Research
Research
Research
Research
348+ open-access research outputs.
We construct and analyze a thermodynamic extension of the recently proposed information geometric regularization of Cao and Sch\"afer. The construction extends their shock-mitigating Hessian metric ge…
We consider machine learning tasks with low-rank functional tree tensor networks (TTN) as the learning model. While in the case of least-squares regression, low-rank functional TTNs can be efficiently…
Vanishing gradients and overfitting are central problems in machine learning, yet are typically analyzed in asymptotic regimes that obscure their dynamical origins. Here we provide a dynamical descrip…
In dually flat manifolds, there is a deep connection between gradient flows and pregeodesics. This was one of the many important contributions of Amari to information geometry. In this paper, we exten…
Generalized Hopfield models with higher-order or exponential interaction terms are known to have substantially larger storage capacities than the classical quadratic model. On the other hand, asso…
Reading constructed a Cambrian lattice $C_\Gamma$ for each oriented finite type Coxeter diagram $\Gamma$. We show that the derived category of representations of $C_\Gamma$ is fractionally Calabi-Yau …
In this paper, we introduce \emph{$\ell^p$-information geometry}, an infinite-dimensional framework that shares key features with the geometry of the space of probability densities \( \mathrm{Dens}(M)…
As large language models (LLMs) evolve into autonomous agents, persistent memory at the API layer is essential for enabling context-aware behavior across LLMs and multi-session interactions. Existing …
Flips in triangulations of convex polygons arise in many different settings. They are isomorphic to rotations in binary trees, define edges in the 1-skeleton of the Associahedron and cover relations i…
We introduce a novel combinatorial structure called pointed building sets, which can be viewed as families of lattices equipped with compatibility relations. To each pointed building set $\mathsf{B}$,…
Consumer-to-consumer (C2C) marketplaces pose distinct retrieval challenges: short, ambiguous queries; noisy, user-generated listings; and strict production constraints. This paper reports our experime…
Flow polytopes of acyclic oriented graphs arise naturally in combinatorial optimization, and the study of their volumes and triangulations has revealed intriguing connections across combinatorics, geo…
While graph neural networks have shown remarkable success in molecular property prediction, current approaches like the Equivariant Subgraph Aggregation Networks (ESAN) treat molecules as bags of inde…
This work focuses on indirect descent methods for optimal control problems governed by nonlinear ordinary differential equations in Banach spaces, viewed as abstract models of distributed dynamics. As…
We construct a smooth orthonormal wavelet $\psi$ such that both $\psi$ and its Fourier transform $\widehat{\psi}$ belong to the extended Gevrey class $\mathcal{E}_{\sigma}(\mathbb{R})$ for $\sigma > 1…
We introduce a new broadly unifying family of combinatorial objects, which we call permutation flows, associated to an acyclic directed graph $G$ together with a framing $F$. This new family is combin…
It is an open problem of Mazari-Armida whether every abstract elementary class of $R$-modules $(\mathbf{K}, \leq_{\mathrm{pure}})$, with $\leq_{\mathrm{pure}}$ the pure submodule relation, is stable. …
The study of cortical dynamics during different states such as decision making, sleep and movement, is an important topic in Neuroscience. Modelling efforts aim to relate the neural rhythms present in…
We establish several independent results concerning extremal, left modular, congruence uniform, and semidistributive lattices. An equivalent characterization of left modular lattices is obtained in te…
Generating expressive and controllable human speech is one of the core goals of generative artificial intelligence, but its progress has long been constrained by two fundamental challenges: the deep e…
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