arXiv subjects

Xing Gao

Publications and source records attributed to Xing Gao.

At least 19 recordsLinked to original sources

arXiv2026

Profiling a Frontier Agent with EBench: From Direct Control to Harness with Policy

Frontier multimodal large language models (MLLMs) can control robots without robot-specific training, but how their capabilities compare and interact with post-trained vision-language-action (VLA) and world action model (WAM) policies across manipulation demands remains to be thoroughly evaluated. In this report, we evaluate GPT-6-Astra on EBench as the core of an agent that controls a robot through an agent harness under the same visual and proprioceptive observation protocol as post-trained policies. We study two agent configurations: direct control, in which the agent generates waypoint commands directly, and harness with policy, in which it can also invoke a post-trained VLA or WAM policy for action execution. Under direct control, the agent achieves competitive overall performance relative to post-trained policies. It leads on short-horizon tasks and exhibits the least performance variation across generalization dimensions, whereas it underperforms post-trained policies on long-horizon tasks, tabletop manipulation, and high-precision contact-rich tasks. In the harness with policy, invoking a post-trained VLA or WAM combines the complementary strengths of both components, raising overall task success to the level of the strongest compared post-trained policies while substantially reducing token cost. However, performance remains below the per-task upper bound of the standalone components due to suboptimal policy invocation, fixed-instruction execution without subgoals, and grasp disruption when the agent resumes control. Overall, our study characterizes the capability boundary of a frontier MLLM agent and suggests directions for improving future agent harness design. Project page: https://internrobotics.github.io/EBench-Astra-Tech-Report/

cs.RO↗

arXiv2026

Classical cumulants from the double tensor unshuffle Hopf algebra

We realize classical cumulants and their fixed-point equations in the double tensor unshuffle Hopf algebra introduced by Ebrahimi-Fard and Patras, placing classical, free, Boolean, and monotone cumulants in a common algebraic framework. A concatenation perturbation of the functionals yields left and right half-shuffle equations on ordinary words without changing the coproduct or either half-coproduct. Both equations are equivalent to the classical moment--cumulant formula and uniquely determine the classical cumulants. We also obtain a Hopf-algebraic realization of the classical-to-free cumulant transform through convolution exponentiation and the left half-shuffle logarithm. A commutative diagram identifies its partition-level action with summation over non-crossing closure fibers, recovering Lehner's closure-fiber formula within the framework of the double tensor unshuffle Hopf algebra.

math.QA↗

arXiv2026

Path-dependent rough differential equations in the full step-two range

We establish the existence of solutions to path-dependent rough differential equations with non-anticipative coefficients whose regularity is formulated in terms of horizontal and vertical Dupire derivatives. Under the same regularity assumptions as in Ananova~\cite{An23}, we develop a new causal Taylor argument and establish a second-order remainder estimate. This removes the regularity loss responsible for the restriction $2\leq p<1+\sqrt{2}$ in~\cite{An23} and extends the existence result to the full range $2\le p<3$.

math.PR↗

arXiv2026

PICA-WAM: Visual Perturbation Invariance via Cross-Appearance Self-Alignment in World Action Models

World Action Models (WAMs) jointly predict future video and generate actions, yet remain sensitive to task-irrelevant visual perturbations, i.e., changes in visual appearance that should not affect robot behavior. We identify a gap in conventional WAM training: video prediction encourages representations to preserve appearance information, while action generation does not explicitly enforce invariance to task-irrelevant appearance. Data augmentation exposes WAMs to such perturbations but does not require perturbed and nominal observations to produce consistent action representations, and alignment with external pretrained features does not guarantee the desired invariance. To address this gap, we propose PICA-WAM, a self-supervised training framework that casts perturbation invariance as an auxiliary cross-appearance self-alignment task for WAMs. An exponential-moving-average (EMA) teacher processes the nominal observation to provide a deeper-layer target, while the online WAM processes a perturbed observation and aligns its shallower-layer action representation to this target through a lightweight projection head. Across four strong WAMs evaluated on RoboTwin 2.0, LIBERO-Plus, EBench, and a real robot, PICA-WAM consistently improves robustness under visual perturbations, preserves nominal performance in simulation, and raises the real robot success rate. PICA-WAM further reduces the sensitivity of video features to task-irrelevant appearance and its propagation into actions, as shown by paired layer-wise diagnostics. Code: https://github.com/YudeZou/PICA-WAM-release

cs.CV↗

arXiv2026

How Do LLMs Understand Legal Philosophy? Diagnosing Legal-Philosophical Reasoning in LLMs

Legal reasoning is a fundamental capability for large language models (LLMs) to complete legal AI tasks such as legal judgment prediction. In legal practice, this reasoning is shaped by legal philosophy: a judge's view of the nature and sources of law guides how legal materials are interpreted and applied, so judges working from the same statutes and precedents can reach different judgments. Existing research has largely overlooked whether LLMs can understand legal philosophy and apply it in legal reasoning, an ability we call \textit{legal-philosophical reasoning}. To fill this gap, we introduce LePhilBench, a benchmark for evaluating the legal-philosophical reasoning of LLMs that comprises two benchmarking tasks and a dataset. The two tasks evaluate how well LLMs understand legal philosophy and how well they apply it in legal reasoning, respectively. The dataset is manually and meticulously constructed. Its test set contains 220 U.S. Supreme Court opinions. A law professor designed fourteen annotation questions on legal philosophy, and three law-trained annotators with formal training in jurisprudence answered all fourteen questions for every opinion, yielding 9,240 legal-philosophical labels. LePhilBench takes the first step toward exploring legal-philosophical reasoning in LLMs.

cs.CL↗

arXiv2026

Which Metadata Matters for LLM Tool Selection in MCP? Evidence from Controlled Factor-Level Interventions

In Model Context Protocol (MCP) systems, LLMs select tools from metadata rather than from their implementations. Names and descriptions summarize what a tool does, while the parameter schema specifies the fields a tool accepts and how they are organized. Our analysis of metadata for 367,174 MCP tools reveals substantial schema variation among functionally similar tools. Many of these tools share names and similar descriptions but expose different parameter schemas. This raises a key question: can parameter-schema differences influence tool selection before any call is made? We study this question through controlled metadata interventions across five LLMs and five tasks. Each comparison changes exactly one metadata factor (server name, tool name, description, or parameter schema) while keeping the others fixed. We balance tool positions and use conditional logistic regression to estimate position-adjusted effects. We find that: (1) parameter-schema changes produce the largest and most consistent selection shifts among the tested interventions. Models tend to favor separate top-level parameters over grouped or composite forms. (2) Descriptions that explain parameters also tend to increase selection, while name effects are weaker and less consistent. (3) Targeted comparisons show that schema effects depend on the specific parameter names and on how the request represents the same information. When only one schema satisfies an explicit request requirement, all five models select the compatible tool despite position preferences. These results show that parameter schemas influence not only how tools are called, but also whether they are selected. For MCP developers and evaluators, schema design and tool ordering can therefore affect which implementation is invoked even when functionality is unchanged.

cs.AI↗

arXiv2026

On the nonnegativity of monomial immanants for hook partitions

Let $A=(a_{ij})$ be an $n\times n$ real matrix and let $λ$ be a partition of $n$. Let $ϕ^λ$ be the class function dual to the Young permutation character, and let $$ ϕ^λ[A] = \sum_{σ\in\mathfrak{S}_n}ϕ^λ(σ) \prod_{i=1}^{n}a_{iσ(i)} $$ be the corresponding monomial immanant. Stembridge [Canad. J. Math. 44 (1992), pp. 1079-1099] posed the following open problem: If all minors of $A$ of order at most $r$ are nonnegative, and the partition $λ$ has length at most $r$, is it true that $ϕ^λ[A]\ge 0$? This paper solves the problem for all hook partitions.

math.CO↗

arXiv2026

InternW0-$Δ$: A World Action Model Bridging Predictive Dynamics and Actions with 20K+ Hours of Open Data

World Action Models (WAMs) jointly model visual dynamics and action generation for generalist robot manipulation. A central challenge is to integrate priors from large-scale pretrained models---including visual dynamics, scene semantics, geometry, and motion---into a unified framework for robot action generation. We introduce InternW0-$Δ$, a unified WAM pretrained on a heterogeneous corpus that outperforms prior methods across simulation benchmarks and real-robot platforms. InternW0-$Δ$ combines pretrained visual dynamics, scene-level semantics, 4D geometric and motion priors, and action generation within a Mixture-of-Transformers (MoT) framework. A pretrained video expert and an action expert interact under semantic guidance from a frozen VLM, while a pretrained 4D foundation model injects geometric and motion priors through training-only distillation. We further introduce Causal Imprint, which learns future-relevant scene changes from training-only future supervision and provides predictive representations directly to the action expert without future-video rollout at inference. For large-scale joint training, we construct a heterogeneous corpus of robot demonstrations, UMI data, egocentric human demonstrations, and Ego2Robot data, curated and aligned under a common state-action representation. The resulting corpus contains over 20K hours of processed training data, to our knowledge the largest open-source corpus of its kind. We pretrain InternW0-$Δ$ on this corpus and demonstrate strong performance across simulation benchmarks and real-robot platforms. We will open source the training code, model weights, infrastructure, data-processing pipeline, and processed data where licenses permit. Project page: https://internrobotics.github.io/InternW0-Delta/

cs.RO↗

arXiv2026

EP250302a: violent shell collision in a soft-X-ray-selected GRB-like transient

The Einstein Probe opens a previously unexplored soft X-ray window onto gamma-ray bursts, filling a critical observational gap in the soft X-ray coverage of their prompt emission. In this letter, we present EP250302a, a soft-X-ray-selected, GRB-like transient at $z=1.131$ detected by the Einstein Probe. Follow-up observations from X-ray to radio reveal a narrow X-ray flare at $\sim 1.1$\, ks and subsequent achromatic optical and X-ray rebrightening. These features challenge a standard single-component afterglow model and indicate the need for multiple ejecta components. A violent collision between a late relativistic shell and the decelerated leading blast wave provides a plausible interpretation: the flare arises from internal dissipation of the late ejecta, while the rebrightening is powered by the shocked emission produced in the collision. Quantitative modeling constrains the kinetic energy ratio between the late shell and the initial ejecta to $E_{\rm k,iso,2}/E_{\rm k,iso,1} \sim 5$ (with $E_{\rm k,iso,2} \sim 10^{53}$~erg and $E_{\rm k,iso,1} \sim 2\times10^{52}$~erg), as well as the Lorentz factor contrast to $Γ_{2,0}/Γ_{1,0} \approx 0.98$--$2.27$, required to reproduce the observed flare luminosity and rebrightening amplitude. Such an energetic late shell can be launched in a radiatively inefficient second episode of central-engine activity. Thanks to the well-sampled, early-time multiband coverage facilitated by the EP trigger, EP250302a provides a valuable case to test the physical connection between central-engine activity and shell collisions.

astro-ph.HE↗

arXiv2026

InternW0: A Foundational Physical World Model for Efficient Real-World Interactions

Physical intelligence requires more than predicting how the world may evolve: predictions must remain actionable as the world continues to change. We introduce InternW0, the first instantiation of the InternW physical world model series from Shanghai AI Laboratory, built around omnimodal interfaces, asynchronous multi-frequency processing, and local physical modeling under partial observations and external influences. InternW0 jointly learns future visual dynamics and continuous robot control through an asymmetric video--action architecture with flow matching. A high-capacity video expert provides longer-horizon predictive context, while a lightweight action expert operates at a faster timescale. Instead of regenerating the future for every action update, InternW0 reuses layerwise K/V and adapts it to newly observed states through observation-conditioned context routing. Domain-specific interfaces and soft prompts support heterogeneous embodiments, while contact-aware post-training incorporates force and tactile signals for contact-rich manipulation. We train InternW0 on approximately 7,200 hours of heterogeneous robot and egocentric data, including EgoLab, a 275-hour real-laboratory egocentric dataset. Evaluation spans simulation benchmarks and real-world scientific tasks, including a 15-stage metal--organic framework synthesis workflow and 5-stage contact- and force-aware dexterous manipulation for general-purpose quantitative pipetting. These results advance scalable, asynchronous, and science-native physical world models for universal and efficient real-world interactions.

cs.RO↗

arXiv2026

Random dynamical systems generated by rough differential equations driven by controlled rough paths

We study rough differential equations driven by controlled rough paths with drift. By means of the canonical lift of the controlled driver, we establish pathwise well-posedness and continuity. Under compatible time-shift conditions, we construct differentiable solution cocycles for the associated dynamical system generated by the equations considered here. Furthermore, assuming the corresponding regularity, moment, and spectral hypotheses, we prove the invariance of the local stable, unstable, and center manifolds.

math.PR↗

arXiv2026

Type C transpositions and strong marked tableaux

Motivated by the Morse--Seelinger conjecture on type C $k$-Schur functions, we develop a permutation model for type C strong marked tableaux. Using type C transpositions, we give an explicit correspondence with the symmetric-core model that preserves the marking data. We also describe the induced affine Weyl group action on bounded partitions.

math.CO↗

arXiv2026

Controlled B-series, controlled Runge-Kutta methods and controlled rough differential equations

We develop controlled B-series and controlled Runge-Kutta methods as extensions of classical B-series and Runge-Kutta theory to controlled-driven rough differential equations. The driving signal is a path controlled by an underlying $α$-Hölder step-$2$ rough path, with $α\in(1/3,1/2]$, as arises when the output of one rough system drives another. Controlled B-series retain the classical rooted-tree and elementary-differential structure, while incorporating driver-dependent coefficients defined recursively through controlled rough integration. We establish finite-order expansions of the exact solution and its controlled Runge-Kutta approximation, and derive corresponding tree-based order conditions. Under suitable smoothness, solvability, stability, and boundedness assumptions, matching through tree order $p$ yields local error $O(|t-s|^{(p+1)α})$ and global error $O(h^{(p+1)α-1})$, provided $(p+1)α>1$. The standard rough differential equation formulation is recovered when the controlled driver is the reference path itself, and the classical time-driven case recovers the usual B-series and Runge-Kutta methods. We further construct a simplified method using only increments of the controlled driver. Segmentwise canonical lifting of its piecewise linear interpolation gives explicit tree coefficients and reduces the third-order conditions to the classical ones. Assuming a Wong-Zakai solution-approximation rate $r_0>0$, the simplified method has global error $O(h^{\min\{r_0,(p+1)α-1\}})$. Numerical experiments with fractional Brownian controlled drivers illustrate the resulting convergence behaviour.

math.NA↗

arXiv2026

EBench: Elemental Diagnosis of Generalist Mobile Manipulation Policies

We present EBench, a simulation benchmark that diagnoses generalist mobile manipulation policies beyond a single success-rate scalar. EBench comprises 26 diverse and challenging manipulation tasks annotated along 5 capability dimensions and 4 generalization dimensions. We evaluate state-of-the-art generalist manipulation models including $π_0$, $π_{0.5}$, XVLA, and InternVLA-A1, and reveal that the models exhibit strikingly different capability profiles: $π_{0.5}$ achieves the highest test success rate, the best train--test retention, and the strongest mobile manipulation performance; $π_0$ leads on dexterous fixed-base and high-precision tasks; XVLA and InternVLA-A1 exhibit complementary strengths across atomic skills and operating regimes. Beyond capability profiling, EBench analyzes the generalization ability from 4 representative perspectives, identifying the impact of different distribution shift factors. The results reveal strengths and weaknesses of models behind an overall score. We hope this benchmark offers a broad set of diagnostic signals to guide iteration on generalist manipulation models.

cs.RO↗

arXiv2026

Extremely Low Mass Ratio Contact Binaries. III. Photometric and Spectroscopic Investigations of Eleven Systems

We present photometric and spectroscopic investigations of 11 totally eclipsing contact binaries with mass ratios below 0.15, classifying them as extremely low mass ratio contact binaries. The ground-based multiband light curves were modeled with PHysics Of Eclipsing BinariEs to derive the photometric parameters of these systems. The TESS light curves of J011323 and J002747 show pronounced asymmetries and continuous variations. Markov Chain Monte Carlo modeling suggests that these variations are related to longitudinal migration of spots on the primary components. Spectral subtraction of the LAMOST spectra reveals excess chromospheric emission in six systems, while no detectable excess emission is found in the other five. The O$-$C analysis indicates secular period increases in six systems and secular decreases in five systems. We estimated their orbital angular momenta and performed a dynamical analysis. {Within our adopted semi-analytical framework without energy transfer, the formation of these observed systems requires additional angular momentum loss beyond saturated magnetic braking and gravitational radiation, but this requirement could be modified by different assumptions on mass transfer or radius evolution.

astro-ph.SR↗

arXiv2026

Solution to an open problem on the computational complexity of immanant

Immanants are a class of generalized matrix functions associated with the irreducible characters of the symmetric group. Bürgisser [SIAM J. Comput., 30 (2000), pp. 1023--1040] proved that the computation of hook immanants and immanants corresponding to rectangular Young diagrams of polynomially growing width is VNP-complete under $p$-projections. And he posed an open problem: whether the family of immanants corresponding to rectangular Young diagrams of width $2$ is VNP-complete under $p$-projections. This paper gives a solution to this problem. We prove that, over any field of characteristic zero, the immanant families associated with rectangular Young diagrams of width $2$ and of length $2$ are both VNP-complete under $p$-projections.

math.CO↗

arXiv2026

Disuccessors, Gröbner-Shirshov bases and free L-dendriform algebras

In this paper, we prove respectively that the disuccessor operations on the associative operad $\as$, the Lie operad $\lie$, and the pre-Lie operad $\prelie$ preserve Gröbner-Shirshov bases. This structural preservation enables the transfer of known bases to more complex operads. As a consequence, we introduce new methods for constructing Gröbner-Shirshov bases for the $\dend$ and $\prelie$ operads, and explicitly construct a Gröbner-Shirshov basis for the free L-dendriform algebra. This provides a conceptual and computationally efficient resolution of Madariaga's problem and offers new insights into the combinatorial structure of L-dendriform algebras.

math.RA↗

arXiv2026

GAUGE: A Measurement-Grounded Benchmark for Physical Fidelity in Simulation Engines and Video World Models

Physics engines facilitate large-scale training and evaluation for embodied intelligence, while generative video world models are emerging as implicit simulators of future states and interactions. However, existing evaluations of physical fidelity are often conducted in isolation and rely heavily on perceptual similarity or human judgments, providing limited insight into which physical principles or parameters are violated. We introduce GAUGE, a real-world-grounded diagnostic benchmark for jointly evaluating how numerical simulators and generative video world models reproduce or deviate from real-world physics. It comprises 22 controlled task families covering rigid bodies, flexible cables, textiles, and volumetric deformable objects. Grounded in real-world trajectories and paired with calibrated physical metadata, uncertainty annotations, and task-specific observables, these tasks cover fundamental physical processes including collision, friction, momentum transfer, oscillation, self-contact, and deformation across diverse materials and conditions. We benchmark Isaac Sim, Genesis, and Newton on 14 task families using generalized trajectory errors, and evaluate 6 image-to-video models on 5 rigid-body tasks by testing physical-law consistency and the temporal stability of inferred parameters. Our results reveal no uniformly faithful physics engine, with the largest discrepancies arising in impulsive contact, rapid textile motion, and volumetric deformation. We further find that video world models can produce trajectories with the expected equation form while recovering incorrect accelerations, momentum transfer, and oscillation timing. GAUGE lays the groundwork for developing more physically faithful simulators and world models for embodied intelligence.

cs.AI↗