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Hongyi Liu

Publications and source records attributed to Hongyi Liu.

At least 19 recordsLinked to original sources
arXiv2026

Spectral dynamics for the Basilica group

The projective spectrum of a tuple $A=(A_0,A_1,\dots,A_n)$ with elements in a unital Banach algebra $\mathcal{A}$ is the collection of $[z_0:z_1:\cdots:z_n]\in \mathbb{P}^n$ such that $z_0A_0+z_1A_1+\dots+z_nA_n$ is not invertible in $\mathcal{A}$. For the tuple $A_{\rho}=(\rho({\bf e}),\rho({\bf a}),\rho({\bf b}))$, where ${\bf e},{\bf a},{\bf b}$ are the three states of the automaton generating the Basilica group $\mathcal{B}$ and $\rho$ is the Koopman representation, a dynamical map $F$ preserving the projective spectrum of $A_{\rho}$ is established. Further, a substantial common subset of the Julia set of $F$ and the projective spectrum of $A_{\rho}$, as well as a large common subset of the Fatou set of $F$ and the projective resolvent set of $A_{\rho}$ is identified. The result provides partial support for the conjecture of equality of the Julia set of $F$ and the projective spectrum of $A_{\rho}$.

math.DS↗
arXiv2026

Blockchain Empowered Trustworthy Agent Networks: Foundations, Taxonomy, and Future Directions

AI agents are evolving from isolated task executors into networked autonomous entities that can communicate, delegate tasks, invoke tools, access external knowledge, and participate in cross-platform service and economic workflows. This evolution gives rise to open agent networks, where heterogeneous agents owned by different stakeholders interact without naturally shared infrastructures for identity, authorization, auditability, reputation, or settlement. This survey and tutorial article reviews the literature over the period 1980--2026 on the evolution from classical multi-agent systems to open agent networks, with a particular focus on LLM-based autonomous agents, agent interoperability protocols, Internet-of-Agents infrastructures, and blockchain-enabled trust mechanisms. We first review this evolution and show how the trust boundary expands from individual execution to cross-agent, cross-platform, and cross-organizational interaction. We then identify a network-level trust crisis that cannot be fully addressed by single-agent safety mechanisms or closed multi-agent coordination techniques, and develop a five-dimensional taxonomy covering entity and capability trust, authorization and delegation trust, information and provenance trust, coordination and group-robustness trust, and accountability and settlement trust. Based on this taxonomy, we examine how blockchain can provide shared identity, verifiable authorization, tamper-evident provenance, auditable collaboration, incentive alignment, and value settlement for trustworthy agent networks. We further synthesize the mapping between agent-network risks, trust requirements, and blockchain-enabled mechanisms, and clarify the role of blockchain as a shared trust layer rather than a replacement for agent security, semantic verification, privacy protection, or robust reasoning.

cs.CR↗
arXiv2026

Frontis-MA1: Training an AI4AI Model towards Recursive Self-Improvement in Machine Learning Engineering

Recursive self-improvement (RSI) requires AI systems that improve the process of building AI (i.e., AI4AI); machine learning engineering (MLE) offers a concrete, executable testbed for studying this capability. We introduce OpenMLE, an open full-stack system for RSI research in MLE, spanning verifiable task environments with execution feedback (OpenMLE-Gym), operator learning (OpenMLE-RL), and long-horizon search (OpenMLE-Evo). On this stack we post-train Frontis-MA1 (35B) as a meta-evolution agent for MLE, aligning post-training and inference around four atomic program-evolution operators (Draft, Improve, Debug, Crossover): the same operators are trained via execution-grounded SFT and RL on data deduplicated against all evaluation benchmarks, then composed into long-horizon search, coupling learning and evolution in a single loop. On MLE-Bench Lite under a 12-hour per-task budget on one RTX 4090 capped at 12 GB VRAM, Frontis-MA1 (35B) improves Medal Average from 39.39% to 60.61% over its base model with OpenMLE-Evo, and reaches 71.21% with OpenMLE-Evo-Max (benchmark-independent experience priors and asynchronous search), exceeding GPT-5.5 + Codex and approaching GPT-5.6 Sol and the 2.8T Kimi K3. On held-out NatureBench Lite, both components transfer: with the framework fixed, swapping in the trained model raises Match-SOTA from 50% to 70%; with the model fixed, swapping in OpenMLE-Evo raises it from 20% to 50%. We release the model weights and the full OpenMLE stack to enable reproducible research on executable AI4AI toward RSI. Code: https://github.com/FrontisAI/OpenRSI

cs.CL↗
arXiv2026

Faithful Autoformalization of Natural Language Assertions

Formal contracts are essential for software testing and verification, yet writing them remains labor-intensive and error-prone. LLMs offer a promising path toward autoformalization: synthesizing executable assertions from natural-language specifications and thereby bridging the gap between informal developer intent and formal executable specifications. We present Monty: an autoformalization framework for assertions that tackles the challenges of expectations of validity of assertions and ambiguity in natural-language. Our techniques are based on filtering formalizations using a novel conformance score metric and validity scores obtained from testing the code against formalized assertions. We evaluate our approach on 541 assertion-generation tasks derived from 22 collection-like Java classes, and show that our technique produces the ground truth more reliably (improving upto 20 points in precision on average) than when using LLMs naively to translate assertions.

cs.SE↗
arXiv2026

Counterexample Guided Learning in the Large using Reasoning Agents

LLMs and LLM agents should improve when given feedback, but identifying when they are able to do so is difficult: feedback is heterogeneous, domain-specific, and difficult to control. We approach this challenge by asking LLMs to perform regular-expression induction, a classical symbolic learning problem where precise mechanisms for feedback exist in the form of counterexamples. In counterexample-guided learning, a learner (LLM) proposes candidate regular expressions from positive/negative-labeled strings, and the teacher (verifier) returns counterexamples showcasing the difference between the candidate and target languages. We identify novel counterexample-guided refinement strategies that enable effective regex learning, such as regularization and symbolic counterexample clusters. We also explore agentic strategies such as reflection and repair loops. Empirically, we find that verifier feedback substantially improves sample efficiency on challenging regex-induction tasks, reducing the number of labeled examples required and enabling learning of complex target expressions where standard prompting fails. For example, on the hardest task groups, our counterexample-guided framework improves success from 3.2% to 38.1% and from 38.9% to 74.1% on two different regex domains. These results suggest that LLMs can benefit from rich feedback beyond treating it as additional data, opening the door for robust verifier-guided methods for LLM-based program synthesis and formal reasoning.

cs.LG↗
arXiv2026

Inter-Landau-Level Pair Tunneling Rigidifies the Long-Wavelength Structure Factor of the {\nu}=1/3 Laughlin State

A textbook chain of reasoning, originating with Girvin, MacDonald, and Platzman, predicts that Landau-level mixing (LLM) at nu=1/3 should soften the long-wavelength structure factor S(L): virtual excitations suppress V_1, the magnetoroton gap closes, and the single-mode approximation then forces S(L) to increase. We test this chain on the Haldane sphere at nu=1/3, N=6, 2Q=15. (i) Perturbatively, via first-order Schrieffer-Wolff dressing of the LLL Laughlin state, fed Lowdin-renormalised pseudopotentials: the dressed state gives Delta S(1) at kappa=10 of approximately +21%, consistent with the GMP prediction (~19% softening of V_1^eff). (ii) Non-perturbatively, via rigorous two-Landau-level (LLL+SLL) exact diagonalisation using a repaired DiagHam 2LL module that retains, for the first time on the sphere, the full inter-LL scattering channels. The response reverses sign: S(1) rigidifies monotonically from 0.118 at kappa->0 to 0.080 at kappa=10, a 32% suppression. Perturbative and non-perturbative results thus disagree in sign, with a gap of ~53 percentage points between +21% (SW) and -32% (full ED). Channel-mask ablation localises the reversal to the DD<->UU pair-tunneling channel (98% of the shift). A four-way decomposition shows the three-body coherent content overpowers the perturbative admixture by ~2.5x. Repaired code: https://github.com/Cannan-1/DiagHamOnSphereOpenSource (v2.0).

cond-mat.str-el↗
arXiv2026

Poincar\'e-Einstein 4-manifolds with cusps

In this paper, we construct Poincar\'e-Einstein 4-manifolds with various kinds of cusps. In particular, we construct: (1) Infinite families of Einstein metrics on $(0,\infty)\times \mathscr{N}$, where $\mathscr{N}\to T^2$ is a principal $\mathbb{S}^1$-bundle over $T^2$, with one Poincar\'e-Einstein end and one end asymptotic to a real or complex hyperbolic cusp. (2) Infinite families of Einstein metrics on $(0,\infty)\times P$, where $P\to \Sigma_{\mathtt{g}}$ is a principal $\mathbb{S}^1$-bundle over a closed Riemann surface $\Sigma_{\mathtt{g}}$ of genus $\mathtt{g}\geq 2$, with one Poincar\'e-Einstein end and one end asymptotic to a bundle of two-dimensional hyperbolic cusps over hyperbolic $\Sigma_{\mathtt{g}}$. Universal covers of (1) and (2) provide new complete negative Einstein metrics on $\mathbb{R}^4$. These Einstein metrics also exhibit interesting degeneration phenomena. With this construction, we give a negative answer to a question of Anderson concerning cusp formation for Poincar\'e-Einstein 4-manifolds.

math.DG↗
arXiv2026

SkillsVote: Lifecycle Governance of Agent Skills from Collection, Recommendation to Evolution

Long-horizon LLM agents generate traces that could become reusable experience, but raw trajectories are noisy, local, and hard to govern. Agent Skills offer a structured artifact for combining procedural guidance, executable resources, and applicability boundaries. Yet open skill ecosystems contain redundant, uneven, environment-sensitive artifacts, and indiscriminate updates can pollute future context. We present SkillsVote, a lifecycle-governance framework for Agent Skills across collection, recommendation, attribution, and evolution. SkillsVote profiles a million-scale open source corpus for environment requirements, quality, and verifiability, and synthesizes tasks for verifiable skills. Before execution, it performs agentic library search over structured skill folders to expose instructional context. After execution, it decomposes trajectories into skill-linked subtasks, attributes outcomes to skill-guided execution, agent exploration, environment, and result signals, and admits only successful reusable discoveries to evidence-gated updates. Experiments on Terminal-Bench 2.0 and SWE-Bench Pro show that SkillsVote improves agent performance on challenging agentic coding benchmarks. The gains arise from two complementary pathways: online evolution over task streams at test time and offline transfer via frozen libraries built from either historical trajectories or curated open source skills.

cs.CL↗
arXiv2026

Towards Robust LLM Post-Training: Automatic Failure Management for Reinforcement Fine-Tuning

Reinforcement fine-tuning (RFT) has become a core paradigm for post-training large language models, yet its training process remains highly fragile. Existing efforts mainly improve reliability at the system level or address specific issues in individual subproblems by modifying RFT algorithms. Despite their effectiveness, they largely overlook the problem of failure management at the training-process level. When training goes wrong, practitioners still rely heavily on expert-driven manual inspection and correction, and automatic failure management for RFT remains largely unexplored. In this paper, we take a first step toward systematic failure management for reinforcement fine-tuning. To understand the empirical structure of RFT failures, we first construct RFT-FaultBench, the first benchmark for fine-grained failures in reinforcement fine-tuning, covering 5 fault families, 16 fault types, 779 training runs, 22,549 train-step records, and 1,457,288 trajectory-level records. Based on this benchmark, we conduct a comprehensive empirical study showing that RFT failures are both observable from training dynamics and distinguishable through their empirical fault fingerprints. Building on these findings, we propose RFT-FM, an automatic failure management framework for reinforcement fine-tuning that unifies anomaly detection, failure diagnosis, and auto remediation in a closed loop. Experimental results show that RFT-FaultBench is neither trivial nor saturated: it exhibits clear anomaly structure while still posing substantial challenges, especially under subtle fault settings. Moreover, RFT-FM shows strong capability in detecting, diagnosing, and mitigating RFT failures.

cs.SE↗
arXiv2026

Dual-Exposure Imaging with Events

By combining complementary benefits of short- and long-exposure images, Dual-Exposure Imaging (DEI) enhances image quality in low-light scenarios. However, existing DEI approaches inevitably suffer from producing artifacts due to spatial displacement from scene motion and image feature discrepancies from different exposure times. To tackle this problem, we propose a novel Event-based DEI (E-DEI) algorithm, which reconstructs high-quality images from dual-exposure image pairs and events, leveraging high temporal resolution of event cameras to provide accurate inter-/intra-frame dynamic information. Specifically, we decompose this complex task into an integration of two sub-tasks, i.e., event-based motion deblurring and low-light image enhancement tasks, which guides us to design E-DEI network as a dual-path parallel feature propagation architecture. We propose a Dual-path Feature Alignment and Fusion (DFAF) module to effectively align and fuse features extracted from dual-exposure images with assistance of events. Furthermore, we build a real-world Dataset containing Paired low-/normal-light Images and Events (PIED). Experiments on multiple datasets show the superiority of our method. The code and dataset are available at github.

cs.CV↗
arXiv2026

Jackpot: Optimal Budgeted Rejection Sampling for Extreme Actor-Policy Mismatch Reinforcement Learning

Reinforcement learning (RL) for large language models (LLMs) remains expensive, particularly because the rollout is expensive. Decoupling rollout generation from policy optimization (e.g., leveraging a more efficient model to rollout) could enable substantial efficiency gains, yet doing so introduces a severe distribution mismatch that destabilizes learning. We propose Jackpot, a framework that leverages Optimal Budget Rejection Sampling (OBRS) to directly reduce the discrepancy between the rollout model and the evolving policy. Jackpot integrates a principled OBRS procedure, a unified training objective that jointly updates the policy and rollout models, and an efficient system implementation enabled by top-$k$ probability estimation and batch-level bias correction. Our theoretical analysis shows that OBRS consistently moves the rollout distribution closer to the target distribution under a controllable acceptance budget. Empirically, \sys substantially improves training stability compared to importance-sampling baselines, achieving performance comparable to on-policy RL when training Qwen3-8B-Base for up to 300 update steps of batchsize 64. Taken together, our results show that OBRS-based alignment brings us a step closer to practical and effective decoupling of rollout generation from policy optimization for RL for LLMs.

cs.AI↗
arXiv2026

NFCDS: A Plug-and-Play Noise Frequency-Controlled Diffusion Sampling Strategy for Image Restoration

Diffusion sampling-based Plug-and-Play (PnP) methods produce images with high perceptual quality but often suffer from reduced data fidelity, primarily due to the noise introduced during reverse diffusion. To address this trade-off, we propose Noise Frequency-Controlled Diffusion Sampling (NFCDS), a spectral modulation mechanism for reverse diffusion noise. We show that the fidelity-perception conflict can be fundamentally understood through noise frequency: low-frequency components induce blur and degrade fidelity, while high-frequency components drive detail generation. Based on this insight, we design a Fourier-domain filter that progressively suppresses low-frequency noise and preserves high-frequency content. This controlled refinement injects a data-consistency prior directly into sampling, enabling fast convergence to results that are both high-fidelity and perceptually convincing--without additional training. As a PnP module, NFCDS seamlessly integrates into existing diffusion-based restoration frameworks and improves the fidelity-perception balance across diverse zero-shot tasks.

cs.CV↗
arXiv2026

Phong-Rodrigues Extrinsic Vector-Field Processing

We introduce a new extrinsic discretization of tangent vector fields on triangle meshes that is continuous, with bounded derivatives that are continuous almost everywhere, supporting pointwise evaluation and integration of differential operators. We achieve this by building a continuous normal field over the mesh via Phong interpolation and using minimal Rodrigues rotations to transport vertex-based tangent vectors into triangle interiors. Unlike most existing discretizations, which typically sacrifice either continuity or the ability to evaluate derivatives pointwise, our approach supports both. Because it is pointwise evaluatable, and using the fact that the covariant derivative can be decomposed into its symmetric, antisymmetric, and scalar components, our discretization supports the construction of standard vector-field processing operators including the connection and Hodge Laplacians, Killing energy, divergence, curl, and the Lie bracket. This framework provides a simple and practical finite-element formulation for vector-field processing on meshes, supporting both integration-based operators and pointwise queries. To our knowledge, ours is the first discretization that jointly enables extrinsic continuous vector fields, bounded derivatives, and pointwise evaluation of this collection of operators.

cs.GR↗
arXiv2026

Distilling the Thought, Watermarking the Answer: A Principle Semantic Guided Watermark for Large Reasoning Models

Reasoning Large Language Models (RLLMs) excelling in complex tasks present unique challenges for digital watermarking, as existing methods often disrupt logical coherence or incur high computational costs. Token-based watermarking techniques can corrupt the reasoning flow by applying pseudo-random biases, while semantic-aware approaches improve quality but introduce significant latency or require auxiliary models. This paper introduces ReasonMark, a novel watermarking framework specifically designed for reasoning-intensive LLMs. Our approach decouples generation into an undisturbed Thinking Phase and a watermarked Answering Phase. We propose a Criticality Score to identify semantically pivotal tokens from the reasoning trace, which are distilled into a Principal Semantic Vector (PSV). The PSV then guides a semantically-adaptive mechanism that modulates watermark strength based on token-PSV alignment, ensuring robustness without compromising logical integrity. Extensive experiments show ReasonMark surpasses state-of-the-art methods by reducing text Perplexity by 0.35, increasing translation BLEU score by 0.164, and raising mathematical accuracy by 0.67 points. These advancements are achieved alongside a 0.34% higher watermark detection AUC and stronger robustness to attacks, all with a negligible increase in latency. This work enables the traceable and trustworthy deployment of reasoning LLMs in real-world applications.

cs.AI↗
arXiv2025

Fail Fast, Win Big: Rethinking the Drafting Strategy in Speculative Decoding via Diffusion LLMs

Diffusion Large Language Models (dLLMs) offer fast, parallel token generation, but their standalone use is plagued by an inherent efficiency-quality tradeoff. We show that, if carefully applied, the attributes of dLLMs can actually be a strength for drafters in speculative decoding with autoregressive (AR) verifiers. Our core insight is that dLLM's speed from parallel decoding drastically lowers the risk of costly rejections, providing a practical mechanism to effectively realize the (elusive) lengthy drafts that lead to large speedups with speculative decoding. We present FailFast, a dLLM-based speculative decoding framework that realizes this approach by dynamically adapting its speculation length. It "fails fast" by spending minimal compute in hard-to-speculate regions to shrink speculation latency and "wins big" by aggressively extending draft lengths in easier regions to reduce verification latency (in many cases, speculating and accepting 70 tokens at a time!). Without any fine-tuning, FailFast delivers lossless acceleration of AR LLMs and achieves up to 4.9$\times$ speedup over vanilla decoding, 1.7$\times$ over the best naive dLLM drafter, and 1.7$\times$ over EAGLE-3 across diverse models and workloads. We open-source FailFast at https://github.com/ruipeterpan/failfast.

cs.LG↗
arXiv2025

PEGS: Physics-Event Enhanced Large Spatiotemporal Motion Reconstruction via 3D Gaussian Splatting

Reconstruction of rigid motion over large spatiotemporal scales remains a challenging task due to limitations in modeling paradigms, severe motion blur, and insufficient physical consistency. In this work, we propose PEGS, a framework that integrates Physical priors with Event stream enhancement within a 3D Gaussian Splatting pipeline to perform deblurred target-focused modeling and motion recovery. We introduce a cohesive triple-level supervision scheme that enforces physical plausibility via an acceleration constraint, leverages event streams for high-temporal resolution guidance, and employs a Kalman regularizer to fuse multi-source observations. Furthermore, we design a motion-aware simulated annealing strategy that adaptively schedules the training process based on real-time kinematic states. We also contribute the first RGB-Event paired dataset targeting natural, fast rigid motion across diverse scenarios. Experiments show PEGS's superior performance in reconstructing motion over large spatiotemporal scales compared to mainstream dynamic methods.

cs.CV↗
arXiv2025

Not-a-Bandit: Provably No-Regret Drafter Selection in Speculative Decoding for LLMs

Speculative decoding is widely used in accelerating large language model (LLM) inference. In this work, we focus on the online draft model selection problem in speculative decoding. We design an algorithm that provably competes with the best draft model in hindsight for each query in terms of either the token acceptance probability or expected acceptance length. In particular, we show that we can accurately evaluate all draft models, instead of only the chosen model without incurring additional queries to the target model, which allows us to improve exponentially over the existing bandit-based approach as the number of draft models increases. Our approach is generically applicable with any speculative decoding methods (single draft, multi-drafts and draft-trees). Moreover, we design system-efficient versions of online learners and demonstrate that the overhead in computation and latency can be substantially reduced. We conduct extensive experiments on open-source LLMs and diverse datasets, demonstrating that our methods substantially outperform the state-of-the-art EAGLE3 and the BanditSpec baseline in a variety of domains where specialized domain-expert drafters are available, especially when long reasoning chains are required.

cs.LG↗
arXiv2025

Poincar\'e-Einstein 4-manifolds with conformally K\"ahler geometry

We study 4-dimensional Poincar\'e-Einstein manifolds whose conformal class contains a K\"ahler metric. Such Einstein metrics are non-K\"ahler and admit a Killing field extending to the conformal infinity, and the Einstein equation reduces to a Toda-type equation. When the Killing field integrates to an $\mathbb{S}^1$-action, we formulate a Dirichlet boundary value problem and establish existence and uniqueness theory. This construction provides a non-perturbative realization of infinite-dimensional families of new Poincar\'e-Einstein metrics whose conformal infinities are of non-positive Yamabe type.

math.DG↗