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Quantifying imperfect cognition via achieved information gain

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arXiv 2025年

作者： Enßlin, Torsten Max Planck Institute for Astrophysics Karl-Schwarzschild-Str. 1 Garching85748 Germany Deutsches Zentrum für Astrophysik Postplatz 1 Görlitz02826 Germany Ludwig-Maximilians-Universität München Geschwister-Scholl-Platz 1 Munich80539 Germany Excellence Cluster ORIGINS Boltzmannstr. 2 Garching85748 Germany

Cognition, the process of information processing in form of inference, communication, and memorization, is the central activity of any intelligence. Its physical realization in a brain, computer, or in any other intelligent system requires resources like time, energy, memory, bandwidth, money, and others. Due to limited resources, many real world intelligent systems perform only imperfect cognition. For understanding the trade-off between accuracy and resource investments in existing systems, e.g. in biology, as well as for the resource-aware optimal design of information processing systems, like computer algorithms and artificial neural networks, a quantification of information obtained in an imperfect cognitive operation is desirable. To this end, we propose the concept of achieved information gain (AIG) of a belief update, which is given by the amount of information obtained by updating from the initial knowledge state to the ideal one, minus the amount a change from the imperfect to the ideal state would yield. AIG has many properties desired for quantifying imperfect cognition. The ratio of achieved to ideally obtainable information measures cognitive fidelity and that of AIG to the necessary cognitive effort measures cognitive efficiency. We provide an axiomatic derivation of AIG, illustrate its application at common scenarios of posterior inaccuracies, and discuss the implication of cognitive efficiency for sustainable resource allocation in computational *** Codes 94A15 Copyright © 2025, The Authors. All rights reserved.

关键词： computation theory

You Keep Using ThatWord:Ways of Thinking about Gender in Computing Research

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Proceedings of the ACM on Human-Computer Interaction 2021年第CSCW1期5卷 1-23页

作者： Keyes, Os May, Chandler Carrell, Annabelle University of Washington 428 Sieg Hall Box 352315 SeattleWA98195-2315 United States Johns Hopkins University 3400 N. Charles Street BaltimoreMD21218 United States

CSCW researchers have long inquired into the ways that identity informs, and is informed by, the design of technological systems. Gender is a regularly considered aspect of identity, with extensive work documenting and exploring gendered experiences and designs with the aim of addressing inequalities in, or through, design. Recent work has questioned the way that we conceptualise and "measure"gender, advocating more nuanced classificatory schemes to avoid silencing or obscuring trans and/or non-binary experiences. Building on and extending this research, our work examines how gender is conceptualised more broadly. Drawing from a range of theoretical perspectives in gender studies, feminist and postcolonial theory, we argue for the treatment of gender as "multiplicitous"when we conceptualise and interpret research, in order to avoid unintentionally perpetuating silencing and inequality even as we work to tackle it. Illustrating our argument with examples from both within and without CSCW, we suggest both new research directions for CSCW scholars inquiring into gender, and sensitising questions that scholars can use when constructing and evaluating studies. © 2021 ACM.

关键词： computation theory

COMPUTING MONOMIAL BASES IN LIE theory USING OSCAR

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arXiv 2024年

作者： Fang, Xin Fourier, Ghislain Göttgens, Lars Wilop, Ben Chair of Algebra and Representation Theory RWTH Aachen University Germany

In this survey, we present a detailed guide on using the computer algebra system OSCAR to compute monomial bases for simple, finite-dimensional modules of simple, complex Lie algebras. We will also demonstrate how to determine monomial bases for the homogeneous coordinate ring of a (partial) flag variety, depending on a chosen birational sequence and a monomial order. This survey will be updated to reflect any advancements in OSCAR’s capabilities in these *** Codes 17B10, 14M25, 14D06, 14M15, 14-04, 97N80 © 2024, CC BY.

关键词： computation theory

Diffusion of Thought: Chain-of-Thought Reasoning in Diffusion Language Models

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arXiv 2024年

作者： Ye, Jiacheng Gong, Shansan Chen, Liheng Zheng, Lin Gao, Jiahui Shi, Han Wu, Chuan Jiang, Xin Li, Zhenguo Bi, Wei Kong, Lingpeng The University of Hong Kong Hong Kong Huawei Noah’s Ark Lab Canada Tencent AI Lab

Recently, diffusion models have garnered significant interest in the field of text processing due to their many potential advantages compared to conventional autoregressive models. In this work, we propose Diffusion-of-Thought (DoT), a novel approach that integrates diffusion models with Chain-of-Thought, a well-established technique for improving the reasoning ability of autoregressive language models. In contrast to autoregressive language models that make decisions in a left-to-right, token-by-token manner, DoT allows reasoning steps to diffuse over time through a diffusion language model and offers greater flexibility in trading-off computation for reasoning performance. Our experimental results demonstrate the effectiveness of DoT in multi-digit multiplication, boolean logic, and grade school math problems, with a small diffusion model outperforming a much larger autoregressive model in both efficiency and accuracy. In addition to that, DoT showcases promising self-correction abilities and benefits from existing reasoning-enhancing techniques like self-consistency decoding. Our findings contribute to the understanding and development of reasoning with diffusion language models. Copyright © 2024, The Authors. All rights reserved.

关键词： computation theory

Maximum Likelihood Estimators of Quantum Probabilities

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arXiv 2024年

作者： Navara, Mirko Ševic, Jan Department of Cybernetics Faculty of Electrical Engineering Czech Technical University Prague Czech Republic

Classical probability theory is based on assumptions which are often violated in practice. Therefore quantum probability is a proposed alter- native not only in quantum physics, but also in other sciences. However, so far it mostly criticizes the classical approach, but does not suggest a working alternative. Maximum likelihood estimators were given very low attention in this context. We show that they can be correctly defined and their computation in closed form is feasible at least in some cases. © 2024, CC BY.

关键词： computation theory

The Role of Affective States in computational Psychiatry

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arXiv 2025年

作者： Benrimoh, David Smith, Ryan Diaconescu, Andreea O. Friesen, Timothy Jalali, Sara Mikus, Nace Gschwandtner, Laura Gandhi, Jay Horga, Guillermo Powers, Albert McGill University Department of Psychiatry Montreal Canada Douglas Research Center Montreal Canada Laureate Institute for Brain Research TulsaOK United States Oxley College of Health and Natural Sciences University of Tulsa TulsaOK United States Krembil Centre for Neuroinformatics CAMH Toronto Canada Department of Psychiatry University of Toronto TorontoON Canada Interacting Minds Centre Aarhus University Aarhus Denmark Department of Cognition- Emotion- and Methods in Psychology University of Vienna Vienna Austria Yale University School of Medicine New HavenCT United States Department of Psychiatry Columbia University New YorkNY United States

Studying psychiatric illness has often been limited by difficulties in connecting symptoms and behavior to neurobiology. computational psychiatry approaches promise to bridge this gap by providing formal accounts of the latent information processing changes that underlie the development and maintenance of psychiatric phenomena. Models based on these theories generate individual-level parameter estimates which can then be tested for relationships to neurobiology. In this review, we explore computational modelling approaches to one key aspect of health and illness: affect. We discuss strengths and limitations of key approaches to modelling affect, with a focus on reinforcement learning, active inference, the hierarchical gaussian filter, and drift-diffusion models. We find that, in this literature, affect is an important source of modulation in decision making, and has a bidirectional influence on how individuals infer both internal and external states. Highlighting the potential role of affect in information processing changes underlying symptom development, we extend an existing model of psychosis, where affective changes are influenced by increasing cortical noise and consequent increases in either perceived environmental instability or expected noise in sensory input, becoming part of a self-reinforcing process generating negatively valenced, over-weighted priors underlying positive symptom development. We then provide testable predictions from this model at computational, neurobiological, and phenomenological levels of description. © 2025, CC BY-NC-ND.

关键词： computation theory

Examples of solvable and nilpotent finite quantum groups

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arXiv 2024年

作者： Glowacki, Gerard Hattori, Masamune Tanaka, Masato

We prove the solvability and nilpotency of Kac–Paljutkin’s finite quantum group and Sekine quantum groups and we classify the solvable series of Kac–Paljutkin’s finite quantum group via Cohen–Westreich’s Burnside theorem. Some semisimple quasitriangular Hopf algebras of dimensions 2pq are also studied. In Appendix A, we give a direct computation of the universal R-matrices for Kac–Paljutkin’s 8-dimensional finite quantum *** Codes 16T05, 16T25, 16T10 Copyright © 2024, The Authors. All rights reserved.

关键词： computation theory

DEHN FUNCTIONS OF SUBGROUPS OF PRODUCTS OF FREE GROUPS PART I: UNIFORM UPPER BOUNDS

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arXiv 2024年

作者： Ascari, Dario Bertolotti, Federica Italiano, Giovanni Isenrich, Claudio Llosa Migliorini, Matteo Department of Mathematics University of the Basque Country Barrio Sarriena Leioa48940 Spain Scuola Normale Superiore Piazza dei Cavalieri 7 Pisa56126 Italy Mathematical Institute University of Oxford Andrew Wiles Building Woodstock Road OxfordOX2 6GG United Kingdom Faculty of Mathematics KIT Englerstr. 2 Karlsruhe76131 Germany

Subgroups of direct products of finitely many finitely generated free groups form a natural class that plays an important role in geometric group theory. Its members include fundamental examples, such as the Stallings–Bieri groups. This raises the problem of understanding their geometric invariants. We prove that finitely presented subgroups of direct products of three free groups, as well as subgroups of finiteness type Fn−1 in a direct product of n free groups, have Dehn function bounded above by N9. This gives a positive answer to a question of Dison within these important subclasses and provides new insights in the context of Bridson’s conjecture stating that finitely presented subgroups of direct products of free groups have polynomially bounded Dehn function. To prove our results we generalise techniques for "pushing fillings" into normal *** Codes 20F65 (Primary) 20F05, 20F67, 20F69, 57M07 (Secondary) Copyright © 2024, The Authors. All rights reserved.

关键词： computation theory

Random Bond perturbations of the O(2) vector model

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arXiv 2024年

作者： Nocchi, Maria Mathematical Institute University of Oxford Radcliffe Observatory Quarter Andrew Wiles Building Woodstock Road OxfordOX2 6GG United Kingdom

We investigate the impact of quenched disorder in the critical O(2) vector model. We first review, in the modern language of Conformal Perturbation theory, the random temperature perturbation in 4 − ϵ. Then, we present a direct computation in 3d. The pure CFT is now strongly interacting, and its CFT data are determined in recent numerical bootstrap studies. We then explore the anisotropic disorder associated with the lowest-dimension charge-2 scalar, which is relevant in 3d. This perturbation breaks locally O(2). However, the symmetry is restored in the IR in a weakly coupled new fixed point. Copyright © 2024, The Authors. All rights reserved.

关键词： computation theory