arXiv preprints from January 1, 2026 through September 22, 2026 — 00:45:12 EST
We give a new proof of Faltings' isogeny theorem. More precisely, we show that Yuan's non-archimedean equidistribution theorem can be used to "pump" homomorphisms and semisimplicity from finite fields to number fields, thereby reducing Faltings' theorem directly to Tate's theorem.
Let $(A,\mathfrak{m})$ be a Gorenstein local ring with $G(A)$ Cohen-Macaulay, and let $M$ be a Cohen-Macaulay $A$-module of finite projective dimension. In \cite{Quasipure}, the authors proved that $e_1(M)\geq \binom{c+1}{2}$, where $c=\operatorname{reg}G(A)$ and $e_i(M)$ is the $i$th Hilbert coefficient of $M$. We first show that...
Continuous measurement of quantum systems gives rise to stochastic dynamics of the conditional quantum state, described by diffusive stochastic master equations. In this paper, we study parameter estimation for such equations when the Hamiltonian and measurement operators depend on unknown parameters. Based on multiple independent...
Frenkel and Wang obtained a representation of the Virasoro algebra by commuting Goulden's cut-and-join operator with the Heisenberg generators. A vertex-operator construction by Lascoux and the author extends this representation to $\mathcal W_{1+\infty}$ by means of differential operators whose eigenvalues are the power sums of the...
Multimodal large language models (MLLMs) process hundreds or thousands of visual tokens per image, incurring prohibitive inference costs. While existing vision token pruning methods mitigate this overhead, they implicitly assume that a single fixed pruning strategy can be applied uniformly across all inputs. Our analysis further...
A confidence-aware multimodal fusion framework (CAMF) is proposed to realize reliable human intention prediction for industrial human-robot collaboration. This framework fuses four heterogeneous modalities including object 6D pose, gaze, skeletal motion and IMU-based hand motion. It embeds a confidence-trend-driven dynamic fusion...
Multimedia applications require precise music annotation-labeled positions, segments, or loops-placed by hand or algorithmically. Machine-learning algorithms are scalable and effective but need annotated training data, scarce for many tasks. TimeCues Studio is an open-source workspace where algorithm-development teams annotate a music...
Despite significant progress in odometry estimation, long-term drift remains a fundamental limitation of incremental pose integration, especially in large-scale or loop-free environments. Existing map-assisted methods can reduce drift, but often depend on dense maps, sensor-specific processing, or complex matching pipelines. We...
Plane geometry remains a significant challenge in AI, requiring the integration of visual perception and mathematical reasoning. While Large Multimodal Models (LMMs) naturally handle visuo-linguistic inputs, they are often computationally intensive and opaque. We demonstrate that a pure Large Language Model (LLM), when equipped with...
Uncertainty estimation for medical vision--language models (VLMs) using conformal prediction has gained increasing attention due to its distribution-free coverage guarantees. However, standard conformal prediction relies on exchangeability between calibration and test data and typically requires a sufficiently large calibration set to...
Transferring the rich priors of large 2D foundation models to sparse 3D LiDAR remains challenging, as training native 3D foundation models at comparable scale is limited by data and annotation scarcity. We introduce a LiDAR-conditioned diffusion model trained on pseudo-labels from off-the-shelf 2D foundation models. The model supports...
Knowledge distillation offers an efficient route to transfer a task-adapted vision-language teacher to a compact student. The training target in current vision-language distillation methods is typically constructed from the teacher prediction and applied uniformly to all training samples, making it unreliable under class and domain...
Streaming talking-head generation produces each frame as its driving audio arrives, yet fidelity and efficiency have so far pulled in opposite directions: end-to-end methods condition a video diffusion model on audio directly and achieve high quality but only at large scale, while cheaper two-stage methods generate an intermediate...
Translating high-level controls from security standards into concrete, system-specific requirements is central to cybersecurity requirements engineering. Large language models (LLMs) can accelerate this labor-intensive, recall-sensitive task, but any single run is unreliable: it misses valid safeguards while introducing plausible...
Reinforcement learning with verifiable rewards (RLVR) has advanced language-model reasoning in domains such as mathematics and code, where objective answers are inexpensive to check. Diagnostic reasoning over complex data lacks this advantage: establishing the true cause of an anomaly often requires costly expert investigation and may...
The lottery ticket hypothesis posits the existence of winning tickets: sparse subnetworks that, when trained in isolation from their original initialization, match the accuracy of the full dense network. The predominant method for discovering such tickets, iterative magnitude pruning, alternates pruning with full retraining from...
High-resolution water mapping supports environmental monitoring and related applications, but accurate pixel-level labels are difficult and costly to produce. Official hydrographic vectors provide scalable weak supervision, but they contain artifacts like boundary noise, temporal mismatch, and omissions of small water structures. We...
Mean field planning on a surface prescribes initial and terminal densities and minimizes a transport energy subject to the continuity equation. Proximal algorithms for this problem repeatedly solve a time--space Poisson equation, whose temporal derivative and surface gradient determine the density and momentum corrections. We study a...
Nonlinear complexity is a fundamental criterion in the evaluation of pseudorandom sequences. The construction of multi-sequences with high nonlinear complexity is both theoretically and practically important in cryptography. Motivated by prior constructions of multi-sequences with high nonlinear complexity in [IEEE Trans. Inf. Theory,...
Tensor compilers such as TinyTC and OpenAI Triton were originally developed for AI workloads, but the same tiling and memory abstractions can be applied to implement efficient high-order stencils for scientific and industrial applications. We demonstrate this for an 8th-order, 25-point acoustic stencil with boundary conditions over an...
We characterize equality in the finite free Stam and entropy-power inequalities, proving that Hermite polynomials are the unique extremizers among simple real-rooted inputs, up to independent translations and scalings. The proof turns this classification into a rigidity problem for projective plane curves. Using hyperbolicity and the...
While AVSR has achieved sub-1% word error rates on the standard LRS3 benchmark, its reliance on broadcast speech obscures whether this reflects true generalization or just domain adaptation. To investigate this gap, we evaluate three AVSR architectures across six conditions: controlled broadcast speech, fixed-grammar utterances,...
Simultaneous assessment of medical imaging and patient records is often required in clinical diagnosis. However, standard machine learning algorithms cannot analyze these data types together. Meanwhile, compliance with HIPAA and GDPR can constrain centralized aggregation of sensitive patient data. This leaves a crucial void of secure...
SceneHI is a framework that lifts high-resolution, illumination-aware priors from 2D diffusion models to perform 3D texture synthesis. It is the first to demonstrate that high-resolution textures, previously limited to 2D synthesis, can be generated directly on 3D objects without model fine-tuning or optimization. Designed for...
We give a simple proof for the existence of weak central polynomials for the algebra of multiplications of a finite-dimensional simple (non-associative) algebra. As an example we present explicit weak central polynomials in the cases of the three-dimensional simple Lie algebra and the Jordan algebra of the two-dimensional vector space...