Cross-Entropy Is All You Need To Invert the Data Generating Process

Supervised learning has become a cornerstone of modern machine learning, yet a comprehensive theory explaining its effectiveness remains elusive. Empirical phenomena, such as neural analogy-making and the linear representation hypothesis, suggest that supervised models can learn interpretable factors of variation in a linear fashion. Recent advances in self-supervised learning, particularly nonlinear Independent Component Analysis, have shown that these methods can recover latent structures by inverting the data generating process. We extend these identifiability results to parametric instance discrimination, then show how insights transfer to the ubiquitous setting of supervised learning with cross-entropy minimization. We prove that even in standard classification tasks, models learn representations of ground-truth factors of variation up to a linear transformation. We corroborate our theoretical contribution with a series of empirical studies. First, using simulated data matching our theoretical assumptions, we demonstrate successful disentanglement of latent factors. Second, we show that on DisLib, a widely-used disentanglement benchmark, simple classification tasks recover latent structures up to linear transformations. Finally, we reveal that models trained on ImageNet encode representations that permit linear decoding of proxy factors of variation. Together, our theoretical findings and experiments offer a compelling explanation for recent observations of linear representations, such as superposition in neural networks. This work takes a significant step toward a cohesive theory that accounts for the unreasonable effectiveness of supervised deep learning.

The Fair Language Model Paradox

Large Language Models (LLMs) are widely deployed in real-world applications, yet little is known about their training dynamics at the token level. Evaluation typically relies on aggregated training loss, measured at the batch level, which overlooks subtle per-token biases arising from (i) varying token-level dynamics and (ii) structural biases introduced by hyperparameters. While weight decay is commonly used to stabilize training, we reveal that it silently introduces performance biases detectable only at the token level. In fact, we empirically show across different dataset sizes, model architectures and sizes ranging from 270M to 3B parameters that as weight decay increases, low-frequency tokens are disproportionately depreciated. This is particularly concerning, as these neglected low-frequency tokens represent the vast majority of the token distribution in most languages, calling for novel regularization techniques that ensure fairness across all available tokens.

ALLoRA: Adaptive Learning Rate Mitigates LoRA Fatal Flaws

Low-Rank Adaptation (LoRA) is the bread and butter of Large Language Model (LLM) finetuning. LoRA learns an additive low-rank perturbation, $AB$, of a pretrained matrix parameter $W$ to align the model to a new task or dataset with $W+AB$. We identify three core limitations to LoRA for finetuning--a setting that employs limited amount of data and training steps. First, LoRA employs Dropout to prevent overfitting. We prove that Dropout is only suitable for long training episodes but fails to converge to a reliable regularizer for short training episodes. Second, LoRA's initialization of $B$ at $0$ creates a slow training dynamic between $A$ and $B$. That dynamic is also exacerbated by Dropout that further slows the escape from $0$ for $B$ which is particularly harmful for short training episodes. Third, the scaling factor multiplying each LoRA additive perturbation creates ``short-sighted'' interactions between the LoRA modules of different layers. Motivated by principled analysis of those limitations, we find an elegant solution: a Dropout-free, scaling-free, LoRA with Adaptive Learning rate--coined ALLoRA. By scaling the per sample and per parameter gradients with a coefficient inversely proportional to parameters' $\ell_2$ norm, ALLoRA alleviates those three limitations. As a by-product, ALLoRA removes two hyper-parameters from LoRA: the scaling factor and the dropout rate. Empirical results show that ALLoRA admits better accuracy than LoRA on various settings, including against recent LoRA variants such as Weight-Decomposed Low-Rank Adaptation (DoRA). Ablation studies show our solution is the optimal in a family of weight-dependent / output-dependent approaches on various LLMs including the latest Llama3.

Self-Supervised Anomaly Detection in the Wild: Favor Joint Embeddings Methods

Accurate anomaly detection is critical in vision-based infrastructure inspection, where it helps prevent costly failures and enhances safety. Self-Supervised Learning (SSL) offers a promising approach by learning robust representations from unlabeled data. However, its application in anomaly detection remains underexplored. This paper addresses this gap by providing a comprehensive evaluation of SSL methods for real-world anomaly detection, focusing on sewer infrastructure. Using the Sewer-ML dataset, we evaluate lightweight models such as ViT-Tiny and ResNet-18 across SSL frameworks, including BYOL, Barlow Twins, SimCLR, DINO, and MAE, under varying class imbalance levels. Through 250 experiments, we rigorously assess the performance of these SSL methods to ensure a robust and comprehensive evaluation. Our findings highlight the superiority of joint-embedding methods like SimCLR and Barlow Twins over reconstruction-based approaches such as MAE, which struggle to maintain performance under class imbalance. Furthermore, we find that the SSL model choice is more critical than the backbone architecture. Additionally, we emphasize the need for better label-free assessments of SSL representations, as current methods like RankMe fail to adequately evaluate representation quality, making cross-validation without labels infeasible. Despite the remaining performance gap between SSL and supervised models, these findings highlight the potential of SSL to enhance anomaly detection, paving the way for further research in this underexplored area of SSL applications.

On the Geometry of Deep Learning

In this paper, we overview one promising avenue of progress at the mathematical foundation of deep learning: the connection between deep networks and function approximation by affine splines (continuous piecewise linear functions in multiple dimensions). In particular, we will overview work over the past decade on understanding certain geometrical properties of a deep network's affine spline mapping, in particular how it tessellates its input space. As we will see, the affine spline connection and geometrical viewpoint provide a powerful portal through which to view, analyze, and improve the inner workings of a deep network.

UniBench: Visual Reasoning Requires Rethinking Vision-Language Beyond Scaling

Significant research efforts have been made to scale and improve vision-language model (VLM) training approaches. Yet, with an ever-growing number of benchmarks, researchers are tasked with the heavy burden of implementing each protocol, bearing a non-trivial computational cost, and making sense of how all these benchmarks translate into meaningful axes of progress. To facilitate a systematic evaluation of VLM progress, we introduce UniBench: a unified implementation of 50+ VLM benchmarks spanning a comprehensive range of carefully categorized capabilities from object recognition to spatial awareness, counting, and much more. We showcase the utility of UniBench for measuring progress by evaluating nearly 60 publicly available vision-language models, trained on scales of up to 12.8B samples. We find that while scaling training data or model size can boost many vision-language model capabilities, scaling offers little benefit for reasoning or relations. Surprisingly, we also discover today's best VLMs struggle on simple digit recognition and counting tasks, e.g. MNIST, which much simpler networks can solve. Where scale falls short, we find that more precise interventions, such as data quality or tailored-learning objectives offer more promise. For practitioners, we also offer guidance on selecting a suitable VLM for a given application. Finally, we release an easy-to-run UniBench code-base with the full set of 50+ benchmarks and comparisons across 59 models as well as a distilled, representative set of benchmarks that runs in 5 minutes on a single GPU.

$\mathbb{X}$-Sample Contrastive Loss: Improving Contrastive Learning with Sample Similarity Graphs

Learning good representations involves capturing the diverse ways in which data samples relate. Contrastive loss - an objective matching related samples - underlies methods from self-supervised to multimodal learning. Contrastive losses, however, can be viewed more broadly as modifying a similarity graph to indicate how samples should relate in the embedding space. This view reveals a shortcoming in contrastive learning: the similarity graph is binary, as only one sample is the related positive sample. Crucially, similarities \textit{across} samples are ignored. Based on this observation, we revise the standard contrastive loss to explicitly encode how a sample relates to others. We experiment with this new objective, called $\mathbb{X}$-Sample Contrastive, to train vision models based on similarities in class or text caption descriptions. Our study spans three scales: ImageNet-1k with 1 million, CC3M with 3 million, and CC12M with 12 million samples. The representations learned via our objective outperform both contrastive self-supervised and vision-language models trained on the same data across a range of tasks. When training on CC12M, we outperform CLIP by $0.6\%$ on both ImageNet and ImageNet Real. Our objective appears to work particularly well in lower-data regimes, with gains over CLIP of $16.8\%$ on ImageNet and $18.1\%$ on ImageNet Real when training with CC3M. Finally, our objective seems to encourage the model to learn representations that separate objects from their attributes and backgrounds, with gains of $3.3$-$5.6$\% over CLIP on ImageNet9. We hope the proposed solution takes a small step towards developing richer learning objectives for understanding sample relations in foundation models.

Occam's Razor for Self Supervised Learning: What is Sufficient to Learn Good Representations?

Deep Learning is often depicted as a trio of data-architecture-loss. Yet, recent Self Supervised Learning (SSL) solutions have introduced numerous additional design choices, e.g., a projector network, positive views, or teacher-student networks. These additions pose two challenges. First, they limit the impact of theoretical studies that often fail to incorporate all those intertwined designs. Second, they slow-down the deployment of SSL methods to new domains as numerous hyper-parameters need to be carefully tuned. In this study, we bring forward the surprising observation that--at least for pretraining datasets of up to a few hundred thousands samples--the additional designs introduced by SSL do not contribute to the quality of the learned representations. That finding not only provides legitimacy to existing theoretical studies, but also simplifies the practitioner's path to SSL deployment in numerous small and medium scale settings. Our finding answers a long-lasting question: the often-experienced sensitivity to training settings and hyper-parameters encountered in SSL come from their design, rather than the absence of supervised guidance.

ScaLES: Scalable Latent Exploration Score for Pre-Trained Generative Networks

We develop Scalable Latent Exploration Score (ScaLES) to mitigate over-exploration in Latent Space Optimization (LSO), a popular method for solving black-box discrete optimization problems. LSO utilizes continuous optimization within the latent space of a Variational Autoencoder (VAE) and is known to be susceptible to over-exploration, which manifests in unrealistic solutions that reduce its practicality. ScaLES is an exact and theoretically motivated method leveraging the trained decoder's approximation of the data distribution. ScaLES can be calculated with any existing decoder, e.g. from a VAE, without additional training, architectural changes, or access to the training data. Our evaluation across five LSO benchmark tasks and three VAE architectures demonstrates that ScaLES enhances the quality of the solutions while maintaining high objective values, leading to improvements over existing solutions. We believe that new avenues to LSO will be opened by ScaLES ability to identify out of distribution areas, differentiability, and computational tractability. Open source code for ScaLES is available at https://github.com/OmerRonen/scales.

Deep Networks Always Grok and Here is Why

Grokking, or delayed generalization, is a phenomenon where generalization in a deep neural network (DNN) occurs long after achieving near zero training error. Previous studies have reported the occurrence of grokking in specific controlled settings, such as DNNs initialized with large-norm parameters or transformers trained on algorithmic datasets. We demonstrate that grokking is actually much more widespread and materializes in a wide range of practical settings, such as training of a convolutional neural network (CNN) on CIFAR10 or a Resnet on Imagenette. We introduce the new concept of delayed robustness, whereby a DNN groks adversarial examples and becomes robust, long after interpolation and/or generalization. We develop an analytical explanation for the emergence of both delayed generalization and delayed robustness based on a new measure of the local complexity of a DNN's input-output mapping. Our local complexity measures the density of the so-called 'linear regions' (aka, spline partition regions) that tile the DNN input space, and serves as a utile progress measure for training. We provide the first evidence that for classification problems, the linear regions undergo a phase transition during training whereafter they migrate away from the training samples (making the DNN mapping smoother there) and towards the decision boundary (making the DNN mapping less smooth there). Grokking occurs post phase transition as a robust partition of the input space emerges thanks to the linearization of the DNN mapping around the training points. Website: https://bit.ly/grok-adversarial