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.

In Search of Forgotten Domain Generalization

Out-of-Domain (OOD) generalization is the ability of a model trained on one or more domains to generalize to unseen domains. In the ImageNet era of computer vision, evaluation sets for measuring a model's OOD performance were designed to be strictly OOD with respect to style. However, the emergence of foundation models and expansive web-scale datasets has obfuscated this evaluation process, as datasets cover a broad range of domains and risk test domain contamination. In search of the forgotten domain generalization, we create large-scale datasets subsampled from LAION -- LAION-Natural and LAION-Rendition -- that are strictly OOD to corresponding ImageNet and DomainNet test sets in terms of style. Training CLIP models on these datasets reveals that a significant portion of their performance is explained by in-domain examples. This indicates that the OOD generalization challenges from the ImageNet era still prevail and that training on web-scale data merely creates the illusion of OOD generalization. Furthermore, through a systematic exploration of combining natural and rendition datasets in varying proportions, we identify optimal mixing ratios for model generalization across these domains. Our datasets and results re-enable meaningful assessment of OOD robustness at scale -- a crucial prerequisite for improving model robustness.

InfoNCE: Identifying the Gap Between Theory and Practice

Previous theoretical work on contrastive learning (CL) with InfoNCE showed that, under certain assumptions, the learned representations uncover the ground-truth latent factors. We argue these theories overlook crucial aspects of how CL is deployed in practice. Specifically, they assume that within a positive pair, all latent factors either vary to a similar extent, or that some do not vary at all. However, in practice, positive pairs are often generated using augmentations such as strong cropping to just a few pixels. Hence, a more realistic assumption is that all latent factors change, with a continuum of variability across these factors. We introduce AnInfoNCE, a generalization of InfoNCE that can provably uncover the latent factors in this anisotropic setting, broadly generalizing previous identifiability results in CL. We validate our identifiability results in controlled experiments and show that AnInfoNCE increases the recovery of previously collapsed information in CIFAR10 and ImageNet, albeit at the cost of downstream accuracy. Additionally, we explore and discuss further mismatches between theoretical assumptions and practical implementations, including extensions to hard negative mining and loss ensembles.

Identifiable Exchangeable Mechanisms for Causal Structure and Representation Learning

Identifying latent representations or causal structures is important for good generalization and downstream task performance. However, both fields have been developed rather independently. We observe that several methods in both representation and causal structure learning rely on the same data-generating process (DGP), namely, exchangeable but not i.i.d. (independent and identically distributed) data. We provide a unified framework, termed Identifiable Exchangeable Mechanisms (IEM), for representation and structure learning under the lens of exchangeability. IEM provides new insights that let us relax the necessary conditions for causal structure identification in exchangeable non--i.i.d. data. We also demonstrate the existence of a duality condition in identifiable representation learning, leading to new identifiability results. We hope this work will pave the way for further research in causal representation learning.

Understanding LLMs Requires More Than Statistical Generalization

The last decade has seen blossoming research in deep learning theory attempting to answer, "Why does deep learning generalize?" A powerful shift in perspective precipitated this progress: the study of overparametrized models in the interpolation regime. In this paper, we argue that another perspective shift is due, since some of the desirable qualities of LLMs are not a consequence of good statistical generalization and require a separate theoretical explanation. Our core argument relies on the observation that AR probabilistic models are inherently non-identifiable: models zero or near-zero KL divergence apart -- thus, equivalent test loss -- can exhibit markedly different behaviors. We support our position with mathematical examples and empirical observations, illustrating why non-identifiability has practical relevance through three case studies: (1) the non-identifiability of zero-shot rule extrapolation; (2) the approximate non-identifiability of in-context learning; and (3) the non-identifiability of fine-tunability. We review promising research directions focusing on LLM-relevant generalization measures, transferability, and inductive biases.

Effective pruning of web-scale datasets based on complexity of concept clusters

Utilizing massive web-scale datasets has led to unprecedented performance gains in machine learning models, but also imposes outlandish compute requirements for their training. In order to improve training and data efficiency, we here push the limits of pruning large-scale multimodal datasets for training CLIP-style models. Today's most effective pruning method on ImageNet clusters data samples into separate concepts according to their embedding and prunes away the most prototypical samples. We scale this approach to LAION and improve it by noting that the pruning rate should be concept-specific and adapted to the complexity of the concept. Using a simple and intuitive complexity measure, we are able to reduce the training cost to a quarter of regular training. By filtering from the LAION dataset, we find that training on a smaller set of high-quality data can lead to higher performance with significantly lower training costs. More specifically, we are able to outperform the LAION-trained OpenCLIP-ViT-B32 model on ImageNet zero-shot accuracy by 1.1p.p. while only using 27.7% of the data and training compute. Despite a strong reduction in training cost, we also see improvements on ImageNet dist. shifts, retrieval tasks and VTAB. On the DataComp Medium benchmark, we achieve a new state-of-the-art ImageNet zero-shot accuracy and a competitive average zero-shot accuracy on 38 evaluation tasks.

An Interventional Perspective on Identifiability in Gaussian LTI Systems with Independent Component Analysis

We investigate the relationship between system identification and intervention design in dynamical systems. While previous research demonstrated how identifiable representation learning methods, such as Independent Component Analysis (ICA), can reveal cause-effect relationships, it relied on a passive perspective without considering how to collect data. Our work shows that in Gaussian Linear Time-Invariant (LTI) systems, the system parameters can be identified by introducing diverse intervention signals in a multi-environment setting. By harnessing appropriate diversity assumptions motivated by the ICA literature, our findings connect experiment design and representational identifiability in dynamical systems. We corroborate our findings on synthetic and (simulated) physical data. Additionally, we show that Hidden Markov Models, in general, and (Gaussian) LTI systems, in particular, fulfil a generalization of the Causal de Finetti theorem with continuous parameters.

Does CLIP's Generalization Performance Mainly Stem from High Train-Test Similarity?

Foundation models like CLIP are trained on hundreds of millions of samples and effortlessly generalize to new tasks and inputs. Out of the box, CLIP shows stellar zero-shot and few-shot capabilities on a wide range of out-of-distribution (OOD) benchmarks, which prior works attribute mainly to today's large and comprehensive training dataset (like LAION). However, it is questionable how meaningful terms like out-of-distribution generalization are for CLIP as it seems likely that web-scale datasets like LAION simply contain many samples that are similar to common OOD benchmarks originally designed for ImageNet. To test this hypothesis, we retrain CLIP on pruned LAION splits that replicate ImageNet's train-test similarity with respect to common OOD benchmarks. While we observe a performance drop on some benchmarks, surprisingly, CLIP's overall performance remains high. This shows that high train-test similarity is insufficient to explain CLIP's OOD performance, and other properties of the training data must drive CLIP to learn more generalizable representations. Additionally, by pruning data points that are dissimilar to the OOD benchmarks, we uncover a 100M split of LAION ($\frac{1}{4}$th of its original size) on which CLIP can be trained to match its original OOD performance.

Provable Compositional Generalization for Object-Centric Learning

Learning representations that generalize to novel compositions of known concepts is crucial for bridging the gap between human and machine perception. One prominent effort is learning object-centric representations, which are widely conjectured to enable compositional generalization. Yet, it remains unclear when this conjecture will be true, as a principled theoretical or empirical understanding of compositional generalization is lacking. In this work, we investigate when compositional generalization is guaranteed for object-centric representations through the lens of identifiability theory. We show that autoencoders that satisfy structural assumptions on the decoder and enforce encoder-decoder consistency will learn object-centric representations that provably generalize compositionally. We validate our theoretical result and highlight the practical relevance of our assumptions through experiments on synthetic image data.

Scale Alone Does not Improve Mechanistic Interpretability in Vision Models

In light of the recent widespread adoption of AI systems, understanding the internal information processing of neural networks has become increasingly critical. Most recently, machine vision has seen remarkable progress by scaling neural networks to unprecedented levels in dataset and model size. We here ask whether this extraordinary increase in scale also positively impacts the field of mechanistic interpretability. In other words, has our understanding of the inner workings of scaled neural networks improved as well? We here use a psychophysical paradigm to quantify mechanistic interpretability for a diverse suite of models and find no scaling effect for interpretability - neither for model nor dataset size. Specifically, none of the nine investigated state-of-the-art models are easier to interpret than the GoogLeNet model from almost a decade ago. Latest-generation vision models appear even less interpretable than older architectures, hinting at a regression rather than improvement, with modern models sacrificing interpretability for accuracy. These results highlight the need for models explicitly designed to be mechanistically interpretable and the need for more helpful interpretability methods to increase our understanding of networks at an atomic level. We release a dataset containing more than 120'000 human responses from our psychophysical evaluation of 767 units across nine models. This dataset is meant to facilitate research on automated instead of human-based interpretability evaluations that can ultimately be leveraged to directly optimize the mechanistic interpretability of models.