Self-supervised learning (SSL) excels at finding general-purpose latent representations from complex data, yet lacks a unifying theoretical framework that explains the diverse existing methods and guides the design of new ones. We cast SSL as latent distribution matching (LDM): learning representations that maximize their log-probability under an assumed latent model (alignment), while maximizing latent entropy to prevent collapse (uniformity). This view unifies independent component analysis with contrastive, non-contrastive, and predictive SSL methods, including stop gradient approaches. Leveraging LDM, we derive a nonlinear, sampling-free Bayesian filtering model with a Kalman-based predictor for high-dimensional timeseries. We further prove that predictive LDM yields identifiable latent representations under mild assumptions, even with nonlinear predictors. Overall, LDM clarifies the assumptions behind established SSL methods and provides principled guidance for developing new approaches.

Self-supervised learning (SSL) methods aim to exploit the abundance of unlabelled data for machine learning (ML), however the underlying principles are often method-specific. An SSL framework derived from biological first principles of embodied learning could unify the various SSL methods, help elucidate learning in the brain, and possibly improve ML. SSL commonly transforms each training datapoint into a pair of views, uses the knowledge of this pairing as a positive (i.e.

L.1 Source Dataset: ImageNet Table 13 and Table 14 describe 5-way 1-shot and 5-way 5-shot CD-FSL performance when ImageNet is used as the source dataset, respectively. Note that Table 14 is added for convenience and this is the same with Table 3 in the main paper.

Data assimilation is the process of estimating the time-evolving state of a dynamical system by integrating model predictions and noisy observations. It is commonly formulated as Bayesian filtering, but classical filters often struggle with accuracy or computational feasibility in high dimensions. Recently, score-based generative models have emerged as a scalable approach for high-dimensional data assimilation, enabling accurate modeling and sampling of complex distributions. However, existing score-based filters often specify the forward process independently of the data assimilation. As a result, the measurement-update step depends on heuristic approximations of the likelihood score, which can accumulate errors and degrade performance over time. Here, we propose a measurement-aware score-based filter (MASF) that defines a measurement-aware forward process directly from the measurement equation. This construction makes the likelihood score analytically tractable: for linear measurements, we derive the exact likelihood score and combine it with a learned prior score to obtain the posterior score. Numerical experiments covering a range of settings, including high-dimensional datasets, demonstrate improved accuracy and stability over existing score-based filters.

High demand for computation resources severely hinders deployment of large-scale Deep Neural Networks (DNN) in resource constrained devices. In this work, we propose a Structured Sparsity Learning (SSL) method to regularize the structures (i.e., filters, channels, filter shapes, and layer depth) of DNNs. SSL can: (1) learn a compact structure from a bigger DNN to reduce computation cost; (2) obtain a hardware-friendly structured sparsity of DNN to efficiently accelerate the DNN's evaluation. Experimental results show that SSL achieves on average 5.1 and 3.1 speedups of convolutional layer computation of AlexNet against CPU and GPU, respectively, with off-the-shelf libraries. These speedups are about twice speedups of non-structured sparsity; (3) regularize the DNN structure to improve classification accuracy. The results show that for CIFAR-10, regularization on layer depth reduces a 20-layer Deep Residual Network (ResNet) to 18 layers while improves the accuracy from 91.25% to 92.60%, which is still higher than that of original ResNet with 32 layers. For AlexNet, SSL reduces the error by 1%.

The premise of semi-supervised learning (SSL) is that combining labeled and unlabeled data yields significantly more accurate models.Despite empirical successes, the theoretical understanding of SSL is still far from complete. In this work, we study SSL for high dimensional sparse Gaussian classification. To construct an accurate classifier a key task is feature selection, detecting the few variables that separate the two classes.For this SSL setting, we analyze information theoretic lower bounds for accurate feature selection as well as computational lower bounds, assuming the low-degree likelihood hardness conjecture. Our key contribution is the identification of a regime in the problem parameters (dimension, sparsity, number of labeled and unlabeled samples) where SSL is guaranteed to be advantageous for classification.Specifically, there is a regime where it is possible to construct in polynomial time an accurate SSL classifier.However, any computationally efficient supervised or unsupervised learning schemes, that separately use only the labeled or unlabeled data would fail. Our work highlights the provable benefits of combining labeled and unlabeled data for classification and feature selection in high dimensions. We present simulations that complement our theoretical analysis.