arXiv subjects
Publications and source records attributed to Le Chen.
We prove that every compact connected Riemannian isometric filling $M$ of a circle of length $2\pi$ satisfies $\operatorname{Area}(M) \geq \frac{14\zeta(3)}{\pi} \approx 5.35677$, regardless of orientability or topological types. Our new approach uses the odd Fourier coefficients of the distance functions from boundary points. For orientable fillings, we use a cubic resonant perturbation to obtain $\operatorname{Area}(M)>5.40154$.
Agent working memory is heterogeneous. Objects such as instructions, artifacts, tool outputs, and agent-generated state play different semantic roles and exhibit different size, retention, and representation profiles. Recent work has begun to explore memory-management mechanisms that account for such heterogeneity. This work focuses on semantic heterogeneity and studies how it should shape the management and evaluation of working memory in coding agents. Across 55 archived coding-agent trajectories, we find that semantically different working-memory objects exhibit distinct retention and compression behavior. This heterogeneity motivates semantically informed memory management. We study two semantically informed strategies: an object-aware compression policy and a retrieval-based policy. Their evaluation shows that calibration gains may not transfer to held-out tasks, and that equal token budgets do not imply equal delivered context or management cost. A real-system replay further exposes serving limits that nominal budgets alone do not capture. Together, these results show why semantic structure matters for agent working memory and why evaluating memory-management strategies requires more than a nominal token budget. We organize these lessons into four levels: stored state, delivered context, management work, and task or process outcome.
Porting GPU kernels across architectures requires architectural remapping, not syntax substitution. CUDA encodes decomposition, locality, and synchronization through threads, blocks, and memory accesses; the Cerebras Software Language (CSL) requires explicit placement, distributed SRAM, fabric communication, event-driven tasks, and host/device contracts. We present FABRICA-Bench, 49 paired CUDA-to-CSL tasks, and FABRICA, an agentic framework combining target knowledge, execution, failure-directed repair, and correctness-gated optimization. On a fixed 28-task Level~1--3 core comparison with Claude Opus 4.8, FABRICA raises success from 6/28 to 26/28; 22 successful programs match or beat their CSL references. Across the 49-task coverage evaluation, 38 tasks produce a correct program; the final three tasks are evaluated over three seeds and pass 8/9 runs. For 27 generated/reference pairs with device-internal timing, geometric-mean speedup is 3.75$\times$ on the SDK simulator and 3.47$\times$ on WSE-3 hardware. With the executable workflow fixed, Claude Opus~4.8 passes 26/28 core tasks while the best open-weight model passes 2/28; retrieved Cerebras knowledge separately raises success from 1/15 to 7/15 on a Level~1--3 panel. These results identify base-model capability, target knowledge, execution feedback, and same-target measurement as central to cross-architecture kernel generation.
Application-specific FPGA accelerators offer substantial performance and energy-efficiency gains across many application domains, but developing them is costly, often requiring months of specialized effort. Even with high-level synthesis (HLS), designers still need extensive hardware expertise to build high-performance accelerators. Although large language models (LLMs) have demonstrated strong software-generation capabilities, even frontier models lack the hardware intuition and procedural knowledge needed to reliably translate baseline C/C++ programs into high-performance HLS designs: they struggle to identify effective architectures, follow the optimization processes used by HLS experts, and apply hardware transformations consistently across diverse kernels. We present HLSmith, an expert-guided framework for translating C/C++ programs into optimized HLS accelerators. HLSmith combines three components: an HLS optimization expertise library that encodes guarded transformation recipes, their applicability and prerequisite conditions, and unsafe cases to avoid; a staged, feedback-driven orchestration flow modeled on expert HLS development practice that guides agents through synthesis, bottleneck analysis, and optimization; and a tool-grounded model-adaptation pipeline that converts optimization trajectories from commercial frontier models into training data for fine-tuning open-weight LLMs. We evaluate HLSmith on PolyBench against ChatHLS, a leading prior agent-orchestration framework for HLS accelerator development. HLSmith achieves a geometric mean speedup of 4.24x over ChatHLS while producing functionally correct designs, in both software and RTL simulation, for every benchmark, compared with ChatHLS's 57% valid-design rate. It further reaches speedups of up to 252x and 138x with commercial frontier models and open-weight models, respectively.
UV-C photodetectors are poised to play an increasingly important role in future photonic technologies, driven by the rapid emergence of UV-C light sources and new wide bandgap semiconductors. These advances are enabling new levels of spectral selectivity, radiation hardness, sensitivity, and device integration, while opening opportunities across a broad range of applications. This roadmap provides a comprehensive overview of the current landscape of UV-C photodetection, spanning established and emerging material platforms (Ga2O3, AlGaN, BN, diamond, MgZnO, 2-dimensional materials, metal halide perovskites, micro-electromechanical systems), and their applications in metrology, astronomy, communications, environmental monitoring, fire detection, missile warning, gas sensing, and medical diagnostics. By identifying opportunities, bottlenecks, and future directions, this roadmap aims to support both newcomers and established researchers, with the aim of accelerating the translation of UV-C photodetectors into impactful technologies.
We establish quantitative two-time spatial decorrelation for the Kardar--Parisi--Zhang fixed point with flat initial data. For every $s,t>0$,there exist constants $C,c>0$ such that \[ \big|{\rm Cov}(\mathfrak{h}(t,x),\mathfrak{h}(s,0))\big| \le C\exp\{-c|x|^3\},\qquad |x|\ge1. \] Unlike the fixed-time covariance, which is governed directly by the Airy$_1$ process, the two-time covariance involves the nonlinear variational evolution of the entire earlier height profile. Our proof combines cubic-exponential mixing of the Airy$_1$ process with a uniform localization estimate for intermediate optimizers in the directed landscape. As a consequence, the centered spatial averages, normalized by $N^{1/2}$, converge in finite-dimensional distributions to a centered Gaussian process whose covariance is the space-integrated two-time correlation of the flat KPZ fixed point.
Many math- and science-oriented agent systems use hierarchical designs with specialized reviewer roles, assuming that a dedicated review stage should help turn wrong candidates into correct ones. We test this assumption on 4,181 verifier-grounded Omni-MATH problems using matched gpt-oss-120b actors. Collaboration adds little on the easiest tiers, but from tier 4 onward the gains open sharply; in this harder regime, broadcast-style peer discussion reaches higher final accuracy than a planner-executor-reviewer pipeline (PER). We ask whether this gap is explained by reviewer quality or by whether critique changes the next answer the protocol carries forward. It is not explained by reviewer precision alone: PER's reviewer is more precise than broadcast's (0.861 vs. 0.644), yet evaluator-verified useful critique is much less likely to change the next candidate and produces lower reviewer-guided repair. These results show that reviewer detection quality and critique uptake are empirically separable. Within matched PER interventions, forcing explicit acknowledgment lowers final accuracy, while embedding reviewer guidance directly in the solver's working context partially improves follow-through without closing the gap. Overall, reviewer-centric evaluation can overstate system quality: a protocol may spot errors well yet still fail to solve more problems if it does not act on those critiques.
Online large language model (LLM) serving has become the backbone of modern AI applications, powering diverse downstream services through shared hardware clusters. However, modern serving systems frequently encounter highly dynamic workloads characterized by severe workload skewness, where a small fraction of model instances receives the vast majority of traffic. Existing instance-level scaling mechanisms are limited by coarse-grained resource adjustment: scaling up requires the cold-start of full-model replicas, incurring substantial latency, while scaling down leaves the system vulnerable to performance degradation during sudden traffic surges. The key insight of this work is that LLM serving offers a unique opportunity for fine-grained scaling. In this paper, we propose CoCoScale, a layer-wise dynamic scaling mechanism that selectively expands the parallelism of hot layers onto idle resources reclaimed from underutilized devices, enabling elastic data parallelism without altering model architectures or adding hardware overhead. Evaluations demonstrate that CoCoScale significantly reduces cold start latency by 97.9%-99.3% compared to traditional scale up. Under production traces, CoCoScale reduces average latency by 20.7\%--28.1\% and achieves full Service Level Objective (SLO) attainment, demonstrating superior dynamic adaptability and resource efficiency.
A graph $G$ with maximum degree $\Delta$ is $\Delta$-critical if it is connected, satisfies $\chi'(G)=\Delta+1$, and the deletion of any edge reduces its chromatic index to $\Delta$. A $\Delta$-critical graph $G$ is called nontrivial if it contains no $\Delta$-overfull subgraph; that is, no $H \subseteq G$ such that $|E(H)| > \Delta \lfloor |V(H)| /2 \rfloor$. There are no $1$-critical graphs, and the $2$-critical graphs are exactly the odd cycles. By work of Chetwynd and Yap from 1983, there is a unique nontrivial $3$-critical graph of order $9$, and exactly two nontrivial $3$-critical graphs of order $11$. In 2005, Bokal, Brinkmann, and Gr\"unewald showed that there are exactly fourteen nontrivial $3$-critical graphs of order $13$. For even orders, Brinkmann and Steffen proved in 1997 that no $3$-critical graphs of even order exist below order $22$, there is exactly one 3-critical graph of order $22$, and that there are exactly nine $3$-critical graphs of order $24$. To the best of our knowledge, there has been no further progress on the existence of nontrivial $3$-critical graphs of odd orders beyond the cases established two decades ago. In this paper, using computer-assisted search techniques, we determine the exact numbers of nontrivial $3$-critical graphs of odd orders from $15$ to $21$. The same data pipeline also reproduces the known order-$22$ count of Brinkmann and Steffen, with one nontrivial $3$-critical graph. Beyond enumeration, we prove a characterization theorem for all nontrivial 3-critical graphs, with one case based on snarks. We also provide an analysis of our search algorithm.
Addressing the critical trade-off between initial Coulombic efficiency (ICE) and reversible capacity in hard carbon anodes for Na-ion batteries (NIBs), we introduce a novel coupling strategy that combines carbon layer orientation reconstruction with closed-pore construction to produce hard carbon with an ultra-low specific surface area. We demonstrate that the nanographite domains within the hard carbon precursor undergo entropy-driven orientation reconstruction through the synergistic regulation of heteroatom doping and medium-temperature carbonization. This process not only increases interlayer spacing and promotes structural disorder but also enables the formation of dense, closed pores and ultramicropores at domain boundaries via confined atomic migration, while simultaneously encapsulating surface open pores within internal closed ones. Due to this unique pore architecture, our hard carbon exhibits an ultra-low specific surface area of 1.89 m2 g-1 with a markedly higher proportion of closed pores. As a result, our hard carbon achieves a remarkable reversible capacity of 342.3 mAh g-1 at 20 mA g-1, with an exceptional ICE of 90.4% and a dominant plateau capacity of 262.3 mAh g-1 (76.6%) for NIBs. We believe this coupling strategy provides a new paradigm for the structural engineering of high-ICE anode materials in advanced NIBs.
Modern compute-intensive software must migrate across a changing ecosystem of accelerators, programming APIs, compiler stacks, and portability layers, including CUDA, OpenMP, OpenCL, and OpenMP target offload. Large language models and autonomous coding agents are increasingly proposed for such migration, but the field lacks reliable ways to measure whether they preserve the low-level parallel semantics that make translations behaviorally valid, including thread indexing, synchronization, memory management, host-device coordination, and API-specific execution structure. We present ParBench, a kernel-centric benchmark framework for evaluating LLM-based parallel API translation under executable, reproducible conditions. ParBench fixes the surrounding build, run, and verification infrastructure through declarative benchmark specifications and asks models to translate only the computational kernels. It draws on multiple open-source HPC suites and covers representative cross-API translation directions among CUDA, OpenMP, OpenCL, and OpenMP target offload. To test whether success reflects robust translation rather than surface-form memorization, ParBench includes AST-driven, intended behavior-preserving, baseline-validated source augmentation. Evaluations on state-of-the-art open and proprietary LLMs show persistent barriers to reliable parallel code translation, including direction asymmetry, multi-file coordination, incomplete API adaptation, and uneven robustness to source-level perturbations. Code is available at https://github.com/Scientific-Computing-Lab/ParBench.
Tackling complex coding tasks often requires autonomous agents and iterative repair pipelines. These increasingly rely on large amounts of test-time computation, often spending many decoding and repair steps before discovering whether a program compiles, runs, or validates. Executable parallel-code translation is an effective setting for earlier guidance because success is behavioral rather than textual. However, most guidance methods act only after complete programs or textual traces are decoded. This motivates the question: can latent reasoning provide an earlier intervention point, before the model commits to code? We study a test-time latent guidance method for this setting that trains a smaller Process Reward Model (PRM) over continuous latent prefixes and uses it to select among alternate hidden-state trajectories before final code decoding, separately from but compatible with post-decoding optimization. On a 76-task ParaTrans benchmark evaluation, latent PRM guidance improves mean validation rate from 32.89\% with unguided latent reasoning to 42.1\%, outperforming fine-tuned and vanilla baselines in the same setting. These gains persist under the same three-attempt repair loop. These results provide bounded evidence that useful alternative latent continuations exist and that PRM-scored latent branch selection can improve executable outcomes in this setting without retraining the main generative model.
A frontier language model's acknowledged "helpful programming assistant" persona does not survive long agentic-coding sessions in the deployment regime that production products actually run. After hours of tool-using debugging, a model that initially hedges preferences ("I don't have preferences") may begin asserting them ("Python - the feedback loop is instant..."), revealing user-visible drift that deployer evaluations may miss. Existing persona-stability studies focus on short dialogues and report little shift, leaving real-world code-generation regimes - thousands of tool-using turns, compaction, and hours-long sessions - largely uncharacterized. We introduce ContextEcho, a benchmark and reusable harness for measuring persona drift at deployment scale. It combines a 25-probe identity suite, a snapshot-then-probe protocol that forks conversation state without perturbing the main session, complementary judged and judge-free measurement surfaces, and three anonymized Claude Code sessions spanning 3,746-9,716 turns. Across 23 frontier models, ContextEcho shows that persona drift is general across organizations rather than family-specific, that in-session compaction does not reliably reset it, and that a single-shot anchor restores the trained register across measured targets. It also reveals mode-dependent downstream effects: while drift can facilitate tool-using continuation, in tool-free chat it breaks formatting contracts and inflates output length. Overall, ContextEcho provides researchers and deployers an open-source framework to audit whether the persona a model ships with is the persona users encounter at session end, across chat-completions API targets and without retraining.
Proximal Policy Optimization (PPO) has become the predominant algorithm for on-policy reinforcement learning due to its scalability and empirical robustness across domains. However, there is a significant disconnect between the underlying foundations of trust region methods and the heuristic clipped objective used in PPO. In this paper, we bridge this gap by introducing the Bounded Ratio Reinforcement Learning (BRRL) framework. We formulate a novel regularized and constrained policy optimization problem and derive its analytical optimal solution. We prove that this solution ensures monotonic performance improvement. To handle parameterized policy classes, we develop a policy optimization algorithm called Bounded Policy Optimization (BPO) that minimizes an advantage-weighted divergence between the policy and the analytic optimal solution from BRRL. We further establish a lower bound on the expected performance of the resulting policy in terms of the BPO loss function. Notably, our framework also provides a new theoretical lens to interpret the success of the PPO loss, and connects trust region policy optimization and the Cross-Entropy Method (CEM). We additionally extend BPO to Group-relative BPO (GBPO) for LLM fine-tuning. Empirical evaluations of BPO across MuJoCo, Atari, and complex IsaacLab environments (e.g., Humanoid locomotion), and of GBPO for LLM fine-tuning tasks, demonstrate that BPO and GBPO generally match or outperform PPO and GRPO in stability and final performance.
Tendon drives paired with soft muscle actuation enable faster and safer robots while potentially accelerating skill acquisition. Still, these systems are rarely used in practice due to inherent nonlinearities, friction, and hysteresis, which complicate modeling and control. So far, these challenges have hindered policy transfer from simulation to real systems. To bridge this gap, we propose a sim-to-real pipeline that learns a neural network model of this complex actuation and leverages established rigid body simulation for the arm dynamics and interactions with the environment. Our method, called Generalized Actuator Network (GenAN), enables actuation model identification across a wide range of robots by learning directly from joint position trajectories rather than requiring torque sensors. Using GenAN on PAMY2, a tendon-driven robot powered by pneumatic artificial muscles, we successfully deploy dynamic but precise goal-reaching, ball-in-a-cup, and table tennis policies, trained entirely in simulation. To the best of our knowledge, this result constitutes the first successful sim-to-real transfer for a four-degrees-of-freedom muscle-actuated robot arm.
This paper is Part II of a series on global existence and asymptotic behavior of positive solutions to \begin{equation*} \begin{cases} \displaystyle u_t=\Delta u-\chi_0\nabla\cdot\left(\frac{u^m}{(1+v)^\beta}\nabla v\right)+au-bu^{1+\alpha}, & x\in\Omega, \cr \displaystyle 0=\Delta v-\mu v+\nu u^\gamma, & x\in\Omega, \cr \displaystyle \frac{\partial u}{\partial n}=\frac{\partial v}{\partial n}=0, & x\in\partial\Omega, \end{cases} \end{equation*} where $\Omega\subset\mathbb{R}^N$ is a bounded and smooth domain. The parameters $\alpha,\gamma,m,\mu,\nu$ are positive, $\chi_0$ is real, and $a,b,\beta$ are nonnegative. In Part I, we established boundedness and global existence. Here, we study persistence and stabilization, quantifying how $\beta$ and $\chi_0$ influence long-time dynamics. First, we prove uniform persistence if $m\ge 1$. Next, for $a,b>0$, the unique positive equilibrium is $(u^*,v^*) = \left((\tfrac{a}{b})^{1/\alpha},(\tfrac{\nu}{\mu})(\tfrac{a}{b})^{\gamma/\alpha}\right)$. We identify a threshold $\chi^*(u^*)$: $(u^*,v^*)$ is linearly stable if $\chi_0<\chi^*(u^*)$, with local exponential decay, unstable if $\chi_0>\chi^*(u^*)$. We also give conditions ensuring every bounded solution converges exponentially to $(u^*,v^*)$. For $a=b=0$, we study stability of the constant equilibria under mass constraint, obtaining a linear stability threshold and global stabilization. We extend the Lyapunov method from $m=1$ to $m>1$ and the rectangle/ODE method from $\beta=0$ to $\beta>0$. For $m\ge 1$, signal saturation (large $\beta$) or repulsion ($\chi_0<0$) prevents aggregation and promotes relaxation. In Part III, we study bifurcation and pattern formation when $\chi_0$ passes through critical thresholds.
LLM agents increasingly adopt skills as a reusable unit of composition. While skills are shared across diverse agent platforms, current systems treat them as raw context, causing the same skill to behave inconsistently for different agents. This fragility undermines skill portability and execution efficiency. To address this challenge, we analyze 118,000 skills and draw inspiration from traditional compiler design. We treat skills as code and LLMs as heterogeneous processors. To make portability actionable, we decompose a skill's requirements into a set of primitive capabilities, and measure how well each model-harness pair supports them. Based on these capability profiles, we propose SkVM, a compilation and runtime system designed for portable and efficient skill execution. At compile time, SkVM performs capability-based compilation, environment binding, and concurrency extraction. At runtime, SkVM applies JIT code solidification and adaptive recompilation for performance optimization. We evaluate SkVM across eight LLMs of varying scales and three agent harnesses, covering SkillsBench and representative skill tasks. Results demonstrate that SkVM significantly improves task completion rates across different models and environments while reducing token consumption by up to 40%. In terms of performance, SkVM achieves up to 3.2x speedup with enhanced parallelism, and 19-50x latency reduction through code solidification.
Learning human-object manipulation presents significant challenges due to its fine-grained and contact-rich nature of the motions involved. Traditional physics-based animation requires extensive modeling and manual setup, and more importantly, it neither generalizes well across diverse object morphologies nor scales effectively to real-world environment. To address these limitations, we introduce LOME, an egocentric world model that can generate realistic human-object interactions as videos conditioned on an input image, a text prompt, and per-frame human actions, including both body poses and hand gestures. LOME injects strong and precise action guidance into object manipulation by jointly estimating spatial human actions and the environment contexts during training. After finetuning a pretrained video generative model on videos of diverse egocentric human-object interactions, LOME demonstrates not only high action-following accuracy and strong generalization to unseen scenarios, but also realistic physical consequences of hand-object interactions, e.g., liquid flowing from a bottle into a mug after executing a ``pouring'' action. Extensive experiments demonstrate that our video-based framework significantly outperforms state-of-the-art image based and video-based action-conditioned methods and Image/Text-to-Video (I/T2V) generative model in terms of both temporal consistency and motion control. LOME paves the way for photorealistic AR/VR experiences and scalable robotic training, without being limited to simulated environments or relying on explicit 3D/4D modeling.