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@arXiv_csLO_bot@mastoxiv.page
2025-09-23 10:08:50

Adhesive category theory for graph rewriting in Rocq
Samuel Arsac (PLUME, LIP, ENS de Lyon), Russ Harmer (PLUME, LIP), Damien Pous (PLUME, LIP)
https://arxiv.org/abs/2509.17392 …

Adhesive category theory for graph rewriting in Rocq
We design a Rocq library about adhesive categories, using Hierarchy Builder (HB). It is built around two hierarchies. The first is for categories, with usual categories at the bottom and adhesive categories at the top, with weaker variants of adhesive categories in between. The second is for morphisms (notably isomorphisms, monomorphisms and regular monomorphisms). Each level of these hierarchies is equipped with several interfaces to define instances. We cover basic categorical concepts such a…

@arXiv_csCL_bot@mastoxiv.page
2025-09-24 10:39:04

Beyond the Leaderboard: Understanding Performance Disparities in Large Language Models via Model Diffing
Sabri Boughorbel, Fahim Dalvi, Nadir Durrani, Majd Hawasly
https://arxiv.org/abs/2509.18792

Beyond the Leaderboard: Understanding Performance Disparities in Large Language Models via Model Diffing
As fine-tuning becomes the dominant paradigm for improving large language models (LLMs), understanding what changes during this process is increasingly important. Traditional benchmarking often fails to explain why one model outperforms another. In this work, we use model diffing, a mechanistic interpretability approach, to analyze the specific capability differences between Gemma-2-9b-it and a SimPO-enhanced variant. Using crosscoders, we identify and categorize latent representations that dif…

@arXiv_mathAT_bot@mastoxiv.page
2025-08-12 08:14:13

On distributional one-category, diagonal distributional complexity, and related invariants
Ekansh Jauhari, John Oprea
https://arxiv.org/abs/2508.06973 https://

On distributional one-category, diagonal distributional complexity, and related invariants
We develop the theory of probabilistic variants of the one-category and diagonal topological complexity, which bound the classical LS-category and topological complexity from below. Unlike any other classical or probabilistic invariants, these invariants are rigid on spaces with finite fundamental group. On Eilenberg-Mac Lane spaces, we identify these new invariants with distributional category and complexity, respectively, and use them to illuminate aspects of the behavior of the latter invari…

@arXiv_mathST_bot@mastoxiv.page
2025-09-24 08:22:04

Markov Combinations of Discrete Statistical Models
Orlando Marigliano, Eva Riccomagno
https://arxiv.org/abs/2509.18983 https://arxiv.org/pdf/2509.18983

Markov Combinations of Discrete Statistical Models
Markov combination is an operation that takes two statistical models and produces a third whose marginal distributions include those of the original models. Building upon and extending existing work in the Gaussian case, we develop Markov combinations for categorical variables and their statistical models. We present several variants of this operation, both algorithmically and from a sampling perspective, and discuss relevant examples and theoretical properties. We describe Markov combinations …

@arXiv_csFL_bot@mastoxiv.page
2025-09-03 08:20:43

Generalised M\"obius Categories and Convolution Kleene Algebras
James Cranch, Georg Struth, Jana Wagemaker
https://arxiv.org/abs/2509.00168 https://ar…

Generalised Möbius Categories and Convolution Kleene Algebras
Convolution algebras on maps from structures such as monoids, groups or categories into semirings, rings or fields abound in mathematics and the sciences. Of special interest in computing are convolution algebras based on variants of Kleene algebras, which are additively idempotent semirings equipped with a Kleene star. Yet an obstacle to the construction of convolution Kleene algebras on a wide class of structures has so far been the definition of a suitable star. We show that a generalisation…

@arXiv_mathST_bot@mastoxiv.page
2025-09-15 07:51:51

Quantifying and testing dependence to categorical variables
Siegfried H\"ormann, Daniel Strenger-Galvis
https://arxiv.org/abs/2509.10268 https://arxiv…

Quantifying and testing dependence to categorical variables
We suggest a dependence coefficient between a categorical variable and some general variable taking values in a metric space. We derive important theoretical properties and study the large sample behaviour of our suggested estimator. Moreover, we develop an independence test which has an asymptotic $χ^2$-distribution if the variables are independent and prove that this test is consistent against any violation of independence. We discuss some extensions, including a variant of the coefficient f…

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