arXiv subjects

Hao Liu

Publications and source records attributed to Hao Liu.

At least 55 records · Page 3Linked to original sources

arXiv2026

Frequency-Conditioned Flow Matching for Vision-Language-Action Models

Robot actions are temporally correlated trajectories whose frequency components encode motion at different scales with highly non-uniform energy distributions. Yet Flow Matching--based vision-language-action (VLA) models typically generate actions in temporal coordinates, without explicitly modeling or systematically leveraging this frequency heterogeneity. We introduce \emph{FreqFM}, a frequency-conditioned Flow Matching framework for VLA models. It raises action frequency from an implicit trajectory property to an explicit conditioning dimension that spans the entire generation pipeline. Concretely, in DCT frequency coordinates, FreqFM constructs a spectrum-matched source distribution, adaptively balances the objective across frequencies, and constrains per-frequency guidance residuals using the corresponding reference transport scales. FreqFM integrates into existing Flow Matching action experts without changing the VLA backbone. Across LIBERO, LIBERO-Plus, and VLA-Arena, FreqFM consistently improves performance, including a 9.3-point gain on LIBERO-Plus, and further demonstrates its effectiveness on six real-robot tasks.

cs.RO↗

arXiv2026

Kolmogorov-Arnold networks in nuclear binding energy prediction

This study explores the application of Kolmogorov-Arnold networks (KANs) in predicting nuclear binding energies, leveraging their ability to decompose complex multiparameter systems into simpler univariate functions. By utilizing data from the Atomic Mass Evaluation (AME2020) and incorporating features such as atomic number, neutron number, and shell effects, KANs achieved a significant lower root mean square error (0.26 MeV), surpassing traditional models. The symbolic regression analysis yielded simplified analytical expressions for binding energies, aligning with classical models like the liquid drop model and the Bethe-Weizsaecker formula. These results highlight KANs' potential in enhancing the interpretability and understanding of nuclear phenomena, paving the way for future applications in nuclear physics and beyond.

nucl-th↗

arXiv2026

A Token is Worth over 1,000 Tokens: Efficient Knowledge Distillation through Low-Rank Clone

Training high-performing Small Language Models (SLMs) remains costly, even with knowledge distillation and pruning from larger teacher models. Existing work often faces three key challenges: (1) information loss from hard pruning, (2) inefficient alignment of representations, and (3) underutilization of informative activations, particularly from Feed-Forward Networks (FFNs). To address these challenges, we introduce Low-Rank Clone (LRC), an efficient pre-training method that constructs SLMs aspiring to behavioral equivalence with strong teacher models. LRC trains a set of low-rank projection matrices that jointly enable soft pruning by compressing teacher weights, and activation clone by aligning student activations, including FFN signals, with those of the teacher. This unified design maximizes knowledge transfer while removing the need for explicit alignment modules. Extensive experiments with open-source teachers (e.g., Llama-3.2-3B-Instruct, Qwen2.5-3B/7B-Instruct) show that LRC matches or surpasses state-of-the-art models trained on trillions of tokens--while using only 20B tokens, achieving over 1,000x training efficiency. Our codes and model checkpoints are available at https://github.com/CURRENTF/LowRankClone and https://huggingface.co/collections/JitaiHao/low-rank-clone-lrc-6828389e96a93f1d4219dfaf.

cs.CL↗

arXiv2026

Channel couplings redirect absorbed flux from peripheral loss to fusion in weakly bound nuclear reactions

In reactions of weakly bound nuclei, the absorption cross section mixes two physically distinct contributions: inner capture associated with compound-nucleus formation, and peripheral losses from breakup, transfer, and other direct reactions. Within a framework that combines an ingoing-wave boundary condition (IWBC) at an inner radius with a complex potential in the external region, we derive the exact flux identity $σ_{\rm abs}=σ_{\rm fusion}+σ_W$ from the radial continuity equation. The resulting partition is exact within the adopted CC/CDCC model space and provides a practical diagnostic of where absorbed flux is removed. Applied to $^6$Li+$^{209}$Bi, the analysis reveals that channel couplings qualitatively reorganize the absorbed flux: the dominant absorption mechanism shifts from peripheral loss at sub-barrier energies to inner capture above the barrier, whereas the single-channel baseline remains peripheral-loss dominated throughout. The resulting IWBC-defined inner-capture cross section tracks the measured complete-fusion excitation function with only a modest dependence on the chosen boundary radius. Together with the exact identity $σ_{\rm abs}=σ_{\rm fusion}+σ_W$, this agreement supports interpreting the peripheral term $σ_W$ as a major spatial contributor to the well-known CF suppression in weakly bound systems.

nucl-th↗

arXiv2026

Exact construction and uniqueness of the coupled-channel Green's function

We present a rigorous construction and uniqueness proof of the matrix Green's function for coupled radial Schrodinger equations with symmetric coupling potentials. The Green's matrix $G(R,R')$ is built from two fundamental sets of $N$ linearly independent solutions, regular and outgoing, of the coupled radial equations. We prove that the associated Wronskian matrix is diagonal with elements $W_n = -k_n$ and independent of the radial coordinate, and demonstrate through the symplectic structure of the $2N$-dimensional phase space that the resulting construction is the unique Green's matrix satisfying the defining equation with correct boundary conditions, continuity at the source point, and the prescribed derivative discontinuity. The construction applies to any system of coupled radial Schrodinger equations with symmetric coupling potentials and open channels, including coupled-channels problems arising in nuclear, atomic, and molecular scattering. As an illustrative application, we show how the Green's matrix enters the nonlocal dynamical polarization potential within the continuum-discretized coupled-channels framework, where retaining the off-diagonal elements captures multistep excitation pathways beyond the weak-coupling approximation.

nucl-th↗

arXiv2026

Assessing continuum channel importance in continuum-discretized coupled-channels via dynamic polarization potential decomposition

A recurring question in continuum-discretized coupled-channels calculations is which continuum channels carry the breakup coupling, both to interpret the reaction and to decide which channels a model space can safely omit. The standard answer is bin deletion: remove a channel, re-solve the coupled equations, and read the change in the elastic $S$ matrix. We show that this cannot isolate an individual channel's contribution. Deleting a channel forces the surviving model space to reorganize, with the neighboring bins rerouting through the off-diagonal Green's function, so the recorded change mixes the channel's own effect with the readjustment of all the others. Working instead from the channel-resolved Feshbach dynamic polarization potential (DPP), whose full-coupling Green's function is a fixed reference shared by every channel, we define an exclusion that removes one channel while holding that reference fixed, returning its contribution to the intact system. The two operations disagree on which continuum bins matter most, for $d$+$^{58}$Ni at 21.6 MeV even sending the intrinsically leading bin to last place under deletion. The DPP further separates each channel's action into a direct path, virtual excitation and return, and a bridge path, relayed through neighboring bins, a split deletion cannot make; it shows the bins act on the elastic channel mainly as bridges, robustly across angular momentum, and that it is this bridge coupling that reorganizes under deletion. A deletion-based channel importance is therefore best read as the truncated calculation's sensitivity to a channel's removal, not as the channel's intrinsic coupling strength.

nucl-th↗

arXiv2026

Quantifying Error Tolerance in Synthetic Data: An Atomic-level Operand vs. Operator Perturbation Study

Synthetic data generation has become a cornerstone for advancing large language models. However, the lack of the quantitative analysis for error tolerance became a critical bottleneck. Consequently, current filtering strategies fluctuate between two extremes: they are either overly aggressive, risking the exclusion of potentially valuable samples, or overly permissive, failing to eliminate erroneous samples effectively. To bridge this gap, this paper introduces Atomic Tree Operation Modeling (ATOM), a framework that decomposes data into functional units ($f(x)\rightarrow y$). ATOM distinguishes benign Operand $x$ perturbations from fatal Operator $f$ perturbations. The former are needlessly discarded by aggressive filtering, while the latter slip through permissive filtering. Our experiments reveal a double dissociation: models are robust to operand perturbations but collapse under operator perturbations. By prioritizing operator over aggressive operand precision, our ATOM-synthesized data outperforms rigorous baselines (e.g., +3.1% gain over LIMA), suggesting that operator diversity matters more than operand precision. Our code is available at https://github.com/Lut-hub/ATOM.

cs.CL↗

arXiv2026

Coherent Absorption Dynamics: The Dual Role of Off-Diagonal Couplings in Weakly Bound Nuclei

Disentangling reaction mechanisms in weakly bound nuclei remains a long-standing challenge, complicated by the common practice of treating absorption as an incoherent sum of channel contributions. Within the continuum-discretized coupled-channels (CDCC) framework, we apply the generalized optical theorem [Nucl. Phys. A 842, 48 (2010)] and show that the total absorption cross section, $σ_A \propto -\langleΨ|W|Ψ\rangle$, decomposes as $σ_A = σ_D + σ_B + σ_{int}$, where $σ_{int}$ is a coherent interference term between channel components. For the systems and complex fragment-target optical potentials considered, $σ_{int}$ is negative and comparable in magnitude to the direct absorption terms. The off-diagonal imaginary couplings play a dual role: they redistribute flux among channels and generate $σ_{int}$, which is required for flux-balance consistency. In calculations for $d+^{93}$Nb and $^6$Li$+^{59}$Co/$^{208}$Pb, retaining the full non-diagonal coupling matrix nearly doubles the breakup-channel absorption for the heavy target, while reducing the total absorption through $σ_{int}$. Neglecting the off-diagonal imaginary couplings $W_{ij}$ ($i \neq j$) is not merely an approximation but leads to a systematically biased physical picture: the total absorption is overestimated while the breakup absorption component is severely underestimated. Experimental analyses that employ incoherent-sum models to extract direct and breakup cross sections from data will inherit this bias. The full coupling matrix is therefore essential for mechanism-resolved cross-section extraction, and we advocate that experimentalists adopt full-coupling CDCC calculations as the standard for consistent interpretation of absorption data in weakly bound systems.

nucl-th↗

arXiv2026

Existence, uniqueness and long-time behavior of the $λ$-dissipative solutions to the two-component Hunter-Saxton system

In this paper, we construct the explicit characteristics for the $λ$-dissipative solutions ($λ\in[0,1]$) to the two-component Hunter--Saxton (2HS) system. Using these characteristics, we provide a comprehensive study of the existence, uniqueness, and asymptotic behavior of these solutions. For the fully dissipative case ($λ=1$), uniqueness follows from the absence of outgoing cusps. In the partially dissipative regime ($0<λ<1$), outgoing cusps are present. We formulate an exact Eulerian dissipation rule which identifies the energy that has already passed through wave breaking by the intrinsic condition $ρ=0$ and $u_x\geq 2/t$. This rule determines the dissipated part of the energy measure and yields uniqueness. This uniqueness applies to the classical Hunter-Saxton equation and seems to be the first uniqueness result for the general $λ$-dissipative solutions. Concerning the large-time dynamics, we show that the density $ρ$ and the singular part of the energy measure decay to zero as $t\to\infty$, indicating that all energy is eventually concentrated in the $u$-component. Moreover, we derive the leading-order asymptotic term, which takes the form of a kink-wave determined by the system's remaining energy. This kink-wave can be explicitly computed from the initial data and the dissipation parameter $λ$.

math.AP↗

arXiv2026

Exact Treatment of Continuum Couplings in Nuclear Optical Potentials via Feshbach Theory

We present a full-coupling construction of the Feshbach effective interaction in a converged continuum-discretized coupled-channels (CDCC) calculation. The method retains the complete Green's function in the excluded continuum space, treating the continuum-continuum couplings to all orders within the discretized CDCC model space, and therefore yields an explicitly non-local dynamic polarization potential. Applied to $d+^{58}$Ni scattering, the projected two-body potential reproduces the parent CDCC elastic observables and gives a reasonable description of the available experimental data, providing a direct numerical check of the projection. The resulting non-local potential exposes the spatial structure generated by virtual breakup, continuum propagation, and absorption in the continuum. Through the generalized optical theorem, we quantify the continuum-coupling contribution to the elastic flux loss and compare it with the elastic-breakup cross section over a broad incident-energy range. The calculation shows that the elastic-breakup fraction increases with energy, whereas the additional absorption associated with continuum components is strongest at intermediate energies.

nucl-th↗

arXiv2026

DPIAgent: Divide, Protocol, Isolate for Agentic Reproduction Test Generation

Reproduction test generation, producing a failing-then-passing test that captures a reported bug, is a critical step in automated software engineering. Existing agentic methods treat this as a monolithic loop, despite the task inherently comprising two subtasks of distinct nature: diagnosing the root cause and writing a fail-to-pass test. Without explicit separation, the agent faces a compound objective with underspecified intermediate goals, leading to goal drift. We propose DPIAgent, a structured agentic framework built on three principles, Divide, Protocol, Isolate (DPI), that mitigates compound-objective ambiguity and goal drift: it Divides the task into single-objective phases of defect exploration and test generation; enforces a handoff Protocol that records the diagnosis and test plan, preventing context loss; and Isolates each phase's action space by tailoring the toolset to its task, preventing irrelevant tools from misleading execution. On SWT-Bench Verified, DPIAgent outperforms seven baselines across three backbone LLMs. With DPI alone it reaches 81.76% success rate on GPT-5, the highest reported among open-source methods, gaining up to 11.88 points over the strongest baseline on GPT-5-Mini; adding test selection further raises it to 86.17%. Our analysis shows that architectural structure and backbone capability are complementary axes rather than substitutes, demonstrating DPI's generalizability across model classes.

cs.SE↗

arXiv2026

PonyEval: Evaluating LLM-Based Program Repair for Capability-Safe and Actor-Oriented Pony Software

Repository-level issue-resolution benchmarks have made executable evaluation central to software-engineering agents, but their language coverage remains concentrated in mainstream ecosystems. Pony presents a different regime: it combines actors, reference capabilities, ahead-of-time compilation, and a rapidly evolving historical toolchain, making both patch generation and faithful replay difficult. We introduce PonyEval, a SWE-bench-style benchmark of 291 real GitHub issue-pull-request pairs from 15 Pony repositories. Every instance binds an issue statement, a historical base commit, a developer gold patch, a black-box test patch, and a reproducible runtime mapping. The frozen release passes an offline audit requiring the issue-specific test to fail on the base state and pass after the gold patch; it contains no duplicate instance identifiers or canonical repository-PR pairs. In a separate full-set semantic selection audit, three isolated machine reviewers label all 291 instances as include or exclude; their Fleiss' kappa is 0.8968, with 249 unanimous inclusions and 32 unanimous exclusions. To replay eleven years of repository history, we reconstruct 72 runtime images covering 289 unique base commits and verify their availability on five heterogeneous compute nodes. We define a matched evaluation with mini-SWE-agent 2.4.6 for GPT-5.6-sol, DeepSeek-V4-Pro, GLM-5.2, MiniMax-M3, and Kimi-K3, followed by strict patch application, compilation, and hidden-test validation. Across the patches actually produced by each model, conditional resolution rates range from 10.21% to 24.68%. These rates characterize the quality of generated patches rather than success over all 291 benchmark tasks.

cs.SE↗

arXiv2026

From Reasoning Strings to Partial Orders: Verifier-Certified Rule Transport through Quotient Policy Optimization

Many computations admit several valid execution orders because independent subgoals or disjoint state updates can commute. Reinforcement learning with verifiable rewards usually treats each successful trace as a separate token sequence, so serialization choices can be mistaken for logical dependencies. We introduce Verifier-Certified Rule Transport (VCRT), which replays adjacent operation pairs with native verifiers. Pairs whose two orders are accepted and reach the same canonical state provide commutation certificates; rejected or state-changing reversals provide anti-diamonds. VCRT uses anti-diamonds to preserve genuine prerequisites and assigns policy credit to the total probability mass of each certified orbit. It also constrains post-swap consistency, source retention, and policy drift. We evaluate leave-one-environment-out transfer across ProofWriter, CLRS, and Lean through a shared anonymized relation-graph interface. All training and checkpoint decisions are frozen before held-out evaluation, which uses one greedy trajectory per item without search or verifier feedback. VCRT obtains a 77.60% macro pass rate versus 64.53% for the strongest matched baseline, a paired gain of 13.06 points (95% bootstrap CI [12.58, 13.54]). Lean accounts for most of this gain at 33.49 points, while ProofWriter and CLRS improve by 2.85 points on average. Mechanism tests consistently favor anti-diamond supervision, whereas No-Orbit is statistically indistinguishable from full VCRT. The evidence does not establish a general benefit from exact orbit aggregation.

cs.LG↗

arXiv2026

VibeWorlding: Can Multimodal Agents Construct 3D Open Worlds End-to-End?

Constructing an interactive 3D open world from a user query is important. However, existing methods are primarily evaluated on idealized, simple queries, making it difficult to systematically analyze and compare how multimodal agents understand user intent, use 3D tools, and reason over textual and visual 3D world information. To this end, we propose VibeWorlding, a unified framework for benchmarking and training vibe worlding agents: a multimodal agent that can autonomously infer user intent, plan scene layout, invoke 3D tools, and reflect on the multimodal feedback in a multi-turn agent-environment interaction process. To achieve this, we first build VWE-BENCH, a benchmark of 2,616 high-quality 3D assets, 323 human-annotated seed 3D worlds, and 6,828 reverse-synthesized multimodal user queries, split into verified queries with ground-truth and unverified queries with carefully designed rubrics. Moreover, we develop VibeWorlding-Gym, a joint multimodal RL post-training framework that integrates (1) a sandbox environment unifying asset retrieval, editing, and image rendering as MCP tools, and (2) a rubric-based verifier that combines physical feasibility and intent fulfillment verification, supporting both fair model evaluation and scalable multimodal RL reward service. Our experiments show that current frontier MLLMs are far from solving the vibe worlding agent task, with even GPT-5.5 and Qwen3.8-Max reaching below 60% success rate, and trace the bottleneck to precise 3D world editing. We further find that RL training can ease this weakness and enable open-source MLLMs to even surpass closed-source frontiers: our VibeWorlder-8B is comparable to frontier MLLMs, while our flagship VibeWorlder-30B-A3B attains the best overall Pass@1 among all evaluated models.

cs.AI↗

arXiv2026

AppEval: A Unified Benchmark for LLM-Based Mobile Application Repair in ArkTS, Swift, and Kotlin

Repository-level LLM agents are typically evaluated on projects whose tests run on the build host. It remains unclear whether their repairs survive the mobile build-install-launch-test boundary, where a missing SDK, offline device, or pre-assertion crash can be mistaken for a program failure. We present AppEval, a benchmark and native-toolchain evaluation framework for mobile application repair across HarmonyOS/ArkTS, iOS/Swift, and Android/Kotlin. Each task separates a hidden behavior test from the reference production fix and is accepted only when the same installed-app target reaches an assertion failure on the defective revision and passes after the fix; infrastructure failures remain a distinct outcome. A common schema maps this contract to each platform's build system, runtime, and test runner. The audited Android partition contains 200 accepted instrumentation tasks from 24 independently buildable repositories. On these tasks, five agents achieve Pass@1 between 22.00% and 90.50%, a 68.50-percentage-point spread under the same dynamic oracle. These results show that mobile repair performance depends strongly on the evaluated agent while demonstrating why runtime-aware acceptance is necessary for meaningful comparison. The quantitative findings in this paper are Android-specific; audited iOS and HarmonyOS results are required before drawing cross-platform generalization conclusions.

cs.SE↗

arXiv2026

OdinEval: A Reproducible Benchmark for LLM-Based Program Repair in the Odin Programming Language

Repository-level repair benchmarks still center on a few mainstream languages, leaving systems languages such as Odin largely untested. We present OdinEval, a reproducible benchmark built from documented defects in public Odin repositories. Each instance binds an issue to base and fix commits, a gold patch, an issue-specific regression test, a historical toolchain, and execution records. Admission requires the test to fail on the base revision and pass after the gold fix. When no usable developer test exists, a black-box test is reviewed independently by three instances of the same model, executed in both historical states, and revised from recorded feedback under a versioned Test Writing Skill. We evaluate six language models on 168 filtered instances under one shared protocol. Kimi-K3 records the highest Resolved score at 66.7%, while Qwen3.8-Max has the highest Repro score at 96.4%. The release includes frozen data, source archives, containers, validators, model patches, and audit manifests.

cs.SE↗

arXiv2026

SimulCost: A Cost-Aware Benchmark and Toolkit for Automating Physics Simulations with LLMs

Evaluating LLM agents for scientific tasks has focused on token costs while ignoring tool-use costs like simulation time and experimental resources. As a result, metrics like pass@k become impractical under realistic budget constraints. To address this gap, we introduce SimulCost, the first benchmark targeting cost-sensitive parameter tuning in physics simulations. SimulCost compares LLM tuning cost-sensitive parameters against traditional scanning approach in both accuracy and computational cost, spanning 2,643 single-round (initial guess) and 2,304 multi-round (adjustment by trial-and-error) tasks across 11 simulators from fluid dynamics, solid mechanics, and plasma physics, whose costs are analytically defined and platform-independent. A twelfth simulator, a production plasma code measurable only by wall clock, is reported separately. Frontier LLMs achieve 45-62% success rates in single-round mode, dropping to 34-50% under high accuracy requirements, rendering their initial guesses unreliable especially for high accuracy tasks. Multi-round mode improves rates to 66-81%, but LLMs are 1.5-2.7x slower than traditional scanning, making them uneconomical choices. We also investigate parameter group correlations for knowledge transfer potential, and the impact of in-context examples and reasoning effort, providing practical implications for deployment and fine-tuning. We open-source SimulCost as a static benchmark and extensible toolkit to facilitate research on improving cost-aware agentic designs for physics simulations, and for expanding new simulation environments. Code and data are available at https://github.com/Rose-STL-Lab/SimulCost-Bench

physics.comp-ph↗

arXiv2026

Step-Level On-Policy Distillation: Interpolating Between On-Policy Distillation and Supervised Fine-Tuning

On-policy distillation (OPD) aligns a student model with a teacher's logit distribution on student-generated trajectories. This approach has achieved strong empirical gains and can often surpass conventional off-policy distillation with substantially less data. However, standard token-level OPD can provide only fragmented corrections along an erroneous student trajectory and cannot unfold a complete and correct repair path. Motivated by this limitation, we propose \emph{Step-Level On-Policy Distillation} (SOPD), which combines the long-horizon correction of supervised fine-tuning (SFT) with the on-policy advantage of OPD to provide step-level supervision over complete student-generated trajectories. We show that, at different limits of step length, SOPD reduces to SFT or approximates OPD. Compared with SFT, the teacher responses in SOPD are conditioned on student trajectories and therefore align more closely with student-visited states; compared with OPD, SOPD provides longer-horizon corrections rather than fragmented token-level guidance. Across both reasoning and agent tasks, SOPD substantially outperforms conventional SFT and OPD. For example, on ALFWorld, SOPD improves the average success rate by 13.4 points over Vanilla OPD. We hope this work offers a new perspective for future research on distillation methods.

cs.CL↗