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Register a new userToward Understanding the Feature Learning Process of Self-supervised Contrastive Learning
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Added by
Zixin Wen
Publication date
2021
fields
Informatics Engineering
and research's language is
English
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How can neural networks trained by contrastive learning extract features from the unlabeled data? Why does contrastive learning usually need much stronger data augmentations than supervised learning to ensure good representations? These questions involve both the optimization and statistical aspects of deep learning, but can hardly be answered by analyzing supervised learning, where the target functions are the highest pursuit. Indeed, in self-supervised learning, it is inevitable to relate to the optimization/generalization of neural networks to how they can encode the latent structures in the data, which we refer to as the feature learning process. In this work, we formally study how contrastive learning learns the feature representations for neural networks by analyzing its feature learning process. We consider the case where our data are comprised of two types of features: the more semantically aligned sparse features which we want to learn from, and the other dense features we want to avoid. Theoretically, we prove that contrastive learning using $mathbf{ReLU}$ networks provably learns the desired sparse features if proper augmentations are adopted. We present an underlying principle called $textbf{feature decoupling}$ to explain the effects of augmentations, where we theoretically characterize how augmentations can reduce the correlations of dense features between positive samples while keeping the correlations of sparse features intact, thereby forcing the neural networks to learn from the self-supervision of sparse features. Empirically, we verified that the feature decoupling principle matches the underlying mechanism of contrastive learning in practice.
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Contrastive learning applied to self-supervised representation learning has seen a resurgence in recent years, leading to state of the art performance in the unsupervised training of deep image models. Modern batch contrastive approaches subsume or significantly outperform traditional contrastive losses such as triplet, max-margin and the N-pairs loss. In this work, we extend the self-supervised batch contrastive approach to the fully-supervised setting, allowing us to effectively leverage label information. Clusters of points belonging to the same class are pulled together in embedding space, while simultaneously pushing apart clusters of samples from different classes. We analyze two possib
While contrastive approaches of self-supervised learning (SSL) learn representations by minimizing the distance between two augmented views of the same data point (positive pairs) and maximizing views from different data points (negative pairs), recent emph{non-contrastive} SSL (e.g., BYOL and SimSiam) show remarkable performance {it without} negative pairs, with an extra learnable predictor and a stop-gradient operation. A fundamental question arises: why do these methods not collapse into trivial representations? We answer this question via a simple theoretical study and propose a novel approach, DirectPred, that emph{directly} sets the linear predictor based on the statistics of its inputs, without gradient training. On ImageNet, it performs comparably with more complex two-layer non-linear predictors that employ BatchNorm and outperforms a linear predictor by $2.5%$ in 300-epoch training (and $5%$ in 60-epoch). DirectPred is motivated by our theoretical study of the nonlinear learning dynamics of non-contrastive SSL in simple linear networks. Our study yields conceptual insights into how non-contrastive SSL methods learn, how they avoid representational collapse, and how multiple factors, like predictor networks, stop-gradients, exponential moving averages, and weight decay all come into play. Our simple theory recapitulates the results of real-world ablation studies in both STL-10 and ImageNet. Code is released https://github.com/facebookresearch/luckmatters/tree/master/ssl.
Machine learning analysis of longitudinal neuroimaging data is typically based on supervised learning, which requires a large number of ground-truth labels to be informative. As ground-truth labels are often missing or expensive to obtain in neuroscience, we avoid them in our analysis by combing factor disentanglement with self-supervised learning to identify changes and consistencies across the multiple MRIs acquired of each individual over time. Specifically, we propose a new definition of disentanglement by formulating a multivariate mapping between factors (e.g., brain age) associated with an MRI and a latent image representation. Then, factors that evolve across acquisitions of longitudinal sequences are disentangled from that mapping by self-supervised learning in such a way that changes in a single factor induce change along one direction in the representation space. We implement this model, named Longitudinal Self-Supervised Learning (LSSL), via a standard autoencoding structure with a cosine loss to disentangle brain age from the image representation. We apply LSSL to two longitudinal neuroimaging studies to highlight its strength in extracting the brain-age information from MRI and revealing informative characteristics associated with neurodegenerative and neuropsychological disorders. Moreover, the representations learned by LSSL facilitate supervised classification by recording faster convergence and higher (or similar) prediction accuracy compared to several other representation learning techniques.
We propose a novel theoretical framework to understand contrastive self-supervised learning (SSL) methods that employ dual pairs of deep ReLU networks (e.g., SimCLR). First, we prove that in each SGD update of SimCLR with various loss functions, including simple contrastive loss, soft Triplet loss and InfoNCE loss, the weights at each layer are updated by a emph{covariance operator} that specifically amplifies initial random selectivities that vary across data samples but survive averages over data augmentations. To further study what role the covariance operator plays and which features are learned in such a process, we model data generation and augmentation processes through a emph{hierarchical latent tree model} (HLTM) and prove that the hidden neurons of deep ReLU networks can learn the latent variables in HLTM, despite the fact that the network receives emph{no direct supervision} from these unobserved latent variables. This leads to a provable emergence of hierarchical features through the amplification of initially random selectivities through contrastive SSL. Extensive numerical studies justify our theoretical findings. Code is released in https://github.com/facebookresearch/luckmatters/tree/master/ssl.
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.
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