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Recent studies have revealed that neural networks learn interpretable algorithms for many simple problems. However, little is known about how these algorithms emerge during training. In this article, I study the training dynamics of a small…
Spectral Embedding (SE) has often been used to map data points from non-linear manifolds to linear subspaces for the purpose of classification and clustering. Despite significant advantages, the subspace structure of data in the original…
Providing the neurobiological basis of information processing in higher animals, spiking neural networks must be able to learn a variety of complicated computations, including the generation of appropriate, possibly delayed reactions to…
Understanding how the brain learns to compute functions reliably, efficiently and robustly with noisy spiking activity is a fundamental challenge in neuroscience. Most sensory and motor tasks can be described as dynamical systems and could…
State-space models (SSMs) offer a powerful framework for dynamical system analysis, wherein the temporal dynamics of the system are assumed to be captured through the evolution of the latent states, which govern the values of the…
Neural forecasting of spatiotemporal time series drives both research and industrial innovation in several relevant application domains. Graph neural networks (GNNs) are often the core component of the forecasting architecture. However, in…
Understanding how network function constrains neural connectivity is a central challenge in neuroscience. An influential approach is to train neural networks with gradient descent on cognitive tasks and characterize the resulting…
Our theoretical understanding of deep learning has not kept pace with its empirical success. While network architecture is known to be critical, we do not yet understand its effect on learned representations and network behavior, or how…
Statistical learning in high-dimensional spaces is challenging without a strong underlying data structure. Recent advances with foundational models suggest that text and image data contain such hidden structures, which help mitigate the…
The integration and transmission of information in the brain are dependent on the interplay between structural and dynamical properties. Implicit in any pursuit aimed at understanding neural dynamics from appropriate sets of mathematically…
While the deployment of deep learning models on edge devices is increasing, these models often lack robustness when faced with dynamic changes in sensed data. This can be attributed to sensor drift, or variations in the data compared to…
A powerful and flexible approach to structured prediction consists in embedding the structured objects to be predicted into a feature space of possibly infinite dimension by means of output kernels, and then, solving a regression problem in…
Networks of model neurons with balanced recurrent excitation and inhibition produce irregular and asynchronous spiking activity. We extend the analysis of balanced networks to include the known dependence of connection probability on the…
Spiking neural networks (SNNs) are biologically inspired energy-efficient models that use sparse binary spike-based communication between neurons, making them attractive for resource-constrained edge devices. Federated learning enables such…
We propose a method for efficiently incorporating constraints into a stochastic gradient Langevin framework for the training of deep neural networks. Constraints allow direct control of the parameter space of the model. Appropriately…
Deep neural networks can be trained in reciprocal space, by acting on the eigenvalues and eigenvectors of suitable transfer operators in direct space. Adjusting the eigenvalues, while freezing the eigenvectors, yields a substantial…
Structural modularity is a pervasive feature of biological neural networks, which have been linked to several functional and computational advantages. Yet, the use of modular architectures in artificial neural networks has been relatively…
Deep neural networks represent a powerful class of function approximators that can learn to compress and reconstruct images. Existing image compression algorithms based on neural networks learn quantized representations with a constant…
Many applications, such as optimization, uncertainty quantification and inverse problems, require repeatedly performing simulations of large-dimensional physical systems for different choices of parameters. This can be prohibitively…
Understanding the operation of biological and artificial networks remains a difficult and important challenge. To identify general principles, researchers are increasingly interested in surveying large collections of networks that are…