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Machine learning models of vastly different modalities and architectures are being trained to predict the behavior of molecules, materials, and proteins. However, it remains unclear whether they learn similar internal representations of…

High-throughput computational materials design promises to greatly accelerate the process of discovering new materials and compounds, and of optimizing their properties. The large databases of structures and properties that result from…

This paper presents a method for uncovering hidden analytic relationships among the fundamental parameters of the Standard Model (SM), a foundational theory in physics that describes the fundamental particles and their interactions, using…

Machine learning has proven to be a valuable tool to approximate functions in high-dimensional spaces. Unfortunately, analysis of these models to extract the relevant physics is never as easy as applying machine learning to a large dataset…

Robustness is key to engineering, automation, and science as a whole. However, the property of robustness is often underpinned by costly requirements such as over-provisioning, known uncertainty and predictive models, and known adversaries.…

Turing theory of pattern formation is among the most popular theoretical means to account for the variety of spatio-temporal structures observed in Nature and, for this reason, finds applications in many different fields. While Turing…

Large language model (LLM)-driven agents are emerging as a powerful new paradigm for solving complex problems. Despite the empirical success of these practices, a theoretical framework to understand and unify their macroscopic dynamics…

Effectively learning from sequential data is a longstanding goal of Artificial Intelligence, especially in the case of long sequences. From the dawn of Machine Learning, several researchers have pursued algorithms and architectures capable…

Many state-of-the-art algorithms for solving hard combinatorial problems in artificial intelligence (AI) include elements of stochasticity that lead to high variations in runtime, even for a fixed problem instance. Knowledge about the…

Overparametrization has become a de facto standard in machine learning. Despite numerous efforts, our understanding of how and where overparametrization helps model accuracy and robustness is still limited. To this end, here we conduct an…

We propose to employ the hierarchical coarse-grained structure in the artificial neural networks explicitly to improve the interpretability without degrading performance. The idea has been applied in two situations. One is a neural network…

An algorithm that learns from a set of examples should ideally be able to exploit the available resources of (a) abundant computing power and (b) domain-specific knowledge to improve its ability to generalize. Connectionist…

In the research area of anomaly detection, novel and promising methods are frequently developed. However, most existing studies exclusively focus on the detection task only and ignore the interpretability of the underlying models as well as…

Relational reasoning is the ability to infer relations that jointly bind multiple entities, attributes, or variables. This ability is central to scientific reasoning, but existing evaluations of relational reasoning in large language models…

To understand the emergence of macroscopic irreversibility from microscopic reversible dynamics, the idea of coarse-graining plays a fundamental role. In this work, we develop a unified inferential framework for macroscopic states, that is,…

Spatio-temporal patterns emerging from an initial quiescent, uniform state is a phenomenon observed in many dynamical systems sustained far from thermodynamic equilibrium, the practical application of which has only recently begun to be…

Quantifying emergence and modeling emergent dynamics in a data-driven manner for complex dynamical systems is challenging due to the lack of direct observations at the micro-level. Thus, it's crucial to develop a framework to identify…

One of the most influential results in neural network theory is the universal approximation theorem [1, 2, 3] which states that continuous functions can be approximated to within arbitrary accuracy by single-hidden-layer feedforward neural…

In pruning, the Lottery Ticket Hypothesis posits that large networks contain sparse subnetworks, or winning tickets, that can be trained in isolation to match the performance of their dense counterparts. However, most existing approaches…

This paper studies a machine learning regression problem as a multivariate approximation problem using the framework of the theory of random functions. An ab initio derivation of a regression method is proposed, starting from postulates of…