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Understanding the neural implementation of complex human behaviors is one of the major goals in neuroscience. To this end, it is crucial to find a true representation of the neural data, which is challenging due to the high complexity of…
This work presents a novel means for understanding learning dynamics and scaling relations in neural networks. We show that certain measures on the spectrum of the empirical neural tangent kernel, specifically entropy and trace, yield…
Data-driven modeling in mechanics is evolving rapidly based on recent machine learning advances, especially on artificial neural networks. As the field matures, new data and models created by different groups become available, opening…
On a variety of tasks, the performance of neural networks predictably improves with training time, dataset size and model size across many orders of magnitude. This phenomenon is known as a neural scaling law. Of fundamental importance is…
Discrete-time modeling of acoustic, mechanical and electrical systems is a prominent topic in the musical signal processing literature. Such models are mostly derived by discretizing a mathematical model, given in terms of ordinary or…
We develop a learning-based algorithm for the distributed formation control of networked multi-agent systems governed by unknown, nonlinear dynamics. Most existing algorithms either assume certain parametric forms for the unknown dynamic…
Accurately modeling robot dynamics is crucial to safe and efficient motion control. In this paper, we develop and apply an iterative learning semi-parametric model, with a neural network, to the task of autonomous racing with a Model…
Discretizing spacetime is often a natural step towards modelling physical systems. For quantum systems, if we also demand a strict bound on the speed of information propagation, we get quantum cellular automata (QCAs). These originally…
The generation of sustained, open-ended complexity from local interactions remains a fundamental challenge in artificial life. Differentiable multi-agent systems, such as Petri Dish Neural Cellular Automata (PD-NCA), exhibit rich…
Human actions captured in video sequences contain two crucial factors for action recognition, i.e., visual appearance and motion dynamics. To model these two aspects, Convolutional and Recurrent Neural Networks (CNNs and RNNs) are adopted…
We propose NECA, a deep representation learning method for categorical data. Built upon the foundations of network embedding and deep unsupervised representation learning, NECA deeply embeds the intrinsic relationship among attribute values…
We say that a Cellular Automata (CA) is coalescing when its execution on two distinct (random) initial configurations in the same asynchronous mode (the same cells are updated in each configuration at each time step) makes both…
How can we tell whether two neural networks utilize the same internal processes for a particular computation? This question is pertinent for multiple subfields of neuroscience and machine learning, including neuroAI, mechanistic…
Cell biomechanics involve a great number of complex phenomena that are fundamental to the evolution of life itself and other associated processes, ranging from the very early stages of embryo-genesis to the maintenance of damaged structures…
Topological dynamics of cellular automata (CA), inherited from classical dynamical systems theory, has been essentially studied in dimension 1. This paper focuses on higher dimensional CA and aims at showing that the situation is different…
Given that observational and numerical climate data are being produced at ever more prodigious rates, increasingly sophisticated and automated analysis techniques have become essential. Deep learning is quickly becoming a standard approach…
Large Language Models demonstrate remarkable mathematical capabilities but at the same time struggle with abstract reasoning and planning. In this study, we explore whether Transformers can learn to abstract and generalize the rules…
Artificial neural networks (ANNs) exhibit a narrow scope of expertise on stationary independent data. However, the data in the real world is continuous and dynamic, and ANNs must adapt to novel scenarios while also retaining the learned…
Cellular automata (CA) have been found as an attractive modeling tool for various applications, such as, pattern recognition, image processing, data compression, encryption, and specially for VLSI design & test. For such applications,…
The ability to predict future events or patterns based on previous experience is crucial for many applications such as traffic control, weather forecasting, or supply chain management. While modern supervised Machine Learning approaches…