arXiv subjects

Zihan Zhang

Publications and source records attributed to Zihan Zhang.

At least 19 recordsLinked to original sources

arXiv2026

Deterministic Constructions of Reed-Solomon Codes Beyond the Johnson Bound

We give a deterministic quasipolynomial-time construction of Reed-Solomon codes that are list-decodable beyond the Johnson radius. Specifically, for every $ε\in(0,1]$ and all sufficiently large $n$, we construct an $[n,k]$ Reed-Solomon code of rate $R=Ω(ε/(1+\log(1/ε)))$ over a field of size $(nk)^{quasi-poly(nk)}$ that is $(1-ε,O(1/ε))$ list-decodable. The construction runs in quasi-poly(nk) time. We also give a deterministic construction of $[n,k]$-MDS$(3)$ Reed-Solomon codes for all integers $1\leq k<n$, with the same asymptotic bounds on field size and construction time. In the constant-rate regime, our field-size bound substantially improves the bound of $O(n^{k^{2k}})$ achieved by Roth's construction (Roth, IEEE TIT 2022). Our constructions exploit a connection to polynomial identity testing for read-once determinants, together with the quasipolynomial isolating-weight construction of Gurjar and Thierauf for linear matroid intersection (Gurjar and Thierauf, STOC 2017 and Computational Complexity 2020).

cs.CC↗

arXiv2026

ADTGuard: Adaptive Depth-Time Safeguard for Streaming Inference in Large Language Models

Large Language Models (LLMs) can generate fluent responses to diverse user requests, yet streaming may expose users to harmful content before generation is complete. Existing guardrails face two limitations in this setting. First, post-hoc moderation at response or chunk boundaries delays intervention, risking harmful exposure when content is released before verification. Second, even with token-level detection, coarse response-level supervision does not specify when harmful content begins, while fixed-layer readouts may miss relevant safety signals at other depths. To address these limitations, we introduce ADTGuard, which checks each token before release, progressively refines token-level training targets, and adapts layer selection to the current prefix. ADTGuard models risk across depth and time through Depth-Time Safety Dynamics (DTSD), which integrates safety evidence across layers at each token and uses it to guide risk accumulation over successive tokens. To adapt the choice of observation layers to the current prefix, we propose the Causal Depth Router (CDR). With only response-level labels available, we further develop Risk-Onset Target Refinement (RTR) to progressively construct token-level training targets for both components. Through extensive experiments across multiple safety benchmarks, we demonstrate that ADTGuard consistently achieves strong streaming detection performance, matching or surpassing state-of-the-art safeguards while requiring only 16M trainable parameters and maintaining competitive per-token latency.

cs.AI↗

arXiv2026

Making Self-Driving Laboratories Auditable:A Unified Framework for Hybrid Actions,Measurements, and Safe Execution

Self-driving laboratories (SDLs) are laboratory systems that couple experimental planning, automated execution, and measurement feedback in a closed loop. Integrating flexible robot control with the typed application programming interfaces (APIs) and continuous measurements exposed by laboratory instruments remains an execution-interface challenge. To address this challenge, we propose a traceable framework comprising four components: LAM (Lab Action Model), OpenSDL, Safe-SDL, and L3-Bench. LAM is a proposed measurement-conditioned policy architecture that extends vision-language-action paradigms to generate both continuous robot trajectories and typed instrument API calls. OpenSDL is an execution substrate with an initial control implementation, designed to map role-level operations to heterogeneous devices, coordinate execution, and record timestamped causal events. The proposed Safe-SDL runtime gate combines pre-dispatch schema and resource checks with signal temporal logic monitoring during execution, including extended waiting periods. L3-Bench (Level-3 Laboratory Benchmark) specifies an episode-level evaluation protocol covering physical outcomes, timing, reproducibility, safety violations, and fault recovery. Together, these components provide an end-to-end design for linking hybrid action generation, monitored device execution, measurement feedback, and experimental evaluation, addressing coordination and traceability challenges in SDL workflows.

cs.RO↗

arXiv2026

A Sharp Bound for Additive Complements

Let $A$ and $B$ be infinite sets of nonnegative integers whose sum contains all sufficiently large integers, and let $A(x)$ and $B(x)$ be their counting functions. We give a discrete proof of the sharp implication \[ \limsup_{x\to\infty}\frac{A(x)B(x)}{x}<\frac32 \quad\Longrightarrow\quad A(x)B(x)-x\longrightarrow+\infty. \] The constant $3/2$ is best possible. Using finite convolution sums, we show that a long gap in one set forces a gap in the other. We then compare the counting functions before and after the gap to obtain the sharp bound.

math.NT↗

arXiv2026

Cheap to Hypothesize, Costly to Verify: The Defense Surface of Agentic Vulnerability Discovery

Autonomous LLM agents turn vulnerability discovery into a repository-scale search: they generate many vulnerability hypotheses but can verify only a subset under a finite budget. We show that autonomous vulnerability discovery exhibits a hypothesis-verification asymmetry, where verifying a candidate hypothesis through reachability analysis, execution, and proof-of-concept construction is substantially more expensive than forming it. Under a finite resource budget, this makes autonomous discovery a resource-bounded selective-verification process, further exposing verification effort as a unique defense surface. We present RedHerring, which inserts certifiably safe decoys that divert verification effort from real vulnerabilities. Each decoy combines a CVE-derived vulnerability chain that attracts verification with a false bridge that keeps its dangerous sink unreachable. A private certificate lets the defender verify this property efficiently, while establishing the same fact from the released repository requires solving a computationally hard problem. RedHerring further adapts each decoy to the target repository so that it reads as ordinary program logic. Across 33 OSS-Fuzz projects, 70 evaluation instances, and five models under matched budgets, RedHerring reduces real vulnerabilities discovered by 38.7-60.4%. Trajectory analysis shows that agents spend 30.6-51.5% of completion tokens and an estimated 32.5-49.9% of runtime verifying decoys, showing that RedHerring redirects a substantial fraction of the fixed search budget toward decoys. When explicitly informed that decoys may be present, the agent adapts its search strategy, yet RedHerring still reduces vulnerabilities discovered by 37.2% relative to an informed Baseline, showing that its effectiveness does not depend on decoy secrecy.

cs.CR↗

arXiv2026

Group-Graph Policy Optimization for Long-Horizon Agentic Reinforcement Learning

Group-based Reinforcement Learning (RL) has significantly enhanced Large Language Models (LLMs) in agentic scenarios. To achieve finer-grained policy updates, recent agentic RL frameworks have shifted from trajectory-level to step-level training. However, long-horizon agentic RL suffers from severe reward sparsity and delay, as feedback is often deferred for dozens of interaction steps. While existing step-level frameworks refine training granularity, their credit assignment remains coarse-grained and still treats agent exploration as isolated, linear trajectories. This oversimplified perspective ignores the inherent graph structure of state transitions, leading to high-variance state-value estimation and myopic, localized credit assignment. To overcome these critical bottlenecks, we propose Group-Graph Policy Optimization (G2PO), a novel group-based RL algorithm tailored for multi-turn agentic tasks. G2PO explicitly transforms linear interaction trajectories into a global state-transition graph. By aggregating identical observations across different trajectories, we introduce group-aggregation state-value estimation that reduces sampling variance and trajectory-dependent bias. Furthermore, we redefine agent actions as transitions between state nodes and propose an edge-centric advantage estimation strategy. By globally standardizing Temporal Difference (TD) errors across the entire graph, G2PO explicitly identifies and prioritizes critical transitions that drive absolute task progress. Extensive experiments on representative long-horizon benchmarks-WebShop, ALFWorld, and AppWorld-demonstrate that G2PO substantially outperforms state-of-the-art prompt-based and RL baselines, achieving remarkable success rate improvements of up to 22.2% over GRPO.

cs.LG↗

arXiv2026

SWE-at-Scale: Scalable Issue Synthesis from Historical Bug Fixes

As coding agents become increasingly capable, robust evaluation requires a broader and more diverse supply of verifiable software engineering (SWE) tasks. However, real-world tasks are constrained by the natural frequency of issue reporting and the substantial cost of manual curation. Furthermore, existing synthetic approaches rely primarily on the pretrained knowledge of large models coupled with heuristic prompting, often failing to capture the authentic, complex mechanics of software failures. To exponentially scale SWE task production, we introduce SWE-at-Scale, a framework that automatically synthesizes realistic issues by reverse-engineering real-world software fixes. Our key insight is that historical fixes encapsulate deep mechanistic knowledge of bug formation: inverting a fix transforms repair supervision into bug-induction supervision grounded in actual development scenarios. SWE-at-Scale transfers these learned bug patterns to novel code contexts, repeatedly sampling diverse bug typologies to construct executable SWE tasks. Extensive experiments show that SWE-at-Scale generates more diverse and realistic SWE tasks than current synthesis baselines while posing greater challenges to state-of-the-art coding agents. Notably, SWE-at-Scale can generate distinct bug types from a single code context, with bug diversity scaling robustly even up to 200 generations per file. Overall, SWE-at-Scale turns finite real-world fixes into reusable supervision for scalable synthesis of realistic, diverse, and challenging SWE tasks.

cs.SE↗

arXiv2026

LoopRPT: Reinforcement Pre-Training for Looped Language Models

Looped language models (LoopLMs) perform iterative latent computation to refine internal representations, offering an alternative to explicit chain-of-thought (CoT) reasoning. However, existing reinforcement learning (RL) paradigms primarily target output tokens, creating a structural mismatch with looped architectures whose reasoning unfolds implicitly. In this work, we propose LoopRPT, a reinforcement pre-training framework tailored for LoopLMs. By reframing next-token prediction as a next-token reasoning task, LoopRPT assigns reinforcement signals directly to latent steps using an EMA teacher reference and noisy latent rollouts. This formulation enables RL to directly shape intermediate representations, compressing effective reasoning into fewer iterations. We instantiate LoopRPT on Ouro across multiple model scales. Results show that LoopRPT improves per-step representation quality and achieves Pareto dominance in accuracy-computation trade-offs. Large gains on hard tokens indicate that LoopRPT enhances early-stage reasoning rather than merely encouraging premature exits. Our findings highlight reinforcement pre-training as a principled paradigm for learning efficient latent reasoning in LoopLMs.

cs.CL↗

arXiv2026

Large-Step Last-Iterate Convergence of Random-Reshuffling Stochastic Gradient Descent

Random reshuffling stochastic gradient descent (RR-SGD) is widely used for finite-sum optimization in machine learning. For convex $L$-smooth components, recent work establishes convergence guarantees for an averaged iterate with component stepsizes as large as order $1/L$. However, the final iterate is a natural output in practice, and existing last-iterate guarantees in this setting require stepsizes that scale inversely with the number of components $n$. We establish an expected objective-gap bound for the last iterate of standard RR-SGD on unconstrained problems with a constant component stepsize satisfying $0<η\lesssim 1/(L(1 + \log(nK)))$, where $K$ is the number of epochs. By retaining the sampling bias at random comparison points, we remove the explicit $1/n$ factor from the stepsize restriction. Combined with existing small-step bounds, our result matches the corresponding averaged-iterate convergence rate up to logarithmic factors.

math.OC↗

arXiv2026

SafeDriveVLA: Navigation-Conditioned World Model Dreaming for Conflict-Aware End-to-End Autonomous Driving

Vision-Language-Action (VLA) models are gaining attention in autonomous driving, inheriting commonsense priors from large language models (LLMs) and widening the navigation interface from a fixed command set to free-form natural-language instructions. However, this open-ended interface exposes a new vulnerability surface: an inattentive driver may issue instructions that are unsafe given the current scene, and a malicious user may issue dangerous ones on purpose. We present the first benchmark suite that evaluates navigation following and conflict awareness together, along with adversarial robustness. Existing VLAs fall short on both: SimLingo completes no language-instructed lane change in closed loop, and all models degrade sharply under conflicting signals. We propose SafeDriveVLA, the first driving VLA that (1) explicitly predicts a three-level navigation-compliance mode to decouple conflict reasoning from action generation, and (2) uses navigation-conditioned world model dreaming to inform this prediction. Unlike prior world models that roll out expert or planned actions, ours dreams of strictly following the navigation signal, showing when following is safe. SafeDriveVLA reaches 88.16 Driving Score (DS) and 68.64% Success Rate (SR) on Bench2Drive, lifts closed-loop language following by 49.3% and reduces collisions under unsafe instructions from 60 to 38 compared to the best SimLingo variant. Video demonstrations are available on our project page.

cs.RO↗

arXiv2026

Auto-AEG: Scalable Data Construction for Open-Vocabulary Audio Event Grounding

Large Audio-Language Models (LALMs) reason fluently about sound yet struggle to localize precisely when events occur, while classical Sound Event Detection (SED) attains frame-level precision only over a closed label set. At the intersection of these paradigms lies the task of Open-Vocabulary Audio Event Grounding: predicting all time intervals of a target sound event described by an arbitrary natural language query. Progress is bottlenecked by data scarcity: no large-scale resource provides open-vocabulary onset/offset supervision, and manual temporal annotation is prohibitively expensive. To address this, we introduce Auto-AEG, a scalable pipeline that constructs such supervision by automatic data construction and model fine-tuning. It pairs programmatically synthesized clips, which carry placement-exact ground-truth intervals for supervised cold-start, with multi-model pseudo-labels on real-world audio that supply the reward signal for reinforcement learning. Training with this pipeline yields large temporal-localization gains on AEGBench, an independent difficulty-stratified benchmark whose annotations we release, and these gains generalize to various held-out SED and audio grounding benchmarks. Our results show that automatically constructed data, coupled with interval-aware reward design, provides an effective data-side route to expanding the temporal localization capability of LALMs.

cs.SD↗

arXiv2026

Optimal Online Regret for Context-Lumpable Bandits

We study stochastic contextual bandits with an unknown context-lumpable structure. The $S$ contexts are partitioned into $r$ blocks, and every arm has the same mean reward across contexts in the same block. Under arbitrary context distributions and without separation assumptions, we design an algorithm with expected regret $\widetilde{O}(\sqrt{r(S+K)T})$, matching the lower bound of Lee et al. (2023) up to logarithmic factors and improving their previous upper bound by a factor of $r$. The algorithm operates over dyadic accuracy levels, using a baseline policy and confidence-based early stopping to control exploration. It then performs cross-context elimination: since rewards are identical within a block, one selected arm eliminates all surviving records from that block, requiring at most $r$ selections at each level. Multi-scale exploration assigns finer accuracies to frequent blocks and coarser accuracies to rare blocks, yielding a near-optimal arm for every block while keeping the weighted policy error small.

cs.LG↗

arXiv2026

Combinatorial Bounds for List Recovery via Discrete Brascamp--Lieb Inequalities

In coding theory, the problem of list recovery asks one to find all codewords $c$ of a given code $C$ which such that at least $1-ρ$ fraction of the symbols of $c$ lie in some predetermined set of $\ell$ symbols for each coordinate of the code. A key question is bounding the maximum possible list size $L$ of such codewords for the given code $C$. In this paper, we give novel combinatorial bounds on the list recoverability of various families of linear and folded linear codes, including random linear codes, random Reed--Solomon codes, explicit folded Reed--Solomon codes, and explicit univariate multiplicity codes. Our main result is that in all of these settings, we show that for code of rate $R$, when $ρ= 1 - R - ε$ approaches capacity, the list size $L$ is at most $(\ell/(R+ε))^{O(R/ε)}$. These results also apply in the average-radius regime. Our result resolves a long-standing open question on whether $L$ can be bounded by a polynomial in $\ell$. In the zero-error regime, our bound on $L$ perfectly matches known lower bounds. The primary technique is a novel application of a discrete entropic Brascamp--Lieb inequality to the problem of list recovery, allowing us to relate the local structure of each coordinate with the global structure of the recovered list. As a result of independent interest, we show that a recent result by Chen and Zhang (STOC 2025) on the list decodability of folded Reed--Solomon codes can be generalized into a novel Brascamp--Lieb type inequality.

cs.IT↗

arXiv2026

Approximation in Contrastive Representation Learning

Contrastive representation learning (CRL) is a fundamental paradigm for learning transferable representations. Recent work identifies its population target as the pointwise mutual information (PMI) $\log\frac{p(x,y)}{p_X(x)p_Y(y)}$ between two modalities $X,Y$, where $p$ is the joint density function and $p_X,p_Y$ are the marginals. However, it remains unclear why standard inner-product scores $f(x)^\top g(y)$ can effectively approximate a generally nonseparable population target PMI. In this paper, we address this question from the aspect of approximation for CRL. By linking PMI to a compact operator, we show that $D$-dimensional inner-product models perform rank-$D$ spectral approximation, with error controlled by the spectral tail. We then study neural network realizations: in general settings, we show that deep neural network scoring functions are universally consistent, and the approximation error rates depend on the smoothness of the PMI function; under structured low-rank data models we obtain improved rates attained by moderate-width encoders. Finally, we establish a fast calibration rate from contrastive excess risk to downstream retrieval error under a density-ratio Tsybakov noise condition.

cs.LG↗

arXiv2026

DS and AMDS Symbol-Pair Codes from Three Families of Simple Root Cyclic Codes

Symbol-pair distances of simple-root cyclic codes are important for evaluating error correction performance under overlapping pair read channels. In this paper, we construct three families of simple-root cyclic codes over finite fields of odd characteristic via generator polynomials. For length $2q+2$, the minimum symbol-pair distance is $10$ for every odd prime power $q\ge 7$, established by excluding invalid support configurations. For length $4q-4$, when $q\equiv 3\pmod 4$ and finite field constraints hold, it is $9$ or $10$. For length $2(q-1)$, reciprocal-polynomial analysis shows it is $11$ or $12$. All obtained codes are MDS or AMDS symbol-pair codes.

cs.IT↗

arXiv2026

Bounds and Limitations on Codes Achieving List Recovery Capacity

In coding theory, list recoverability is a fundamental concept which robustly captures how ``spread-out'' codewords are in a code. More formally, given a code $C \subseteq Σ^n$ and input lists $S_1, \dots, S_n \subseteq Σ$ of size at most $\ell$, list recoverability requires that there are at most $L$ codewords $c \in C$ such that $c_i \in S_i$ for at least $(1-ρ)n$ choices of $i \in [n]$. List recovery is an important question which has found applications in many areas, including complexity theory, property testing, compressed sensing, streaming algorithms, and cryptography. As our first main result, we establish a tight ``generalized singleton bound''. Formally, we show that for constant $\ell, L,ρ$ and sufficiently large alphabets $Σ$, if we define $R^*=\frac{L+1-\ell}{L}-\frac{L+1}{L}ρ$, it is possible for a $(ρ,\ell,L)$ list-recoverable code to have rate $R^*-ε$ but impossible to have rate $R^*+ε$. One direction of our result already directly generalizes and improves a weaker impossibility result due to Goldberg, Shangguan, and Tamo. For our second main result, we prove that there is a fundamental shortcoming in existing methods that aim to construct explicit, optimal list-recoverable codes. Indeed, recent work has constructed explicit codes achieving list-decoding capacity (along with other related properties) using a framework introduced in the work of Alon--Edmonds--Luby (AEL). We give a meta-analysis of such constructions by presenting an ``AEL framework'' which captures all such recent constructions in the literature. Within this framework, we show that no AEL-based code can break a recently-identified list-recovery barrier for additive and linear codes.

cs.IT↗

arXiv2026

DualSpecSE: A Dual-Path Speech Enhancement Network Integrating Mel and Complex Spectrograms

In this paper, we propose DualSpecSE, a speech enhancement framework that jointly models Mel-spectrogram and complex spectrogram in a dual-path architecture for improved ASR performance and higher-quality speech reconstruction. The Mel branch learns coarse-grained acoustic representations and produces enhanced Mel-spectrograms for direct ASR usage, while the complex branch refines fine-grained spectral details for high-fidelity waveform reconstruction. Built upon the cross-band and narrow-band blocks from CleanMel, DualSpecSE introduces an interaction module and a fusion module to enable effective information exchange between the two branches. The model simultaneously outputs enhanced Mel and complex spectrogram without requiring a pretrained vocoder. Experimental results demonstrate consistent improvements in speech fidelity, perceptual quality, and ASR performance. Codes and audio samples are available.

eess.AS↗

arXiv2026

Curvature bounds for the cost of coherence in conditional optimal transport

We study the gap between the integrated direction-wise kinetic minima and the minimum expected Dirichlet energy of a joint particle realization of a prescribed two-parameter family of conditional probability measures. Under regular coarea assumptions with compact connected fibres and a star-shaped parameter domain, we derive a curvature lower bound valid for every admissible law of Sobolev maps realizing the prescribed smooth positive conditional measures. Our method combines the weighted-Poisson characterization of local optimal-transport velocities with an exact energy-residual identity, a weak Stokes formula, and explicit transport constructions. The minimum excess vanishes exactly when the Lie-bracket curvature vanishes throughout the parameter domain, whereas at a nonzero-curvature centre it is of order $r^4$ as $r\to0$ on squares of half-side length $r$ with unnormalized area measure. In a two-phase torus model fitted to electricity-demand data, numerical tests illustrate this quartic order for explicit couplings, with radial transport approximately halving the ordered construction's excess on the tested small squares.

math.OC↗