from access to a clean object-centric training dataset like Imagenet. Finally, we propose an approach to leverage unstructured videos to learn representations that possess higher viewpoint invariance. Our results show that the learned representations outperform MOCOv2 trained on the same data in terms of invariances encoded and the performance on downstream image classification and semantic segmentation tasks.

The joint-embedding predictive architecture (JEPA) recently has shown impressive results in extracting visual representations from unlabeled imagery under a masking strategy. However, we reveal its disadvantages, notably its insufficient understanding of local semantics. This deficiency originates from masked modeling in the embedding space, resulting in a reduction of discriminative power and can even lead to the neglect of critical local semantics. To bridge this gap, we introduce DMT-JEPA, a novel masked modeling objective rooted in JEPA, specifically designed to generate discriminative latent targets from neighboring information. Our key idea is simple: we consider a set of semantically similar neighboring patches as a target of a masked patch. To be specific, the proposed DMT-JEPA (a) computes feature similarities between each masked patch and its corresponding neighboring patches to select patches having semantically meaningful relations, and (b) employs lightweight cross-attention heads to aggregate features of neighboring patches as the masked targets. Consequently, DMT-JEPA demonstrates strong discriminative power, offering benefits across a diverse spectrum of downstream tasks. Through extensive experiments, we demonstrate our effectiveness across various visual benchmarks, including ImageNet-1K image classification, ADE20K semantic segmentation, and COCO object detection tasks. Code is available at: https://github.com/DMTJEPA/DMTJEPA.

The performance of algorithms for neural architecture search strongly depends on the parametrization of the search space. We use contrastive learning to identify networks across different initializations based on their data Jacobians, and automatically produce the first architecture embeddings independent from the parametrization of the search space. Using our contrastive embeddings, we show that traditional black-box optimization algorithms, without modification, can reach state-of-the-art performance in Neural Architecture Search. As our method provides a unified embedding space, we perform for the first time transfer learning between search spaces. Finally, we show the evolution of embeddings during training, motivating future studies into using embeddings at different training stages to gain a deeper understanding of the networks in a search space.

Modern representation learning increasingly relies on unsupervised and self-supervised methods trained on large-scale unlabeled data. While these approaches achieve impressive generalization across tasks and domains, evaluating embedding quality without labels remains an open challenge. In this work, we propose Persistence, a topology-aware metric based on persistent homology that quantifies the geometric structure and topological richness of embedding spaces in a fully unsupervised manner. Unlike metrics that assume linear separability or rely on covariance structure, Persistence captures global and multi-scale organization. Empirical results across diverse domains show that Persistence consistently achieves top-tier correlations with downstream performance, outperforming existing unsupervised metrics and enabling reliable model and hyperparameter selection.

Fine-grained and instance-level recognition methods are commonly trained and evaluated on specific domains, in a model per domain scenario. Such an approach, however, is impractical in real large-scale applications. In this work, we address the problem of universal image embedding, where a single universal model is trained and used in multiple domains. First, we leverage existing domain-specific datasets to carefully construct a new large-scale public benchmark for the evaluation of universal image embeddings, with 241k query images, 1.4M index images and 2.8M training images across 8 different domains and 349k classes. We define suitable metrics, training and evaluation protocols to foster future research in this area. Second, we provide a comprehensive experimental evaluation on the new dataset, demonstrating that existing approaches and simplistic extensions lead to worse performance than an assembly of models trained for each domain separately. Finally, we conducted a public research competition on this topic, leveraging industrial datasets, which attracted the participation of more than 1k teams worldwide. This exercise generated many interesting research ideas and findings which we present in detail. Project webpage: https://cmp.felk.cvut.cz/univ_emb/

This paper studies the problem of generalized zero-shot learning which requires the model to train on image-label pairs from some seen classes and test on the task of classifying new images from both seen and unseen classes. Most previous models try to learn a fixed one-directional mapping between visual and semantic space, while some recently proposed generative methods try to generate image features for unseen classes so that the zero-shot learning problem becomes a traditional fully-supervised classification problem. In this paper, we propose a novel model that provides a unified framework for three different approaches: visual-> semantic mapping, semantic->visual mapping, and metric learning. Specifically, our proposed model consists of a feature generator that can generate various visual features given class embeddings as input, a regressor that maps each visual feature back to its corresponding class embedding, and a discriminator that learns to evaluate the closeness of an image feature and a class embedding. All three components are trained under the combination of cyclic consistency loss and dual adversarial loss. Experimental results show that our model not only preserves higher accuracy in classifying images from seen classes, but also performs better than existing state-of-the-art models in in classifying images from unseen classes.

Symmetry-based neural networks often constrain the architecture in order to achieve invariance or equivariance to a group of transformations. In this paper, we propose an alternative that avoids this architectural constraint by learning to produce a canonical representation of the data. These canonicalization functions can readily be plugged into non-equivariant backbone architectures. We offer explicit ways to implement them for many groups of interest. We show that this approach enjoys universality while providing interpretable insights. Our main hypothesis is that learning a neural network to perform canonicalization is better than using predefined heuristics. Our results show that learning the canonicalization function indeed leads to better results and that the approach achieves excellent performance in practice.

We show that standard Transformers without graph-specific modifications can lead to promising results in graph learning both in theory and practice. Given a graph, we simply treat all nodes and edges as independent tokens, augment them with token embeddings, and feed them to a Transformer. With an appropriate choice of token embeddings, we prove that this approach is theoretically at least as expressive as an invariant graph network (2-IGN) composed of equivariant linear layers, which is already more expressive than all message-passing Graph Neural Networks (GNN). When trained on a large-scale graph dataset (PCQM4Mv2), our method coined Tokenized Graph Transformer (TokenGT) achieves significantly better results compared to GNN baselines and competitive results compared to Transformer variants with sophisticated graph-specific inductive bias. Our implementation is available at https://github.com/jw9730/tokengt.

In this article, we introduce a new parameterized family of topological invariants, taking the form of candidate decompositions, for multi-parameter persistence modules. We prove that our candidate decompositions are controllable approximations: when restricting to modules that can be decomposed into interval summands, we establish theoretical results about the approximation error between our candidate decompositions and the true underlying module in terms of the standard interleaving and bottleneck distances. Moreover, even when the underlying module does not admit such a decomposition, our candidate decompositions are nonetheless stable invariants; small perturbations in the underlying module lead to small perturbations in the candidate decomposition. Then, we introduce MMA (Multipersistence Module Approximation): an algorithm for computing stable instances of such invariants, which is based on fibered barcodes and exact matchings, two constructions that stem from the theory of single-parameter persistence. By design, MMA can handle an arbitrary number of filtrations, and has bounded complexity and running time. Finally, we present empirical evidence validating the generalization capabilities and running time speed-ups of MMA on several data sets.

Embedding words in high-dimensional vector spaces has proven valuable in many natural language applications. In this work, we investigate whether similarly-trained embeddings of integers can capture concepts that are useful for mathematical applications. We probe the integer embeddings for mathematical knowledge, apply them to a set of numerical reasoning tasks, and show that by learning the representations from mathematical sequence data, we can substantially improve over number embeddings learned from English text corpora.

Several recent publications have proposed methods for mapping images into continuous semantic embedding spaces. In some cases the embedding space is trained jointly with the image transformation. In other cases the semantic embedding space is established by an independent natural language processing task, and then the image transformation into that space is learned in a second stage. Proponents of these image embedding systems have stressed their advantages over the traditional classification framing of image understanding, particularly in terms of the promise for zero-shot learning -- the ability to correctly annotate images of previously unseen object categories. In this paper, we propose a simple method for constructing an image embedding system from any existing image classifier and a semantic word embedding model, which contains the n class labels in its vocabulary. Our method maps images into the semantic embedding space via convex combination of the class label embedding vectors, and requires no additional training. We show that this simple and direct method confers many of the advantages associated with more complex image embedding schemes, and indeed outperforms state of the art methods on the ImageNet zero-shot learning task.

In this paper, we address the challenging problem of open-world instance segmentation. Existing works have shown that vanilla visual networks are biased toward learning appearance information, \eg texture, to recognize objects. This implicit bias causes the model to fail in detecting novel objects with unseen textures in the open-world setting. To address this challenge, we propose a learning framework, called view-Consistent LeaRning (v-CLR), which aims to enforce the model to learn appearance-invariant representations for robust instance segmentation. In v-CLR, we first introduce additional views for each image, where the texture undergoes significant alterations while preserving the image's underlying structure. We then encourage the model to learn the appearance-invariant representation by enforcing the consistency between object features across different views, for which we obtain class-agnostic object proposals using off-the-shelf unsupervised models that possess strong object-awareness. These proposals enable cross-view object feature matching, greatly reducing the appearance dependency while enhancing the object-awareness. We thoroughly evaluate our method on public benchmarks under both cross-class and cross-dataset settings, achieving state-of-the-art performance. Project page: https://visual-ai.github.io/vclr

Self-supervised learning converts raw perceptual data such as images to a compact space where simple Euclidean distances measure meaningful variations in data. In this paper, we extend this formulation by adding additional geometric structure to the embedding space by enforcing transformations of input space to correspond to simple (i.e., linear) transformations of embedding space. Specifically, in the contrastive learning setting, we introduce an equivariance objective and theoretically prove that its minima forces augmentations on input space to correspond to rotations on the spherical embedding space. We show that merely combining our equivariant loss with a non-collapse term results in non-trivial representations, without requiring invariance to data augmentations. Optimal performance is achieved by also encouraging approximate invariance, where input augmentations correspond to small rotations. Our method, CARE: Contrastive Augmentation-induced Rotational Equivariance, leads to improved performance on downstream tasks, and ensures sensitivity in embedding space to important variations in data (e.g., color) that standard contrastive methods do not achieve. Code is available at https://github.com/Sharut/CARE.

Contrastive representation learning has been outstandingly successful in practice. In this work, we identify two key properties related to the contrastive loss: (1) alignment (closeness) of features from positive pairs, and (2) uniformity of the induced distribution of the (normalized) features on the hypersphere. We prove that, asymptotically, the contrastive loss optimizes these properties, and analyze their positive effects on downstream tasks. Empirically, we introduce an optimizable metric to quantify each property. Extensive experiments on standard vision and language datasets confirm the strong agreement between both metrics and downstream task performance. Remarkably, directly optimizing for these two metrics leads to representations with comparable or better performance at downstream tasks than contrastive learning. Project Page: https://tongzhouwang.info/hypersphere Code: https://github.com/SsnL/align_uniform , https://github.com/SsnL/moco_align_uniform

We propose Masked Siamese Networks (MSN), a self-supervised learning framework for learning image representations. Our approach matches the representation of an image view containing randomly masked patches to the representation of the original unmasked image. This self-supervised pre-training strategy is particularly scalable when applied to Vision Transformers since only the unmasked patches are processed by the network. As a result, MSNs improve the scalability of joint-embedding architectures, while producing representations of a high semantic level that perform competitively on low-shot image classification. For instance, on ImageNet-1K, with only 5,000 annotated images, our base MSN model achieves 72.4% top-1 accuracy, and with 1% of ImageNet-1K labels, we achieve 75.7% top-1 accuracy, setting a new state-of-the-art for self-supervised learning on this benchmark. Our code is publicly available.

Supervised contrastive loss (SCL) is a competitive and often superior alternative to the cross-entropy loss for classification. While prior studies have demonstrated that both losses yield symmetric training representations under balanced data, this symmetry breaks under class imbalances. This paper presents an intriguing discovery: the introduction of a ReLU activation at the final layer effectively restores the symmetry in SCL-learned representations. We arrive at this finding analytically, by establishing that the global minimizers of an unconstrained features model with SCL loss and entry-wise non-negativity constraints form an orthogonal frame. Extensive experiments conducted across various datasets, architectures, and imbalance scenarios corroborate our finding. Importantly, our experiments reveal that the inclusion of the ReLU activation restores symmetry without compromising test accuracy. This constitutes the first geometry characterization of SCL under imbalances. Additionally, our analysis and experiments underscore the pivotal role of batch selection strategies in representation geometry. By proving necessary and sufficient conditions for mini-batch choices that ensure invariant symmetric representations, we introduce batch-binding as an efficient strategy that guarantees these conditions hold.

Attributes act as intermediate representations that enable parameter sharing between classes, a must when training data is scarce. We propose to view attribute-based image classification as a label-embedding problem: each class is embedded in the space of attribute vectors. We introduce a function that measures the compatibility between an image and a label embedding. The parameters of this function are learned on a training set of labeled samples to ensure that, given an image, the correct classes rank higher than the incorrect ones. Results on the Animals With Attributes and Caltech-UCSD-Birds datasets show that the proposed framework outperforms the standard Direct Attribute Prediction baseline in a zero-shot learning scenario. Label embedding enjoys a built-in ability to leverage alternative sources of information instead of or in addition to attributes, such as e.g. class hierarchies or textual descriptions. Moreover, label embedding encompasses the whole range of learning settings from zero-shot learning to regular learning with a large number of labeled examples.

Learning high-quality feature embeddings efficiently and effectively is critical for the performance of web-scale machine learning systems. A typical model ingests hundreds of features with vocabularies on the order of millions to billions of tokens. The standard approach is to represent each feature value as a d-dimensional embedding, introducing hundreds of billions of parameters for extremely high-cardinality features. This bottleneck has led to substantial progress in alternative embedding algorithms. Many of these methods, however, make the assumption that each feature uses an independent embedding table. This work introduces a simple yet highly effective framework, Feature Multiplexing, where one single representation space is used across many different categorical features. Our theoretical and empirical analysis reveals that multiplexed embeddings can be decomposed into components from each constituent feature, allowing models to distinguish between features. We show that multiplexed representations lead to Pareto-optimal parameter-accuracy tradeoffs for three public benchmark datasets. Further, we propose a highly practical approach called Unified Embedding with three major benefits: simplified feature configuration, strong adaptation to dynamic data distributions, and compatibility with modern hardware. Unified embedding gives significant improvements in offline and online metrics compared to highly competitive baselines across five web-scale search, ads, and recommender systems, where it serves billions of users across the world in industry-leading products.

We investigate novel random graph embeddings that can be computed in expected polynomial time and that are able to distinguish all non-isomorphic graphs in expectation. Previous graph embeddings have limited expressiveness and either cannot distinguish all graphs or cannot be computed efficiently for every graph. To be able to approximate arbitrary functions on graphs, we are interested in efficient alternatives that become arbitrarily expressive with increasing resources. Our approach is based on Lov\'asz' characterisation of graph isomorphism through an infinite dimensional vector of homomorphism counts. Our empirical evaluation shows competitive results on several benchmark graph learning tasks.

Transformer architectures rely on explicit position encodings in order to preserve a notion of word order. In this paper, we argue that existing work does not fully utilize position information. For example, the initial proposal of a sinusoid embedding is fixed and not learnable. In this paper, we first review absolute position embeddings and existing methods for relative position embeddings. We then propose new techniques that encourage increased interaction between query, key and relative position embeddings in the self-attention mechanism. Our most promising approach is a generalization of the absolute position embedding, improving results on SQuAD1.1 compared to previous position embeddings approaches. In addition, we address the inductive property of whether a position embedding can be robust enough to handle long sequences. We demonstrate empirically that our relative position embedding method is reasonably generalized and robust from the inductive perspective. Finally, we show that our proposed method can be adopted as a near drop-in replacement for improving the accuracy of large models with a small computational budget.

We present network embedding algorithms that capture information about a node from the local distribution over node attributes around it, as observed over random walks following an approach similar to Skip-gram. Observations from neighborhoods of different sizes are either pooled (AE) or encoded distinctly in a multi-scale approach (MUSAE). Capturing attribute-neighborhood relationships over multiple scales is useful for a diverse range of applications, including latent feature identification across disconnected networks with similar attributes. We prove theoretically that matrices of node-feature pointwise mutual information are implicitly factorized by the embeddings. Experiments show that our algorithms are robust, computationally efficient and outperform comparable models on social networks and web graphs.

In many computer vision applications, images are acquired with arbitrary or random rotations and translations, and in such setups, it is desirable to obtain semantic representations disentangled from the image orientation. Examples of such applications include semiconductor wafer defect inspection, plankton microscope images, and inference on single-particle cryo-electron microscopy (cryo-EM) micro-graphs. In this work, we propose Invariant Representation Learning with Implicit Neural Representation (IRL-INR), which uses an implicit neural representation (INR) with a hypernetwork to obtain semantic representations disentangled from the orientation of the image. We show that IRL-INR can effectively learn disentangled semantic representations on more complex images compared to those considered in prior works and show that these semantic representations synergize well with SCAN to produce state-of-the-art unsupervised clustering results.

This work introduces a model that can recognize objects in images even if no training data is available for the objects. The only necessary knowledge about the unseen categories comes from unsupervised large text corpora. In our zero-shot framework distributional information in language can be seen as spanning a semantic basis for understanding what objects look like. Most previous zero-shot learning models can only differentiate between unseen classes. In contrast, our model can both obtain state of the art performance on classes that have thousands of training images and obtain reasonable performance on unseen classes. This is achieved by first using outlier detection in the semantic space and then two separate recognition models. Furthermore, our model does not require any manually defined semantic features for either words or images.

In this paper we introduce a novel family of attributed graphs for the purpose of shape discrimination. Our graphs typically arise from variations on the Mapper graph construction, which is an approximation of the Reeb graph for point cloud data. Our attributions enrich these constructions with (persistent) homology in ways that are provably stable, thereby recording extra topological information that is typically lost in these graph constructions. We provide experiments which illustrate the use of these invariants for shape representation and classification. In particular, we obtain competitive shape classification results when using our topologically attributed graphs as inputs to a simple graph neural network classifier.

While many unsupervised learning models focus on one family of tasks, either generative or discriminative, we explore the possibility of a unified representation learner: a model which uses a single pre-training stage to address both families of tasks simultaneously. We identify diffusion models as a prime candidate. Diffusion models have risen to prominence as a state-of-the-art method for image generation, denoising, inpainting, super-resolution, manipulation, etc. Such models involve training a U-Net to iteratively predict and remove noise, and the resulting model can synthesize high fidelity, diverse, novel images. The U-Net architecture, as a convolution-based architecture, generates a diverse set of feature representations in the form of intermediate feature maps. We present our findings that these embeddings are useful beyond the noise prediction task, as they contain discriminative information and can also be leveraged for classification. We explore optimal methods for extracting and using these embeddings for classification tasks, demonstrating promising results on the ImageNet classification task. We find that with careful feature selection and pooling, diffusion models outperform comparable generative-discriminative methods such as BigBiGAN for classification tasks. We investigate diffusion models in the transfer learning regime, examining their performance on several fine-grained visual classification datasets. We compare these embeddings to those generated by competing architectures and pre-trainings for classification tasks.

Text embeddings are essential for many tasks, such as document retrieval, clustering, and semantic similarity assessment. In this paper, we study how to contrastively train text embedding models in a compute-optimal fashion, given a suite of pre-trained decoder-only language models. Our innovation is an algorithm that produces optimal configurations of model sizes, data quantities, and fine-tuning methods for text-embedding models at different computational budget levels. The resulting recipe, which we obtain through extensive experiments, can be used by practitioners to make informed design choices for their embedding models. Specifically, our findings suggest that full fine-tuning and low-rank adaptation fine-tuning produce optimal models at lower and higher computational budgets respectively.

Text-to-image (T2I) models can effectively capture the content or style of reference images to perform high-quality customization. A representative technique for this is fine-tuning using low-rank adaptations (LoRA), which enables efficient model customization with reference images. However, fine-tuning with a limited number of reference images often leads to overfitting, resulting in issues such as prompt misalignment or content leakage. These issues prevent the model from accurately following the input prompt or generating undesired objects during inference. To address this problem, we examine the text embeddings that guide the diffusion model during inference. This study decomposes the text embedding matrix and conducts a component analysis to understand the embedding space geometry and identify the cause of overfitting. Based on this, we propose DECOR, which projects text embeddings onto a vector space orthogonal to undesired token vectors, thereby reducing the influence of unwanted semantics in the text embeddings. Experimental results demonstrate that DECOR outperforms state-of-the-art customization models and achieves Pareto frontier performance across text and visual alignment evaluation metrics. Furthermore, it generates images more faithful to the input prompts, showcasing its effectiveness in addressing overfitting and enhancing text-to-image customization.

Siamese networks have become a common structure in various recent models for unsupervised visual representation learning. These models maximize the similarity between two augmentations of one image, subject to certain conditions for avoiding collapsing solutions. In this paper, we report surprising empirical results that simple Siamese networks can learn meaningful representations even using none of the following: (i) negative sample pairs, (ii) large batches, (iii) momentum encoders. Our experiments show that collapsing solutions do exist for the loss and structure, but a stop-gradient operation plays an essential role in preventing collapsing. We provide a hypothesis on the implication of stop-gradient, and further show proof-of-concept experiments verifying it. Our "SimSiam" method achieves competitive results on ImageNet and downstream tasks. We hope this simple baseline will motivate people to rethink the roles of Siamese architectures for unsupervised representation learning. Code will be made available.

End-to-end training from scratch of current deep architectures for new computer vision problems would require Imagenet-scale datasets, and this is not always possible. In this paper we present a method that is able to take advantage of freely available multi-modal content to train computer vision algorithms without human supervision. We put forward the idea of performing self-supervised learning of visual features by mining a large scale corpus of multi-modal (text and image) documents. We show that discriminative visual features can be learnt efficiently by training a CNN to predict the semantic context in which a particular image is more probable to appear as an illustration. For this we leverage the hidden semantic structures discovered in the text corpus with a well-known topic modeling technique. Our experiments demonstrate state of the art performance in image classification, object detection, and multi-modal retrieval compared to recent self-supervised or natural-supervised approaches.

Recent studies indicate that large multimodal models (LMMs) are highly robust against natural distribution shifts, often surpassing previous baselines. Despite this, domain-specific adaptation is still necessary, particularly in specialized areas like healthcare. Due to the impracticality of fine-tuning LMMs given their vast parameter space, this work investigates in-context learning (ICL) as an effective alternative for enhancing LMMs' adaptability. We find that the success of ICL heavily relies on the choice of demonstration, mirroring challenges seen in large language models but introducing unique complexities for LMMs facing distribution shifts. Our study addresses this by evaluating an unsupervised ICL method, TopKNearestPR, which selects in-context examples through a nearest example search based on feature similarity. We uncover that its effectiveness is limited by the deficiencies of pre-trained vision encoders under distribution shift scenarios. To address these challenges, we propose InvariantSelectPR, a novel method leveraging Class-conditioned Contrastive Invariance (CCI) for more robust demonstration selection. Specifically, CCI enhances pre-trained vision encoders by improving their discriminative capabilities across different classes and ensuring invariance to domain-specific variations. This enhancement allows the encoders to effectively identify and retrieve the most informative examples, which are then used to guide LMMs in adapting to new query samples under varying distributions. Our experiments show that InvariantSelectPR substantially improves the adaptability of LMMs, achieving significant performance gains on benchmark datasets, with a 34.2%uparrow accuracy increase in 7-shot on Camelyon17 and 16.9%uparrow increase in 7-shot on HAM10000 compared to the baseline zero-shot performance.

Text-attributed graphs are widely used across domains, offering rich opportunities for zero-shot learning via graph-text alignment. However, existing methods struggle with tasks requiring fine-grained pattern recognition, particularly on heterophilic graphs. Through empirical and theoretical analysis, we identify an over-abstraction problem: current approaches operate at excessively large hyperbolic radii, compressing multi-scale structural information into uniform high-level abstractions. This abstraction-induced information loss obscures critical local patterns essential for accurate predictions. By analyzing embeddings in hyperbolic space, we demonstrate that optimal graph learning requires faithful preservation of fine-grained structural details, better retained by representations positioned closer to the origin. To address this, we propose H4G, a framework that systematically reduces embedding radii using learnable block-diagonal scaling matrices and M\"obius matrix multiplication. This approach restores access to fine-grained patterns while maintaining global receptive ability with minimal computational overhead. Experiments show H4G achieves state-of-the-art zero-shot performance with 12.8\% improvement on heterophilic graphs and 8.4\% on homophilic graphs, confirming that radius reduction enables faithful multi-scale representation for advancing zero-shot graph learning.

Hyperbolic embeddings offer excellent quality with few dimensions when embedding hierarchical data structures like synonym or type hierarchies. Given a tree, we give a combinatorial construction that embeds the tree in hyperbolic space with arbitrarily low distortion without using optimization. On WordNet, our combinatorial embedding obtains a mean-average-precision of 0.989 with only two dimensions, while Nickel et al.'s recent construction obtains 0.87 using 200 dimensions. We provide upper and lower bounds that allow us to characterize the precision-dimensionality tradeoff inherent in any hyperbolic embedding. To embed general metric spaces, we propose a hyperbolic generalization of multidimensional scaling (h-MDS). We show how to perform exact recovery of hyperbolic points from distances, provide a perturbation analysis, and give a recovery result that allows us to reduce dimensionality. The h-MDS approach offers consistently low distortion even with few dimensions across several datasets. Finally, we extract lessons from the algorithms and theory above to design a PyTorch-based implementation that can handle incomplete information and is scalable.

We show how perceptual embeddings of the visual system can be constructed at inference-time with no training data or deep neural network features. Our perceptual embeddings are solutions to a weighted least squares (WLS) problem, defined at the pixel-level, and solved at inference-time, that can capture global and local image characteristics. The distance in embedding space is used to define a perceptual similarity metric which we call LASI: Linear Autoregressive Similarity Index. Experiments on full-reference image quality assessment datasets show LASI performs competitively with learned deep feature based methods like LPIPS (Zhang et al., 2018) and PIM (Bhardwaj et al., 2020), at a similar computational cost to hand-crafted methods such as MS-SSIM (Wang et al., 2003). We found that increasing the dimensionality of the embedding space consistently reduces the WLS loss while increasing performance on perceptual tasks, at the cost of increasing the computational complexity. LASI is fully differentiable, scales cubically with the number of embedding dimensions, and can be parallelized at the pixel-level. A Maximum Differentiation (MAD) competition (Wang & Simoncelli, 2008) between LASI and LPIPS shows that both methods are capable of finding failure points for the other, suggesting these metrics can be combined.

Learning visual representations with self-supervised learning has become popular in computer vision. The idea is to design auxiliary tasks where labels are free to obtain. Most of these tasks end up providing data to learn specific kinds of invariance useful for recognition. In this paper, we propose to exploit different self-supervised approaches to learn representations invariant to (i) inter-instance variations (two objects in the same class should have similar features) and (ii) intra-instance variations (viewpoint, pose, deformations, illumination, etc). Instead of combining two approaches with multi-task learning, we argue to organize and reason the data with multiple variations. Specifically, we propose to generate a graph with millions of objects mined from hundreds of thousands of videos. The objects are connected by two types of edges which correspond to two types of invariance: "different instances but a similar viewpoint and category" and "different viewpoints of the same instance". By applying simple transitivity on the graph with these edges, we can obtain pairs of images exhibiting richer visual invariance. We use this data to train a Triplet-Siamese network with VGG16 as the base architecture and apply the learned representations to different recognition tasks. For object detection, we achieve 63.2% mAP on PASCAL VOC 2007 using Fast R-CNN (compare to 67.3% with ImageNet pre-training). For the challenging COCO dataset, our method is surprisingly close (23.5%) to the ImageNet-supervised counterpart (24.4%) using the Faster R-CNN framework. We also show that our network can perform significantly better than the ImageNet network in the surface normal estimation task.

Advances in embedding models for text, image, audio, and video drive progress across multiple domains, including retrieval-augmented generation, recommendation systems, vehicle/person reidentification, and face recognition. Many applications in these domains require an efficient method to retrieve items that are close to a given query in the embedding space while satisfying a filter condition based on the item's attributes, a problem known as Filtered Approximate Nearest Neighbor Search (FANNS). In this work, we present a comprehensive survey and taxonomy of FANNS methods and analyze how they are benchmarked in the literature. By doing so, we identify a key challenge in the current FANNS landscape: the lack of diverse and realistic datasets, particularly ones derived from the latest transformer-based text embedding models. To address this, we introduce a novel dataset consisting of embedding vectors for the abstracts of over 2.7 million research articles from the arXiv repository, accompanied by 11 real-world attributes such as authors and categories. We benchmark a wide range of FANNS methods on our novel dataset and find that each method has distinct strengths and limitations; no single approach performs best across all scenarios. ACORN, for example, supports various filter types and performs reliably across dataset scales but is often outperformed by more specialized methods. SeRF shows excellent performance for range filtering on ordered attributes but cannot handle categorical attributes. Filtered-DiskANN and UNG excel on the medium-scale dataset but fail on the large-scale dataset, highlighting the challenge posed by transformer-based embeddings, which are often more than an order of magnitude larger than earlier embeddings. We conclude that no universally best method exists.

With the growing popularity of RAG, the capabilities of embedding models are gaining increasing attention. Embedding models are primarily trained through contrastive loss learning, with negative examples being a key component. Previous work has proposed various hard negative mining strategies, but these strategies are typically employed as preprocessing steps. In this paper, we propose the conan-embedding model, which maximizes the utilization of more and higher-quality negative examples. Specifically, since the model's ability to handle preprocessed negative examples evolves during training, we propose dynamic hard negative mining method to expose the model to more challenging negative examples throughout the training process. Secondly, contrastive learning requires as many negative examples as possible but is limited by GPU memory constraints. Therefore, we use a Cross-GPU balancing Loss to provide more negative examples for embedding training and balance the batch size across multiple tasks. Moreover, we also discovered that the prompt-response pairs from LLMs can be used for embedding training. Our approach effectively enhances the capabilities of embedding models, currently ranking first on the Chinese leaderboard of Massive text embedding benchmark

We present Transformation Invariance and Covariance Contrast (TiCo) for self-supervised visual representation learning. Similar to other recent self-supervised learning methods, our method is based on maximizing the agreement among embeddings of different distorted versions of the same image, which pushes the encoder to produce transformation invariant representations. To avoid the trivial solution where the encoder generates constant vectors, we regularize the covariance matrix of the embeddings from different images by penalizing low rank solutions. By jointly minimizing the transformation invariance loss and covariance contrast loss, we get an encoder that is able to produce useful representations for downstream tasks. We analyze our method and show that it can be viewed as a variant of MoCo with an implicit memory bank of unlimited size at no extra memory cost. This makes our method perform better than alternative methods when using small batch sizes. TiCo can also be seen as a modification of Barlow Twins. By connecting the contrastive and redundancy-reduction methods together, TiCo gives us new insights into how joint embedding methods work.

The success of machine learning algorithms generally depends on data representation, and we hypothesize that this is because different representations can entangle and hide more or less the different explanatory factors of variation behind the data. Although specific domain knowledge can be used to help design representations, learning with generic priors can also be used, and the quest for AI is motivating the design of more powerful representation-learning algorithms implementing such priors. This paper reviews recent work in the area of unsupervised feature learning and deep learning, covering advances in probabilistic models, auto-encoders, manifold learning, and deep networks. This motivates longer-term unanswered questions about the appropriate objectives for learning good representations, for computing representations (i.e., inference), and the geometrical connections between representation learning, density estimation and manifold learning.

Deep metric learning has been widely applied in many computer vision tasks, and recently, it is more attractive in zero-shot image retrieval and clustering(ZSRC) where a good embedding is requested such that the unseen classes can be distinguished well. Most existing works deem this 'good' embedding just to be the discriminative one and thus race to devise powerful metric objectives or hard-sample mining strategies for leaning discriminative embedding. However, in this paper, we first emphasize that the generalization ability is a core ingredient of this 'good' embedding as well and largely affects the metric performance in zero-shot settings as a matter of fact. Then, we propose the Energy Confused Adversarial Metric Learning(ECAML) framework to explicitly optimize a robust metric. It is mainly achieved by introducing an interesting Energy Confusion regularization term, which daringly breaks away from the traditional metric learning idea of discriminative objective devising, and seeks to 'confuse' the learned model so as to encourage its generalization ability by reducing overfitting on the seen classes. We train this confusion term together with the conventional metric objective in an adversarial manner. Although it seems weird to 'confuse' the network, we show that our ECAML indeed serves as an efficient regularization technique for metric learning and is applicable to various conventional metric methods. This paper empirically and experimentally demonstrates the importance of learning embedding with good generalization, achieving state-of-the-art performances on the popular CUB, CARS, Stanford Online Products and In-Shop datasets for ZSRC tasks. \textcolor[rgb]{1, 0, 0}{Code available at http://www.bhchen.cn/}.

In this work, we demonstrate that the contextualized word vectors derived from pretrained masked language model-based encoders share a common, perhaps undesirable pattern across layers. Namely, we find cases of persistent outlier neurons within BERT and RoBERTa's hidden state vectors that consistently bear the smallest or largest values in said vectors. In an attempt to investigate the source of this information, we introduce a neuron-level analysis method, which reveals that the outliers are closely related to information captured by positional embeddings. We also pre-train the RoBERTa-base models from scratch and find that the outliers disappear without using positional embeddings. These outliers, we find, are the major cause of anisotropy of encoders' raw vector spaces, and clipping them leads to increased similarity across vectors. We demonstrate this in practice by showing that clipped vectors can more accurately distinguish word senses, as well as lead to better sentence embeddings when mean pooling. In three supervised tasks, we find that clipping does not affect the performance.

Modern deep learning-based recommendation systems exploit hundreds to thousands of different categorical features, each with millions of different categories ranging from clicks to posts. To respect the natural diversity within the categorical data, embeddings map each category to a unique dense representation within an embedded space. Since each categorical feature could take on as many as tens of millions of different possible categories, the embedding tables form the primary memory bottleneck during both training and inference. We propose a novel approach for reducing the embedding size in an end-to-end fashion by exploiting complementary partitions of the category set to produce a unique embedding vector for each category without explicit definition. By storing multiple smaller embedding tables based on each complementary partition and combining embeddings from each table, we define a unique embedding for each category at smaller memory cost. This approach may be interpreted as using a specific fixed codebook to ensure uniqueness of each category's representation. Our experimental results demonstrate the effectiveness of our approach over the hashing trick for reducing the size of the embedding tables in terms of model loss and accuracy, while retaining a similar reduction in the number of parameters.

Outfits in online fashion data are composed of items of many different types (e.g. top, bottom, shoes) that share some stylistic relationship with one another. A representation for building outfits requires a method that can learn both notions of similarity (for example, when two tops are interchangeable) and compatibility (items of possibly different type that can go together in an outfit). This paper presents an approach to learning an image embedding that respects item type, and jointly learns notions of item similarity and compatibility in an end-to-end model. To evaluate the learned representation, we crawled 68,306 outfits created by users on the Polyvore website. Our approach obtains 3-5% improvement over the state-of-the-art on outfit compatibility prediction and fill-in-the-blank tasks using our dataset, as well as an established smaller dataset, while supporting a variety of useful queries.

Learning image representations without human supervision is an important and active research field. Several recent approaches have successfully leveraged the idea of making such a representation invariant under different types of perturbations, especially via contrastive-based instance discrimination training. Although effective visual representations should indeed exhibit such invariances, there are other important characteristics, such as encoding contextual reasoning skills, for which alternative reconstruction-based approaches might be better suited. With this in mind, we propose a teacher-student scheme to learn representations by training a convolutional net to reconstruct a bag-of-visual-words (BoW) representation of an image, given as input a perturbed version of that same image. Our strategy performs an online training of both the teacher network (whose role is to generate the BoW targets) and the student network (whose role is to learn representations), along with an online update of the visual-words vocabulary (used for the BoW targets). This idea effectively enables fully online BoW-guided unsupervised learning. Extensive experiments demonstrate the interest of our BoW-based strategy which surpasses previous state-of-the-art methods (including contrastive-based ones) in several applications. For instance, in downstream tasks such Pascal object detection, Pascal classification and Places205 classification, our method improves over all prior unsupervised approaches, thus establishing new state-of-the-art results that are also significantly better even than those of supervised pre-training. We provide the implementation code at https://github.com/valeoai/obow.

We define and investigate the problem of c-approximate window search: approximate nearest neighbor search where each point in the dataset has a numeric label, and the goal is to find nearest neighbors to queries within arbitrary label ranges. Many semantic search problems, such as image and document search with timestamp filters, or product search with cost filters, are natural examples of this problem. We propose and theoretically analyze a modular tree-based framework for transforming an index that solves the traditional c-approximate nearest neighbor problem into a data structure that solves window search. On standard nearest neighbor benchmark datasets equipped with random label values, adversarially constructed embeddings, and image search embeddings with real timestamps, we obtain up to a 75times speedup over existing solutions at the same level of recall.

Hyperbolic spaces have recently gained momentum in the context of machine learning due to their high capacity and tree-likeliness properties. However, the representational power of hyperbolic geometry is not yet on par with Euclidean geometry, mostly because of the absence of corresponding hyperbolic neural network layers. This makes it hard to use hyperbolic embeddings in downstream tasks. Here, we bridge this gap in a principled manner by combining the formalism of Möbius gyrovector spaces with the Riemannian geometry of the Poincaré model of hyperbolic spaces. As a result, we derive hyperbolic versions of important deep learning tools: multinomial logistic regression, feed-forward and recurrent neural networks such as gated recurrent units. This allows to embed sequential data and perform classification in the hyperbolic space. Empirically, we show that, even if hyperbolic optimization tools are limited, hyperbolic sentence embeddings either outperform or are on par with their Euclidean variants on textual entailment and noisy-prefix recognition tasks.

We aim at constructing a high performance model for defect detection that detects unknown anomalous patterns of an image without anomalous data. To this end, we propose a two-stage framework for building anomaly detectors using normal training data only. We first learn self-supervised deep representations and then build a generative one-class classifier on learned representations. We learn representations by classifying normal data from the CutPaste, a simple data augmentation strategy that cuts an image patch and pastes at a random location of a large image. Our empirical study on MVTec anomaly detection dataset demonstrates the proposed algorithm is general to be able to detect various types of real-world defects. We bring the improvement upon previous arts by 3.1 AUCs when learning representations from scratch. By transfer learning on pretrained representations on ImageNet, we achieve a new state-of-theart 96.6 AUC. Lastly, we extend the framework to learn and extract representations from patches to allow localizing defective areas without annotations during training.

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.

Masked Autoencoder (MAE) is a self-supervised approach for representation learning, widely applicable to a variety of downstream tasks in computer vision. In spite of its success, it is still not fully uncovered what and how MAE exactly learns. In this paper, with an in-depth analysis, we discover that MAE intrinsically learns pattern-based patch-level clustering from surprisingly early stages of pretraining. Upon this understanding, we propose self-guided masked autoencoder, which internally generates informed mask by utilizing its progress in patch clustering, substituting the naive random masking of the vanilla MAE. Our approach significantly boosts its learning process without relying on any external models or supplementary information, keeping the benefit of self-supervised nature of MAE intact. Comprehensive experiments on various downstream tasks verify the effectiveness of the proposed method.

Camouflaged object detection (COD), segmenting objects that are elegantly blended into their surroundings, is a valuable yet challenging task. Existing deep-learning methods often fall into the difficulty of accurately identifying the camouflaged object with complete and fine object structure. To this end, in this paper, we propose a novel boundary-guided network (BGNet) for camouflaged object detection. Our method explores valuable and extra object-related edge semantics to guide representation learning of COD, which forces the model to generate features that highlight object structure, thereby promoting camouflaged object detection of accurate boundary localization. Extensive experiments on three challenging benchmark datasets demonstrate that our BGNet significantly outperforms the existing 18 state-of-the-art methods under four widely-used evaluation metrics. Our code is publicly available at: https://github.com/thograce/BGNet.

Training deep neural networks on images represented as grids of pixels has brought to light an interesting phenomenon known as adversarial examples. Inspired by how humans reconstruct abstract concepts, we attempt to codify the input bitmap image into a set of compact, interpretable elements to avoid being fooled by the adversarial structures. We take the first step in this direction by experimenting with image vectorization as an input transformation step to map the adversarial examples back into the natural manifold of MNIST handwritten digits. We compare our method vs. state-of-the-art input transformations and further discuss the trade-offs between a hand-designed and a learned transformation defense.

Self-supervised learning (SSL) has emerged as a powerful paradigm for learning representations without labeled data, often by enforcing invariance to input transformations such as rotations or blurring. Recent studies have highlighted two pivotal properties for effective representations: (i) avoiding dimensional collapse-where the learned features occupy only a low-dimensional subspace, and (ii) enhancing uniformity of the induced distribution. In this work, we introduce T-REGS, a simple regularization framework for SSL based on the length of the Minimum Spanning Tree (MST) over the learned representation. We provide theoretical analysis demonstrating that T-REGS simultaneously mitigates dimensional collapse and promotes distribution uniformity on arbitrary compact Riemannian manifolds. Several experiments on synthetic data and on classical SSL benchmarks validate the effectiveness of our approach at enhancing representation quality.

While LLMs are powerful embedding backbones, their application in training-free settings faces two structural challenges: causal attention restricts early tokens from accessing subsequent context, and the next-token prediction objective biases representations toward generation rather than semantic compression. To address these limitations, we propose KV-Embedding, a framework that activates the latent representation power of frozen LLMs. Our method leverages the observation that the key-value (KV) states of the final token at each layer encode a compressed view of the sequence. By re-routing these states as a prepended prefix, we enable all tokens to access sequence-level context within a single forward pass. To ensure model-agnostic applicability, we introduce an automated layer selection strategy based on intrinsic dimensionality. Evaluations on MTEB across Qwen, Mistral, and Llama backbones show that KV-Embedding outperforms existing training-free baselines by up to 10%, while maintaining robust performance on sequences up to 4,096 tokens. These results demonstrate that internal state manipulation offers an efficient alternative to input modification, and we hope this work encourages further exploration of LLM internals for representation learning.

We show that deep belief networks with binary hidden units can approximate any multivariate probability density under very mild integrability requirements on the parental density of the visible nodes. The approximation is measured in the L^q-norm for qin[1,infty] (q=infty corresponding to the supremum norm) and in Kullback-Leibler divergence. Furthermore, we establish sharp quantitative bounds on the approximation error in terms of the number of hidden units.

Neural net classifiers trained on data with annotated class labels can also capture apparent visual similarity among categories without being directed to do so. We study whether this observation can be extended beyond the conventional domain of supervised learning: Can we learn a good feature representation that captures apparent similarity among instances, instead of classes, by merely asking the feature to be discriminative of individual instances? We formulate this intuition as a non-parametric classification problem at the instance-level, and use noise-contrastive estimation to tackle the computational challenges imposed by the large number of instance classes. Our experimental results demonstrate that, under unsupervised learning settings, our method surpasses the state-of-the-art on ImageNet classification by a large margin. Our method is also remarkable for consistently improving test performance with more training data and better network architectures. By fine-tuning the learned feature, we further obtain competitive results for semi-supervised learning and object detection tasks. Our non-parametric model is highly compact: With 128 features per image, our method requires only 600MB storage for a million images, enabling fast nearest neighbour retrieval at the run time.

Small sample sizes are common in many disciplines, which necessitates pooling roughly similar datasets across multiple institutions to study weak but relevant associations between images and disease outcomes. Such data often manifest shift/imbalance in covariates (i.e., secondary non-imaging data). Controlling for such nuisance variables is common within standard statistical analysis, but the ideas do not directly apply to overparameterized models. Consequently, recent work has shown how strategies from invariant representation learning provides a meaningful starting point, but the current repertoire of methods is limited to accounting for shifts/imbalances in just a couple of covariates at a time. In this paper, we show how viewing this problem from the perspective of Category theory provides a simple and effective solution that completely avoids elaborate multi-stage training pipelines that would otherwise be needed. We show the effectiveness of this approach via extensive experiments on real datasets. Further, we discuss how this style of formulation offers a unified perspective on at least 5+ distinct problem settings, from self-supervised learning to matching problems in 3D reconstruction.

Attention-based graph neural networks (GNNs), such as graph attention networks (GATs), have become popular neural architectures for processing graph-structured data and learning node embeddings. Despite their empirical success, these models rely on labeled data and the theoretical properties of these models have yet to be fully understood. In this work, we propose a novel attention-based node embedding framework for graphs. Our framework builds upon a hierarchical kernel for multisets of subgraphs around nodes (e.g. neighborhoods) and each kernel leverages the geometry of a smooth statistical manifold to compare pairs of multisets, by "projecting" the multisets onto the manifold. By explicitly computing node embeddings with a manifold of Gaussian mixtures, our method leads to a new attention mechanism for neighborhood aggregation. We provide theoretical insights into generalizability and expressivity of our embeddings, contributing to a deeper understanding of attention-based GNNs. We propose both efficient unsupervised and supervised methods for learning the embeddings. Through experiments on several node classification benchmarks, we demonstrate that our proposed method outperforms existing attention-based graph models like GATs. Our code is available at https://github.com/BorgwardtLab/fisher_information_embedding.

Learning structured representations of the visual world in terms of objects promises to significantly improve the generalization abilities of current machine learning models. While recent efforts to this end have shown promising empirical progress, a theoretical account of when unsupervised object-centric representation learning is possible is still lacking. Consequently, understanding the reasons for the success of existing object-centric methods as well as designing new theoretically grounded methods remains challenging. In the present work, we analyze when object-centric representations can provably be learned without supervision. To this end, we first introduce two assumptions on the generative process for scenes comprised of several objects, which we call compositionality and irreducibility. Under this generative process, we prove that the ground-truth object representations can be identified by an invertible and compositional inference model, even in the presence of dependencies between objects. We empirically validate our results through experiments on synthetic data. Finally, we provide evidence that our theory holds predictive power for existing object-centric models by showing a close correspondence between models' compositionality and invertibility and their empirical identifiability.

This paper studies a conceptually simple extension of Masked Autoencoders (MAE) to spatiotemporal representation learning from videos. We randomly mask out spacetime patches in videos and learn an autoencoder to reconstruct them in pixels. Interestingly, we show that our MAE method can learn strong representations with almost no inductive bias on spacetime (only except for patch and positional embeddings), and spacetime-agnostic random masking performs the best. We observe that the optimal masking ratio is as high as 90% (vs. 75% on images), supporting the hypothesis that this ratio is related to information redundancy of the data. A high masking ratio leads to a large speedup, e.g., > 4x in wall-clock time or even more. We report competitive results on several challenging video datasets using vanilla Vision Transformers. We observe that MAE can outperform supervised pre-training by large margins. We further report encouraging results of training on real-world, uncurated Instagram data. Our study suggests that the general framework of masked autoencoding (BERT, MAE, etc.) can be a unified methodology for representation learning with minimal domain knowledge.

Contrastive learning has recently shown immense potential in unsupervised visual representation learning. Existing studies in this track mainly focus on intra-image invariance learning. The learning typically uses rich intra-image transformations to construct positive pairs and then maximizes agreement using a contrastive loss. The merits of inter-image invariance, conversely, remain much less explored. One major obstacle to exploit inter-image invariance is that it is unclear how to reliably construct inter-image positive pairs, and further derive effective supervision from them since no pair annotations are available. In this work, we present a comprehensive empirical study to better understand the role of inter-image invariance learning from three main constituting components: pseudo-label maintenance, sampling strategy, and decision boundary design. To facilitate the study, we introduce a unified and generic framework that supports the integration of unsupervised intra- and inter-image invariance learning. Through carefully-designed comparisons and analysis, multiple valuable observations are revealed: 1) online labels converge faster and perform better than offline labels; 2) semi-hard negative samples are more reliable and unbiased than hard negative samples; 3) a less stringent decision boundary is more favorable for inter-image invariance learning. With all the obtained recipes, our final model, namely InterCLR, shows consistent improvements over state-of-the-art intra-image invariance learning methods on multiple standard benchmarks. We hope this work will provide useful experience for devising effective unsupervised inter-image invariance learning. Code: https://github.com/open-mmlab/mmselfsup.

In state-of-the-art self-supervised learning (SSL) pre-training produces semantically good representations by encouraging them to be invariant under meaningful transformations prescribed from human knowledge. In fact, the property of invariance is a trivial instance of a broader class called equivariance, which can be intuitively understood as the property that representations transform according to the way the inputs transform. Here, we show that rather than using only invariance, pre-training that encourages non-trivial equivariance to some transformations, while maintaining invariance to other transformations, can be used to improve the semantic quality of representations. Specifically, we extend popular SSL methods to a more general framework which we name Equivariant Self-Supervised Learning (E-SSL). In E-SSL, a simple additional pre-training objective encourages equivariance by predicting the transformations applied to the input. We demonstrate E-SSL's effectiveness empirically on several popular computer vision benchmarks, e.g. improving SimCLR to 72.5% linear probe accuracy on ImageNet. Furthermore, we demonstrate usefulness of E-SSL for applications beyond computer vision; in particular, we show its utility on regression problems in photonics science. Our code, datasets and pre-trained models are available at https://github.com/rdangovs/essl to aid further research in E-SSL.

Token embeddings, a mapping from discrete lexical symbols to continuous vectors, are at the heart of any language model (LM). However, lexical symbol meanings can also be determined and even redefined by their structural role in a long context. In this paper, we ask: is it possible for a language model to be performant without any fixed token embeddings? Such a language model would have to rely entirely on the co-occurence and repetition of tokens in the context rather than the a priori identity of any token. To answer this, we study lexinvariantlanguage models that are invariant to lexical symbols and therefore do not need fixed token embeddings in practice. First, we prove that we can construct a lexinvariant LM to converge to the true language model at a uniform rate that is polynomial in terms of the context length, with a constant factor that is sublinear in the vocabulary size. Second, to build a lexinvariant LM, we simply encode tokens using random Gaussian vectors, such that each token maps to the same representation within each sequence but different representations across sequences. Empirically, we demonstrate that it can indeed attain perplexity comparable to that of a standard language model, given a sufficiently long context. We further explore two properties of the lexinvariant language models: First, given text generated from a substitution cipher of English, it implicitly implements Bayesian in-context deciphering and infers the mapping to the underlying real tokens with high accuracy. Second, it has on average 4X better accuracy over synthetic in-context reasoning tasks. Finally, we discuss regularizing standard language models towards lexinvariance and potential practical applications.

Previous robustness approaches for deep learning models such as data augmentation techniques via data transformation or adversarial training cannot capture real-world variations that preserve the semantics of the input, such as a change in lighting conditions. To bridge this gap, we present NaTra, an adversarial training scheme that is designed to improve the robustness of image classification algorithms. We target attributes of the input images that are independent of the class identification, and manipulate those attributes to mimic real-world natural transformations (NaTra) of the inputs, which are then used to augment the training dataset of the image classifier. Specifically, we apply Batch Inverse Encoding and Shifting to map a batch of given images to corresponding disentangled latent codes of well-trained generative models. Latent Codes Expansion is used to boost image reconstruction quality through the incorporation of extended feature maps. Unsupervised Attribute Directing and Manipulation enables identification of the latent directions that correspond to specific attribute changes, and then produce interpretable manipulations of those attributes, thereby generating natural transformations to the input data. We demonstrate the efficacy of our scheme by utilizing the disentangled latent representations derived from well-trained GANs to mimic transformations of an image that are similar to real-world natural variations (such as lighting conditions or hairstyle), and train models to be invariant to these natural transformations. Extensive experiments show that our method improves generalization of classification models and increases its robustness to various real-world distortions

Deep neural networks learn fragile "shortcut" features, rendering them difficult to interpret (black box) and vulnerable to adversarial attacks. This paper proposes semantic features as a general architectural solution to this problem. The main idea is to make features locality-sensitive in the adequate semantic topology of the domain, thus introducing a strong regularization. The proof of concept network is lightweight, inherently interpretable and achieves almost human-level adversarial test metrics - with no adversarial training! These results and the general nature of the approach warrant further research on semantic features. The code is available at https://github.com/314-Foundation/white-box-nn

Recent advances in zero-shot image recognition suggest that vision-language models learn generic visual representations with a high degree of semantic information that may be arbitrarily probed with natural language phrases. Understanding an image, however, is not just about understanding what content resides within an image, but importantly, where that content resides. In this work we examine how well vision-language models are able to understand where objects reside within an image and group together visually related parts of the imagery. We demonstrate how contemporary vision and language representation learning models based on contrastive losses and large web-based data capture limited object localization information. We propose a minimal set of modifications that results in models that uniquely learn both semantic and spatial information. We measure this performance in terms of zero-shot image recognition, unsupervised bottom-up and top-down semantic segmentations, as well as robustness analyses. We find that the resulting model achieves state-of-the-art results in terms of unsupervised segmentation, and demonstrate that the learned representations are uniquely robust to spurious correlations in datasets designed to probe the causal behavior of vision models.

Traditional neural word embeddings are usually dependent on a richer diversity of vocabulary. However, the language models recline to cover major vocabularies via the word embedding parameters, in particular, for multilingual language models that generally cover a significant part of their overall learning parameters. In this work, we present a new compact embedding structure to reduce the memory footprint of the pre-trained language models with a sacrifice of up to 4% absolute accuracy. The embeddings vectors reconstruction follows a set of subspace embeddings and an assignment procedure via the contextual relationship among tokens from pre-trained language models. The subspace embedding structure calibrates to masked language models, to evaluate our compact embedding structure on similarity and textual entailment tasks, sentence and paraphrase tasks. Our experimental evaluation shows that the subspace embeddings achieve compression rates beyond 99.8% in comparison with the original embeddings for the language models on XNLI and GLUE benchmark suites.

Nonlinear manifolds are widespread in deep visual features, where Euclidean distances often fail to capture true similarity. This limitation becomes particularly severe in prototype-based interpretable fine-grained recognition, where subtle semantic distinctions are essential. To address this challenge, we propose a novel paradigm for prototype-based recognition that anchors similarity within the intrinsic geometry of deep features. Specifically, we distill the latent manifold structure of each class into a diffusion space and introduce a differentiable Nystr\"om interpolation, making the geometry accessible to both unseen samples and learnable prototypes. To ensure efficiency, we employ compact per-class landmark sets with periodic updates. This design keeps the embedding aligned with the evolving backbone, enabling fast and scalable inference. Extensive experiments on the CUB-200-2011 and Stanford Cars datasets show that our GeoProto framework produces prototypes focusing on semantically aligned parts, significantly outperforming Euclidean prototype networks.

We present a unified framework for studying the identifiability of representations learned from simultaneously observed views, such as different data modalities. We allow a partially observed setting in which each view constitutes a nonlinear mixture of a subset of underlying latent variables, which can be causally related. We prove that the information shared across all subsets of any number of views can be learned up to a smooth bijection using contrastive learning and a single encoder per view. We also provide graphical criteria indicating which latent variables can be identified through a simple set of rules, which we refer to as identifiability algebra. Our general framework and theoretical results unify and extend several previous works on multi-view nonlinear ICA, disentanglement, and causal representation learning. We experimentally validate our claims on numerical, image, and multi-modal data sets. Further, we demonstrate that the performance of prior methods is recovered in different special cases of our setup. Overall, we find that access to multiple partial views enables us to identify a more fine-grained representation, under the generally milder assumption of partial observability.

Customized text-to-image generation, which aims to learn user-specified concepts with a few images, has drawn significant attention recently. However, existing methods usually suffer from overfitting issues and entangle the subject-unrelated information (e.g., background and pose) with the learned concept, limiting the potential to compose concept into new scenes. To address these issues, we propose the DETEX, a novel approach that learns the disentangled concept embedding for flexible customized text-to-image generation. Unlike conventional methods that learn a single concept embedding from the given images, our DETEX represents each image using multiple word embeddings during training, i.e., a learnable image-shared subject embedding and several image-specific subject-unrelated embeddings. To decouple irrelevant attributes (i.e., background and pose) from the subject embedding, we further present several attribute mappers that encode each image as several image-specific subject-unrelated embeddings. To encourage these unrelated embeddings to capture the irrelevant information, we incorporate them with corresponding attribute words and propose a joint training strategy to facilitate the disentanglement. During inference, we only use the subject embedding for image generation, while selectively using image-specific embeddings to retain image-specified attributes. Extensive experiments demonstrate that the subject embedding obtained by our method can faithfully represent the target concept, while showing superior editability compared to the state-of-the-art methods. Our code will be made published available.

Similarity between training examples is used to curate pretraining datasets for language models by many methods -- for diversification and to select examples similar to high-quality data. However, similarity is typically measured with off-the-shelf embedding models that are generic or trained for tasks such as retrieval. This paper introduces a framework to analyze the suitability of embedding models specifically for data curation in the language model pretraining setting. We quantify the correlation between similarity in the embedding space to similarity in pretraining loss between different training examples, and how diversifying in the embedding space affects pretraining quality. We analyze a variety of embedding models in our framework, with experiments using the Pile dataset for pretraining a 1.7B parameter decoder-only language model. We find that the embedding models we consider are all useful for pretraining data curation. Moreover, a simple approach of averaging per-token embeddings proves to be surprisingly competitive with more sophisticated embedding models -- likely because the latter are not designed specifically for pretraining data curation. Indeed, we believe our analysis and evaluation framework can serve as a foundation for the design of embedding models that specifically reason about similarity in pretraining datasets.

Foundational image-language models have generated considerable interest due to their efficient adaptation to downstream tasks by prompt learning. Prompt learning treats part of the language model input as trainable while freezing the rest, and optimizes an Empirical Risk Minimization objective. However, Empirical Risk Minimization is known to suffer from distributional shifts which hurt generalizability to prompts unseen during training. By leveraging the regularization ability of Bayesian methods, we frame prompt learning from the Bayesian perspective and formulate it as a variational inference problem. Our approach regularizes the prompt space, reduces overfitting to the seen prompts and improves the prompt generalization on unseen prompts. Our framework is implemented by modeling the input prompt space in a probabilistic manner, as an a priori distribution which makes our proposal compatible with prompt learning approaches that are unconditional or conditional on the image. We demonstrate empirically on 15 benchmarks that Bayesian prompt learning provides an appropriate coverage of the prompt space, prevents learning spurious features, and exploits transferable invariant features. This results in better generalization of unseen prompts, even across different datasets and domains. Code available at: https://github.com/saic-fi/Bayesian-Prompt-Learning

In disentangled representation learning, a model is asked to tease apart a dataset's underlying sources of variation and represent them independently of one another. Since the model is provided with no ground truth information about these sources, inductive biases take a paramount role in enabling disentanglement. In this work, we construct an inductive bias towards encoding to and decoding from an organized latent space. Concretely, we do this by (i) quantizing the latent space into discrete code vectors with a separate learnable scalar codebook per dimension and (ii) applying strong model regularization via an unusually high weight decay. Intuitively, the latent space design forces the encoder to combinatorially construct codes from a small number of distinct scalar values, which in turn enables the decoder to assign a consistent meaning to each value. Regularization then serves to drive the model towards this parsimonious strategy. We demonstrate the broad applicability of this approach by adding it to both basic data-reconstructing (vanilla autoencoder) and latent-reconstructing (InfoGAN) generative models. For reliable evaluation, we also propose InfoMEC, a new set of metrics for disentanglement that is cohesively grounded in information theory and fixes well-established shortcomings in previous metrics. Together with regularization, latent quantization dramatically improves the modularity and explicitness of learned representations on a representative suite of benchmark datasets. In particular, our quantized-latent autoencoder (QLAE) consistently outperforms strong methods from prior work in these key disentanglement properties without compromising data reconstruction.

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)%.