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Many problems in statistics and machine learning require the reconstruction of a rank-one signal matrix from noisy data. Enforcing additional prior information on the rank-one component is often key to guaranteeing good recovery…
We achieved a new milestone in the difficult task of enabling agents to learn about their environment autonomously. Our neuro-symbolic architecture is trained end-to-end to produce a succinct and effective discrete state transition model…
We consider the solution of saddle-point systems with a tree-based block structure, introducing a parallelizable direct method for their solution. As our key contribution, we then propose several structure-exploiting preconditioners to be…
Symbolic regression aims to discover human-interpretable equations that explain observational data. However, existing approaches rely heavily on discrete structure search (e.g., genetic programming), which often leads to high computational…
Problems arising in Earth's mantle convection involve finding the solution to Stokes systems with large viscosity contrasts. These systems contain localized features which, even with adaptive mesh refinement, result in linear systems that…
A long-term research proposal on the algebraic structure, the representations and the possible applications of paraparticle algebras is structured in three modules: The first part stems from an attempt to classify the inequivalent gradings…
We present the COGnitive Neural GENerative system (CogNGen), a cognitive architecture that combines two neurobiologically-plausible, computational models: predictive processing and hyperdimensional/vector-symbolic models. We draw…
We study the class structure of finite-alphabet Markov chains with arbitrary memory length. To capture the structural constraints induced by prohibited transitions, we introduce the skeleton of a higher-order transition kernel, defined as a…
Motivated by the remarkable success of Bayesian additive regression trees (BART) in regression modelling, we propose a novel nonparametric Bayesian method, termed Functional BART (FBART), tailored specifically for function-on-scalar…
Despite deep learning models running well-defined mathematical functions, we lack a formal mathematical framework for describing model architectures. Ad-hoc notation, diagrams, and pseudocode poorly handle nonlinear broadcasting and the…
Previous mechanical meta-structures used for mechanical memory storage, computing and information processing are severely constrained by low information density and/or non-robust structural stiffness to stably protect the maintained…
Retrieval-Augmented Generation (RAG) helps large language models (LLMs) answer knowledge-intensive and time-sensitive questions by conditioning generation on external evidence. However, most RAG systems still retrieve unstructured chunks…
This paper presents a comprehensive cross-platform evaluation of reasoning capabilities in contemporary foundation models, establishing an infrastructure-agnostic benchmark across three computational paradigms: HPC supercomputing…
Regression is essential across many domains but remains challenging in high-dimensional settings, where existing methods often lose spatial structure or demand heavy storage. In this work, we address the problem of matrix-valued regression,…
Establishing stable mappings between natural language expressions and visual percepts is a foundational problem for both cognitive science and artificial intelligence. Humans routinely ground linguistic reference in noisy, ambiguous…
Efficient spatial indexing is crucial for processing large-scale spatial data. Traditional spatial indexes, such as STR-Tree and Quad-Tree, organize spatial objects based on coarse approximations, such as their minimum bounding rectangles…
Retrieval-augmented generation (RAG) enhances large language models with external knowledge, and tree-based RAG organizes documents into hierarchical indexes to support queries at multiple granularities. However, existing Tree-RAG methods…
Recent years have seen dramatic progress in the development of techniques for measuring the activity and connectivity of large populations of neurons in the brain. However, as these techniques grow ever more powerful---allowing us to even…
Genetic circuit design remains a laborious, expert-driven process despite decades of progress in synthetic biology. We study this problem through code generation: models produce Python code in pysbol3 to construct genetic circuits in the…
Learning precise surrogate models of complex computer simulations and physical machines often require long-lasting or expensive experiments. Furthermore, the modeled physical dependencies exhibit nonlinear and nonstationary behavior.…