Embrace the Gap: VAEs Perform Independent Mechanism Analysis

Variational autoencoders (VAEs) are a popular framework for modeling complex data distributions; they can be efficiently trained via variational inference by maximizing the evidence lower bound (ELBO), at the expense of a gap to the exact (log-)marginal likelihood. While VAEs are commonly used for representation learning, it is unclear why ELBO maximization would yield useful representations, since unregularized maximum likelihood estimation cannot invert the data-generating process. Yet, VAEs often succeed at this task. We seek to elucidate this apparent paradox by studying nonlinear VAEs in the limit of near-deterministic decoders. We first prove that, in this regime, the optimal encoder approximately inverts the decoder -- a commonly used but unproven conjecture -- which we refer to as {\em self-consistency}. Leveraging self-consistency, we show that the ELBO converges to a regularized log-likelihood. This allows VAEs to perform what has recently been termed independent mechanism analysis (IMA): it adds an inductive bias towards decoders with column-orthogonal Jacobians, which helps recovering the true latent factors. The gap between ELBO and log-likelihood is therefore welcome, since it bears unanticipated benefits for nonlinear representation learning. In experiments on synthetic and image data, we show that VAEs uncover the true latent factors when the data generating process satisfies the IMA assumption.

Visual Representation Learning Does Not Generalize Strongly Within the Same Domain

An important component for generalization in machine learning is to uncover underlying latent factors of variation as well as the mechanism through which each factor acts in the world. In this paper, we test whether 17 unsupervised, weakly supervised, and fully supervised representation learning approaches correctly infer the generative factors of variation in simple datasets (dSprites, Shapes3D, MPI3D). In contrast to prior robustness work that introduces novel factors of variation during test time, such as blur or other (un)structured noise, we here recompose, interpolate, or extrapolate only existing factors of variation from the training data set (e.g., small and medium-sized objects during training and large objects during testing). Models that learn the correct mechanism should be able to generalize to this benchmark. In total, we train and test 2000+ models and observe that all of them struggle to learn the underlying mechanism regardless of supervision signal and architectural bias. Moreover, the generalization capabilities of all tested models drop significantly as we move from artificial datasets towards more realistic real-world datasets. Despite their inability to identify the correct mechanism, the models are quite modular as their ability to infer other in-distribution factors remains fairly stable, providing only a single factor is out-of-distribution. These results point to an important yet understudied problem of learning mechanistic models of observations that can facilitate generalization.

How Well do Feature Visualizations Support Causal Understanding of CNN Activations?

One widely used approach towards understanding the inner workings of deep convolutional neural networks is to visualize unit responses via activation maximization. Feature visualizations via activation maximization are thought to provide humans with precise information about the image features that cause a unit to be activated. If this is indeed true, these synthetic images should enable humans to predict the effect of an intervention, such as whether occluding a certain patch of the image (say, a dog's head) changes a unit's activation. Here, we test this hypothesis by asking humans to predict which of two square occlusions causes a larger change to a unit's activation. Both a large-scale crowdsourced experiment and measurements with experts show that on average, the extremely activating feature visualizations by Olah et al. (2017) indeed help humans on this task ($67 \pm 4\%$ accuracy; baseline performance without any visualizations is $60 \pm 3\%$). However, they do not provide any significant advantage over other visualizations (such as e.g. dataset samples), which yield similar performance ($66 \pm 3\%$ to $67 \pm 3\%$ accuracy). Taken together, we propose an objective psychophysical task to quantify the benefit of unit-level interpretability methods for humans, and find no evidence that feature visualizations provide humans with better "causal understanding" than simple alternative visualizations.

Partial success in closing the gap between human and machine vision

A few years ago, the first CNN surpassed human performance on ImageNet. However, it soon became clear that machines lack robustness on more challenging test cases, a major obstacle towards deploying machines "in the wild" and towards obtaining better computational models of human visual perception. Here we ask: Are we making progress in closing the gap between human and machine vision? To answer this question, we tested human observers on a broad range of out-of-distribution (OOD) datasets, adding the "missing human baseline" by recording 85,120 psychophysical trials across 90 participants. We then investigated a range of promising machine learning developments that crucially deviate from standard supervised CNNs along three axes: objective function (self-supervised, adversarially trained, CLIP language-image training), architecture (e.g. vision transformers), and dataset size (ranging from 1M to 1B). Our findings are threefold. (1.) The longstanding robustness gap between humans and CNNs is closing, with the best models now matching or exceeding human performance on most OOD datasets. (2.) There is still a substantial image-level consistency gap, meaning that humans make different errors than models. In contrast, most models systematically agree in their categorisation errors, even substantially different ones like contrastive self-supervised vs. standard supervised models. (3.) In many cases, human-to-model consistency improves when training dataset size is increased by one to three orders of magnitude. Our results give reason for cautious optimism: While there is still much room for improvement, the behavioural difference between human and machine vision is narrowing. In order to measure future progress, 17 OOD datasets with image-level human behavioural data are provided as a benchmark here: https://github.com/bethgelab/model-vs-human/

Self-Supervised Learning with Data Augmentations Provably Isolates Content from Style

Self-supervised representation learning has shown remarkable success in a number of domains. A common practice is to perform data augmentation via hand-crafted transformations intended to leave the semantics of the data invariant. We seek to understand the empirical success of this approach from a theoretical perspective. We formulate the augmentation process as a latent variable model by postulating a partition of the latent representation into a content component, which is assumed invariant to augmentation, and a style component, which is allowed to change. Unlike prior work on disentanglement and independent component analysis, we allow for both nontrivial statistical and causal dependencies in the latent space. We study the identifiability of the latent representation based on pairs of views of the observations and prove sufficient conditions that allow us to identify the invariant content partition up to an invertible mapping in both generative and discriminative settings. We find numerical simulations with dependent latent variables are consistent with our theory. Lastly, we introduce Causal3DIdent, a dataset of high-dimensional, visually complex images with rich causal dependencies, which we use to study the effect of data augmentations performed in practice.

Adapting ImageNet-scale models to complex distribution shifts with self-learning

While self-learning methods are an important component in many recent domain adaptation techniques, they are not yet comprehensively evaluated on ImageNet-scale datasets common in robustness research. In extensive experiments on ResNet and EfficientNet models, we find that three components are crucial for increasing performance with self-learning: (i) using short update times between the teacher and the student network, (ii) fine-tuning only few affine parameters distributed across the network, and (iii) leveraging methods from robust classification to counteract the effect of label noise. We use these insights to obtain drastically improved state-of-the-art results on ImageNet-C (22.0% mCE), ImageNet-R (17.4% error) and ImageNet-A (14.8% error). Our techniques yield further improvements in combination with previously proposed robustification methods. Self-learning is able to reduce the top-1 error to a point where no substantial further progress can be expected. We therefore re-purpose the dataset from the Visual Domain Adaptation Challenge 2019 and use a subset of it as a new robustness benchmark (ImageNet-D) which proves to be a more challenging dataset for all current state-of-the-art models (58.2% error) to guide future research efforts at the intersection of robustness and domain adaptation on ImageNet scale.

Fast Minimum-norm Adversarial Attacks through Adaptive Norm Constraints

Evaluating adversarial robustness amounts to finding the minimum perturbation needed to have an input sample misclassified. The inherent complexity of the underlying optimization requires current gradient-based attacks to be carefully tuned, initialized, and possibly executed for many computationally-demanding iterations, even if specialized to a given perturbation model. In this work, we overcome these limitations by proposing a fast minimum-norm (FMN) attack that works with different $\ell_p$-norm perturbation models ($p=0, 1, 2, \infty$), is robust to hyperparameter choices, does not require adversarial starting points, and converges within few lightweight steps. It works by iteratively finding the sample misclassified with maximum confidence within an $\ell_p$-norm constraint of size $\epsilon$, while adapting $\epsilon$ to minimize the distance of the current sample to the decision boundary. Extensive experiments show that FMN significantly outperforms existing attacks in terms of convergence speed and computation time, while reporting comparable or even smaller perturbation sizes.

Contrastive Learning Inverts the Data Generating Process

Contrastive learning has recently seen tremendous success in self-supervised learning. So far, however, it is largely unclear why the learned representations generalize so effectively to a large variety of downstream tasks. We here prove that feedforward models trained with objectives belonging to the commonly used InfoNCE family learn to implicitly invert the underlying generative model of the observed data. While the proofs make certain statistical assumptions about the generative model, we observe empirically that our findings hold even if these assumptions are severely violated. Our theory highlights a fundamental connection between contrastive learning, generative modeling, and nonlinear independent component analysis, thereby furthering our understanding of the learned representations as well as providing a theoretical foundation to derive more effective contrastive losses.

Exemplary Natural Images Explain CNN Activations Better than Feature Visualizations

Feature visualizations such as synthetic maximally activating images are a widely used explanation method to better understand the information processing of convolutional neural networks (CNNs). At the same time, there are concerns that these visualizations might not accurately represent CNNs' inner workings. Here, we measure how much extremely activating images help humans to predict CNN activations. Using a well-controlled psychophysical paradigm, we compare the informativeness of synthetic images (Olah et al., 2017) with a simple baseline visualization, namely exemplary natural images that also strongly activate a specific feature map. Given either synthetic or natural reference images, human participants choose which of two query images leads to strong positive activation. The experiment is designed to maximize participants' performance, and is the first to probe intermediate instead of final layer representations. We find that synthetic images indeed provide helpful information about feature map activations (82% accuracy; chance would be 50%). However, natural images-originally intended to be a baseline-outperform synthetic images by a wide margin (92% accuracy). Additionally, participants are faster and more confident for natural images, whereas subjective impressions about the interpretability of feature visualization are mixed. The higher informativeness of natural images holds across most layers, for both expert and lay participants as well as for hand- and randomly-picked feature visualizations. Even if only a single reference image is given, synthetic images provide less information than natural images (65% vs. 73%). In summary, popular synthetic images from feature visualizations are significantly less informative for assessing CNN activations than natural images. We argue that future visualization methods should improve over this simple baseline.