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Function encoders are a recent technique that learn neural network basis functions to form compact, adaptive representations of Hilbert spaces of functions. We show that function encoders provide a principled connection to feature learning…

Machine Learning · Computer Science 2025-09-26 Su Ann Low , Quentin Rommel , Kevin S. Miller , Adam J. Thorpe , Ufuk Topcu

A total set of states for which we have no resolution of the identity (a `pre-basis'), is considered in a finite dimensional Hilbert space. A dressing formalism renormalizes them into density matrices which resolve the identity, and makes…

Mathematical Physics · Physics 2017-08-30 A. Vourdas

We introduce one- and two-dimensional `exponential shapelets': orthonormal basis functions that efficiently model isolated features in data. They are built from eigenfunctions of the quantum mechanical hydrogen atom, and inherit mathematics…

Instrumentation and Methods for Astrophysics · Physics 2019-03-27 Joel Bergé , Richard Massey , Quentin Baghi , Pierre Touboul

Linear causal disentanglement is a recent method in causal representation learning to describe a collection of observed variables via latent variables with causal dependencies between them. It can be viewed as a generalization of both…

Machine Learning · Statistics 2024-07-08 Paula Leyes Carreno , Chiara Meroni , Anna Seigal

Attribution is crucial in question answering (QA) with Large Language Models (LLMs).SOTA question decomposition-based approaches use long form answers to generate questions for retrieving related documents. However, the generated questions…

Computation and Language · Computer Science 2025-11-17 Zhichao Yan , Jiaoyan Chen , Jiapu Wang , Xiaoli Li , Ru Li , Jeff Z. Pan

The general decomposition theory of exponential operators is briefly reviewed. A general scheme to construct independent determining equations for the relevant decomposition parameters is proposed using Lyndon words. Explicit formulas of…

Mathematical Physics · Physics 2009-12-04 Zengo Tsuboi , Masuo Suzuki

Trustworthiness of artificially intelligent agents is vital for the acceptance of human-machine teaming in industrial manufacturing environments. Predictable behaviours and explainable (and understandable) rationale allow humans…

Artificial Intelligence · Computer Science 2023-05-22 Vedran Galetić , Alistair Nottle

A universal minimal spinor set of linear differential equations describing anyons and ordinary integer and half-integer spin fields is constructed with the help of deformed Heisenberg algebra with reflection. The construction is generalized…

High Energy Physics - Theory · Physics 2010-01-05 Mikhail Plyushchay

A quantum model exhibits Hilbert space fragmentation (HSF) if its Hilbert space decomposes into exponentially many dynamically disconnected subspaces, known as Krylov subspaces. A model may however have different HSFs depending on the…

Statistical Mechanics · Physics 2026-01-05 Bo-Ting Chen , Yu-Ping Wang , Biao Lian

There are two main lines of research on visual question answering (VQA): compositional model with explicit multi-hop reasoning, and monolithic network with implicit reasoning in the latent feature space. The former excels in…

Computer Vision and Pattern Recognition · Computer Science 2020-10-13 Ruixue Tang , Chao Ma

Concept-based explanation approach is a popular model interpertability tool because it expresses the reasons for a model's predictions in terms of concepts that are meaningful for the domain experts. In this work, we study the problem of…

Machine Learning · Computer Science 2021-05-25 Mohammad Taha Bahadori , David E. Heckerman

We describe an algorithm to decompose rational functions from which we determine the poset of groups fixing these functions.

Number Theory · Mathematics 2008-08-21 John McKay , David Sevilla

Estimating causal effects from observational data (at either an individual -- or a population -- level) is critical for making many types of decisions. One approach to address this task is to learn decomposed representations of the…

Machine Learning · Computer Science 2021-11-15 Negar Hassanpour , Russell Greiner

We offer a new formalism for global explanations of pairwise feature dependencies and interactions in supervised models. Building upon SHAP values and SHAP interaction values, our approach decomposes feature contributions into synergistic,…

Machine Learning · Computer Science 2021-07-28 Jan Ittner , Lukasz Bolikowski , Konstantin Hemker , Ricardo Kennedy

Deep learning models have achieved remarkable success in different areas of machine learning over the past decade; however, the size and complexity of these models make them difficult to understand. In an effort to make them more…

Computer Vision and Pattern Recognition · Computer Science 2022-06-20 Vikram V. Ramaswamy , Sunnie S. Y. Kim , Nicole Meister , Ruth Fong , Olga Russakovsky

Nonlinear state-space modelling is a very powerful black-box modelling approach. However powerful, the resulting models tend to be complex, described by a large number of parameters. In many cases interpretability is preferred over…

Systems and Control · Electrical Eng. & Systems 2020-06-24 Jan Decuyper , Koen Tiels , Mark C. Runacres , Johan Schoukens

Question answering models struggle to generalize to novel compositions of training patterns, such to longer sequences or more complex test structures. Current end-to-end models learn a flat input embedding which can lose input syntax…

Computation and Language · Computer Science 2021-11-08 Yu Gai , Paras Jain , Wendi Zhang , Joseph E. Gonzalez , Dawn Song , Ion Stoica

In this paper, we introduce a new class of confluent hypergeometric functions of many variables, study their properties, and determine a system of partial differential equations that this function satisfies. It turns out that all the…

Analysis of PDEs · Mathematics 2019-08-21 Tuhtasin Ergashev

Mechanistic interpretability aims to explain neural model behaviour by reverse-engineering learned computational structure into human-understandable components. Without a formal framework, however, mechanistic explanations cannot be…

Machine Learning · Computer Science 2026-05-12 Ward Gauderis , Thomas Dooms , Steven T. Holmer , Kola Ayonrinde , Geraint A. Wiggins

We study generalized polar decompositions of densely defined, closed linear operators in Hilbert spaces and provide some applications to relatively (form) bounded and relatively (form) compact perturbations of self-adjoint, normal, and…

Functional Analysis · Mathematics 2008-11-11 Fritz Gesztesy , Mark Malamud , Marius Mitrea , Serguei Naboko