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Yoshihiro Maruyama

Publications and source records attributed to Yoshihiro Maruyama.

16 recordsLinked to original sources
arXiv2026

Foundations of Equivariant Deep Learning: Unifying Graph and Sheaf Neural Networks

Symmetry is everywhere in nature and society. Geometric deep learning builds architectures respecting group symmetries, whereas topological deep learning organizes computation through cells, incidence relations, and local-to-global structure. In this paper, we extend geometric deep learning beyond simple group actions and unify it with topological deep learning. Specifically, we develop order-equivariant neural networks (OENN), which generalize standard graph message passing and sheaf neural networks via the theory of equivariant vector bundles over face posets (or face categories). We (i) characterize all linear order-equivariant maps, (ii) build OENN layers, and (iii) prove universal approximation theorems (UATs) for continuous order-equivariant maps, which are new results even when restricted to sheaf neural networks. We illustrate the framework on graph and sheaf models. Our results can also be seen as extending the known UAT for graph neural networks to a more general setting that subsumes sheaf neural networks as well. In the appendix, we show that OENN can be connected, via the action groupoid Grothendieck construction, to CENN (category-equivariant neural network), which gives the categorical general form of equivariant neural networks, allowing us to leverage categorical symmetry in data and extending geometric deep learning from groups of symmetries to categories of transformations.

cs.LG↗
arXiv2026

Modeling the Disjunction Effect within Classical Probability: A New Decision Process Model and Comparison with Quantum-like Models

The disjunction effect in human decision making is often taken to show that the classical law of total probability is violated, motivating quantum-like models. We re-examine this claim for the Prisoner's Dilemma disjunction effect. Under the mental-event reading of the opponent-choice events, the conventional classical decision-process model implicitly builds in a certainty-only premise: its standard partition assumptions leave no room for ambiguity, forcing every participant to be certain that the opponent will defect or will cooperate. We relax this by introducing a new classical model in which each participant carries a continuous expectation parameter representing the anticipated likelihood of opponent defection, and the participant pool is partitioned by expectation level; the resulting ambiguity set is precisely the union of the interior expectation bins. In contrast, under the quantum-like event semantics, ambiguous pure states are generic (dense and of full unitarily invariant measure on the unit sphere), so "certainty states" are mathematically exceptional. We prove that an instance of our classical model can realize any empirically observed triple of defection rates across the three information conditions, including strong disjunction-effect patterns, while strictly obeying the classical law of total probability. We further prove that for any such triple produced by a standard quantum-like model of the same experiment, there exists a classical instance reproducing it exactly. In this sense, classical and quantum-like approaches have the same observable-rate expressiveness; their substantive difference lies in how ambiguity is represented and in their respective event semantics, not in a breakdown of classical probability.

q-bio.NC↗
arXiv2025

Categorical Equivariant Deep Learning: Category-Equivariant Neural Networks and Universal Approximation Theorems

We develop a theory of category-equivariant neural networks (CENNs) that unifies group/groupoid-equivariant networks, poset/lattice-equivariant networks, graph and sheaf neural networks. Equivariance is formulated as naturality in a topological category with Radon measures. Formulating linear and nonlinear layers in the categorical setup, we prove the equivariant universal approximation theorem in the general setting: the class of finite-depth CENNs is dense in the space of continuous equivariant transformations. We instantiate the framework for groups/groupoids, posets/lattices, graphs and cellular sheaves, deriving universal approximation theorems for them in a systematic manner. Categorical equivariant deep learning thus allows us to expand the horizons of equivariant deep learning beyond group actions, encompassing not only geometric symmetries but also contextual and compositional symmetries.

cs.LG↗
arXiv2025

Algorithm for Interpretable Graph Features via Motivic Persistent Cohomology

We present the Chromatic Persistence Algorithm (CPA), an event-driven method for computing persistent cohomological features of weighted graphs via graphic arrangements, a classical object in computational geometry. We establish rigorous complexity results: CPA is exponential in the worst case, fixed-parameter tractable in treewidth, and nearly linear for common graph families such as trees, cycles, and series-parallel graphs. Finally, we demonstrate its practical applicability through a controlled experiment on molecular-like graph structures.

cs.CG↗
arXiv2025

Top-K Exterior Power Persistent Homology: Algorithm, Structure, and Stability

Exterior powers play important roles in persistent homology in computational geometry. In the present paper we study the problem of extracting the $K$ longest intervals of the exterior-power layers of a tame persistence module. We prove a structural decomposition theorem that organizes the exterior-power layers into monotone per-anchor streams with explicit multiplicities, enabling a best-first algorithm. We also show that the Top-$K$ length vector is $2$-Lipschitz under bottleneck perturbations of the input barcode, and prove a comparison-model lower bound. Our experiments confirm the theory, showing speedups over full enumeration in high overlap cases. By enabling efficient extraction of the most prominent features, our approach makes higher-order persistence feasible for large datasets and thus broadly applicable to machine learning, data science, and scientific computing.

cs.CG↗
arXiv2025

Learning with Category-Equivariant Architectures for Human Activity Recognition

We propose CatEquiv, a category-equivariant neural network for Human Activity Recognition (HAR) from inertial sensors that systematically encodes temporal, amplitude, and structural symmetries. We introduce a symmetry category that jointly represents cyclic time shifts, positive gain scalings, and the sensor-hierarchy poset, capturing the categorical symmetry structure of the data. CatEquiv achieves equivariance with respect to the categorical symmetry product. On UCI-HAR under out-of-distribution perturbations, CatEquiv attains markedly higher robustness compared with circularly padded CNNs and plain CNNs. These results demonstrate that enforcing categorical symmetries yields strong invariance and generalization without additional model capacity.

cs.CV↗
arXiv2025

Learning with Category-Equivariant Representations for Human Activity Recognition

Human activity recognition is challenging because sensor signals shift with context, motion, and environment; effective models must therefore remain stable as the world around them changes. We introduce a categorical symmetry-aware learning framework that captures how signals vary over time, scale, and sensor hierarchy. We build these factors into the structure of feature representations, yielding models that automatically preserve the relationships between sensors and remain stable under realistic distortions such as time shifts, amplitude drift, and device orientation changes. On the UCI Human Activity Recognition benchmark, this categorical symmetry-driven design improves out-of-distribution accuracy by approx. 46 percentage points (approx. 3.6x over the baseline), demonstrating that abstract symmetry principles can translate into concrete performance gains in everyday sensing tasks via category-equivariant representation theory.

cs.LG↗
arXiv2025

Accelerating Machine Learning Systems via Category Theory: Applications to Spherical Attention for Gene Regulatory Networks

How do we enable artificial intelligence models to improve themselves? This is central to exponentially improving generalized artificial intelligence models, which can improve their own architecture to handle new problem domains in an efficient manner that leverages the latest hardware. However, current automated compilation methods are poor, and efficient algorithms require years of human development. In this paper, we use neural circuit diagrams, based in category theory, to prove a general theorem related to deep learning algorithms, guide the development of a novel attention algorithm catered to the domain of gene regulatory networks, and produce a corresponding efficient kernel. The algorithm we propose, spherical attention, shows that neural circuit diagrams enable a principled and systematic method for reasoning about deep learning architectures and providing high-performance code. By replacing SoftMax with an $L^2$ norm as suggested by diagrams, it overcomes the special function unit bottleneck of standard attention while retaining the streaming property essential to high-performance. Our diagrammatically derived \textit{FlashSign} kernel achieves comparable performance to the state-of-the-art, fine-tuned FlashAttention algorithm on an A100, and $3.6\times$ the performance of PyTorch. Overall, this investigation shows neural circuit diagrams' suitability as a high-level framework for the automated development of efficient, novel artificial intelligence architectures.

math.CT↗
arXiv2023

Fibered Universal Algebra for First-Order Logics

We extend Lawvere-Pitts prop-categories (aka. hyperdoctrines) to develop a general framework for providing "algebraic" semantics for nonclassical first-order logics. This framework includes a natural notion of substitution, which allows first-order logics to be considered as structural closure operators just as propositional logics are in abstract algebraic logic. We then establish an extension of the homomorphism theorem from universal algebra for generalized prop-categories and characterize two natural closure operators on the prop-categorical semantics. The first closes a class of structures (which are interpreted as morphisms of prop-categories) under the satisfaction of their common first-order theory and the second closes a class of prop-categories under their associated first-order consequence. It turns out these closure operators have characterizations that closely mirror Birkhoff's characterization of the closure of a class of algebras under the satisfaction of their common equational theory and Blok and Jónsson's characterization of closure under equational consequence, respectively. These "algebraic" characterizations of the first-order closure operators are unique to the prop-categorical semantics and do not have analogs, for example, in the Tarskian semantics for classical first-order logic. The prop-categories we consider are much more general than traditional intuitionistic prop-categories or triposes (i.e., topos representing indexed partially ordered sets). Nonetheless, to our knowledge, our results are still new even when restricted to these special classes of prop-categories.

math.LO↗
arXiv2023

Computing with Categories in Machine Learning

Category theory has been successfully applied in various domains of science, shedding light on universal principles unifying diverse phenomena and thereby enabling knowledge transfer between them. Applications to machine learning have been pursued recently, and yet there is still a gap between abstract mathematical foundations and concrete applications to machine learning tasks. In this paper we introduce DisCoPyro as a categorical structure learning framework, which combines categorical structures (such as symmetric monoidal categories and operads) with amortized variational inference, and can be applied, e.g., in program learning for variational autoencoders. We provide both mathematical foundations and concrete applications together with comparison of experimental performance with other models (e.g., neuro-symbolic models). We speculate that DisCoPyro could ultimately contribute to the development of artificial general intelligence.

cs.LG↗
arXiv2022

A Probabilistic Generative Model of Free Categories

Applied category theory has recently developed libraries for computing with morphisms in interesting categories, while machine learning has developed ways of learning programs in interesting languages. Taking the analogy between categories and languages seriously, this paper defines a probabilistic generative model of morphisms in free monoidal categories over domain-specific generating objects and morphisms. The paper shows how acyclic directed wiring diagrams can model specifications for morphisms, which the model can use to generate morphisms. Amortized variational inference in the generative model then enables learning of parameters (by maximum likelihood) and inference of latent variables (by Bayesian inversion). A concrete experiment shows that the free category prior achieves competitive reconstruction performance on the Omniglot dataset.

cs.AI↗
arXiv2021

Philosophical Specification of Empathetic Ethical Artificial Intelligence

In order to construct an ethical artificial intelligence (AI) two complex problems must be overcome. Firstly, humans do not consistently agree on what is or is not ethical. Second, contemporary AI and machine learning methods tend to be blunt instruments which either search for solutions within the bounds of predefined rules, or mimic behaviour. An ethical AI must be capable of inferring unspoken rules, interpreting nuance and context, possess and be able to infer intent, and explain not just its actions but its intent. Using enactivism, semiotics, perceptual symbol systems and symbol emergence, we specify an agent that learns not just arbitrary relations between signs but their meaning in terms of the perceptual states of its sensorimotor system. Subsequently it can learn what is meant by a sentence and infer the intent of others in terms of its own experiences. It has malleable intent because the meaning of symbols changes as it learns, and its intent is represented symbolically as a goal. As such it may learn a concept of what is most likely to be considered ethical by the majority within a population of humans, which may then be used as a goal. The meaning of abstract symbols is expressed using perceptual symbols of raw sensorimotor stimuli as the weakest (consistent with Ockham's Razor) necessary and sufficient concept, an intensional definition learned from an ostensive definition, from which the extensional definition or category of all ethical decisions may be obtained. Because these abstract symbols are the same for both situation and response, the same symbol is used when either performing or observing an action. This is akin to mirror neurons in the human brain. Mirror symbols may allow the agent to empathise, because its own experiences are associated with the symbol, which is also associated with the observation of another agent experiencing something that symbol represents.

cs.AI↗
arXiv2021

Intensional Artificial Intelligence: From Symbol Emergence to Explainable and Empathetic AI

We argue that an explainable artificial intelligence must possess a rationale for its decisions, be able to infer the purpose of observed behaviour, and be able to explain its decisions in the context of what its audience understands and intends. To address these issues we present four novel contributions. Firstly, we define an arbitrary task in terms of perceptual states, and discuss two extremes of a domain of possible solutions. Secondly, we define the intensional solution. Optimal by some definitions of intelligence, it describes the purpose of a task. An agent possessed of it has a rationale for its decisions in terms of that purpose, expressed in a perceptual symbol system grounded in hardware. Thirdly, to communicate that rationale requires natural language, a means of encoding and decoding perceptual states. We propose a theory of meaning in which, to acquire language, an agent should model the world a language describes rather than the language itself. If the utterances of humans are of predictive value to the agent's goals, then the agent will imbue those utterances with meaning in terms of its own goals and perceptual states. In the context of Peircean semiotics, a community of agents must share rough approximations of signs, referents and interpretants in order to communicate. Meaning exists only in the context of intent, so to communicate with humans an agent must have comparable experiences and goals. An agent that learns intensional solutions, compelled by objective functions somewhat analogous to human motivators such as hunger and pain, may be capable of explaining its rationale not just in terms of its own intent, but in terms of what its audience understands and intends. It forms some approximation of the perceptual states of humans.

cs.AI↗
arXiv2020

Feature visualization of Raman spectrum analysis with deep convolutional neural network

We demonstrate a recognition and feature visualization method that uses a deep convolutional neural network for Raman spectrum analysis. The visualization is achieved by calculating important regions in the spectra from weights in pooling and fully-connected layers. The method is first examined for simple Lorentzian spectra, then applied to the spectra of pharmaceutical compounds and numerically mixed amino acids. We investigate the effects of the size and number of convolution filters on the extracted regions for Raman-peak signals using the Lorentzian spectra. It is confirmed that the Raman peak contributes to the recognition by visualizing the extracted features. A near-zero weight value is obtained at the background level region, which appears to be used for baseline correction. Common component extraction is confirmed by an evaluation of numerically mixed amino acid spectra. High weight values at the common peaks and negative values at the distinctive peaks appear, even though the model is given one-hot vectors as the training labels (without a mix ratio). This proposed method is potentially suitable for applications such as the validation of trained models, ensuring the reliability of common component extraction from compound samples for spectral analysis.

cs.CV↗
arXiv2014

Duality Theory and Categorical Universal Logic: With Emphasis on Quantum Structures

Categorical Universal Logic is a theory of monad-relativised hyperdoctrines (or fibred universal algebras), which in particular encompasses categorical forms of both first-order and higher-order quantum logics as well as classical, intuitionistic, and diverse substructural logics. Here we show there are those dual adjunctions that have inherent hyperdoctrine structures in their predicate functor parts. We systematically investigate into the categorical logics of dual adjunctions by utilising Johnstone-Dimov-Tholen's duality-theoretic framework. Our set-theoretical duality-based hyperdoctrines for quantum logic have both universal and existential quantifiers (and higher-order structures), giving rise to a universe of Takeuti-Ozawa's quantum sets via the tripos-to-topos construction by Hyland-Johnstone-Pitts. The set-theoretical hyperdoctrinal models of quantum logic, as well as all quantum hyperdoctrines with cartesian base categories, turn out to give sound and complete semantics for Faggian-Sambin's first-order quantum sequent calculus over cartesian type theory; in addition, quantum hyperdoctrines with monoidal base categories are sound and complete for the calculus over linear type theory. We finally consider how to reconcile Birkhoff-von Neumann's quantum logic and Abramsky-Coecke's categorical quantum mechanics (which is modernised quantum logic as an antithesis to the traditional one) via categorical universal logic.

quant-ph↗