arXiv subjects

Wenkai Yang

Publications and source records attributed to Wenkai Yang.

At least 19 recordsLinked to original sources

arXiv2026

Infinite Generalized Sidon Sets with a Negative Answer to a Problem of Szemerédi

We construct infinite $B_h$ sets that repeatedly attain the density scale of finite $B_h$ sets. For every integer $h\geq2$ and every finite $B_h$ set $F$ of positive integers, we obtain an infinite $B_h$ set $A\supseteq F$ such that $$ \limsup_{x\to\infty}\frac{A(x)}{x^{1/h}}=\frac1h, \qquad \liminf_{x\to\infty}\frac{A(x)}{x^{1/h}}=0. $$ The key is to preserve density while preventing additive relations between successive blocks. A positional encoding of the finite-field moment curve has $q$ elements in an interval of length $O_h(q^h)$, while, for each $1\leq r<h$, sums arising from distinct $r$-element multisets are separated by more than $q$. This separation allows whole blocks to be appended to a prescribed finite set without a further dilation. In particular, our result gives a negative answer to a problem posed by Szemerédi \cite{szemeredi}.

math.CO↗

arXiv2026

IC-ThermBench: An Open, Progressive Benchmark for Generalizable 2.5D/3D-IC Thermal Learning

Standardized benchmarks are fundamental to reliable progress in AI for EDA, including learning-based thermal modeling. However, existing thermal prediction studies often rely on different datasets, simulators, data splits, preprocessing pipelines, and metrics, while most datasets and implementations remain unavailable, making fair and reproducible comparison difficult. We introduce IC-ThermBench, an open and progressive benchmark that combines established 3D-IC steady-state, transient, and industrial package tasks with a new 50,000-sample 2.5D chiplet extension designed to evaluate progressively broader represented physical variation and cross-package OOD transfer. Five Generalization Scopes cover 3D-IC fixed-design prediction, Within-Family Generalization under layout, material, and boundary-condition variation, and Cross-Package OOD transfer to unseen package systems. We evaluate eight representative baselines under common data, splits, labels, and metrics. Performance degrades gradually from S2 to S4 as represented physical support broadens, but Cross-Package OOD produces a much sharper degradation: the best RMSE and MAE increase from 1.216 and 0.938~K at S4 to 15.99 and 15.00~K at S5, respectively. With only 10 labeled samples per OOD case, target-domain adaptation reduces the best MAE to 2.60~K. IC-ThermBench further provides a unified generation, training, inference, and evaluation pipeline, enabling reproducible and fair comparison of existing and new thermal predictor.

cs.CE↗

arXiv2026

On a classical zero-sum invariant II: Disproof of a long-standing conjecture

For a nontrivial finite abelian group $G$, let $ν(G)$ be the smallest {nonnegative} integer $\ell$ such that every zero-sum free sequence $T$ over $G$ of length at least $\ell$ has the following property: all nonzero elements of $G$ that do not occur as a subsequence sum of $T$ lie in a proper coset of some subgroup of $G$. It is easy to check that $\mathsf d (G)-1 \le ν(G) \le \mathsf d (G)$, where $\mathsf d (G)$ is the small Davenport constant of $G$. A conjecture by Gao from the year 2000 stated that equality should always hold at the lower bound. This conjecture has since been confirmed for many families of groups (including all p-groups and groups of rank at most two). In this paper, we disprove the conjecture.

math.CO↗

arXiv2026

Counting Admissible Sets of Integers: A Proof of the Erdős--Nicolas--Sárközy Conjecture

A finite set of positive integers is admissible if any two of its subsets with the same sum have the same cardinality. In 1991, Erdős, Nicolas and Sárközy conjectured that $\log a(N)\asymp\sqrt N$, where $a(N)$ denotes the number of nonempty admissible subsets of $\{1,\ldots,N\}$. We prove this conjecture by showing that there are absolute constants $c,C>0$ such that $\exp(c\sqrt N)\le a(N)\le\exp(C\sqrt N)$ for every integer $N\ge4$. The same bounds hold for the number of admissible sets with maximum $N$. For the upper bound, we show that every sufficiently large admissible set $A\subseteq\{1,\ldots,N\}$ contains a subset of proportional size whose doubling constant is $O(N/|A|^2)$.

math.CO↗

arXiv2026

Additive bases and the zero-sum invariant $\mathsf{N}(G)$ for groups $C_p\oplus C_{np}$

Let $G$ be a finite abelian group, and let $c_0(G)$ be the least integer such that every regular sequence over $G$ of at least this length is an additive basis. Let $\mathsf N(G)$ be the least integer $l$ such that every weak-regular sequence $S$ over $G$ with $|S|\ge l$ has a nonempty zero-sum subsequence $T$ satisfying $\mathsf v_g(T)=\mathsf v_g(S)$ for some $g\mid S$. We obtain a common upper bound for $c_0(C_q\oplus C_{nq})$ for groups of odd order, where $q$ is prime, and prove $\mathsf N(G)\ge r(n_r-1)+1$ when $G=C_{n_1}\oplus\cdots\oplus C_{n_r}$ with $1<n_1\mid\cdots\mid n_r$. If $n\ge1$ and $p\ge3$ is the smallest prime divisor of $np$, we obtain $\mathsf N(C_p\oplus C_{np^2})=2np^2-1$ and give upper bounds for $\mathsf N(C_p\oplus C_{np})$ when $p\nmid n$. We also determine $\mathsf N(C_n)$ for two infinite families of cyclic groups arising in earlier work.

math.CO↗

arXiv2026

DeepSeek Elastic Compute (DSec): A Sandbox Infrastructure for Effective Agentic Training at Scale

Large-scale agentic training and evaluation with large language models (LLMs) rely on isolated, stateful execution environments in which models inspect repositories, invoke tools, execute commands, and interact with task-specific services. These workloads create sandboxes in large bursts, span heterogeneous functionality and isolation requirements, retain state across long interactions, and draw from large image corpora with limited reuse. Supporting them therefore requires an elastic execution platform rather than a single sandbox runtime. This report presents DeepSeek Elastic Compute (DSec), a production sandbox platform that exposes FnCall, container, microVM, and full-VM sandbox backends through a unified SDK. DSec coordinates placement and lifecycle management across the cluster, composes environments from independently versioned layers, combines memory sharing, reclamation, and CPU scheduling for high-density execution, and loads image data on demand from Fire-Flyer File System (3FS), a cluster-wide distributed filesystem. DSec is co-designed with the reinforcement learning (RL) framework, decouples stateful rollout execution from preemptible GPU training, coordinates sandbox lifecycle with training to preserve rollout state while reclaiming idle resources, and mitigates agent misbehavior such as reward hacking. A single production-scale unit of DSec spans around 160 nodes, serving about 3 million sandboxes per day; in production, it supports over 380,000 concurrent sandboxes and sustains over 5,000 sandbox creations per second. Our evaluation and deployment experience show that these mechanisms reduce environment setup and image-distribution overhead, improve memory efficiency, and preserve latency-sensitive performance under high-density overcommit.

cs.DC↗

arXiv2026

Certified Multi-Turn Robustness for LLM Safety via Compositional Bounds and Safety Persistence

Large language models (LLMs) are vulnerable to multi-turn jailbreak attacks that progressively manipulate conversation context. Existing certified robustness methods are limited to single-turn inputs; naive multi-turn composition yields bounds that degrade exponentially in the number of turns. We introduce Multi-Turn Certified Robustness (MTCR), a framework that models conversational safety via State-Adversarial MDPs and defines $k$-turn certified robustness as the worst-case safety probability across $k$ adversarial turns. MTCR comprises: (i) compositional certification via embedding-space mode decomposition, yielding tighter certified lower bounds than naive multiplication; (ii) $(α,β)$-safety persistence, improving the degradation rate from $\underline{p}^{k}$ to $β^k$ (with $β> \underline{p}$) and yielding interpretable horizon estimates; (iii) matching information-theoretic upper bounds establishing tightness; and (iv) a unified algorithm combining these results. Experiments on six LLMs under $ε$-bounded and Crescendo-style attacks confirm that empirical safety consistently exceeds the certified bounds.

cs.AI↗

arXiv2026

On a classical zero-sum invariant

Let $G$ be a nontrivial, finite abelian group. Then $ν(G)$ is the smallest integer $\ell$ such that every zero-sum free sequence $T$ over $G$ of length at least $\ell$ has the following property: all nonzero elements of $G$ that do not occur as a subsequence sum of $T$ lie in a proper coset of some subgroup of $G$. We study the invariant $ν(G)$, which was introduced in Zero-Sum Theory in the 1960s.

math.NT↗

arXiv2026

Self-Attention to Operator Learning-based 3D-IC Thermal Simulation

Thermal management in 3D ICs is increasingly challenging due to higher power densities. Traditional PDE-solving-based methods, while accurate, are too slow for iterative design. Machine learning approaches like FNO provide faster alternatives but suffer from high-frequency information loss and high-fidelity data dependency. We introduce Self-Attention U-Net Fourier Neural Operator (SAU-FNO), a novel framework combining self-attention and U-Net with FNO to capture long-range dependencies and model local high-frequency features effectively. Transfer learning is employed to fine-tune low-fidelity data, minimizing the need for extensive high-fidelity datasets and speeding up training. Experiments demonstrate that SAU-FNO achieves state-of-the-art thermal prediction accuracy and provides an 842x speedup over traditional FEM methods, making it an efficient tool for advanced 3D IC thermal simulations.

cs.LG↗

arXiv2026

DSpark: Confidence-Scheduled Speculative Decoding with Semi-Autoregressive Generation

Speculative decoding accelerates Large Language Model (LLM) inference by decoupling draft generation from target verification. While recent parallel drafters efficiently propose long token sequences in a single forward pass, they suffer from rapid acceptance decay due to a lack of inter-token dependencies. Furthermore, indiscriminately verifying these extended blocks wastes critical batch capacity on tokens with high rejection risks, severely degrading throughput in high-concurrency serving systems. We introduce DSpark, a speculative decoding framework that unifies high-throughput parallel generation with adaptive, load-aware verification. To maintain draft quality, DSpark utilizes a semi-autoregressive architecture, coupling a parallel backbone with a lightweight sequential module, to introduce intra-block dependency modeling and mitigate suffix decay. To optimize system efficiency, DSpark employs confidence-scheduled verification, dynamically tailoring the verification length for each request based on estimated prefix survival probabilities and engine-specific throughput profiles. On offline benchmarks across diverse domains, DSpark substantially improves the accepted length over state-of-the-art autoregressive and parallel drafters. When deployed within the DeepSeek-V4 serving system under live user traffic, DSpark successfully mitigates verification waste. Compared to the established production baseline (MTP-1), DSpark accelerates per-user generation speeds by 60 to 85 percent at matched throughput levels. More importantly, by preventing severe throughput degradation under strict interactivity constraints, it enables performance tiers that were previously unattainable, shifting the Pareto frontier of our serving system.

cs.AI↗

arXiv2026

Rethinking Continual Experience Internalization for Self-Evolving LLM Agents

Experience internalization converts contextual experience from past interactions into reusable parametric capability, offering a promising path toward continual learning in large language models (LLMs). While prior work has predominantly focused on single-iteration transfer, we discover that under multi-iteration experience learning, existing methods suffer from a progressive capability collapse rather than compounding improvement. We systematically examine this failure through three vital dimensions of experience internalization: (1) Experience Granularity: We find that principle-level experience is more durable than instance-level experience, as it effectively abstracts transferable strategies away from trajectory-specific details. (2) Experience Injection Pattern: Our analysis reveals that step-wise injection significantly outperforms global injection by aligning experience with intermediate decision states, a property that is critical for long-horizon tool use. (3) Internalization Regime: We demonstrate that off-policy context-distillation on high-quality teacher trajectories provides a substantially more stable training signal than on-policy context-distillation, which is inherently limited by local corrections on student-induced flawed states. Together, these insights yield a simple yet robust recipe for stable and sustainable experience internalization, providing concrete guidance for engineering self-evolving and continually learning LLMs.

cs.CL↗

arXiv2026

AgentProcessBench: Diagnosing Step-Level Process Quality in Tool-Using Agents

While Large Language Models (LLMs) have evolved into tool-using agents, they remain brittle in long-horizon interactions. Unlike mathematical reasoning where errors are often rectifiable via backtracking, tool-use failures frequently induce irreversible side effects, making accurate step-level verification critical. However, existing process-level benchmarks are predominantly confined to closed-world mathematical domains, failing to capture the dynamic and open-ended nature of tool execution. To bridge this gap, we introduce AgentProcessBench, the first benchmark dedicated to evaluating step-level effectiveness in realistic, tool-augmented trajectories. The benchmark comprises 1,000 diverse trajectories and 8,509 human-labeled step annotations with 89.1% inter-annotator agreement. It features a ternary labeling scheme to capture exploration and an error propagation rule to reduce labeling ambiguity. Extensive experiments reveal key insights: (1) weaker policy models exhibit inflated ratios of correct steps due to early termination; (2) distinguishing neutral and erroneous actions remains a significant challenge for current models; and (3) process-derived signals provide complementary value to outcome supervision, significantly enhancing test-time scaling. We hope AgentProcessBench can foster future research in reward models and pave the way toward general agents. The code and data are available at https://github.com/RUCBM/AgentProcessBench.

cs.AI↗

arXiv2026

Therm-FM: Foundation Model is ALL YOU NEED for 3D-ICs Thermal Simulation

Data-driven thermal predictors for 3D-ICs are often trained from scratch for each chip design using many high-fidelity finite-element simulations, leading to high data-generation cost and costly cross-design reuse. We propose Therm-FM, a neural operator framework that adapts a pretrained partial differential equation (PDE) foundation model to steady-state and transient 3D-IC thermal simulation. The motivation is that steady-state and transient chip-level heat conduction respectively share elliptic and parabolic operator structures with diffusion-type PDEs, allowing pretrained diffusion priors to provide an effective initialization for thermal-field prediction under heterogeneous materials, dense TSV/microbump interconnects, and package-level boundary conditions. To further reduce data-generation cost, Therm-FM incorporates a thermal-equivalent multi-fidelity training strategy that uses low-cost approximate simulations for thermal-domain adaptation and limited high-fidelity samples for calibration. Experiments on public HotSpot benchmarks and industrial 3D-IC package benchmarks show that Therm-FM achieves up to a 10.6x reduction in mean error and surpasses prior best accuracy with less than 20% of the training data. In cross-chip adaptation, it matches or surpasses full-data baselines in several metrics using only 10--30 target samples. We release datasets, source code, and pretrained models at https://github.com/haiyangxin/Therm-FM.

cs.CE↗

arXiv2026

Real-Space Imaging of Guided Exciton Polaritons in Free-standing Monolayer WSe2

Monolayers of transition metal dichalcogenides (TMDCs), known for their strong excitonic states with high binding energies in the visible spectrum at room temperature, offer great potential for polariton-driven devices. While polariton guided modes in bulk TMDCs have been reported the real space experimental observation of 2D exciton-polariton guided modes in a monolayer remains challenging due to various mode cut-off conditions that arise as the TMDC layer becomes thinner, including cut-off frequency, mode confinement and boundary conditions. Here using scanning near-field optical microscopy (s-SNOM), we directly visualized the real-space propagation of these guided modes for the first time in an angstrom-thick, suspended monolayer of WSe2. Through numerical simulations we have also validated that the guided mode can only exist in a monolayer WSe2 when symmetric cladding conditions are closely applied. By tuning the excitation laser energy and analysing the guided mode distribution, we observed a pronounced back-bending dispersion around the A exciton, indicating strong light-matter interactions, and confirmed the existence of the fundamental TE0 exciton polariton (EP) propagation mode. The unique dispersion characteristics of these modes were further validated through theoretical modelling of the mode in free-standing monolayer WSe2. Our findings provide crucial experimental evidence of guided mode EPs in atomically thin TMDCs, opening new possibilities for nanoscale photonic applications.

physics.optics↗

arXiv2026

Rethinking On-Policy Distillation of Large Language Models: Phenomenology, Mechanism, and Recipe

On-policy distillation (OPD) has become a core technique in the post-training of large language models, yet its training dynamics remain poorly understood. This paper provides a systematic investigation of OPD dynamics and mechanisms. We first identify that two conditions govern whether OPD succeeds or fails: (i) the student and teacher should share compatible thinking patterns; and (ii) even with consistent thinking patterns and higher scores, the teacher must offer genuinely new capabilities beyond what the student has seen during training. We validate these findings through weak-to-strong reverse distillation, showing that same-family 1.5B and 7B teachers are distributionally indistinguishable from the student's perspective. Probing into the token-level mechanism, we show that successful OPD is characterized by progressive alignment on high-probability tokens at student-visited states, a small shared token set that concentrates most of the probability mass (97%-99%). We further propose two practical strategies to recover failing OPD: off-policy cold start and teacher-aligned prompt selection. Finally, we show that OPD's apparent free lunch of dense token-level reward comes at a cost, raising the question of whether OPD can scale to long-horizon distillation.

cs.LG↗

arXiv2026

Learning beyond Teacher: Generalized On-Policy Distillation with Reward Extrapolation

On-policy distillation (OPD), which aligns the student with the teacher's logit distribution on student-generated trajectories, has demonstrated strong empirical gains in improving student performance and often outperforms off-policy distillation and reinforcement learning (RL) paradigms. In this work, we first theoretically show that OPD is a special case of dense KL-constrained RL where the reward function and the KL regularization are always weighted equally and the reference model can by any model. Then, we propose the Generalized On-Policy Distillation (G-OPD) framework, which extends the standard OPD objective by introducing a flexible reference model and a reward scaling factor that controls the relative weight of the reward term against the KL regularization. Through comprehensive experiments on math reasoning and code generation tasks, we derive two novel insights: (1) Setting the reward scaling factor to be greater than 1 (i.e., reward extrapolation), which we term ExOPD, consistently improves over standard OPD across a range of teacher-student size pairings. In particular, in the setting where we merge the knowledge from different domain experts, obtained by applying domain-specific RL to the same student model, back into the original student, ExOPD enables the student to even surpass the teacher's performance boundary and outperform the domain teachers. (2) Building on ExOPD, we further find that in the strong-to-weak distillation setting (i.e., distilling a smaller student from a larger teacher), performing reward correction by choosing the reference model as the teacher's base model before RL yields a more accurate reward signal and further improves distillation performance. However, this choice assumes access to the teacher's pre-RL variant and incurs more computational overhead. We hope our work offers new insights for future research on OPD.

cs.LG↗

arXiv2025

Light matter interaction in van der Waals heterostructures with Mie voids

Recently introduced concept of Mie voids allows to enhance the field localization inside air cavities embedded in high-index materials. Mie voids provide an alternative approach to conventional dielectric resonators that confine optical fields within bulk high-index materials. Building on this concept, here we present a hybrid photonic platform that integrates monolayer WS2 with Mie void resonators patterned in a high-index Bi2Te3 substrate. By carefully aligning the dipolar void resonance with the excitonic transition of WS2, we achieve substantially enhanced photoluminescence and second-harmonic generation. Far-field imaging of the harmonic fields reveals spatially resolved hotspots that directly map localized resonant modes, with their positions tunable by cavity geometry and pump wavelength. This approach enables real-space control of nonlinear emission at the single-resonator level, offering a robust and reconfigurable platform for next-generation nonlinear photonics and surface-enhanced optical sensing.

physics.optics↗

arXiv2025

Accelerating IC Thermal Simulation Data Generation via Block Krylov and Operator Action

Recent advances in data-driven approaches, such as neural operators (NOs), have shown substantial efficacy in reducing the solution time for integrated circuit (IC) thermal simulations. However, a limitation of these approaches is requiring a large amount of high-fidelity training data, such as chip parameters and temperature distributions, thereby incurring significant computational costs. To address this challenge, we propose a novel algorithm for the generation of IC thermal simulation data, named block Krylov and operator action (BlocKOA), which simultaneously accelerates the data generation process and enhances the precision of generated data. BlocKOA is specifically designed for IC applications. Initially, we use the block Krylov algorithm based on the structure of the heat equation to quickly obtain a few basic solutions. Then we combine them to get numerous temperature distributions that satisfy the physical constraints. Finally, we apply heat operators on these functions to determine the heat source distributions, efficiently generating precise data points. Theoretical analysis shows that the time complexity of BlocKOA is one order lower than the existing method. Experimental results further validate its efficiency, showing that BlocKOA achieves a 420-fold speedup in generating thermal simulation data for 5000 chips with varying physical parameters and IC structures. Even with just 4% of the generation time, data-driven approaches trained on the data generated by BlocKOA exhibits comparable performance to that using the existing method.

cs.AI↗