arXiv subjects

Zijian Song

Publications and source records attributed to Zijian Song.

At least 19 recordsLinked to original sources

arXiv2026

MaxProof: Scaling Mathematical Proof with Generative-Verifier RL and Population-Level Test-Time Scaling

We present MaxProof, a population-level test-time scaling framework for competition-level mathematical proof in the MiniMax-M3 series. M3 first trains three proof-oriented capabilities -- proof generation, proof verification, and critique-conditioned proof repair -- using a defense-in-depth generative verifier engineered for low false-positive rate. These capabilities are merged into a single released M3 model. At test time, MaxProof treats the model as a generator, verifier, refiner, and ranker, searches over a population of candidate proofs, and returns one final proof through tournament selection. With MaxProof test-time scaling, the M3 model reaches 35/42 on IMO 2025 and 36/42 on USAMO 2026, exceeding the human gold-medal threshold on both.

cs.LG↗

arXiv2026

IndusAgent: Reinforcing Open-Vocabulary Industrial Anomaly Detection with Agentic Tools

Multimodal large language models (MLLMs) have shown remarkable capability in bridging visual perception and textual reasoning, enabling zero-shot understanding across diverse industrial scenarios. However, their performance in open-vocabulary industrial anomaly detection (IAD) is often limited by domain-misaligned reasoning and hallucinated structural inferences. To address these challenges, we propose \textbf{IndusAgent}, a tool-augmented agentic framework for open-vocabulary IAD. Specifically, we first construct \textbf{Indus-CoT}, a structured dataset that integrates global visual observations, high-resolution local patches, and expert normalcy priors, providing supervision for fine-tuning the model on rigorous industrial inspection trajectories. Building on this, IndusAgent dynamically orchestrates a set of external tools, including dynamic region cropping, high-frequency feature enhancement, and prior retrieval, thus enabling the agent to actively resolve visual ambiguities and disentangle subtle anomalies. Furthermore, we introduce a gated reinforcement learning objective that jointly optimizes anomaly classification, localization accuracy, anomaly type reasoning, and efficient tool usage, ensuring that tool invocation occurs only when beneficial. Extensive evaluations on five industrial anomaly benchmarks, including MVTec-AD, VisA, MPDD, DTD, and SDD, demonstrate that IndusAgent achieves state-of-the-art zero-shot performance among all existing methods, validating our robustness and generalization capacity.

cs.CV↗

arXiv2026

Robotic Manipulation is Vision-to-Geometry Mapping: Vision-Geometry Backbones over Language and Video Models

At its core, robotic manipulation is a problem of vision-to-geometry mapping ($f(v) \rightarrow G$). Physical actions are fundamentally defined by geometric properties like 3D positions and spatial relationships. Consequently, we argue that the foundation for generalizable robotic control should be a vision-geometry backbone, rather than the widely adopted vision-language or video models. Conventional VLA and video-predictive models rely on backbones pretrained on large-scale 2D image-text or temporal pixel data. While effective, their representations are largely shaped by semantic concepts or 2D priors, which do not intrinsically align with the precise 3D geometric nature required for physical manipulation. Driven by this insight, we propose the Vision-Geometry-Action (VGA) model, which directly conditions action generation on pretrained 3D representations. Specifically, VGA replaces conventional language or video backbones with a pretrained 3D world model, establishing a seamless vision-to-geometry mapping that translates visual inputs directly into physical actions. To further enhance geometric consistency, we introduce Progressive Volumetric Modulation and jointly train action and 3D property prediction to preserve geometric representations. Extensive experiments validate the effectiveness of our approach. Across simulation benchmarks, VGA outperforms leading VLA, 3D-VLA, and WAM baselines, including $\pi_{0.5}$, OpenVLA-OFT, GeoVLA, and Motus. In real-world deployments, VGA surpasses $\pi_{0.5}$ under unseen viewpoints and accurately follows language instructions for target grasping. These results highlight that operating on native 3D representations, rather than relying primarily on language or video priors, offers a promising direction toward generalizable physical intelligence. Project page: https://hcplab-sysu.github.io/VisionGeometryActionModel.

cs.RO↗

arXiv2026

Mixed-state Phases from Higher-order SSPTs with Kramers-Wannier Symmetry

Mixed-state phases have recently attracted significant attention as a generalization beyond their pure-state counterparts. Prominent examples include mixed-state symmetry-protected topological (mSPT) phases and the strong-to-weak symmetry breaking (SWSSB) phases. It has been shown recently that mSPT phases admit a holographic dual description in terms of higher-order subsystem SPT phases. In this work, we investigate the mixed-state phases obtained by tracing out the bulk degrees of freedom of higher-order subsystem SPT phases protected by non-invertible symmetries. We find that the resulting mixed states exhibit the coexistence of the symmetry-protected topological order and SWSSB. We also use the interface as a probe to characterize the mixed state phases, and specifically, when there is no local modification to preserve the symmetries across the interface, the two sides of the interface are in distinct phases.

cond-mat.str-el↗

arXiv2026

Learning Physics from Pretrained Video Models: A Multimodal Continuous and Sequential World Interaction Models for Robotic Manipulation

The scarcity of large-scale robotic data has motivated the repurposing of foundation models from other modalities for policy learning. In this work, we introduce PhysGen (Learning Physics from Pretrained Video Generation Models), a scalable continuous and sequential world interaction framework that leverages autoregressive video generation to solve robotic manipulation tasks. By treating the pretrained video model as a proxy for a physics simulator, PhysGen models the dynamic interplay between the external environment and robot actions. We introduce a multimodal continuous representation that unifies video and action into shared physical tokens, bridging the gap between discrete video generation and continuous robotic control. This approach enables the seamless transfer of implicit physical knowledge-such as object permanence and dynamics-from video pretraining to downstream manipulation.To ensure efficient convergence, we incorporate causal masking, inverse kinematics, Lookahead Multi-Token Prediction (L-MTP), and key-value (KV) caching. Experimental results on the Libero and ManiSkill benchmarks demonstrate that PhysGen consistently outperforms robust baselines, surpassing OpenVLA and WorldVLA by margins of 13.8% and 8.8%, respectively. Notably, in real-world scenarios, PhysGen matches the performance of large-scale action-pretrained models like $\pi_0$ without requiring prior action-specific pretraining, demonstrating superior capability in physically complex tasks such as grasping transparent objects. These findings validate the potential of extracting physical intuition from pretrained video generators to facilitate generalizable robotic manipulation.

cs.RO↗

arXiv2026

RADAR: Benchmarking Vision-Language-Action Generalization via Real-World Dynamics, Spatial-Physical Intelligence, and Autonomous Evaluation

VLA models have achieved remarkable progress in embodied intelligence; however, their evaluation remains largely confined to simulations or highly constrained real-world settings. This mismatch creates a substantial reality gap, where strong benchmark performance often masks poor generalization in diverse physical environments. We identify three systemic shortcomings in current benchmarking practices that hinder fair and reliable model comparison. (1) Existing benchmarks fail to model real-world dynamics, overlooking critical factors such as dynamic object configurations, robot initial states, lighting changes, and sensor noise. (2) Current protocols neglect spatial--physical intelligence, reducing evaluation to rote manipulation tasks that do not probe geometric reasoning. (3) The field lacks scalable fully autonomous evaluation, instead relying on simplistic 2D metrics that miss 3D spatial structure or on human-in-the-loop systems that are costly, biased, and unscalable. To address these limitations, we introduce RADAR (Real-world Autonomous Dynamics And Reasoning), a benchmark designed to systematically evaluate VLA generalization under realistic conditions. RADAR integrates three core components: (1) a principled suite of physical dynamics; (2) dedicated tasks that explicitly test spatial reasoning and physical understanding; and (3) a fully autonomous evaluation pipeline based on 3D metrics, eliminating the need for human supervision. We apply RADAR to audit multiple state-of-the-art VLA models and uncover severe fragility beneath their apparent competence. Performance drops precipitously under modest physical dynamics, with the expectation of 3D IoU declining from 0.261 to 0.068 under sensor noise. Moreover, models exhibit limited spatial reasoning capability. These findings position RADAR as a necessary bench toward reliable and generalizable real-world evaluation of VLA models.

cs.RO↗

arXiv2026

Anyon Permutations in Quantum Double Models through Constant-depth Circuits

We provide explicit constant-depth local unitary circuits that realize general anyon permutations in Kitaev's quantum double models. This construction can be naturally understood through a correspondence between anyon permutation symmetries of two-dimensional topological orders and self-dualities in one-dimensional systems, where local gates implement self-duality transformations on the boundaries of microscopic regions. From this holographic perspective, general anyon permutations in the $D(G)$ quantum double correspond to compositions of three classes of one-dimensional self-dualities, including gauging of certain subgroups of $G$, stacking with $G$ symmetry-protected topological phases, and outer automorphisms of the group $G$. We construct circuits realizing the first class by employing self-dual unitary gauging maps, and present transversal circuits for the latter two classes.

quant-ph↗

arXiv2025

Human-Centric Open-Future Task Discovery: Formulation, Benchmark, and Scalable Tree-Based Search

Recent progress in robotics and embodied AI is largely driven by Large Multimodal Models (LMMs). However, a key challenge remains underexplored: how can we advance LMMs to discover tasks that assist humans in open-future scenarios, where human intentions are highly concurrent and dynamic. In this work, we formalize the problem of Human-centric Open-future Task Discovery (HOTD), focusing particularly on identifying tasks that reduce human effort across plausible futures. To facilitate this study, we propose HOTD-Bench, which features over 2K real-world videos, a semi-automated annotation pipeline, and a simulation-based protocol tailored for open-set future evaluation. Additionally, we propose the Collaborative Multi-Agent Search Tree (CMAST) framework, which decomposes complex reasoning through a multi-agent system and structures the reasoning process through a scalable search tree module. In our experiments, CMAST achieves the best performance on the HOTD-Bench, significantly surpassing existing LMMs. It also integrates well with existing LMMs, consistently improving performance.

cs.CV↗

arXiv2025

Strong-to-weak spontaneous symmetry breaking of higher-form non-invertible symmetries in Kitaev's quantum double model

Topological orders can be understood as spontaneous symmetry breaking of higher-form symmetries. In the non-Abelian case, the broken higher-form symmetries are notably non-invertible. In this work, we extend this framework to mixed states, where symmetries can be either strong or weak. In particular, we investigate the strong-to-weak spontaneous symmetry breaking (SWSSB) of non-invertible higher-form symmetries in non-Abelian Kitaev's quantum double models under decoherence. We further show that the resulting decohered quantum double mixed states form a locally indistinguishable set, which also constitutes an information convex set. Importantly, we emphasize that the dimension of this convex set equals the ground-state degeneracy of the corresponding pure state, highlighting that the quantum information encoded in the ground-state subspace is degraded into classical information captured by the convex set of decohered density matrices.

quant-ph↗

arXiv2025

AutoDrive-R$^2$: Incentivizing Reasoning and Self-Reflection Capacity for VLA Model in Autonomous Driving

Vision-Language-Action (VLA) models in autonomous driving systems have recently demonstrated transformative potential by integrating multimodal perception with decision-making capabilities. However, the interpretability and coherence of the decision process and the plausibility of action sequences remain largely underexplored. To address these issues, we propose AutoDrive-R$^2$, a novel VLA framework that enhances both reasoning and self-reflection capabilities of autonomous driving systems through chain-of-thought (CoT) processing and reinforcement learning (RL). Specifically, we first propose an innovative CoT dataset named nuScenesR$^2$-6K for supervised fine-tuning, which effectively builds cognitive bridges between input information and output trajectories through a four-step logical chain with self-reflection for validation. Moreover, to maximize both reasoning and self-reflection during the RL stage, we further employ the Group Relative Policy Optimization (GRPO) algorithm within a physics-grounded reward framework that incorporates spatial alignment, vehicle dynamic, and temporal smoothness criteria to ensure reliable and realistic trajectory planning. Extensive evaluation results across both nuScenes and Waymo datasets demonstrates the state-of-the-art performance and robust generalization capacity of our proposed method.

cs.RO↗

arXiv2025

Physical Autoregressive Model for Robotic Manipulation without Action Pretraining

The scarcity of manipulation data has motivated the use of pretrained large models from other modalities in robotics. In this work, we build upon autoregressive video generation models to propose a Physical Autoregressive Model (PAR), where physical tokens combine frames and actions to represent the joint evolution of the robot and its environment. PAR leverages the world knowledge embedded in video pretraining to understand physical dynamics without requiring action pretraining, enabling accurate video prediction and consistent action trajectories. It also adopts a DiT-based de-tokenizer to model frames and actions as continuous tokens, mitigating quantization errors and facilitating mutual enhancement. Furthermore, we incorporate a causal mask with inverse kinematics, parallel training, and the KV-cache mechanism to further improve performance and efficiency. Experiments on the ManiSkill benchmark show that PAR achieves a 100\% success rate on the PushCube task, matches the performance of action-pretrained baselines on other tasks, and accurately predicts future videos with tightly aligned action trajectories. These findings underscore a promising direction for robotic manipulation by transferring world knowledge from autoregressive video pretraining. The project page is here: https://hcplab-sysu.github.io/PhysicalAutoregressiveModel/

cs.CV↗

arXiv2025

SIRI-Bench: Challenging VLMs' Spatial Intelligence through Complex Reasoning Tasks

Large Language Models (LLMs) have undergone rapid progress, largely attributed to reinforcement learning on complex reasoning tasks. In contrast, while spatial intelligence is fundamental for Vision-Language Models (VLMs) in real-world interaction, the systematic study of their complex spatial reasoning remains underexplored. To bridge this gap, we introduce SIRI-Bench, a benchmark designed to evaluate VLMs' structural spatial intelligence through spatial-grounded reasoning tasks. SIRI-Bench comprises 9,000 video-question-answer triplets, where each problem is embedded in a realistic 3D scene. The benchmark is carefully designed so that solving each problem requires both spatial comprehension and structural reasoning. To facilitate large-scale data synthesis, we develop an Automatic Scene Creation Engine that employs collaborative LLM agents to translate abstract mathematical problems into faithful 3D scenes. Experimental results reveal that state-of-the-art VLMs struggle significantly on SIRI-Bench, underscoring the challenge of structural spatial reasoning. We hope that our study will bring researchers' attention to spatially grounded reasoning and advance VLMs in visual problem-solving.

cs.CV↗

arXiv2025

Non-Clifford gates between stabilizer codes via non-Abelian topological order

We propose protocols to implement non-Clifford logical gates between stabilizer codes by entangling into a non-Abelian topological order as an intermediate step. Generalizing previous approaches, we provide a framework that generates a large class of non-Clifford and non-diagonal logical gates between qudit surface codes by gauging the topological symmetry of symmetry-enriched topological orders. As our main example, we concretely detail a protocol that utilizes the quantum double of $S_3$ to generate a controlled-charge conjugation ($C\mathcal{C}$) gate between a qubit and qutrit surface code. Both the preparation of non-Abelian states and logical state injection between the Abelian and non-Abelian codes are executed via finite-depth quantum circuits with measurement and feedforward. We discuss aspects of the fault-tolerance of our protocol, presenting insights on how to construct a heralded decoder for the quantum double of $S_3.$ We also outline how analogous protocols can be used to obtain logical gates between qudit surface codes by entangling into $\mathcal{D}(G),$ where $G$ is a semidirect product of Abelian groups. This work serves as a step towards classifying the computational power of non-Abelian quantum phases beyond the paradigm of anyon braiding on near-term quantum devices.

quant-ph↗

arXiv2025

Enhancing Pre-Trained Model-Based Class-Incremental Learning through Neural Collapse

Class-Incremental Learning (CIL) is a critical capability for real-world applications, enabling learning systems to adapt to new tasks while retaining knowledge from previous ones. Recent advancements in pre-trained models (PTMs) have significantly advanced the field of CIL, demonstrating superior performance over traditional methods. However, understanding how features evolve and are distributed across incremental tasks remains an open challenge. In this paper, we propose a novel approach to modeling feature evolution in PTM-based CIL through the lens of neural collapse (NC), a striking phenomenon observed in the final phase of training, which leads to a well-separated, equiangular feature space. We explore the connection between NC and CIL effectiveness, showing that aligning feature distributions with the NC geometry enhances the ability to capture the dynamic behavior of continual learning. Based on this insight, we introduce Neural Collapse-inspired Pre-Trained Model-based CIL (NCPTM-CIL), a method that dynamically adjusts the feature space to conform to the elegant NC structure, thereby enhancing the continual learning process. Extensive experiments demonstrate that NCPTM-CIL outperforms state-of-the-art methods across four benchmark datasets. Notably, when initialized with ViT-B/16-IN1K, NCPTM-CIL surpasses the runner-up method by 6.73% on VTAB, 1.25% on CIFAR-100, and 2.5% on OmniBenchmark.

cs.LG↗

arXiv2024

Neural Collapse Inspired Knowledge Distillation

Existing knowledge distillation (KD) methods have demonstrated their ability in achieving student network performance on par with their teachers. However, the knowledge gap between the teacher and student remains significant and may hinder the effectiveness of the distillation process. In this work, we introduce the structure of Neural Collapse (NC) into the KD framework. NC typically occurs in the final phase of training, resulting in a graceful geometric structure where the last-layer features form a simplex equiangular tight frame. Such phenomenon has improved the generalization of deep network training. We hypothesize that NC can also alleviate the knowledge gap in distillation, thereby enhancing student performance. This paper begins with an empirical analysis to bridge the connection between knowledge distillation and neural collapse. Through this analysis, we establish that transferring the teacher's NC structure to the student benefits the distillation process. Therefore, instead of merely transferring instance-level logits or features, as done by existing distillation methods, we encourage students to learn the teacher's NC structure. Thereby, we propose a new distillation paradigm termed Neural Collapse-inspired Knowledge Distillation (NCKD). Comprehensive experiments demonstrate that NCKD is simple yet effective, improving the generalization of all distilled student models and achieving state-of-the-art accuracy performance.

cs.CV↗

arXiv2024

Domain walls from SPT-sewing

We introduce a systematic method for constructing gapped domain walls of topologically ordered systems by gauging a lower-dimensional symmetry-protected topological (SPT) order. Based on our construction, we propose a correspondence between 1d SPT phases with a non-invertible $G\times \text{Rep}(G)\times G$ symmetry and invertible domain walls in the quantum double associated with the group $G$. We prove this correspondence when $G$ is Abelian and provide evidence for the general case by studying the quantum double model for $G=S_3$. We also use our method to construct \emph{anchoring domain walls}, which are novel exotic domain walls in the 3d toric code that transform point-like excitations to semi-loop-like excitations anchored on these domain walls.

quant-ph↗

arXiv2024

Magic Boundaries of 3D Color Codes

We investigate boundaries of 3D color codes and provide a systematic classification into 101 distinct boundary types, including two novel classes. The first class consists of 1 boundary and is generated by sweeping the codimension-1 (2D) $T$-domain wall across the system and attaching it to the $X$-boundary that condenses only magnetic fluxes. Since the $T$-domain wall cannot condense on the $X$-boundary, a new magic boundary is produced, where the boundary stabilizers contain $XS$-stabilizers going beyond the conventional Pauli stabilizer formalism, and hence contains 'magic'. Neither electric nor magnetic excitations can condense on such a magic boundary, and only the composite of the magnetic flux and codimension-2 (1D) $S$-domain wall can condense on it, which makes the magic boundary going beyond the classification of the Lagrangian subgroup. The second class consists of 70 boundaries and is generated by sweeping the $S$-domain wall across a codimension-1 submanifold and attaching it to the boundary. This generates a codimension-2 (1D) nested boundary at the intersection. We also connect these novel boundaries to their previously discovered counterpart in the $\mathbb{Z}_2^3$ gauge theory, equivalent to three copies of 3D toric codes, where the $S$ and $T$ domain walls correspond to gauged symmetry-protected topological (SPT) defects. New boundaries are produced whenever the corresponding symmetry of the SPT defect remains unbroken on the boundary. Applications of the magic boundaries include implementing fault-tolerant non-Clifford logical gates, e.g., in the context of fractal topological codes.

quant-ph↗

arXiv2023

XVTP3D: Cross-view Trajectory Prediction Using Shared 3D Queries for Autonomous Driving

Trajectory prediction with uncertainty is a critical and challenging task for autonomous driving. Nowadays, we can easily access sensor data represented in multiple views. However, cross-view consistency has not been evaluated by the existing models, which might lead to divergences between the multimodal predictions from different views. It is not practical and effective when the network does not comprehend the 3D scene, which could cause the downstream module in a dilemma. Instead, we predicts multimodal trajectories while maintaining cross-view consistency. We presented a cross-view trajectory prediction method using shared 3D Queries (XVTP3D). We employ a set of 3D queries shared across views to generate multi-goals that are cross-view consistent. We also proposed a random mask method and coarse-to-fine cross-attention to capture robust cross-view features. As far as we know, this is the first work that introduces the outstanding top-down paradigm in BEV detection field to a trajectory prediction problem. The results of experiments on two publicly available datasets show that XVTP3D achieved state-of-the-art performance with consistent cross-view predictions.

cs.CV↗