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.

Get rich quick: exact solutions reveal how unbalanced initializations promote rapid feature learning

While the impressive performance of modern neural networks is often attributed to their capacity to efficiently extract task-relevant features from data, the mechanisms underlying this rich feature learning regime remain elusive, with much of our theoretical understanding stemming from the opposing lazy regime. In this work, we derive exact solutions to a minimal model that transitions between lazy and rich learning, precisely elucidating how unbalanced layer-specific initialization variances and learning rates determine the degree of feature learning. Our analysis reveals that they conspire to influence the learning regime through a set of conserved quantities that constrain and modify the geometry of learning trajectories in parameter and function space. We extend our analysis to more complex linear models with multiple neurons, outputs, and layers and to shallow nonlinear networks with piecewise linear activation functions. In linear networks, rapid feature learning only occurs with balanced initializations, where all layers learn at similar speeds. While in nonlinear networks, unbalanced initializations that promote faster learning in earlier layers can accelerate rich learning. Through a series of experiments, we provide evidence that this unbalanced rich regime drives feature learning in deep finite-width networks, promotes interpretability of early layers in CNNs, reduces the sample complexity of learning hierarchical data, and decreases the time to grokking in modular arithmetic. Our theory motivates further exploration of unbalanced initializations to enhance efficient feature learning.

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.

Towards Nonlinear Disentanglement in Natural Data with Temporal Sparse Coding

We construct an unsupervised learning model that achieves nonlinear disentanglement of underlying factors of variation in naturalistic videos. Previous work suggests that representations can be disentangled if all but a few factors in the environment stay constant at any point in time. As a result, algorithms proposed for this problem have only been tested on carefully constructed datasets with this exact property, leaving it unclear whether they will transfer to natural scenes. Here we provide evidence that objects in segmented natural movies undergo transitions that are typically small in magnitude with occasional large jumps, which is characteristic of a temporally sparse distribution. We leverage this finding and present SlowVAE, a model for unsupervised representation learning that uses a sparse prior on temporally adjacent observations to disentangle generative factors without any assumptions on the number of changing factors. We provide a proof of identifiability and show that the model reliably learns disentangled representations on several established benchmark datasets, often surpassing the current state-of-the-art. We additionally demonstrate transferability towards video datasets with natural dynamics, Natural Sprites and KITTI Masks, which we contribute as benchmarks for guiding disentanglement research towards more natural data domains.