arXiv subjects

Yuchen Yang

Publications and source records attributed to Yuchen Yang.

At least 37 records · Page 2Linked to original sources

arXiv2026

Bounded Representatives in Critical Sobolev-Hodge Spaces

Let $n\geq 2$, $1\leq \ell\leq n-1$, and $1<p<\infty$. We prove that every $v\in \dot W^{n/p,p}(\mathbb{R}^n;Λ^\ell)$ has a representative $u\in \dot W^{n/p,p}\cap L^\infty$ with $du=dv$ and $\max{|u|{\dot W^{n/p,p}},|u|{L^\infty}}\lesssim |v|{\dot W^{n/p,p}}$. Equivalently, $d[\dot W^{n/p,p}Λ^\ell]=d[(\dot W^{n/p,p}\cap L^\infty)Λ^\ell]$ with equivalent quotient norms. The proof reduces the selection problem to an endpoint graph estimate for a Riesz potential and the exact Hodge projection. Its main analytic input is a finite-dimensional-input Maz'ya--$Φ$ inequality for operator-valued homogeneous kernels. For the Riesz/Hodge pair, a nonlinear spherical profile built from the projected kernel has exact atomic cancellation and is coercive by the identity $\int{S^{n-1}}P(θ),d\barσ=(\ell/n)\operatorname{Id}$. Frequency-localized graph closure and Hahn--Banach duality then return a bounded representative.

math.FA↗

arXiv2026

The Minimum Cardinality of a Dependent Finite Gabor System Is Four

Recent work produced a linearly dependent system of twelve time--frequency shifts of a Schwartz function, disproving the HRT conjecture. We show that four shifts already suffice, and hence that four is the smallest possible cardinality of a dependent finite Gabor system. More precisely, set $α=\frac13+10^{-12}\sqrt2$ and $β=\frac13+10^{-12}\sqrt3$. We construct a nonzero complex-valued function $f\in\mathcal S(\mathbb R)$ and $λ\ne0$ such that $\left(I+\frac12W(1,0)+\frac12W(0,1/2)\right)W(α,β/2)f=λf$, where $W$ denotes the Weyl time--frequency shift. Since every system of at most three shifts of a nonzero $L^2(\mathbb R)$ function is linearly independent, this gives the sharp cardinality threshold. The construction uses the rank-two Zak bundle naturally associated with the covolume-$1/2$ lattice generated by $(1,0)$ and $(0,1/2)$. At the rational translation $(1/3,1/3)$, the three-step return has a uniformly dominated contracting line. A finite outward-rounded interval certificate proves that this line is topologically trivial. A quantitative perturbation argument carries the dominated line to the explicit algebraic translation above. A winding calculation and a Diophantine cohomological equation then flatten its scalar multiplier, and inverse Zak folding produces the required Schwartz function.

math.FA↗

arXiv2026

A Finite E-Group of Nilpotency Class Three

A group is an E-group if every element commutes with each of its endomorphic images. Caranti asked whether a finite E-group can have nilpotency class three. We prove that the $3$-group of order $3^{84}$ introduced by Abdollahi, Faghihi, and Mohammadi Hassanabadi, and later shown by Abdollahi, Faghihi, Linton, and O'Brien to have the corresponding automorphism property, is an E-group. Let $P$ denote this group and put $V=P/Φ(P)\cong \mathbb{F}_3^9$. The nine power relations of $P$ determine a linear map $q:V\longrightarrowΛ^2 V$. We prove that $q$ has no nonzero proper subspace $U$ satisfying $q(U)\subseteqΛ^2 U$. Since the image induced by any endomorphism of $P$ on $V$ has precisely this closure property, every endomorphism acts on $V$ either invertibly or trivially. The invertible case is the known A-group case. In the trivial case the image first lies in $Φ(P)=P'$, and the power relations then force it into $Ω_1(P')=Z(P)$. Thus every element commutes with every endomorphic image. The tensor rigidity is reduced to an exact finite calculation on the $9841$ points of $\mathrm{PG}(8,3)$.

math.GR↗

arXiv2026

HijackKV: New Threat in Position-Independent KV Cache Reuse

Key-Value (KV) cache reduces inference latency in large language models (LLMs). Traditional prefix-based reuse has low cache hit rates across inference requests because it requires exact token and position matches. To improve efficiency, recent system optimizations introduce position-independent KV reuse, allowing KV cache to be reused whenever identical text chunks appear, regardless of their position in the sequence. We show this design introduces a new threat, KV Cache Hijacking. Since KV caches are retrieved by token match but encode the context in which they were originally computed, the KV tied to a benign-looking token chunk may encode an attacker-controlled prefix. When later reused in a victim query, this contaminated KV silently hijacks the model's behavior, even if no attacker-controlled text appears in the input. We introduce HIJACKKV, the first attack framework that systematically exploits this vulnerability, demonstrating its severity and practicality. HIJACKKV optimizes an attacker-controlled prefix, so that the KV computed for a subsequent common benign text encodes the attacker's goal, while the text remains unchanged for future cache hits. HIJACKKV achieves an average 94% success rate in a single attempt, remains effective under realistic constraints including low hit rates (10%) and frequent recomputation (50%), persists over multi-turn interactions, and transfers across models in black-box settings. We further provide design insights for building secure KV reuse systems.

cs.CR↗

arXiv2026

A Proof of the Dittert Conjecture via Boundary Rigidity

Let $\mathcal{K}_n$ be the simplex of nonnegative $n \times n$ matrices whose entries sum to $n$. For $A$ in $\mathcal{K}_n$, with row sums $r_1,\ldots,r_n$ and column sums $c_1,\ldots,c_n$, define $Φ(A)=\prod_{i=1}^n r_i+\prod_{j=1}^n c_j-\mathrm{per}(A)$. Dittert conjectured that $Φ$ is uniquely maximized by the uniform matrix $U_n=J_n/n$, with maximum $2-n!/n^n$. We prove the conjecture for every $n \geq 2$. Hwang's theorem already determines every positive maximizer, so the essential problem is to exclude maximizers on the boundary of $\mathcal{K}_n$. A reduction of Cheon and Wanless supplies two zero entries in distinct rows and columns. In order four, we classify all admissible support strata and exclude them by exact Karush-Kuhn-Tucker identities together with a Bernstein-form positivity certificate. For all $n \geq 5$, an attained-stratum averaging argument compresses a hypothetical boundary maximizer to a seven-parameter matrix with one multiplicity $m=n-2$. A symbolic odd-variable expansion, a cofactor identity at the two missing entries, and uniform coefficient inequalities then contradict the one-sided multiplier conditions. This argument is uniform in $m$ and uses no finite enumeration. We also give independent spectral proofs in dimensions 7 through 13 and prescribed-zero proofs in dimensions 14 and 15. Every dimension-dependent calculation is certified over the rationals and recorded explicitly in the appendices.

math.RA↗

arXiv2026

An Explicit Counterexample to Stanley's Rankwise Lower-Bound Conjecture for Differential Posets

In Problem 6 of his 1988 paper on differential posets, Stanley asked for the least possible cardinality of a fixed rank of an $r$-differential poset and suggested that the minimum should be attained by $Y^r$, the $r$-fold Cartesian power of Young's lattice. We disprove the resulting universal coefficientwise lower bound. For every $r\geq 3$, we construct an infinite $r$-differential poset $P^{(r)}$ satisfying $\lvert P^{(r)}_4\rvert=\lvert (Y^r)_4\rvert-\lfloor r/3\rfloor$. For $r=3$, the construction replaces thirteen rank-four lower-cover blocks of $Y^3$ by twelve blocks with the same point and pair incidence multiplicities, producing the initial rank sequence $1,3,9,22,50$ instead of $1,3,9,22,51$. A reflection extension then yields an infinite differential poset. The construction does not address the cases $r=1$ and $r=2$.

math.CO↗

arXiv2026

A Negative Answer to Stanley's Problem 4 on Differential Posets

In Problem 4 of his 1988 paper on differential posets, Stanley asked whether the weighted $k$-multichain series of an arbitrary differential poset is always a rational multiple of the $k$th power of its rank series. We answer this question in the negative. Already for $k=2$, we construct a locally finite $1$-differential poset $P$ for which $M_{P,2}(q)/F_P(q)^2$ is not rational over any field of characteristic zero. The construction uses Wagner's crown reflection. At each sufficiently high rank there are two valid one-rank extensions with the same required Gram matrix and with new rank sizes differing by one. We show that the first quotient coefficient affected by that rank distinguishes the two choices. Choosing successively between them and diagonalizing against the rational power series produces the required poset. The same coefficient argument also yields continuum many distinct quotient series, of which continuum many are nonrational.

math.CO↗

arXiv2026

Self-complementary completions on six vertices

Let $\cthreshold(n)$ be the largest integer $q$ such that every loopless digraph on $n$ vertices with at most $q$ arcs is isomorphic to a spanning subdigraph of a self-complementary digraph of order $n$. We prove that $\cthreshold(6)=7$. The upper bound is witnessed by \[ \bK{3}\dunion (x\longrightarrow y\longrightarrow z), \] and follows from a direct argument with a self-complementing permutation. We also determine the complete eight-arc obstruction layer: it consists of five isomorphism classes, or three after converse digraphs are identified. All five are arc-minimal. Each nevertheless packs with an isomorphic copy of itself, so ordinary packing is strictly weaker than same-order self-complementary completion already at this first failure layer.

math.CO↗

arXiv2026

An Exact Counterexample to Carlson's Associated-Prime Depth Conjecture from a Group of Order 128

In Question~3.1 of his 1995 paper on depth and transfer, Carlson asked whether the depth of a finite-group cohomology ring is always realized by the dimension of one of its associated primes. We give a negative answer. Let \[ G=\SG{128}{859},\qquad k=\kbar. \] An exact presentation certificate proves that $\depth H^*(G;k)=2$. Okuyama's associated-prime theorem would convert an associated prime of dimension two into a rank-two elementary abelian subgroup $E\leq G$ satisfying $\depth H^*(C_G(E);k)=2$. We enumerate all $75$ rank-two elementary abelian subgroups of $G$ and obtain six centralizer types. Duflot's theorem gives depth at least three for four types, while exact ideal-quotient certificates exhibit regular sequences of length three for the remaining two. Hence every rank-two centralizer has cohomological depth at least three, so $H^*(G;k)$ has no associated prime of dimension two. The finite group presentation, the three cohomology-ring presentations, the enumeration summary, and the exact algebraic certificates are included for independent verification.

math.GR↗

arXiv2026

PagedWeight: Efficient MoE LLM Serving with Dynamic Quality-Aware Weight Quantization

Mixture-of-Experts (MoE) is a popular class of large language models (LLMs), offering high efficiency and accuracy. However, in KV-cache-intensive serving scenarios, MoEs often exhibit a tension between the GPU memory requirements of the model weights and the growing KV cache. We propose PagedWeight, a novel management method for MoE LLM serving that dynamically quantizes MoE model's weights at runtime and balances expert-weight precision with the KV cache sizes. PagedWeight exposes and effectively navigates the complex tradeoff between the model's task accuracy, memory consumption, and throughput/latency. Across several memory-sensitive MoE serving scenarios, PagedWeight improves the quality-memory tradeoff over several existing quantization baselines. PagedWeight achieves FP16-equivalent accuracy with up to 72.0% GPU memory savings and 1.94$\times$ throughput improvement, and improves quality over quantization methods by up to 39.3% at a similar memory budget with at most 4.1% throughput loss.

cs.LG↗

arXiv2026

Rethinking Forgery Attacks on Semantic Watermarks in Black-Box Settings: A Geometric Distortion Perspective

Recent studies have shown that semantic watermarks, which embed information into the initial noise of latent diffusion models (LDMs), are vulnerable to black-box forgery attacks. However, existing methods primarily rely on empirical evidence and lack a rigorous theoretical understanding of the conditions under which such attacks succeed or fail. To bridge this gap, we rethink the nature of such attacks through the lens of rate-distortion in the latent space. Our analysis identifies an irreducible distortion floor due to structural mismatches between proxy and target models, which fundamentally limits the fidelity of forged watermarks. We further characterize this distortion as structured geometric deviations on the latent manifold, in the form of global drift and local deformation rather than stochastic noise. Leveraging these insights, we propose a scheme-agnostic detection method that distinguishes forged samples before watermark verification. Extensive experiments demonstrate the effectiveness of our method across diverse black-box scenarios, while preserving robustness to common distortions.

cs.CR↗

arXiv2026

AREAL-DTA: Dynamic Tree Attention for Efficient Reinforcement Learning of Large Language Models

Reinforcement learning (RL)-based post-training for large language models (LLMs) is computationally expensive, as it generates many rollout sequences that frequently share long token prefixes. Existing RL frameworks usually process these sequences independently during policy training, i.e., repeatedly recomputing identical prefixes in both the forward and backward passes of policy gradient computation, leading to substantial inefficiencies in computation resources and memory usage. Although prefix sharing naturally induces a tree structure over rollouts, packed tree-mask approaches scale poorly in RL settings. In this paper, we introduce AReaL-DTA, which efficiently exploits prefix sharing in RL training. AReaL-DTA employs a depth-first search (DFS)-based execution strategy that dynamically traverses the rollout prefix tree during both forward and backward computation, materializing only a single root-to-leaf path at a time. To further improve scalability, AReaL-DTA incorporates a load-balanced distributed batching mechanism that dynamically constructs and processes prefix trees across multiple GPUs. On $τ^2$-bench, AReaL-DTA improves training throughput by up to $8.31\times$ over dense training and up to $1.70\times$ over sparse training. Our code is available at https://github.com/areal-project/AReaL/tree/feat/dta.

cs.LG↗

arXiv2026

CMI-RewardBench: Evaluating Music Reward Models with Compositional Multimodal Instruction

While music generation models have evolved to handle complex multimodal inputs mixing text, lyrics, and reference audio, evaluation mechanisms have lagged behind. In this paper, we bridge this critical gap by establishing a comprehensive ecosystem for music reward modeling under Compositional Multimodal Instruction (CMI), where the generated music may be conditioned on text descriptions, lyrics, and audio prompts. We first introduce CMI-Pref-Pseudo, a large-scale preference dataset comprising 110k pseudo-labeled samples, and CMI-Pref, a high-quality, human-annotated corpus tailored for fine-grained alignment tasks. To unify the evaluation landscape, we propose CMI-RewardBench, a unified benchmark that evaluates music reward models on heterogeneous samples across musicality, text-music alignment, and compositional instruction alignment. Leveraging these resources, we develop CMI reward models (CMI-RMs), a parameter-efficient reward model family capable of processing heterogeneous inputs. We evaluate their correlation with human judgment scores on musicality and alignment on CMI-Pref along with previous datasets. Further experiments demonstrate that CMI-RM not only correlates strongly with human judgments, but also enables effective inference-time scaling via top-k filtering. Code is available at GitHub (https://github.com/Haiwen-Xia/CMI-RewardBench). Model weights: CMI-RM (https://huggingface.co/HaiwenXia/CMI-RM). Datasets: CMI-Pref-Pseudo (https://huggingface.co/datasets/HaiwenXia/cmi-pref-pseudo) and CMI-Pref (https://huggingface.co/datasets/HaiwenXia/cmi-pref)

cs.SD↗

arXiv2026

D^2SD: Accelerating Speculative Decoding with Dual Diffusion Draft Models

Speculative decoding accelerates autoregressive large language model inference by drafting multiple tokens and verifying them in a single target-model forward pass. Recent diffusion-based drafters generate an entire block of tokens in parallel but usually commit to a single draft sequence per verification: once the first mismatch occurs, all subsequent draft tokens are discarded, resulting in a limited acceptance rate. Naively batching more draft candidate sequences only introduces a marginal improvement, as redundant or poorly placed branches increase the cost of drafting and verification without proportionally increasing the number of accepted tokens. We propose D^2SD, a dual diffusion draft speculative decoding framework that organizes candidates into a confidence-guided prefix tree, where the first diffusion drafter generates a block along with per-position confidence scores that are used to identify the most likely rejection boundary and select the top-K prefix ranges for recovery; the second variable-prefix diffusion drafter re-anchors at each selected prefix and proposes alternative continuations in one batched pass; the resulting shared-prefix candidates are jointly verified via cascade attention. Empirically, D^2SD shows clear improvements over both the underlying diffusion approach and strong autoregressive speculative decoding baselines.

cs.DC↗

arXiv2026

PromptCOS: Towards Content-only System Prompt Copyright Auditing for LLMs

System prompts are critical for shaping the behavior and output quality of large language model (LLM)-based applications, driving substantial investment in optimizing high-quality prompts beyond traditional handcrafted designs. However, as system prompts become valuable intellectual property, they are increasingly vulnerable to prompt theft and unauthorized use, highlighting the urgent need for effective copyright auditing, especially watermarking. Existing methods rely on verifying subtle logit distribution shifts triggered by a query. We observe that this logit-dependent verification framework is impractical in real-world content-only settings, primarily because (1) random sampling makes content-level generation unstable for verification, and (2) stronger instructions needed for content-level signals compromise prompt fidelity. To overcome these challenges, we propose PromptCOS, the first content-only system prompt copyright auditing method based on content-level output similarity. PromptCOS achieves watermark stability by designing a cyclic output signal as the conditional instruction's target. It preserves prompt fidelity by injecting a small set of auxiliary tokens to encode the watermark, leaving the main prompt untouched. Furthermore, to ensure robustness against malicious removal, we optimize cover tokens, i.e., critical tokens in the original prompt, to ensure that removing auxiliary tokens causes severe performance degradation. Experimental results show that promptCOS achieves high effectiveness (99.3% average watermark similarity), strong distinctiveness (60.8% higher than the best baseline), high fidelity (accuracy degradation no greater than 0.6%), robustness (resilience against four potential attack categories), and high computational efficiency (up to 98.1% cost saving).

cs.CR↗

arXiv2026

ZipMoE: Efficient On-Device MoE Serving via Lossless Compression and Cache-Affinity Scheduling

While Mixture-of-Experts (MoE) architectures substantially bolster the expressive power of large-language models, their prohibitive memory footprint severely impedes the practical deployment on resource-constrained edge devices, especially when model behavior must be preserved without relying on lossy quantization. In this paper, we present ZipMoE, an efficient and semantically lossless on-device MoE serving system. ZipMoE exploits the synergy between the hardware properties of edge devices and the statistical redundancy inherent to MoE parameters via a caching-scheduling co-design with provable performance guarantee. Fundamentally, our design shifts the paradigm of on-device MoE inference from an I/O-bound bottleneck to a compute-centric workflow that enables efficient parallelization. We implement a prototype of ZipMoE and conduct extensive experiments on representative edge computing platforms using popular open-source MoE models and real-world workloads. Our evaluation reveals that ZipMoE achieves up to $72.77\%$ inference latency reduction and up to $6.76\times$ higher throughput than the state-of-the-art systems.Our code is available at: https://github.com/npnothard/ZipMoE-ICML26.

cs.DC↗

arXiv2026

AgentKernelArena: Generalization-Aware Benchmarking of GPU Kernel Optimization Agents

GPU kernel optimization is increasingly critical for efficient deep learning systems, but writing high-performance kernels still requires substantial low-level expertise. Recent AI coding agents can iteratively read code, invoke compilers and profilers, and refine implementations, yet existing kernel benchmarks evaluate single LLM calls rather than full agent workflows, and none include both kernel-to-kernel optimization and unseen-configuration generalization testing. We present AgentKernelArena, an open-source benchmark for measuring AI coding agents on GPU kernel optimization. The benchmark contains 196 tasks spanning HIP-to-HIP optimization, Triton-to-Triton optimization, and PyTorch-to-HIP translation, and evaluates complete agent workflows in isolated workspaces using gated compilation, correctness, and performance checks, centralized scoring and an unseen-configuration generalization protocol that tests whether optimizations transfer to input configurations the agent never observed. Across production agents including Cursor Agent, Claude Code, and Codex Agent, we find near-perfect compilation and high correctness rates on most task categories, with the strongest configurations achieving mean speedups of up to 6.89x on PyTorch-to-HIP, 6.69x on HIP-to-HIP, and 2.13x on Triton-to-Triton tasks. Our unseen-configuration evaluation shows that HIP-to-HIP and Triton-to-Triton optimizations largely transfer to unseen input shapes, while PyTorch-to-HIP exhibits substantial correctness drops, indicating that agents generating kernels from scratch frequently hardcode shape-specific assumptions. AgentKernelArena is designed as a modular, extensible framework for rigorous evaluation of agentic GPU kernel optimization across agents, tasks, and hardware targets.

cs.CL↗

arXiv2026

ARQ: A Mixed-Precision Quantization Framework for Accurate and Certifiably Robust DNNs

Mixed precision quantization has become an important technique for optimizing the execution of deep neural networks (DNNs). Certified robustness, which provides provable guarantees about a model's ability to withstand different adversarial perturbations, has rarely been addressed in quantization due to the unacceptably high cost of certifying robustness. This paper introduces ARQ, an innovative mixed-precision quantization method that not only preserves the clean accuracy of the smoothed classifiers, but also maintains their certified robustness. ARQ uses reinforcement learning to find accurate and robust DNN quantization, while efficiently leveraging randomized smoothing, a popular class of statistical DNN verification algorithms. ARQ consistently performs better than multiple state-of-the-art quantization techniques across all the benchmarks and the input perturbation levels. The performance of ARQ quantized networks reaches that of the original DNN with floating-point weights, while using only 1.5% instructions and the highest certified radius. ARQ's code is available at https://github.com/uiuc-arc/ARQ.

cs.LG↗