arXiv subjects

Haowei Lin

Publications and source records attributed to Haowei Lin.

At least 19 recordsLinked to original sources

arXiv2026

Multi-marginal optimal transport on sub-Riemannian manifolds

In this paper, we study multi-marginal optimal transport on ideal sub-Riemannian manifolds. We establish a sub-Riemannian barycentric balance condition and prove the existence of a solution to the Monge problem under an additional assumption. We also investigate the absolute continuity of Wasserstein barycenters. Our results extend and improve upon those of Pass, Pinamonti, and Vedovato (Methods Appl. Anal. 28 (2021), 61-76) on the Heisenberg group, answering two open questions raised in their work.

math.DG↗

arXiv2026

SLDBench v2: Active Scaling Law Discovery

Scaling laws predict large-model performance from small experiments, but finding a reliable law itself requires costly experiments. SLDBench tests whether language-model agents can discover scaling laws when all experimental results are given upfront. We introduce SLDBench v2 with two extensions. First, we expand the corpus from 8 to 127 scenarios spanning language-model pretraining, downstream performance, and vision-language transfer, and select 30 challenging scenarios on which a reference power-law fit reaches $R^2 \le 0.8$; they represent at least $1.09 \times 10^{23}$ FLOPs of source-reported training compute. Second, we introduce active scaling law discovery: an agent chooses which experiments to run, pays each one's recorded cost (e.g., training FLOPs), and revises its law as outcomes arrive, and is scored on the same hidden extrapolation targets as in the passive setting. Across 8 frontier agent systems, median $R^2$ drops from 0.72-0.75 (passive) to 0.24-0.57 (active), and prediction error rises 1.5-4.7 times, depending on the system. Agents favor cheap experiments, spending 8-44% of the full-pool cost on average; low-cost acquisition can yield strong predictions, but cheap purchases also leave experimental conditions needed for extrapolation unobserved. Experimental planning thus remains a key open challenge for agents that assist model development in the prevailing AI-for-AI study. Project page: https://lingbei-meng.github.io/SLDBench-v2/.

cs.LG↗

arXiv2026

L2G-SR: Learning to Guide LLM-based Symbolic Regression

Symbolic regression searches for an equation that explains observed data. Numerical error is commonly used to guide the search, but it alone can favor an accurate surrogate over a candidate with the right structure. We propose L2G-SR, a framework for LLM-based symbolic regression that guides search with a learned structural verifier. We construct structural supervision signal using tree edit distance (TED), accounting for commutative operators and alternative expression forms. A verifier first aligns numerical observations with the formulas, then learns to score a candidate's structural similarity to the target formula. At search time, the target formula is hidden and the verifier complements numerical error in parent selection. An analyst then uses verifier feedback and diagnostic tools to propose revisions, which a generator converts into refined expressions. On LLM-SRBench, L2G-SR achieves state-of-the-art numerical fit, equation level accuracy and TED across the evaluated LLM backbones and domains. L2G-SR demonstrates the value of learned structural guidance for LLM-based symbolic regression.

cs.AI↗

arXiv2026

WebCraftBench: Evaluating Web Application Generation from a Software Testing Perspective

Human evaluation provides a direct measure of the quality of LLM-generated web applications. However, fitting human judgments through automated evaluation remains challenging. Static benchmarks can credit functionality that exists in source code but is unreachable at runtime. Interactive benchmarks exercise the application, yet incomplete exploration can cause them to miss implemented functionality and confound application defects with agent execution failures. To address these limitations, we propose WebCraftBench, an interactive benchmark for evaluating web application generation from a software testing perspective. WebCraftBench instruments each generated application and uses code coverage to guide an agent in exploring its functionality through user-simulated interactions. It then abstracts the interaction trace into a state-transition graph and evaluates the application along three dimensions: visual aesthetics, usability, and requirement alignment. By separating exploration from scoring, WebCraftBench collects runtime evidence without constraining exploration to predefined acceptance criteria. WebCraftBench comprises 369 real-world user requirements and 5,088 acceptance criteria. Evaluation of 17 frontier LLMs reveals distinct strengths across the three dimensions, with no model leading on every dimension. On 197 validated sessions sampled from an internal arena, WebCraftBench achieves 85.3\% agreement with human preferences, with agreement generally increasing as the score difference between paired applications grows. Further experiments show that coverage guidance improves exploration coverage and the model rankings remain stable when the judge model is replaced.

cs.SE↗

arXiv2026

Harbor Adapters and Harbor-Index: Infrastructure and a Curated Meta-Dataset for Large-Scale Agentic Evaluation

Evaluating agents on the growing number of agentic benchmarks is challenging because they often require complex environments and agent integrations. We introduce Harbor Adapters, a unified evaluation infrastructure for agentic benchmarks. Our work makes three contributions. First, we develop benchmark adapters that port more than 80 benchmarks to evaluate arbitrary agents, and validate them through rigorous code review and parity experiments. Second, we conduct a large-scale evaluation of 8 models spanning capability tiers across 54 benchmarks; every model is run with Terminus-2 and with one of 3 native harnesses. This enables a broader analysis of agent capabilities and failure modes than was previously possible. Third, we introduce Harbor-Index, a curated set of 82 difficult, diverse, and high-quality tasks spanning 29 benchmarks, refined from the adapted suite through difficulty filtering, AI and human audit, and an audit-and-fix loop. Harbor-Index preserves the challenge and breadth of large-scale agentic evaluations while being affordable to run; no evaluated model-harness configuration exceeds 30% pass rate, and the strongest (GPT-5.5 with Codex) reaches 28.0%. We release the adapters, evaluation results, in-depth analysis, and Harbor-Index as open-source artifacts to support more reliable and comprehensive evaluation of language-model agents.

cs.AI↗

arXiv2026

Test-Time Scaling for Scientific Equation Discovery

Test-time scaling (TTS) improves language model reasoning by allocating additional test-time compute, but prior work mainly studies closed-ended tasks such as math and coding. We study TTS for automated equation discovery, an open-ended setting where models search over candidate equations and rely on observed datapoints for feedback. We formulate LLM-driven equation discovery as an iterative search process that unifies Best-of-N, sequential refinement, tree search, and evolution-style methods under a common compute-allocation view. To isolate allocation effects from prompt engineering and other heuristics, we compare minimal parallel controllers under fixed budgets. On LLM-SRBench equation-discovery tasks, we find that search width is the dominant allocation parameter: the best width in our sweep generally increases with the compute budget, while the population--branching split and controller choice matter less. Appropriate width selection also improves wall-clock efficiency by increasing parallelism. These results suggest that, given an informative verifier, controlling exploration and exploitation is central to scaling LLM-based equation discovery.

cs.CL↗

arXiv2026

Spend Less, Fit Better: Budget-Efficient Scaling Law Fitting via Active Experiment Selection

Scaling laws are used to plan multi-million-dollar training runs, but fitting those laws can itself cost millions. In modern large-scale workflows, assembling a sufficiently informative set of pilot experiments is already a major budget-allocation problem rather than a routine preprocessing step. We formulate scaling-law fitting as budget-aware sequential experimental design: given a finite pool of runnable experiments with heterogeneous costs, choose which runs to execute so as to maximize extrapolation accuracy in a high-cost target region. We propose $\mathrm{SL}^2$ (Scaling Laws, Spend Less), an uncertainty-aware method for sequentially allocating experimental budget toward the runs most useful for target-region extrapolation. Across a diverse benchmark of scaling-law tasks, $\mathrm{SL}^2$ outperforms classical design-based baselines, and often approaches the performance of fitting on the full experimental set while using only about 10\% of the total training budget. Our code is available at https://github.com/PlanarG/active-sl.

cs.LG↗

arXiv2026

Settling the Optimal Exponent Relating Sumsets and Difference Sets

For a finite nonempty subset $A$ of an abelian group, let $σ(A)=|A+A|/|A|$ and $δ(A)=|A-A|/|A|$. The classical sum-difference inequalities state that $$σ(A)^{1/2}\leqδ(A)\leqσ(A)^2.$$ The exponent $2$ in the second inequality is known to be optimal, whereas it has remained open whether the exponent $1/2$ in the first inequality can be improved. We settle this question by constructing an explicit family of finite sets $A_K\subset\mathbb{Z}$ such that $$\frac{\logσ(A_K)}{\logδ(A_K)}\longrightarrow 2,$$ hence the exponent $1/2$ in the first inequality is also optimal. The construction and its proof were developed with the assistance of Hyra, an AI research agent based on the open-weights Hy3 model.

math.CO↗

arXiv2026

Structured Scaling of AI Discovery Across Diverse Scientific Domains

Scientific discovery often requires many cycles of proposing, testing, and refining candidate solutions. Language models can increasingly participate in these loops, but simply generating more attempts does not ensure progress: parallel searches may duplicate one another and iterative refinement may become trapped in poor directions. The central challenge is therefore not only to scale AI-driven discovery, but to structure that scaling so that evaluation signals compound over time. Here we introduce SimpleTES (Simple Test-time Evaluation-driven Scaling), a framework that focuses on the structured scaling of AI discovery loops, organizing evaluator queries across independent trajectories, iterative refinement, local candidate selection, and the selective reuse of evaluated histories. Drawing on structural features of scientific communities, SimpleTES uses a single open-source GPT-OSS model to establish new state-of-the-art solutions across 28 open-ended problems in diverse scientific domains ranging from quantum physics and astronomy to biology, AI, and mathematics. These include a 24.5% reduction in quantum circuit compilation overhead, up to 23% lower propulsive cost for deep-space trajectories, a 2.17x faster lasso-path solver, an 8.5% lower-error whole-brain neural-activity predictor, the fastest reported TriMul kernel, and new mathematical constructions beyond prior human or AI records. We further post-train the model for long-horizon discovery by assigning each attempt the final outcome of the trajectory it helped produce. This improves performance on both training and held-out mathematics problems, further advancing the frontier. Together, these results establish structured scaling as a general mechanism for advancing AI scientific discovery.

cs.LG↗

arXiv2026

SceneActBench: Can Agents Act on the 3D Scenes They See?

Vision-language model (VLM) agents increasingly use tools to act on 3D scenes rather than only describe them. Existing 3D benchmarks score textual responses or single-object operations, leaving agent action on complete multi-object 3D scenes under evaluated. We present SceneActBench, a benchmark for visually conditioned action across five 3D tasks under a unified agent-environment loop. Given PNG images or sampled video frames and, where applicable, supplied 3D assets, an agent acts on a 3D environment. We evaluate each final output against hidden ground truth with task-specific geometric metrics. SceneActBench comprises five tasks built from 210 source instances, yielding 520 task cases including paired input conditions. Every task runs through one fixed agent loop to keep the comparison fair. Across eleven proprietary VLM configurations, Overall scores span 38.6-50.2, and none performs consistently well across tasks. We further analyse where and how failures manifest.

cs.AI↗

arXiv2026

Sub-Finslerian Interpolation Inequalities

In this paper, we prove that forward ideal sub-Finslerian manifolds support interpolation inequalities for optimal transport, extending the results of Barilari and Rizzi, arXiv:1705.05380, from the sub-Riemannian to the sub-Finslerian setting. A key role is played by the introduction of sub-Finslerian Jacobi fields and the establishment of optimal transport theory on sub-Finslerian manifolds. By combining this transport framework with sub-Finslerian Jacobian estimates, we characterize the generalized distortion coefficients. As an application, we deduce several fundamental geometric inequalities, including the Brunn-Minkowski and Borell-Brascamp-Lieb inequalities. Finally, for the case of the Randers sub-Finslerian Heisenberg group, whose metric is defined by a sub-Riemannian metric perturbed by a drift term, we explicitly show that it satisfies the measure contraction property.

math.DG↗

arXiv2026

UniCode: Augmenting Evaluation for Code Reasoning

Current coding benchmarks often inflate Large Language Model (LLM) capabilities due to static paradigms and data contamination, enabling models to exploit statistical shortcuts rather than genuine reasoning. To address this, we introduce UniCode, a generative evaluation framework that systematically probes LLM limits via: (1) multi-dimensional augmentation transforming seed problems into complex variations to disrupt fixed algorithmic patterns; (2) a highly reliable, automated test generation pipeline for scalable evaluation; and (3) fine-grained metrics for rich error signals. Experiments reveal a 31.2% performance collapse in state-of-the-art models on UniCode, primarily driven by deficiencies in conceptual modeling and scalability reasoning rather than syntactic errors. Furthermore, we uncover a seed-problem regression where models revert to memorized seed logic rather than following new specifications, signaling a reliance on shortcuts over reasoning. This work validates UniCode as a robust framework to expose model fragility and foster reasoning-oriented code intelligence.

cs.SE↗

arXiv2026

Can Current Agents Close the Discovery-to-Application Gap? A Case Study in Minecraft

Discovering causal regularities and applying them to build functional systems--the discovery-to-application loop--is a hallmark of general intelligence, yet evaluating this capacity has been hindered by the vast complexity gap between scientific discovery and real-world engineering. We introduce SciCrafter, a Minecraft-based benchmark that operationalizes this loop through parameterized redstone circuit tasks. Agents must ignite lamps in specified patterns (e.g., simultaneously or in timed sequences); scaling target parameters substantially increases construction complexity and required knowledge, forcing genuine discovery rather than reliance on memorized solutions. Evaluating frontier models including GPT-5.2, Gemini-3-Pro, and Claude-Opus-4.5 under a general-purpose code agent scaffold, we find that all plateau at approximately 26% success rate. To diagnose these failures, we decompose the loop into four capacities--knowledge gap identification, experimental discovery, knowledge consolidation, and knowledge application--and design targeted interventions whose marginal contributions serve as proxies for corresponding gaps. Our analysis reveals that although the general knowledge application capability still remains as the biggest gap across all models, for frontier models the knowledge gap identification starts to become a major hurdle--indicating the bottleneck is shifting from solving problems right to raising the right problems for current AI. We release SciCrafter as a diagnostic probe for future research on AI systems that navigate the full discovery-to-application loop.

cs.AI↗

arXiv2026

Preference Goal Tuning: Post-Training as Latent Control for Frozen Policies

Goal-conditioned policies enable decision-making models to execute diverse behaviors based on specified goals, yet their downstream performance is often highly sensitive to the choice of instructions or prompts. To bypass the limitations of discrete text prompts, we formulate post-training adaptation as a latent control problem, where the goal embedding serves as a continuous control variable to modulate the behavior of a frozen policy. We propose Preference Goal Tuning (PGT), a framework that optimizes this latent control variable to align the induced trajectory distribution with task preferences. Unlike standard fine-tuning that updates policy parameters, PGT keeps the policy frozen and updates only the latent goal using a trajectory-level preference objective. This approach essentially searches for the optimal conditioning input that maximizes the likelihood of preferred behaviors while suppressing undesirable ones. We evaluate PGT on the Minecraft SkillForge benchmark across 17 tasks. With minimal data, PGT achieves average relative improvements of 72.0\% and 81.6\% on two foundation policies, consistently outperforming expert-crafted prompts. Crucially, by decoupling task alignment (latent goal) from physical dynamics (frozen policy), PGT surpasses full fine-tuning by 13.4\% in out-of-distribution settings, demonstrating superior robustness and generalization.

cs.AI↗

arXiv2026

Can Language Models Discover Scaling Laws?

Discovering scaling laws for predicting model performance at scale is a fundamental and open-ended challenge, mostly reliant on slow, case specific human experimentation. To investigate the potential for LLMs to automate this process, we collect over 5,000 experiments from existing literature and curate eight diverse scaling law discovery tasks. While existing agents struggle to produce accurate law formulas, this paper introduces SLDAgent, an evolution-based agent that co-optimize the scaling law model and the parameters, enabling it to autonomously explore complex relationships between variables. For the first time, we demonstrates that SLDAgent can automatically discover laws that exhibit consistently more accurate extrapolation than their established, human-derived counterparts across all tasks. Through comprehensive analysis, we elucidate why these discovered laws are superior and verify their practical utility in both pretraining and finetuning applications. This work establishes a new paradigm for agentic scientific discovery, showing that AI systems can understand their own scaling behavior, and can contribute novel and practical knowledge back to the research community.

cs.LG↗

arXiv2026

Terminal-Bench: Benchmarking Agents on Hard, Realistic Tasks in Command Line Interfaces

AI agents may soon become capable of autonomously completing valuable, long-horizon tasks in diverse domains. Current benchmarks either do not measure real-world tasks, or are not sufficiently difficult to meaningfully measure frontier models. To this end, we present Terminal-Bench 2.0: a carefully curated hard benchmark composed of 89 tasks in computer terminal environments inspired by problems from real workflows. Each task features a unique environment, human-written solution, and comprehensive tests for verification. We show that frontier models and agents score less than 65\% on the benchmark and conduct an error analysis to identify areas for model and agent improvement. We publish the dataset and evaluation harness to assist developers and researchers in future work at https://www.tbench.ai/ .

cs.SE↗

arXiv2025

Peptide2Mol: A Diffusion Model for Generating Small Molecules as Peptide Mimics for Targeted Protein Binding

Structure-based drug design has seen significant advancements with the integration of artificial intelligence (AI), particularly in the generation of hit and lead compounds. However, most AI-driven approaches neglect the importance of endogenous protein interactions with peptides, which may result in suboptimal molecule designs. In this work, we present Peptide2Mol, an E(3)-equivariant graph neural network diffusion model that generates small molecules by referencing both the original peptide binders and their surrounding protein pocket environments. Trained on large datasets and leveraging sophisticated modeling techniques, Peptide2Mol not only achieves state-of-the-art performance in non-autoregressive generative tasks, but also produces molecules with similarity to the original peptide binder. Additionally, the model allows for molecule optimization and peptidomimetic design through a partial diffusion process. Our results highlight Peptide2Mol as an effective deep generative model for generating and optimizing bioactive small molecules from protein binding pockets.

cs.LG↗

arXiv2025

A Neural Symbolic Model for Space Physics

In this study, we unveil a new AI model, termed PhyE2E, to discover physical formulas through symbolic regression. PhyE2E simplifies symbolic regression by decomposing it into sub-problems using the second-order derivatives of an oracle neural network, and employs a transformer model to translate data into symbolic formulas in an end-to-end manner. The resulting formulas are refined through Monte-Carlo Tree Search and Genetic Programming. We leverage a large language model to synthesize extensive symbolic expressions resembling real physics, and train the model to recover these formulas directly from data. A comprehensive evaluation reveals that PhyE2E outperforms existing state-of-the-art approaches, delivering superior symbolic accuracy, precision in data fitting, and consistency in physical units. We deployed PhyE2E to five applications in space physics, including the prediction of sunspot numbers, solar rotational angular velocity, emission line contribution functions, near-Earth plasma pressure, and lunar-tide plasma signals. The physical formulas generated by AI demonstrate a high degree of accuracy in fitting the experimental data from satellites and astronomical telescopes. We have successfully upgraded the formula proposed by NASA in 1993 regarding solar activity, and for the first time, provided the explanations for the long cycle of solar activity in an explicit form. We also found that the decay of near-Earth plasma pressure is proportional to r^2 to Earth, where subsequent mathematical derivations are consistent with satellite data from another independent study. Moreover, we found physical formulas that can describe the relationships between emission lines in the extreme ultraviolet spectrum of the Sun, temperatures, electron densities, and magnetic fields. The formula obtained is consistent with the properties that physicists had previously hypothesized it should possess.

astro-ph.SR↗