arXiv preprints from January 1, 2026 through September 24, 2026 — 01:51:46 EST
Training modern deep learning models is increasingly constrained by GPU memory and compute limits. While Randomized Numerical Linear Algebra (RandNLA) offers proven techniques to compress these models, the lack of a unified, production-grade library prevents widely adopting these methods. We present Panther, a PyTorch-compatible...
Large language models (LLMs) process and predict sequences containing text to answer questions, and address tasks including document summarization, providing recommendations, writing software and solving quantitative problems. We provide a mathematical framework for LLMs by describing the encoding of text sequences into sequences of...
Floating point arithmetic is costly on FPGA platforms due to wide datapaths, normalization, and carry propagation, motivating alternative numerical representations that improve throughput and efficiency. This paper presents the Hybrid Residue Floating Numerical Architecture (HRFNA), a fully specified numerical system that combines...
We present a novel system for camera-based measurement and visualization of muscle work based on the Hill-Type-Muscle-Model: the exercise exertion muscle-work monitor (\textit{XEM}$^{2}$). Our aim is to complement and, thus, address issues of established measurement techniques that offer imprecise data for non-uniform movements...
The integration of electromagnetic metasurfaces into wireless communications enables intelligent control of the propagation environment. Recently, flexible intelligent metasurfaces (FIMs) have evolved beyond conventional reconfigurable intelligent surfaces (RISs), enabling three-dimensional surface deformation for adaptive wave...
We develop low distortion embeddings with outliers from arbitrary metrics into hierarchically separated trees (HSTs). In particular, we develop an efficient algorithm that for any $ε>0$, given an input metric $(X,d)$, and a probabilistic embedding of all but $k$ points from $X$ into HSTs with distortion $c$, samples from a...
We consider a (left) coherent ring R. We prove that if the character module of every Ding injective (left) R-module is Gorenstein flat, then the class of Gorenstein flat (right) R-modules, GF, is preenveloping. We show that this is the case when every injective (left) R-module has finite flat dimension. In particular, GF is...
The prevalence and low cost of LLMs have led to a rise of synthetic content. From review sites to court documents, "natural" content has been contaminated by data points that appear similar to natural data, but are in fact LLM-generated. In this work we revisit fundamental learning theory questions in this, now ubiquitous, setting. We...
Two broad positions within statistics define a treatment effect, on the one hand, as a parameter of a statistical model, and on the other, as an appropriate population-level difference in outcomes or counterfactual outcomes under the different treatment regimes. This short expository paper presents some simple but consequential...
It is obvious that emotions are causal variables of motivation, as they elicit states, forces and energies that trigger and guide labor behavior. Thus, a motivational tension that is not informed by needs alone, but also by emotions, intention, goals and means to achieve them is therefore generated within the mental, emotional and...
As digital tools increasingly mediate mental health care, self-clone chatbots can offer a uniquely novel approach to intra-personal exploration and self-derived support. Trained to replicate users' conversational patterns, self-clones allow users to talk to themselves through their digital replicas. Despite the promises, these systems...
Rank-metric codes, defined as sets of matrices over a finite field with the rank distance, have gained significant attention due to their applications in network coding and connections to diverse mathematical areas. Initially studied by Delsarte in 1978 and later rediscovered by Gabidulin, these codes have become a central topic in...
The determinants of modular Collatz graphs and the modular Conway amusical permutation graph are determined, and some interesting number theoretic properties are described.
Strong, correlated noise in recurrent neural circuits often passes through nonlinear transfer functions, complicating dynamical mean-field analyses of complex phenomena such as transients and bifurcations. We introduce a method that replaces nonlinear functions of Ornstein-Uhlenbeck (OU) noise with a Gaussian-equivalent process...
We show that the non-log version of Kato's ramification filtration on the Brauer group of a separated and finite type regular scheme over a positive characteristic local field coincides with the evaluation filtration. This extends a recent result of Bright-Newton to positive characteristics. Among several applications, we extend some...
We present a multi-epoch test of f(T) gravity with nonminimal torsion-matter coupling, combining early- and late-Universe observations. At the MeV scale, Big-Bang Nucleosynthesis constrains the fractional variation of the weak freeze-out temperature, |δτ_f/τ_f|, thereby mapping light-element abundances into limits on deviations from...
This study presents an integrated framework for enhancing the safety and operational efficiency of robotic arms in laparoscopic surgery by addressing minimum distance estimation between multi-arm manipulators and the associated collision-aware warning. By combining analytical modeling, real time simulation, and machine learning, the...
Motivation: The multiple sequence alignment (MSA) problem has been extensively studied, with numerous approaches developed over recent years. With the rapid growth of sequence data, there is an increasing need for fast and accurate MSA tools that scale effectively to large datasets. Building on our previous work on CLAM, we are able...
The integration of Large Language Models (LLMs) into the public health policy sector offers a transformative approach to navigating the vast repositories of regulatory guidance maintained by agencies such as the Centers for Disease Control and Prevention (CDC). However, the propensity for LLMs to generate hallucinations, defined as...
Millimeter-wave oscillators underpin key applications in communication, spectroscopy, radar, and astronomy, yet their achievable spectral purity remains limited. Approaches that directly generate millimeter-wave carriers are fundamentally limited by quantum and thermal phase-noise processes. Here we show that these limits can be...
In their 1991 paper "Algebraic Reconstruction of Types and Effects," Pierre Jouvelot and David Gifford presented a type-and-effect reconstruction algorithm based on an algebraic structure of effects. Their work is considered a milestone in the development of type-and-effect systems, and has inspired numerous subsequent works in the...
The standard proof of the equivalence of Fourier type on \(\mathbb R^d\) and on the torus \(\mathbb T^d\) is usually stated in terms of an implicit constant which can be expressed in terms of the global minimiser of the functions \[f_r(x)=\sum_{m\in\mathbb{Z}}\left|\frac{\sin(π(x+m))}{π(x+m)}\right|^{2r},\qquad x\in [0,1], \ r\ge 1.\]...
Few-normal shot anomaly detection (FNSAD) aims to detect abnormal regions in images using only a few normal training samples, making the task highly challenging due to limited supervision and the diversity of potential defects. Recent approaches leverage vision-language models such as CLIP with prompt-based learning to align image and...
Magnetars are now known to be among the most strongly polarized celestial sources in X-rays. Here we report on the $500\,\mathrm{ks}$ observation of the magnetar 1E 1547.0-5408 performed by the Imaging X-ray Polarimetry Explorer (IXPE) in March 2025. The IXPE spectrum is well reproduced by a single thermal component with blackbody...
We study the generalized Ramsey numbers $f(Q_n, C_{k}, q)$, that is, the minimum number of colors needed to edge-color the hypercube $Q_n$ so that every copy of the cycle $C_{k}$ has at least $q$ colors. Our main result is that for any integers $k,q$ satisfying $k \geq 6$ and $3 \leq q \leq k/2+1$, we have $f(Q_n, C_{k}, q)= o\left(...