arXiv subjects

Peiyao Xiao

Publications and source records attributed to Peiyao Xiao.

14 recordsLinked to original sources

arXiv2026

HLE-Verified: A Systematic Verification and Structured Revision of Humanity's Last Exam

Humanity's Last Exam (HLE) has become a widely used benchmark for evaluating frontier large language models on challenging, multi-domain questions. However, community-led analyses have raised concerns that HLE contains a non-trivial number of noisy items, which can bias evaluation results and distort cross-model comparisons. To address this challenge, we introduce HLE-Verified, a verified and revised version of HLE with a transparent verification protocol and fine-grained error taxonomy. Our construction follows a two-stage validation-and-repair workflow resulting in a certified benchmark. In Stage I, each item undergoes binary validation of the problem and final answer through domain-expert review and model-based cross-checks, yielding 668 verified items. In Stage II, flawed but fixable items are revised under strict constraints preserving the original evaluation intent, through dual independent expert repairs, model-assisted auditing, and final adjudication, resulting in 1,143 revised-and-certified items. The remaining 689 items are released as a documented uncertain set with explicit uncertainty sources and expertise tags for future refinement. We evaluate eight state-of-the-art language models on HLE and HLE-Verified, observing an average absolute accuracy gain of 7--10 percentage points on HLE-Verified. The improvement is particularly pronounced on items where the original problem statement and/or reference answer is erroneous, with gains of 30--40 percentage points. Our analyses further reveal a strong association between model confidence and the presence of errors in the problem statement or reference answer, supporting the effectiveness of our revisions. Overall, HLE-Verified improves HLE-style evaluations by reducing annotation noise and enabling more faithful measurement of model capabilities. Data is available at: https://huggingface.co/datasets/skylenage/HLE-Verified

cs.CL↗

arXiv2026

ReciNet: Reciprocal Space-Aware Long-Range Modeling for Crystalline Property Prediction

Predicting properties of crystals from their structures is a fundamental yet challenging task in materials science. Unlike molecules, crystal structures exhibit infinite periodic arrangements of atoms, requiring methods capable of capturing both local and global information effectively. However, current works fall short of capturing long-range interactions within periodic structures. To address this, we leverage \emph{reciprocal space}, the natural domain for periodic crystals, and construct a Fourier series representation from fractional coordinates and reciprocal lattice vectors with learnable filters. Building on this, we introduce the reciprocal space-based geometry network (\textbf{ReciNet}), a novel architecture that integrates geometric GNNs and reciprocal blocks to model short-range and long-range interactions. Experiments on comprehensive benchmarks JARVIS, Materials Project, and MatBench demonstrate that ReciNet achieves outstanding predictive accuracy across a range of crystal property prediction tasks. Additionally, we explore a model extension for multi-property prediction with the mixture-of-experts, which demonstrates high computational efficiency and reveals positive transfer between correlated properties. These findings highlight the potential of our model as a scalable and accurate solution for crystal property prediction.

cs.LG↗

arXiv2026

FeynmanBench: Benchmarking Multimodal LLMs on Diagrammatic Physics Reasoning

Current multimodal benchmarks for scientific reasoning primarily evaluate local information extraction -- models recognize symbols and values and then perform textual inference. They do not assess whether models can reason over the global structural properties of formal diagrams, such as topology, conservation constraints, and the consistent mapping between visual patterns and algebraic expressions. We introduce FeynmanBench, a benchmark of over 2,000 tasks centered on Feynman diagrams spanning the electromagnetic, weak, and strong interactions of the Standard Model. Each instance couples a diagram image with minimal textual conventions and requires models to recover the full physical content -- vertex inventory, propagator types, topological connectivity, momentum routing, and the complete scattering amplitude. An automated generation and verification pipeline produces the diagrams, annotations, and reference answers under standardized rules. Evaluating 19 state-of-the-art multimodal LLMs, we find a consistent failure pattern: models achieve 70--95\% on local recognition (vertex and propagator identification) but collapse to 13--17\% on topological reconstruction (CP3), and near zero on full algebraic derivation (CP5). FeynmanBench offers a controlled testbed for multimodal reasoning over formal scientific diagrams and highlights fundamental limitations of current architectures in topology-sensitive scientific reasoning.

cs.AI↗

arXiv2026

SPM-Bench: Benchmarking Large Language Models for Scanning Probe Microscopy

As LLMs achieved breakthroughs in general reasoning, their proficiency in specialized scientific domains reveals pronounced gaps in existing benchmarks due to data contamination, insufficient complexity, and prohibitive human labor costs. Here we present SPM-Bench, an original, PhD-level multimodal benchmark specifically designed for scanning probe microscopy (SPM). We propose a fully automated data synthesis pipeline that ensures both high authority and low-cost. By employing Anchor-Gated Sieve (AGS) technology, we efficiently extract high-value image-text pairs from arXiv and journal papers published between 2023 and 2025. Through a hybrid cloud-local architecture where VLMs return only spatial coordinates "llbox" for local high-fidelity cropping, our pipeline achieves extreme token savings while maintaining high dataset purity. To accurately and objectively evaluate the performance of the LLMs, we introduce the Strict Imperfection Penalty F1 (SIP-F1) score. This metric not only establishes a rigorous capability hierarchy but also, for the first time, quantifies model "personalities" (Conservative, Aggressive, Gambler, or Wise). By correlating these results with model-reported confidence and perceived difficulty, we expose the true reasoning boundaries of current AI in complex physical scenarios. These insights establish SPM-Bench as a generalizable paradigm for automated scientific data synthesis.

cs.AI↗

arXiv2026

BilliardPhys-Bench: Benchmarking Physical Reasoning and Visual Dynamics of Multimodal LLMs

Current multimodal models handle static image recognition well, but intuitive physical reasoning remains a weakness. Predicting how objects will move and interact from a single image is still difficult for these systems. We present BilliardPhys-Bench, a benchmark for physical reasoning in synthetic billiards environments. Its procedural engine generates randomized scenarios with friction and elastic collisions. The benchmark tests three abilities: (1) predicting ball-to-ball collisions, (2) reasoning about wall bounces, and (3) estimating final ball positions after motion stops. We evaluate recent MLLMs from the GPT, Claude, Gemini, and Qwen families. Performance drops as simulation time increases and scene geometry grows more complex. We also observe a consistent failure mode we call "stasis bias": when the correct physical outcome is harder to infer, models tend to predict no interaction. These findings show where current MLLMs break down on visual dynamics and point toward the need for better physical inductive biases in multimodal architectures.

cs.AI↗

arXiv2026

CrystalXRD-Bench: Benchmarking Vision-Language Models for XRD Peak Indexing Across Diverse Crystalline Materials

Miller-index identification from powder XRD patterns requires capabilities untested by existing multimodal benchmarks: the model must read a narrow peak location from a rendered scientific curve and then connect that observation to multi-step crystallographic reasoning. We introduce CrystalXRD-Bench, a 250-sample benchmark built from 10 public crystallographic databases for a single task: recover the full set of HKLs contributing to the highest-intensity peak in an XRD pattern. Each sample pairs the rendered XRD image with the source CIF text and chemical formula, so visual extraction errors and reasoning errors can be examined side by side. We evaluate seven vision-language models. The best Jaccard score is 0.5888 (GPT-5.4) with an exact-match rate of 37.6%, yet six of seven models remain below Jaccard 0.50; the task is far from solved. Error patterns vary systematically: double-peak cases are especially brittle, recall-heavy models gain coverage by over-predicting HKLs, and access to CIF text does not close the gap in crystallographic calculation. Alongside model rankings, the benchmark identifies the conditions under which current VLMs fail on quantitative scientific figures. All data and evaluation code will be publicly available.

cs.AI↗

arXiv2026

DeepMTL2R: A Library for Deep Multi-task Learning to Rank

This paper presents DeepMTL2R, an open-source deep learning framework for Multi-task Learning to Rank (MTL2R), where multiple relevance criteria must be optimized simultaneously. DeepMTL2R integrates heterogeneous relevance signals into a unified, context-aware model by leveraging the self-attention mechanism of transformer architectures, enabling effective learning across diverse and potentially conflicting objectives. The framework includes 21 state-of-the-art multi-task learning algorithms and supports multi-objective optimization to identify Pareto-optimal ranking models. By capturing complex dependencies and long-range interactions among items and labels, DeepMTL2R provides a scalable and expressive solution for modern ranking systems and facilitates controlled comparisons across MTL strategies. We demonstrate its effectiveness on a publicly available dataset, report competitive performance, and visualize the resulting trade-offs among objectives. DeepMTL2R is available at \href{https://github.com/amazon-science/DeepMTL2R}{https://github.com/amazon-science/DeepMTL2R}.

cs.LG↗

arXiv2025

LDC-MTL: Balancing Multi-Task Learning through Scalable Loss Discrepancy Control

Multi-task learning (MTL) has been widely adopted for its ability to simultaneously learn multiple tasks. While existing gradient manipulation methods often yield more balanced solutions than simple scalarization-based approaches, they typically incur a significant computational overhead of $\mathcal{O}(K)$ in both time and memory, where $K$ is the number of tasks. In this paper, we propose LDC-MTL, a simple and scalable loss discrepancy control approach for MTL, formulated from a bilevel optimization perspective. Our method incorporates two key components: (i) a bilevel formulation for fine-grained loss discrepancy control, and (ii) a scalable first-order bilevel algorithm that requires only $\mathcal{O}(1)$ time and memory. Theoretically, we prove that LDC-MTL guarantees convergence not only to a stationary point of the bilevel problem with loss discrepancy control but also to an $ε$-accurate Pareto stationary point for all $K$ loss functions under mild conditions. Extensive experiments on diverse multi-task datasets demonstrate the superior performance of LDC-MTL in both accuracy and efficiency.

cs.LG↗

arXiv2025

Achieving ${O}(ε^{-1.5})$ Complexity in Hessian/Jacobian-free Stochastic Bilevel Optimization

In this paper, we revisit the bilevel optimization problem, in which the upper-level objective function is generally nonconvex and the lower-level objective function is strongly convex. Although this type of problem has been studied extensively, it still remains an open question how to achieve an ${O}(ε^{-1.5})$ sample complexity in Hessian/Jacobian-free stochastic bilevel optimization without any second-order derivative computation. To fill this gap, we propose a novel Hessian/Jacobian-free bilevel optimizer named FdeHBO, which features a simple fully single-loop structure, a projection-aided finite-difference Hessian/Jacobian-vector approximation, and momentum-based updates. Theoretically, we show that FdeHBO requires ${O}(ε^{-1.5})$ iterations (each using ${O}(1)$ samples and only first-order gradient information) to find an $ε$-accurate stationary point. As far as we know, this is the first Hessian/Jacobian-free method with an ${O}(ε^{-1.5})$ sample complexity for nonconvex-strongly-convex stochastic bilevel optimization.

math.OC↗

arXiv2025

MGDA Converges under Generalized Smoothness, Provably

Multi-objective optimization (MOO) is receiving more attention in various fields such as multi-task learning. Recent works provide some effective algorithms with theoretical analysis but they are limited by the standard $L$-smooth or bounded-gradient assumptions, which typically do not hold for neural networks, such as Long short-term memory (LSTM) models and Transformers. In this paper, we study a more general and realistic class of generalized $\ell$-smooth loss functions, where $\ell$ is a general non-decreasing function of gradient norm. We revisit and analyze the fundamental multiple gradient descent algorithm (MGDA) and its stochastic version with double sampling for solving the generalized $\ell$-smooth MOO problems, which approximate the conflict-avoidant (CA) direction that maximizes the minimum improvement among objectives. We provide a comprehensive convergence analysis of these algorithms and show that they converge to an $ε$-accurate Pareto stationary point with a guaranteed $ε$-level average CA distance (i.e., the gap between the updating direction and the CA direction) over all iterations, where totally $\mathcal{O}(ε^{-2})$ and $\mathcal{O}(ε^{-4})$ samples are needed for deterministic and stochastic settings, respectively. We prove that they can also guarantee a tighter $ε$-level CA distance in each iteration using more samples. Moreover, we analyze an efficient variant of MGDA named MGDA-FA using only $\mathcal{O}(1)$ time and space, while achieving the same performance guarantee as MGDA.

cs.LG↗

arXiv2024

Theoretical Study of Conflict-Avoidant Multi-Objective Reinforcement Learning

Multi-task reinforcement learning (MTRL) has shown great promise in many real-world applications. Existing MTRL algorithms often aim to learn a policy that optimizes individual objective functions simultaneously with a given prior preference (or weights) on different tasks. However, these methods often suffer from the issue of \textit{gradient conflict} such that the tasks with larger gradients dominate the update direction, resulting in a performance degeneration on other tasks. In this paper, we develop a novel dynamic weighting multi-task actor-critic algorithm (MTAC) under two options of sub-procedures named as CA and FC in task weight updates. MTAC-CA aims to find a conflict-avoidant (CA) update direction that maximizes the minimum value improvement among tasks, and MTAC-FC targets at a much faster convergence rate. We provide a comprehensive finite-time convergence analysis for both algorithms. We show that MTAC-CA can find a $ε+ε_{\text{app}}$-accurate Pareto stationary policy using $\mathcal{O}({ε^{-5}})$ samples, while ensuring a small $ε+\sqrt{ε_{\text{app}}}$-level CA distance (defined as the distance to the CA direction), where $ε_{\text{app}}$ is the function approximation error. The analysis also shows that MTAC-FC improves the sample complexity to $\mathcal{O}(ε^{-3})$, but with a constant-level CA distance. Our experiments on MT10 demonstrate the improved performance of our algorithms over existing MTRL methods with fixed preference.

cs.LG↗

arXiv2023

SimFBO: Towards Simple, Flexible and Communication-efficient Federated Bilevel Learning

Federated bilevel optimization (FBO) has shown great potential recently in machine learning and edge computing due to the emerging nested optimization structure in meta-learning, fine-tuning, hyperparameter tuning, etc. However, existing FBO algorithms often involve complicated computations and require multiple sub-loops per iteration, each of which contains a number of communication rounds. In this paper, we propose a simple and flexible FBO framework named SimFBO, which is easy to implement without sub-loops, and includes a generalized server-side aggregation and update for improving communication efficiency. We further propose System-level heterogeneity robust FBO (ShroFBO) as a variant of SimFBO with stronger resilience to heterogeneous local computation. We show that SimFBO and ShroFBO provably achieve a linear convergence speedup with partial client participation and client sampling without replacement, as well as improved sample and communication complexities. Experiments demonstrate the effectiveness of the proposed methods over existing FBO algorithms.

cs.LG↗

arXiv2023

Direction-oriented Multi-objective Learning: Simple and Provable Stochastic Algorithms

Multi-objective optimization (MOO) has become an influential framework in many machine learning problems with multiple objectives such as learning with multiple criteria and multi-task learning (MTL). In this paper, we propose a new direction-oriented multi-objective problem by regularizing the common descent direction within a neighborhood of a direction that optimizes a linear combination of objectives such as the average loss in MTL. This formulation includes GD and MGDA as special cases, enjoys the direction-oriented benefit as in CAGrad, and facilitates the design of stochastic algorithms. To solve this problem, we propose Stochastic Direction-oriented Multi-objective Gradient descent (SDMGrad) with simple SGD type of updates, and its variant SDMGrad-OS with an efficient objective sampling in the setting where the number of objectives is large. For a constant-level regularization parameter $λ$, we show that SDMGrad and SDMGrad-OS provably converge to a Pareto stationary point with improved complexities and milder assumptions. For an increasing $λ$, this convergent point reduces to a stationary point of the linear combination of objectives. We demonstrate the superior performance of the proposed methods in a series of tasks on multi-task supervised learning and reinforcement learning. Code is provided at https://github.com/ml-opt-lab/sdmgrad.

cs.LG↗

arXiv2023

Communication-Efficient Federated Hypergradient Computation via Aggregated Iterative Differentiation

Federated bilevel optimization has attracted increasing attention due to emerging machine learning and communication applications. The biggest challenge lies in computing the gradient of the upper-level objective function (i.e., hypergradient) in the federated setting due to the nonlinear and distributed construction of a series of global Hessian matrices. In this paper, we propose a novel communication-efficient federated hypergradient estimator via aggregated iterative differentiation (AggITD). AggITD is simple to implement and significantly reduces the communication cost by conducting the federated hypergradient estimation and the lower-level optimization simultaneously. We show that the proposed AggITD-based algorithm achieves the same sample complexity as existing approximate implicit differentiation (AID)-based approaches with much fewer communication rounds in the presence of data heterogeneity. Our results also shed light on the great advantage of ITD over AID in the federated/distributed hypergradient estimation. This differs from the comparison in the non-distributed bilevel optimization, where ITD is less efficient than AID. Our extensive experiments demonstrate the great effectiveness and communication efficiency of the proposed method.

cs.LG↗