Identifying Interpretable Visual Features in Artificial and Biological Neural Systems

Single neurons in neural networks are often interpretable in that they represent individual, intuitively meaningful features. However, many neurons exhibit $\textit{mixed selectivity}$, i.e., they represent multiple unrelated features. A recent hypothesis proposes that features in deep networks may be represented in $\textit{superposition}$, i.e., on non-orthogonal axes by multiple neurons, since the number of possible interpretable features in natural data is generally larger than the number of neurons in a given network. Accordingly, we should be able to find meaningful directions in activation space that are not aligned with individual neurons. Here, we propose (1) an automated method for quantifying visual interpretability that is validated against a large database of human psychophysics judgments of neuron interpretability, and (2) an approach for finding meaningful directions in network activation space. We leverage these methods to discover directions in convolutional neural networks that are more intuitively meaningful than individual neurons, as we confirm and investigate in a series of analyses. Moreover, we apply the same method to three recent datasets of visual neural responses in the brain and find that our conclusions largely transfer to real neural data, suggesting that superposition might be deployed by the brain. This also provides a link with disentanglement and raises fundamental questions about robust, efficient and factorized representations in both artificial and biological neural systems

Minimalistic Unsupervised Learning with the Sparse Manifold Transform

We describe a minimalistic and interpretable method for unsupervised learning, without resorting to data augmentation, hyperparameter tuning, or other engineering designs, that achieves performance close to the SOTA SSL methods. Our approach leverages the sparse manifold transform, which unifies sparse coding, manifold learning, and slow feature analysis. With a one-layer deterministic sparse manifold transform, one can achieve 99.3% KNN top-1 accuracy on MNIST, 81.1% KNN top-1 accuracy on CIFAR-10 and 53.2% on CIFAR-100. With a simple gray-scale augmentation, the model gets 83.2% KNN top-1 accuracy on CIFAR-10 and 57% on CIFAR-100. These results significantly close the gap between simplistic ``white-box'' methods and the SOTA methods. Additionally, we provide visualization to explain how an unsupervised representation transform is formed. The proposed method is closely connected to latent-embedding self-supervised methods and can be treated as the simplest form of VICReg. Though there remains a small performance gap between our simple constructive model and SOTA methods, the evidence points to this as a promising direction for achieving a principled and white-box approach to unsupervised learning

Topographic VAEs learn Equivariant Capsules

In this work we seek to bridge the concepts of topographic organization and equivariance in neural networks. To accomplish this, we introduce the Topographic VAE: a novel method for efficiently training deep generative models with topographically organized latent variables. We show that such a model indeed learns to organize its activations according to salient characteristics such as digit class, width, and style on MNIST. Furthermore, through topographic organization over time (i.e. temporal coherence), we demonstrate how predefined latent space transformation operators can be encouraged for observed transformed input sequences -- a primitive form of unsupervised learned equivariance. We demonstrate that this model successfully learns sets of approximately equivariant features (i.e. "capsules") directly from sequences and achieves higher likelihood on correspondingly transforming test sequences. Equivariance is verified quantitatively by measuring the approximate commutativity of the inference network and the sequence transformations. Finally, we demonstrate approximate equivariance to complex transformations, expanding upon the capabilities of existing group equivariant neural networks

Causal Triplet: An Open Challenge for Intervention-centric Causal Representation Learning

Recent years have seen a surge of interest in learning high-level causal representations from low-level image pairs under interventions. Yet, existing efforts are largely limited to simple synthetic settings that are far away from real-world problems. In this paper, we present Causal Triplet, a causal representation learning benchmark featuring not only visually more complex scenes, but also two crucial desiderata commonly overlooked in previous works: (i) an actionable counterfactual setting, where only certain object-level variables allow for counterfactual observations whereas others do not; (ii) an interventional downstream task with an emphasis on out-of-distribution robustness from the independent causal mechanisms principle. Through extensive experiments, we find that models built with the knowledge of disentangled or object-centric representations significantly outperform their distributed counterparts. However, recent causal representation learning methods still struggle to identify such latent structures, indicating substantial challenges and opportunities for future work. Our code and datasets will be available at https://sites.google.com/view/causaltriplet.Comment: Conference on Causal Learning and Reasoning (CLeaR) 202

Nonlinear Independent Component Analysis for Principled Disentanglement in Unsupervised Deep Learning

A central problem in unsupervised deep learning is how to find useful representations of high-dimensional data, sometimes called "disentanglement". Most approaches are heuristic and lack a proper theoretical foundation. In linear representation learning, independent component analysis (ICA) has been successful in many applications areas, and it is principled, i.e. based on a well-defined probabilistic model. However, extension of ICA to the nonlinear case has been problematic due to the lack of identifiability, i.e. uniqueness of the representation. Recently, nonlinear extensions that utilize temporal structure or some auxiliary information have been proposed. Such models are in fact identifiable, and consequently, an increasing number of algorithms have been developed. In particular, some self-supervised algorithms can be shown to estimate nonlinear ICA, even though they have initially been proposed from heuristic perspectives. This paper reviews the state-of-the-art of nonlinear ICA theory and algorithms

Selected Inductive Biases in Neural Networks To Generalize Beyond the Training Domain

Die künstlichen neuronalen Netze des computergesteuerten Sehens können mit den vielf\"altigen Fähigkeiten des menschlichen Sehens noch lange nicht mithalten. Im Gegensatz zum Menschen können künstliche neuronale Netze durch kaum wahrnehmbare Störungen durcheinandergebracht werden, es mangelt ihnen an Generalisierungsfähigkeiten über ihre Trainingsdaten hinaus und sie benötigen meist noch enorme Datenmengen für das Erlernen neuer Aufgaben. Somit sind auf neuronalen Netzen basierende Anwendungen häufig auf kleine Bereiche oder kontrollierte Umgebungen beschränkt und lassen sich schlecht auf andere Aufgaben übertragen. In dieser Dissertation, werden vier Veröffentlichungen besprochen, die sich mit diesen Einschränkungen auseinandersetzen und Algorithmen im Bereich des visuellen Repräsentationslernens weiterentwickeln. In der ersten Veröffentlichung befassen wir uns mit dem Erlernen der unabhängigen Faktoren, die zum Beispiel eine Szenerie beschreiben. Im Gegensatz zu vorherigen Arbeiten in diesem Forschungsfeld verwenden wir hierbei jedoch weniger künstliche, sondern natürlichere Datensätze. Dabei beobachten wir, dass die zeitlichen Änderungen von Szenerien beschreibenden, natürlichen Faktoren (z.B. die Positionen von Personen in einer Fußgängerzone) einer verallgemeinerten Laplace-Verteilung folgen. Wir nutzen die verallgemeinerte Laplace-Verteilung als schwaches Lernsignal, um neuronale Netze für mathematisch beweisbares Repräsentationslernen unabhängiger Faktoren zu trainieren. Wir erzielen in den disentanglement_lib Wettbewerbsdatensätzen vergleichbare oder bessere Ergebnisse als vorherige Arbeiten – dies gilt auch für die von uns beigesteuerten Datensätze, welche natürliche Faktoren beinhalten. Die zweite Veröffentlichung untersucht, ob verschiedene neuronale Netze bereits beobachtete, eine Szenerie beschreibende Faktoren generalisieren können. In den meisten bisherigen Generalisierungswettbewerben werden erst während der Testphase neue Störungsfaktoren hinzugefügt - wir hingegen garantieren, dass die für die Testphase relevanten Variationsfaktoren bereits während der Trainingsphase teilweise vorkommen. Wir stellen fest, dass die getesteten neuronalen Netze meist Schwierigkeiten haben, die beschreibenden Faktoren zu generalisieren. Anstatt die richtigen Werte der Faktoren zu bestimmen, neigen die Netze dazu, Werte in zuvor beobachteten Bereichen vorherzusagen. Dieses Verhalten ist bei allen untersuchten neuronalen Netzen recht ähnlich. Trotz ihrer begrenzten Generalisierungsfähigkeiten, können die Modelle jedoch modular sein: Obwohl sich einige Faktoren während der Trainingsphase in einem zuvor ungesehenen Wertebereich befinden, können andere Faktoren aus einem bereits bekannten Wertebereich größtenteils dennoch korrekt bestimmt werden. Die dritte Veröffentlichung präsentiert ein adversielles Trainingsverfahren für neuronale Netze. Das Verfahren ist inspiriert durch lokale Korrelationsstrukturen häufiger Bildartefakte, die z.B. durch Regen, Unschärfe oder Rauschen entstehen können. Im Klassifizierungswettbewerb ImageNet-C zeigen wir, dass mit unserer Methode trainierte Netzwerke weniger anfällig für häufige Störungen sind als einige, die mit bestehenden Methoden trainiert wurden. Schließlich stellt die vierte Veröffentlichung einen generativen Ansatz vor, der bestehende Ansätze gemäß mehrerer Robustheitsmetriken beim MNIST Ziffernklassifizierungswettbewerb übertrifft. Perzeptiv scheint unser generatives Modell im Vergleich zu früheren Ansätzen stärker auf das menschliche Sehen abgestimmt zu sein, da Bilder von Ziffern, die für unser generatives Modell mehrdeutig sind, auch für den Menschen mehrdeutig erscheinen können. Diese Arbeit liefert also Möglichkeiten zur Verbesserung der adversiellen Robustheit und der Störungstoleranz sowie Erweiterungen im Bereich des visuellen Repräsentationslernens. Somit nähern wir uns im Bereich des maschinellen Lernens weiter der Vielfalt menschlicher Fähigkeiten an.Artificial neural networks in computer vision have yet to approach the broad performance of human vision. Unlike humans, artificial networks can be derailed by almost imperceptible perturbations, lack strong generalization capabilities beyond the training data and still mostly require enormous amounts of data to learn novel tasks. Thus, current applications based on neural networks are often limited to a narrow range of controlled environments and do not transfer well across tasks. This thesis presents four publications that address these limitations and advance visual representation learning algorithms. In the first publication, we aim to push the field of disentangled representation learning towards more realistic settings. We observe that natural factors of variation describing scenes, e.g., the position of pedestrians, have temporally sparse transitions in videos. We leverage this sparseness as a weak form of learning signal to train neural networks for provable disentangled visual representation learning. We achieve competitive results on the disentanglement_lib benchmark datasets and our own contributed datasets, which include natural transitions. The second publication investigates whether various visual representation learning approaches generalize along partially observed factors of variation. In contrast to prior robustness benchmarks that add unseen types of perturbations during test time, we compose, interpolate, or extrapolate the factors observed during training. We find that the tested models mostly struggle to generalize to our proposed benchmark. Instead of predicting the correct factors, models tend to predict values in previously observed ranges. This behavior is quite common across models. Despite their limited out-of-distribution performances, the models can be fairly modular as, even though some factors are out-of-distribution, other in-distribution factors are still mostly inferred correctly. The third publication presents an adversarial noise training method for neural networks inspired by the local correlation structure of common corruptions caused by rain, blur, or noise. On the ImageNet-C classification benchmark, we show that networks trained with our method are less susceptible to common corruptions than those trained with existing methods. Finally, the fourth publication introduces a generative approach that outperforms existing approaches according to multiple robustness metrics on the MNIST digit classification benchmark. Perceptually, our generative model is more aligned with human vision compared to previous approaches, as images of digits at our model's decision boundary can also appear ambiguous to humans. In a nutshell, this work investigates ways of improving adversarial and corruption robustness, and disentanglement in visual representation learning algorithms. Thus, we alleviate some limitations in machine learning and narrow the gap towards human capabilities

On the Transfer of Disentangled Representations in Realistic Settings

Learning meaningful representations that disentangle the underlying structure of the data generating process is considered to be of key importance in machine learning. While disentangled representations were found to be useful for diverse tasks such as abstract reasoning and fair classification, their scalability and real-world impact remain questionable. We introduce a new high-resolution dataset with 1M simulated images and over 1,800 annotated real-world images of the same setup. In contrast to previous work, this new dataset exhibits correlations, a complex underlying structure, and allows to evaluate transfer to unseen simulated and real-world settings where the encoder i) remains in distribution or ii) is out of distribution. We propose new architectures in order to scale disentangled representation learning to realistic high-resolution settings and conduct a large-scale empirical study of disentangled representations on this dataset. We observe that disentanglement is a good predictor for out-of-distribution (OOD) task performance.Comment: Published at ICLR 202