Search arXiv⌕ Search

SEARCH · Search arXiv

Results for “math.FA”

Search indexed arXiv papers on artificial intelligence, large language models, computer vision and robotics. Read source abstracts and follow links to arXiv.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

933 records · Page 2Linked to original sources
arXiv2026

Sim-FA: A GPGPU Simulator Framework for Fine-Grained Asynchronous Pipeline Analysis

To efficiently support Large Language Models (LLMs), modern GPGPU architectures have introduced new features and programming paradigms, such as warp specialization. These features enable temporal overlap between the producer and consumer, as well as between matrix multiplication and activation function operations, substantially improving performance. To conduct effective AI infrastructure and computer architecture research, cycle-accurate simulators that support these new features, together with analytical models that faithfully capture workload characteristics, are essential. However, existing academic tools provide limited support for these emerging requirements. Existing cycle-accurate simulators do not incorporate new NVIDIA GPU features, such as the Tensor Memory Accelerator (TMA), in a timely manner. Moreover, existing analytical models can misestimate DRAM traffic under certain configurations. In this paper, we build Sim-FA, a cycle-accurate simulation framework for Hopper TMA/WGMMA pipelines. We first develop an operator-agnostic trace frontend that instruments kernels at the Triton TTGIR level and validates it on 23 GEMM shapes, achieving 5.49\% MAPE against H800, confirming that the simulator core is not tied to any single operator. Because FlashAttention-3 introduces additional complexity beyond standard TMA/WGMMA kernels (asymmetric producer-consumer pipelines, softmax, ping-pong synchronization), we further build an FA3-specialized frontend that achieves 5.7\% MAPE with a maximum error of 12.7\%. Within the same framework, SimFA-python serves as an analytical fast path for large-scale design-space exploration where cycle-accurate simulation is prohibitively slow; validated against cuTile kernels on Blackwell (GB10), it explains why existing analytical models can produce inaccurate traffic estimates.

cs.AR↗
arXiv2026

Modern Transformers Are Implicit Hybrids: From Functional Differentiation to Principled Hybrid Architecture Design

Hybrid architectures combining Full Attention (FA) and Linear Attention (LA) are increasingly prominent, yet their allocation remains heuristic. We seek an evidence-grounded basis in head-level functional organization learned by RoPE-based Transformers. Behavioral probes do not yield a complete taxonomy, so we propose two intervention metrics: RoPE Frequency Importance Score (RFIS), measuring how each frequency affects a head's attention distribution, and RoPE Positional Dependence (RPD), isolating dependence on rotary positional modulation. On Qwen3-series models and Llama3.1, RFIS suggests and RPD verifies a complete taxonomy of retrieval and positional heads separated by a salient mid-low-frequency band. Controlled Transformers show that this boundary follows the training-length positional scale; we term it the Global Positional Band (GPBand). The analysis suggests a potential cause of zero-shot length-extrapolation failure and yields two principles: positional modeling should operate only locally, with global access through position-independent retrieval; and both functions should be assigned at head granularity with layer-specific allocation. We instantiate them in Head-wise Hybrid Architecture (HwH), using NoPE FA for global retrieval and LA for local positional modeling. With an FA-to-LA ratio below 1:3, HwH retains strong language modeling and commonsense reasoning while improving retrieval and substantially strengthening zero-shot long-context extrapolation over Transformer, LA, and a layer-wise hybrid baseline. Ablations validate both principles and component roles, highlighting principled hybrid architecture design as a promising route toward future foundation models.

cs.LG↗
arXiv2026

TalkFa: A Unified Benchmark for Farsi Dialogue Generation and Understanding

Farsi, spoken by more than 120 million people, lacks a comprehensive benchmark for dialogue generation and understanding. We introduce TALKFA, a unified benchmark comprising three complementary datasets: (1) WIKI-FADIAL, 4.2K Wikipedia-grounded dialogues for knowledge-grounded generation; (2) DAILYDIALOG-FA, 6.6K dialogues annotated for dialogue acts and emotions; and (3) PLAYDIAL-FA, 2.1K theatrical dialogues with sentiment labels. While LLMs assist data construction, every dialogue undergoes multi-stage review and revision by native Farsi speakers, and only the final human-approved dialogues are released. Experiments with six LLAMA and MISTRAL models show that LoRA substantially improves dialogue generation while requiring only 25-50% of the training data to recover over 90% of the final performance gains. Across classification tasks, FABERT achieves the best dialogue-act performance, LORA-MISTRAL-7B performs best on emotion recognition, and MISTRAL-24B achieves the highest sentiment score. Human evaluation and independent external validation demonstrate the reliability of the benchmark, while comparisons with GPT-4.1 as an LLM judge reveal that automatic metrics substantially overestimate dialogue quality. Zero-shot evaluation with frontier LLMs further shows that TalkFa remains a challenging benchmark. We will release all datasets, annotation guidelines, code, and checkpoints.

cs.CL↗
arXiv2026

Robust Speech Emotion Recognition under Tone-Word Conflict: A Benchmark and Framework

Speech emotion recognition (SER) is a crucial component of human-computer interaction, attracting extensive attention from both industry and academia. However, existing SER systems typically assume alignment between vocal tone and lexical semantics, overlooking the real-world scenarios that involve tone-word conflict-where the emotion conveyed by speech contradicts the literal meaning of the words. To bridge this gap, we introduce TWIN-SER (Tone-Word Incongruent SER), a benchmark for systematic evaluation under acoustic-semantic incongruence, and show that state-of-the-art models degrade severely under such incongruence. To address this, we propose DAS (Disentangled Acoustic-Semantic fusion), a framework that mitigates tone-word conflict by explicitly disentangling acoustic and semantic pathways, selecting informative high-energy embeddings, and adaptively fusing them via a lightweight query-based attention mechanism. Specifically, DAS comprises three crucial modules: i) a heterogeneous feature extraction module that separately captures complementary acoustic and semantic representations from raw input; ii) a high-energy embedding selection module that identifies and retains the most discriminative embeddings; and iii) a Q-Former combination module that bridges the two pathways through cross-attention, enabling robust emotion prediction under incongruent conditions. Extensive experiments demonstrate that DAS consistently outperforms existing methods in tone-word conflict scenarios, as well as in standard in-domain and zero-shot settings. Our code and datasets are available at https://github.com/24DavidHuang/FAS

eess.AS↗
arXiv2026

WeAgent-MMSearch: Native Text-Vision Interaction for Multimodal Search Agents

Multimodal search agents extend parametric knowledge with newly emerging and long-tail evidence from the open web. Yet many existing agentic search environments often expose retrieved evidence only as text and omit tool-returned images from subsequent context, reducing visually grounded trajectories to text-only reasoning. Long-horizon interaction also compounds tool-call, response-length, timeout, and budget failures, which can discard salvageable trajectories, waste rollout computation, and disturb policy updates. To address these issues, we introduce WeAgent-Harness, a multimodal agentic harness that supports native text-vision interaction and runtime recovery. Retrieved images receive persistent disk references, allowing the model to inspect, process, and cite them throughout the trajectory. Based on this harness, we develop WeAgent-MMSearch, an integrated system spanning data construction, agentic post-training, and multimodal rollout. For data construction, a strong MLLM uses WeAgent-Harness to discover, synthesize, and verify MMSearch-style tasks and collect expert trajectories. During post-training, our Failure-Aware GSPO (FA-GSPO) recovers salvageable abnormal rollouts and filters invalid ones to improve bounded multimodal planning and search. We also introduce VisTarget-Bench, a 150-task human-verified benchmark that pairs each question with a held-out target image, distinguishing image-retrieval failures from visual-perception failures. Evaluation on VisTarget-Bench and seven public benchmarks shows that agentic post-training improves the average score by 19.22 points, enabling our model to outperform similarly sized open-source models and rival models with roughly ten times its parameter count.

cs.AI↗
arXiv2005

The maximum entropy state

We give an algorithm for calculating the maximum entropy state as the least fixed point of a Scott continuous mapping on the domain of classical states in their Bayesian order.

math.PR↗
arXiv2025

Turing complete Navier-Stokes steady states via cosymplectic geometry

In this article, we construct stationary solutions to the Navier-Stokes equations on certain Riemannian $3$-manifolds that exhibit Turing completeness, in the sense that they are capable of performing universal computation. This universality arises on manifolds admitting nonvanishing harmonic 1-forms, thus showing that computational universality is not obstructed by viscosity, provided the underlying geometry satisfies a mild cohomological condition. The proof makes use of a correspondence between nonvanishing harmonic $1$-forms and cosymplectic geometry, which extends the classical correspondence between Beltrami fields and Reeb flows on contact manifolds.

math.DG↗
arXiv2026

Two Adjoint Perspectives on Fokker-Planck Optimization: A Microscopic-Macroscopic Correspondence

The Fokker-Planck equation admits both a macroscopic Eulerian description through probability densities and a microscopic Lagrangian description through stochastic trajectories. Consequently, optimization problems constrained by the Fokker-Planck equation can be formulated from either perspective. Surprisingly, the corresponding adjoint equations appear to be fundamentally different: the macroscopic adjoint is governed by the backward Kolmogorov equation, whereas the microscopic adjoint evolves pathwise along stochastic trajectories. In this note, we reconcile these two formulations by establishing their correspondence in the continuum setting. We further show that, although their discrete gradients no longer coincide after discretization, both provide consistent numerical approximations of the continuum gradient. Explicit convergence rates are established for both discretization strategies.

math.NA↗
arXiv2026

Multiplicative comparisons of Rényi entropies for weighted Bernoulli sums

We establish improved multiplicative bounds relating the Rényi entropies of different orders for weighted sums of independent Bernoulli random variables. In particular, we prove a logarithmic bound between the zeroth-order and infinity-order Rényi entropies, which yields a polynomial improvement over the square-root bound of Jain, Sah, and Sawhney. Additionally, we obtain explicit constant-factor bounds for comparisons among Rényi entropies of nonzero orders.

math.PR↗
arXiv2026

Set Theory in the Foundation of Math; Internal Classes and External Sets

Usual math sets have special types: countable, compact, open, occasionally Borel, rarely projective, etc. Each such set is described by a single set theory formula with parameters unrelated to formulas. Exotic expressions involving sets related to formulas of unbounded quantifier depth appear mostly in esoteric or foundational studies. Recognizing the internal to math (formula-specified) and external (parameter-based) aspects of math objects greatly simplifies foundations. I postulate that external sets (not internally specified, constituting the domain of quantifiable variables) are hereditarily countable and independent of purely formula-defined classes, i.e. with finite algorithmic information about them. Variables for classes are not explicitly quantified. This opens a way to eliminate all non-integer quantifiers in set theory sentences. The restrictions seem to require almost no changes in math papers, only reinterpreting some formalities.

cs.LO↗
arXiv2026

Harmonic higher weight distributions, Simonis' approach of MacWilliams identity and moments

We present a combinatorial proof of Simonis type MacWilliams identity for harmonic higher weight distributions of linear codes. Furthermore, we investigate the statistical moments of the harmonic higher weight enumerators for random linear codes. Defining the enumerators via rank functions of the generator matrices of linear codes, we prove that its expectation vanishes for all non-trivial harmonic functions due to the inherent symmetry of random matrices, and we also derive an explicit, non-trivial formula for the covariance.

math.CO↗
arXiv2026

Shannon's problem on the monotonicity of entropy and a Conjecture of Tao

Let $X_1,X_2,\ldots$ be i.i.d. finitely supported random variables in a torsion-free abelian group, and write $S_k=X_1+\cdots+X_k$, and $H(S_k)$ is the Shannon entropy $S_k$, for all $k \ge 1$. We prove that, for every fixed $n\geq1$, \[ H(S_{n+1})-H(S_n) \geq \frac12\log\frac{n+1}{n} -o_{H(X_1)\to\infty}(1), \] uniformly over the ambient group and the input law. This proves a conjecture of Tao [29] in 2010.

math.PR↗
arXiv2026

Geometric integrators for adiabatically closed simple thermodynamic systems

A variational formulation for non-equilibrium thermodynamics was developed by Gay-Balmaz and Yoshimura. In a recent article, the first two authors of the present paper introduced partially cosymplectic structures as a geometric framework for thermodynamic systems, recovering the evolution equations obtained variationally. In this paper, we develop a discrete variational principle for adiabatically closed simple thermodynamic systems, which can be utilised to construct numerical integrators for the dynamics of such systems. The effectiveness of our method is illustrated with several examples.

math-ph↗
arXiv2026

A counterexample to Kusner's conjecture on equilateral sets

We disprove Kusner's 1983 conjecture that every equilateral set in $\ell_p^n$ with $2 57$. This is the first equilateral set of more than $n+1$ points in $\ell_p^n$ for any finite $p\ge2$. The construction persists on an open interval of exponents around $5$; since Ge, Xu and Zhou recently proved the conjecture for $2\le p\le4$, the infimum of exponents at which it fails lies in $[4,5)$. The configuration is the unique solution of an explicit polynomial system with rational coefficients in a rational box, established in exact arithmetic.

math.MG↗
arXiv2026

Edge codes constructed from unicyclic graphs

Jaramillo-Velez recently introduced edge codes, a new class of toric evaluation codes constructed from the edges of a (hyper)graph $\mathcal{H}$. In the case that $\mathcal{H}$ is a tree, Jaramillo-Velez computed both the minimum distance and the weight distribution of the associated code. In this paper, we study edge codes associated to unicyclic graphs. Our most striking result is that computing the parameters of these codes is subtle in the case that the induced cycle has an even length because these values will depend on certain conditions regarding the length of the cycle and the size of the base field.

math.CO↗
arXiv2025

Quantum channel discrimination against jammers

We study the problem of quantum channel discrimination between two channels with an adversary input party (a.k.a. a jammer). This setup interpolates between the best-case channel discrimination as studied by (Wang & Wilde, 2019) and the worst-case channel discrimination as studied by (Fang, Fawzi, & Fawzi, 2025), thereby generalizing both frameworks. To address this problem, we introduce the notion of minimax channel divergence and establish several of its key mathematical properties. We prove the Stein's lemma in this new setting, showing that the optimal type-II error exponent in the asymptotic regime under parallel strategies is characterized by the regularized minimax channel divergence.

quant-ph↗