arXiv preprints from January 1, 2026 through September 11, 2026 — 02:16:15 EST
The Word Problem has been a subject of intensive mathematical study for over a century, initially driving advances in combinatorial group theory and more recently emerging as a foundational hardness assumption in post-quantum cryptography (PQC). While generally undecidable, several families of infinite non-abelian groups exhibit...
In this paper, we study Ricci solitons on the three-dimensional solvable Lie group $\mathrm{Sol}^{3}_{m,n}$ equipped with a left-invariant Riemannian metric, viewed as a generalization of the classical $\mathrm{Sol}^{3}$ geometry. We investigate harmonic maps, harmonic sections, and geodesic curves, including the geodesic properties...
Featuring Hessian-driven damping, two inertial primal dual dynamical systems are proposed for solving smooth saddle point problems with bilinear coupling. For convex-concave functions, we establish a convergence rate $\mathcal{O}\left( \frac{1}{t^2} \right)$ for the primal dual gap; for strongly convex-strongly concave functions, we...
Diffusion MRI (dMRI) relies on diffusion-weighted echo-planar imaging, which is highly susceptible to eddy-current-induced geometric distortions. These distortions vary across diffusion volumes according to gradient strength and direction, causing between-volume misalignment that can bias downstream microstructural analyses. Current...
Large language models (LLMs) are increasingly used as general-purpose translation systems, but their behavior is usually evaluated under a single prompt shape: translate one source sentence into one target language. In practice, users may ask for one target language, for several related languages at once, or for translations...
Collaborative Perception (CP) improves autonomous systems' awareness of their surroundings by sharing sensor data, intermediate features, and detection results. In real-world deployments, however, collaborating vehicles often use heterogeneous sensors, perception models, datasets, and training domains, creating feature-space shifts...
We study peer review at ICLR, a large machine-learning conference whose complete review record, including rejected submissions, is public. Reviewers score each submission; for the borderline band whose scores do not settle an outcome, an area chair makes a discretionary accept-or-reject call. We ask whether that call is even-handed:...
Collaborative robots are well-suited to maritime missions that benefit from coordination, such as the exploration of unknown reef structures, inspection of subsea infrastructure, or search-and-rescue operations. These missions typically provide sparse feedback signals for measuring progress and require adherence to safety and...
It is common for two-dimensional embeddings of high-dimensional data to be read far beyond what they can support. Distances in and between clusters, the meaning behind empty spaces, and the amount of structure hidden at each point are generally invisible in the output of methods such as t-SNE and UMAP. This is because the information...
Gill (arXiv:2402.13376) introduced the probabilistic automatic complexity $A_P(w)$ of a finite string $w$: the least number of states of a probabilistic finite automaton (PFA) for which $w$ is the unique most probably accepted string of its length. He asked whether $A_P$ is unbounded, noting that no string with $A_P > 3$ was known...
Martinsson and Steiner recently proved that the fractional chromatic number of any $d$-degenerate triangle-free graph $G$ satisfies $χ_f(G) = O\left(\frac{d}{\log d}\right)$. They further conjectured a sharp leading constant $1 + o(1)$. In this paper, we confirm their upper bound conjecture for graphs having girth at least $5$. Our...
Two linear error-correcting codes $\cal{C}_1, \cal{C}_2 \subseteq \mathbb{F}_q^n$ are called linearly equivalent if there is a linear isometry mapping $\cal{C}_1$ to $\cal{C}_2$. In this work, we generalize the notion of linear equivalence and study the minimum distortion $\cal{D}(\cal{C}_1, \cal{C}_2)$ of a linear mapping between...
Reinforcement learning with verifiable rewards (RLVR) is bottlenecked by rollout generation, yet many sampled prompts produce saturated groups (all responses correct or all incorrect) whose zero reward variance yields no policy-gradient signal. Existing remedies either oversample a larger candidate pool and discard saturated prompts...
Line-haul trucking costs are dominated by three comparably sized components: energy, driver labor, and equipment. Most efficiency technologies address only one component at a time. This paper presents Robostreet Flow, a freight architecture that jointly optimizes the vehicle, convoy formation, and operating model to minimize cost per...
Psychometric calibration for educational tests typically requires costly human response data. Large language models (LLMs) simulated examinees offer a promising route to early calibration, but their responses are too accurate and too uniform. We propose Cognitive Diagnostic Profiling (CDP), a zero-shot framework that prompts LLMs to...
Mixture-of-experts (MoE) inference first aligns routed tokens into padded expert blocks, then executes packed quantized matrix multiplication over those blocks. This preprocessing is often treated as bookkeeping. In one pre-specified Qwen3-Coder AWQ layer-6 fixture on a pinned vLLM/Marlin build and RTX 3090 runtime, we show that the...
To operate effectively across diverse contexts, robots must not only perform manipulation tasks accurately but also adapt how their actions unfold to the task, object, and interaction setting. We ask whether this execution-level variation can be learned as a reusable behavioral factor shared across tasks. We present \textbf{MoMo}, a...
Stealth, the discipline of achieving an objective without revealing your presence, capabilities, or collected intelligence, is what separates sophisticated operators from detectable ones. Elite security researchers and advanced persistent threats achieve their objectives unnoticed; autonomous agents increasingly inherit the same...
Agentic systems act, so a defect in the evidence they retrieve becomes a wrong action with a currency cost. The most dangerous enterprise defects are metadata-borne: a stale price or a superseded record, perfectly well-formed in the payload and betrayed only by freshness, lineage, or provenance. Such a defect never enters the agent's...
Contemporary LLM-based coding agents produce code as black-box outputs: the rationale behind each line is hidden, the evolution of the code through benchmark-driven repair is ephemeral, and post-hoc auditing is impossible. We present a code generation concept that addresses these shortcomings through three complementary mechanisms:...
Relating low-level executable code to a high-level account of its behavior has been a central concern of programming-language research for decades. From formally verified compilers to translation validators, certifying compilers, and proof-carrying code, each approach chooses between laborious but foundational mechanized proofs and...
Let p be an odd prime and K/Qp a finite unramified extension of degree f > 1. Let Z(r) be the reduced special fiber of the Emerton-Gee stack of two-dimensional crystalline representations of Hodge type r of the absolute Galois group of K. We study the collection of stacks Z(r) as r varies over p-bounded Hodge types, as a set partially...
Editing character motion often requires transferring a gesture or gait from one or more reference motions while preserving the source action, timing, root trajectory, and unselected body regions. Existing motion datasets, however, rarely provide paired targets for arbitrary part-local content--reference combinations, and...
We extend the Caffarelli-Hardt-Simon perturbation argument for truncated regular minimal cones to the special Lagrangian setting and prove a bridge principle for regular special Lagrangian cones in the spirit of Nathan Smale. Our bridge principle yields a general existence theorem for conically singular special Lagrangian submanifolds...
Alon and Füredi proved that at least $n$ affine hyperplanes are required to cover $\{0,1\}^n\setminus\{\textbf{0}\}$ while avoiding the origin, and that this bound is sharp. We study how small the largest Boolean intersection among the hyperplanes can be in a cover attaining this minimum. Let $F(n)$ denote the minimum possible value...