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While state-of-the-art contrastive Self-Supervised Learning (SSL) models produce results competitive with their supervised counterparts, they lack the ability to infer latent variables. In contrast, prescribed latent variable (LV) models…
Long-tailed semi-supervised learning poses a significant challenge in training models with limited labeled data exhibiting a long-tailed label distribution. Current state-of-the-art LTSSL approaches heavily rely on high-quality…
We consider a noninteracting disordered system designed to model particle diffusion, relaxation in glasses, and impurity bands of semiconductors. Disorder originates in the random spatial distribution of sites. We find strong numerical…
In the present work we explore the potential of models of the discrete nonlinear Schr\"odinger (DNLS) type to support spatially localized and temporally quasiperiodic solutions on top of a finite background. Such solutions are rigorously…
Self-supervised learning (SSL) approaches have brought tremendous success across many tasks and domains. It has been argued that these successes can be attributed to a link between SSL and identifiable representation learning: Temporal…
A simple and natural introduction to the concept and formalism of spontaneous wave function collapse can and should be based on textbook knowledge of standard quantum state collapse and monitoring. This approach explains the origin of noise…
We study a recently proposed modified Schr\"{o}dinger equation having an added nonlinear term, which gives rise to disentanglement. The process of quantum measurement is explored for the case of a pair of coupled spins. We find that the…
In this work we review the theory of the spherical collapse model and critically analyse the aspects of the numerical implementation of its fundamental equations. By extending a recent work by Herrera et al. 2017, we show how different…
Recent successes in self-supervised learning (SSL) model spatial co-occurrences of visual features either by masking portions of an image or by aggressively cropping it. Here, we propose a new way to model spatial co-occurrences by aligning…
We design and analyse a semi-implicit finite volume scheme for the two-dimensional rotating shallow water (RSW) equations that is energy stable, well-balanced (capable of preserving discrete geostrophic steady states), consistent, and…
Supervised-contrastive loss (SCL) is an alternative to cross-entropy (CE) for classification tasks that makes use of similarities in the embedding space to allow for richer representations. In this work, we propose methods to engineer the…
Self-Supervised Learning (SSL) is an important paradigm for learning representations from unlabelled data, and SSL with neural networks has been highly successful in practice. However current theoretical analysis of SSL is mostly restricted…
Why do we never see a table in a superposition of here and there? This problem gets a solution by so called collapse models assuming the collapse as a genuinely physical process. Here we consider two specific collapse models and apply them…
Compressive sensing (CS) is a mathematically elegant tool for reducing the sampling rate, potentially bringing context-awareness to a wider range of devices. Nevertheless, practical issues with the sampling and reconstruction algorithms…
Diffusion models have become the dominant paradigm in text-to-image generation, and test-time scaling (TTS) improves sample quality by allocating additional computation at inference. Existing TTS methods, however, resample the entire image,…
We analyze a class of linear shell models subject to stochastic forcing in finitely many degrees of freedom. The unforced systems considered formally conserve energy. Despite being formally conservative, we show that these dynamical systems…
Last couple of years have witnessed a tremendous progress in self-supervised learning (SSL), the success of which can be attributed to the introduction of useful inductive biases in the learning process to learn meaningful visual…
In recent years, the introduction of self-supervised contrastive learning (SSCL) has demonstrated remarkable improvements in representation learning across various domains, including natural language processing and computer vision. By…
Efficient continual learning techniques have been a topic of significant research over the last few years. A fundamental problem with such learning is severe degradation of performance on previously learned tasks, known also as catastrophic…
Despite its empirical success, the theoretical foundations of self-supervised contrastive learning (CL) are not yet fully established. In this work, we address this gap by showing that standard CL objectives implicitly approximate a…