Tootfinder

Rethinking LLM Training through Information Geometry and Quantum Metrics
Riccardo Di Sipio
https://arxiv.org/abs/2506.15830 https://a…

Rethinking LLM Training through Information Geometry and Quantum Metrics
Optimization in large language models (LLMs) unfolds over high-dimensional parameter spaces with non-Euclidean structure. Information geometry frames this landscape using the Fisher information metric, enabling more principled learning via natural gradient descent. Though often impractical, this geometric lens clarifies phenomena such as sharp minima, generalization, and observed scaling laws. We argue that curvature-aware approaches deepen our understanding of LLM training. Finally, we specula…

Transfer-matrix approach to the Blume-Capel model on the triangular lattice
Dimitrios Mataragkas, Alexandros Vasilopoulos, Nikolaos G. Fytas, Dong-Hee Kim
https://arxiv.org/abs/2506.16483

Transfer-matrix approach to the Blume-Capel model on the triangular lattice
We investigate the spin-$1$ Blume-Capel model on an infinite strip of the triangular lattice using the transfer-matrix method combined with a sparse-matrix factorization technique. Through finite-size scaling analysis of numerically exact spectra for strip widths up to $L = 19$, we accurately locate the tricritical point improving upon recent Monte Carlo estimates. In the first-order regime, we observe exponential scaling of the spectral gap, reflecting the linear growth of interfacial tension …

DRIVE Through the Unpredictability:From a Protocol Investigating Slip to a Metric Estimating Command Uncertainty
Nicolas Samson, William Larriv\'ee-Hardy, William Dubois, \'Elie Roy-Brouard, Edith Brotherton, Dominic Baril, Julien L\'epine, Fran\c{c}ois Pomerleau
https://arxiv.org/abs/2506.16593

DRIVE Through the Unpredictability:From a Protocol Investigating Slip to a Metric Estimating Command Uncertainty
Off-road autonomous navigation is a challenging task as it is mainly dependent on the accuracy of the motion model. Motion model performances are limited by their ability to predict the interaction between the terrain and the UGV, which an onboard sensor can not directly measure. In this work, we propose using the DRIVE protocol to standardize the collection of data for system identification and characterization of the slip state space. We validated this protocol by acquiring a dataset with two…

Explicit Constructions of Sum-Rank Metric Codes from Quadratic Kummer Extensions
Zhu Yunlong, Zhao Chang-An
https://arxiv.org/abs/2506.18653 https://

Explicit Constructions of Sum-Rank Metric Codes from Quadratic Kummer Extensions
This paper presents new constructions of sum-rank metric codes derived from algebraic function fields, while the existing results about such codes remain limited. A central challenge in this field involves the determination of parameters. We address this challenge through quadratic Kummer extensions, and propose two general constructions of $2\times2$ sum-rank codes. The novel sum-rank metric code constructions derived from algebraic function fields demonstrate superior code lengths compared to…

🇺🇦 #NowPlaying on KEXP's #MiddayShow
Black Rebel Motorcycle Club:
🎵 Carried From the Start
#BlackRebelMotorcycleClub
https://open.spotify.com/track/6Hh1RE0f2jpotIH9mrdp62

Subgraph Entropy
Tawfiq Ahmed, Tarik Aougab, Matt Clay
https://arxiv.org/abs/2506.18838 https://arxiv.org/pdf/2506.18838

Subgraph Entropy
Given $r \geq 3$, we prove that there exists $λ>0$ depending only on $r$ so that if $G$ is a metric graph of rank $r$ with metric entropy $1$, then there exists a proper subgraph $H$ of $G$ with metric entropy at least $λ$. This answers a question of the second two authors together with Rieck. We interpret this as a graph theoretic version of the Bers Lemma from hyperbolic geometry, and explain some connections to the pressure metric on the Culler-Vogtmann Outer Space.

Multi-field TDiff theories: the mixed regime case
Antonio L. Maroto, Prado Mart\'in-Moruno, Diego Tessainer
https://arxiv.org/abs/2507.16616 https://…

Multi-field TDiff theories: the mixed regime case
We study theories breaking diffeomorphism (Diff) invariance down to the subgroup of transverse diffeomorphisms (TDiff), consisting of multiple scalar fields in a cosmological background. In particular, we focus on models involving a field dominated by its kinetic term and a field dominated by its potential, coupled to gravity through power-law functions of the metric determinant. The Diff symmetry breaking results in the individual energy-momentum tensors not being conserved, although the total…

Diffusion-Based Hypothesis Testing and Change-Point Detection
Sean Moushegian, Taposh Banerjee, Vahid Tarokh
https://arxiv.org/abs/2506.16089 https://

Diffusion-Based Hypothesis Testing and Change-Point Detection
Score-based methods have recently seen increasing popularity in modeling and generation. Methods have been constructed to perform hypothesis testing and change-point detection with score functions, but these methods are in general not as powerful as their likelihood-based peers. Recent works consider generalizing the score-based Fisher divergence into a diffusion-divergence by transforming score functions via multiplication with a matrix-valued function or a weight matrix. In this paper, we ext…

Theories of the gravity gauge type in de Sitter space
Julian Lang, Yasha Neiman
https://arxiv.org/abs/2506.16707 https://arxiv.org/pd…

Theories of the gravity+gauge type in de Sitter space
We study theories of the "General Relativity + Yang-Mills" type in 4d spacetime with cosmological constant, focusing on formulations where the basic variables are connections and curvatures (but no metric). We present a new Lagrangian for GR coupled to Yang-Mills, which uses the same kind of variables for both sectors, and has a manifest double-copy structure. This Lagrangian comes in both non-chiral (real) and chiral (complex) versions. The chiral version makes it easy to isolate the self-dual…

Emergent field theory
Erick I. Duque
https://arxiv.org/abs/2507.16163 https://arxiv.org/pdf/2507.16163…

Emergent field theory
The uniqueness theorems for general relativity and Yang-Mills theories can be circumvented by dropping the ubiquitous, yet often implicit, assumption that physical fields, such as the spacetime metric, are fundamental. The novel concept of emergent fields makes it possible to construct modified theories of gravity and forces where the spacetime metric and strength tensor fields emerge from a covariance analysis in the canonical formulation with nontrivial relations to the fundamental phase spac…