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Zhichao Liu

Publications and source records attributed to Zhichao Liu.

At least 19 recordsLinked to original sources
arXiv2026

GigaBrain-WBC-0.5: A Behavior World Model for Robust Humanoid Whole-Body Tracking with Environment Interaction

General-purpose motion trackers enable humanoid robots to follow diverse whole-body motions while maintaining balance, but are trained only on flat ground, failing to exploit bipedal mobility over complex terrain. Cross-terrain controllers, meanwhile, are task-specific or accept only low-dimensional locomotion commands. We introduce InterTrack, the first behavior world model (BWM) for robust whole-body tracking with environment interaction. Its Transformer jointly predicts the next action, state, and behavior distribution, learning environment-conditioned dynamics. To scale interaction training data, an automatic annotation pipeline reconstructs 3D support geometry from retargeted motions. At deployment, the policy handles commands implausible in the current environment in a "best-effort" manner. Quantitatively, InterTrack achieves an 81.3% success rate on terrain interaction (4.3 times the best evaluated baseline) and a 99.3% fall-recovery rate, while also improving free-space tracking and outperforming three leading tracking baselines across all of these regimes. To our knowledge, we provide the first demonstration of real-time cross-terrain whole-body teleoperation on a humanoid robot, alongside object interaction, stable responses to missing supports, and robust recovery from falls.

cs.RO↗
arXiv2026

Every compact operator is a commutator of compact operators

We prove that every compact operator $T$ on a separable infinite-dimensional complex Hilbert space is a commutator of two compact operators, thereby answering a question of Pearcy and Topping. Moreover, the compact factors $A$ and $B$ can be chosen such that $[A, B] = T$ and $\max\{\Vert{}A\Vert{},\Vert{}B\Vert{}\}\leq c\Vert{}T\Vert{}^{1/2}$ for a universal constant $c$.

math.FA↗
arXiv2026

Maximal Algebraic Ideals in Nonunital $C^*$-Algebras

Motivated by Ozawa's question of whether every maximal algebraic two-sided ideal in a $C^*$-algebra must be closed, we study the existence of maximal algebraic two-sided ideals in nonunital $C^*$-algebras. We formulate singular-distribution estimates intrinsically through lower semicontinuous 2-quasitraces and apply them to control algebraic ideal membership. This allows us to develop a novel criterionthe, the admissible quasitracial projection scale, for establishing the nonexistence of maximal ideals in nonunital $C^*$-algebras. This criterion applies to a wide class of simple $C^*$-algebras, including: (i) all $A\otimes K$ where $A$ is unital, simple, stably finite, $QT_2^1(A)$ nonempty, and the radius of comparison $rc(A)$ is finite, as well as all their hereditary $C^*$-subalgebras whenever $A$ satisfies further assumptions that A is of real rank zero and A has finitely many extreme quasitraces; (ii) all nonunital, simple, separable, stably finite, $Z$-stable $C^*$-algebras A that have an approximate identity consisting of increasing projections $(p_n)$ and for which the simplex $QT_2^1(A,p_1)$ of normalized traces at $p_1$ has finitely many extreme points. We also show that a large class of $C^*$-algebras E constructed from extensions of $C^*$-algebras above such that $E$ still has no maximal ideals. In particular, for these classes, Ozawa's question could be settled in an unexpected manner.

math.OA↗
arXiv2026

GigaBrain-0.7: Scaling Embodied Foundation Models to Emergent Capabilities with a Three-System Architecture

Vision-language-action (VLA) models have become a dominant paradigm for generalist embodied agents, demonstrating strong complex and long-horizon task completion in structured settings. Yet it remains an open question whether current VLA systems can benefit from more effective architectural design, scale to substantially larger and more heterogeneous data regimes, and achieve broader generalization across tasks and embodiments. To this end, we present GigaBrain-0.7, an embodied foundation model with substantially improved generalization across diverse robot embodiments. Specifically, GigaBrain-0.7 unifies understanding, prediction, and action through a three-system architecture, scales pretraining to over 37,000 hours of heterogeneous embodied data, and introduces one-stage alignment training that jointly optimizes vision-language understanding and multi-embodiment action generation. Compared with the preceding GigaBrain-0 series and prior state-of-the-art models including $π_{0.5}$, GigaBrain-0.7 achieves substantial improvements in foundation zero-shot capabilities, language-conditioned instruction following, and post-training task success rates. In particular, on our in-house Maker H01 platform and mainstream robot embodiments, GigaBrain-0.7 demonstrates strong task adaptability and completion ability across both home and industrial scenarios. All training code and pretrained model weights will be released.

cs.RO↗
arXiv2026

Bockstein operations and AD algebras with unbounded torsion in $K_1$

Eilers showed that for AD algebras of real rank zero with bounded torsion in $\mathrm{K}_1$, the coefficient transformations $κ$ are redundant in the classification by ordered scaled total $K$-theory. In this paper we treat the unbounded torsion case and prove that, in contrast, $κ$ becomes necessary. Specifically, we construct two non-isomorphic unital AD algebras of real rank zero, $E_0$ and $E_1$, such that their ordered scaled total $K$-theory invariants agree when the $κ$-maps are forgotten, i.e., \[ \bigl( \underline{\mathrm{K}}(E_0), \underline{\mathrm{K}}(E_0)_+, [1_{E_0}] \bigr)_{\underline{\mathrm{K}}_{\langleκ\rangle}} \cong \bigl( \underline{\mathrm{K}}(E_1), \underline{\mathrm{K}}(E_1)_+, [1_{E_1}] \bigr)_{\underline{\mathrm{K}}_{\langleκ\rangle}} \] but are not isomorphic under the full $Λ$-module structure: \[ \bigl( \underline{\mathrm{K}}(E_0), \underline{\mathrm{K}}(E_0)_+, [1_{E_0}] \bigr)_Λ \not\cong \bigl( \underline{\mathrm{K}}(E_1), \underline{\mathrm{K}}(E_1)_+, [1_{E_1}] \bigr)_Λ .\] This completes the picture for the necessity of all three operations $ρ$, $β$, and $κ$ in this context.

math.OA↗
arXiv2026

Long-Horizon-Terminal-Bench: Testing the Limits of Agents on Long-Horizon Terminal Tasks with Dense Reward-Based Grading

AI agents have become capable of autonomously completing short, well-specified tasks. However, existing terminal benchmarks largely focus on simple problems that finish within minutes and are evaluated only by their final outcome. This setup overlooks intermediate progress and partial solutions, yielding sparse reward signals and an incomplete picture of agent capability. We introduce Long-Horizon-Terminal-Bench, a terminal benchmark of 46 long-horizon tasks spanning nine categories, including experiment reproduction, software engineering, multimodal analysis, interactive games, and scientific computing. Each task follows a Terminal-Bench-style setup with a reference solution or simulation engine, but is further decomposed into fine-grained graded subtasks. This design enables dense intermediate rewards and partial credit, allowing evaluation to capture not only whether an agent reaches the final goal, but also how far it progresses on open-ended workflows. Tasks in Long-Horizon-Terminal-Bench typically require hundreds of episodes and minutes to hours of execution, stressing long-horizon planning, long-context management, and iterative debugging rather than one-shot problem solving. We evaluate 15 frontier models and find that agents consume on average 9.9M tokens per task, with roughly 231 episodes and 85.3 minutes of execution time per run, making Long-Horizon-Terminal-Bench more demanding than prior terminal-based benchmarks. Even the strongest tested model achieves 15.2% pass@1 at a partial-reward threshold of 0.95 and 10.9% at a perfect-reward threshold of 1.0, while the mean pass rate across models is 4.3% and 1.7% under the two thresholds, respectively. These results reveal headroom for improvement. We further analyze failure modes and error patterns, and release Long-Horizon-Terminal-Bench to support future progress on long-horizon terminal agents.

cs.AI↗
arXiv2026

A Path-Survival Analytical Framework for SCL Decoding of Polar Codes

A theoretical analysis of CRC-aided successive cancellation list (CA-SCL) decoding for polar codes remains an open problem, despite its widespread practical adoption. While low-density parity-check (LDPC) codes benefit from mature analytical tools, such as density evolution (DE), for predicting the performance of belief-propagation (BP) decoding, similar techniques are not directly applicable to CA-SCL decoding. This limitation stems from the complex path-pruning mechanism inherent in CA-SCL decoding. In this paper, we propose an analytical framework based on a novel path-survival model that captures the evolution of the correct path's rank during decoding. The proposed framework enables efficient prediction of CA-SCL decoding performance without requiring exhaustive list-specific Monte Carlo simulations. Extensive numerical evaluations demonstrate its effectiveness across a wide range of code lengths, code rates, list sizes, and channel models.

cs.IT↗
arXiv2026

Towards Long-Horizon Interpretability: Efficient and Faithful Multi-Token Attribution for Reasoning LLMs

Token attribution methods provide intuitive explanations for language model outputs by identifying causally important input tokens. However, as modern LLMs increasingly rely on extended reasoning chains, existing schemes face two critical challenges: (1) efficiency bottleneck, where attributing a target span of M tokens within a context of length N requires O(M*N) operations, making long-context attribution prohibitively slow; and (2) faithfulness drop, where intermediate reasoning tokens absorb attribution mass, preventing importance from propagating back to the original input. To address these, we introduce FlashTrace, an efficient multi-token attribution method that employs span-wise aggregation to compute attribution over multi-token targets in a single pass, while maintaining faithfulness. Moreover, we design a recursive attribution mechanism that traces importance through intermediate reasoning chains back to source inputs. Extensive experiments on long-context retrieval (RULER) and multi-step reasoning (MATH, MorehopQA) tasks demonstrate that FlashTrace achieves over 130x speedup over existing baselines while maintaining superior faithfulness. We further analyze the dynamics of recursive attribution, showing that even a single recursive hop improves faithfulness by tracing importance through the reasoning chain.

cs.LG↗
arXiv2026

WebTrap: Stealthy Mid-Task Hijacking of Browser Agents During Navigation

Browser agents are increasingly deployed in long-horizon tasks, which require executing extended action chains to accomplish user goals. However, this prolonged execution process provides attackers with more opportunities to inject malicious instructions. Existing prompt injection attacks against browser agents expose two key gaps: (1) low effectiveness, as attacks optimized for toy baselines fail to achieve end-to-end goals in real-world scenarios with complex environments and longer steps; (2) weak stealthiness, since most attacks pit the attack goal against the user goal, causing a significant drop in system usability under attack. To address these gaps, we propose WebTrap, a mid-task hijacking injection attack. It employs multi-step instruction fusion steering to seamlessly combine both goals, enabling the agent to resume the original user task after executing the attack goal. Furthermore, we design a context-grounded generation method to align the injected content with the task environment and system instructions, maximizing the hijacking success rate. Extensive experiments on two browser agent tasks, based on extended WASP and InjecAgent environments, demonstrate that our method achieves a high attack success rate while preserving the usability of the original system. We find that WebTrap exploits the agent's navigation vulnerabilities, binding the two goals so tightly that standard defense mechanisms cannot restore the system to normal operation. These findings reveal a critical vulnerability in agent systems during long-horizon tasks that they can be stealthily hijacked.

cs.CR↗
arXiv2026

First Frame Is the Place to Go for Video Content Customization

What role does the first frame play in video generation models? Traditionally, it's viewed as the spatial-temporal starting point of a video, merely a seed for subsequent animation. In this work, we reveal a fundamentally different perspective: video models implicitly treat the first frame as a conceptual memory buffer that stores visual entities for later reuse during generation. Leveraging this insight, we show that it's possible to achieve robust and generalized video content customization in diverse scenarios, using only 20-50 training examples without architectural changes or large-scale finetuning. This unveils a powerful, overlooked capability of video generation models for reference-based video customization.

cs.CV↗
arXiv2026

GigaWorld-Policy: An Efficient Action-Centered World--Action Model

World-Action Models (WAM) initialized from pre-trained video generation backbones have demonstrated remarkable potential for robot policy learning. However, existing approaches face two critical bottlenecks that hinder performance and deployment. First, jointly reasoning over future visual dynamics and corresponding actions incurs substantial inference overhead. Second, joint modeling often entangles visual and motion representations, making motion prediction accuracy heavily dependent on the quality of future video forecasts. To address these issues, we introduce GigaWorld-Policy, an action-centered WAM that learns 2D pixel-action dynamics while enabling efficient action decoding, with optional video generation. Specifically, we formulate policy training into two coupled components: the model predicts future action sequences conditioned on the current observation, and simultaneously generates future videos conditioned on the predicted actions and the same observation. The policy is supervised by both action prediction and video generation, providing richer learning signals and encouraging physically plausible actions through visual-dynamics constraints. With a causal design that prevents future-video tokens from influencing action tokens, explicit future-video generation is optional at inference time, allowing faster action prediction during deployment. To support this paradigm, we curate a diverse, large-scale robot dataset to pre-train an action-centered video generation model, which is then adapted as the backbone for robot policy learning. Experimental results on real-world robotic platforms show that GigaWorld-Policy runs 9x faster than the leading WAM baseline, Motus, while improving task success rates by 7%. Moreover, compared with pi-0.5, GigaWorld-Policy improves performance by 95% on RoboTwin 2.0.

cs.CV↗
arXiv2026

MM-Zero: Self-Evolving Multi-Model Vision Language Models From Zero Data

Self-evolving has emerged as a key paradigm for improving foundational models such as Large Language Models (LLMs) and Vision Language Models (VLMs) with minimal human intervention. While recent approaches have demonstrated that LLM agents can self-evolve from scratch with little to no data, VLMs introduce an additional visual modality that typically requires at least some seed data, such as images, to bootstrap the self-evolution process. In this work, we present Multi-model Multimodal Zero (MM-Zero), the first RL-based framework to achieve zero-data self-evolution for VLM reasoning. Moving beyond prior dual-role (Proposer and Solver) setups, MM-Zero introduces a multi-role self-evolving training framework comprising three specialized roles: a Proposer that generates abstract visual concepts and formulates questions; a Coder that translates these concepts into executable code (e.g., Python, SVG) to render visual images; and a Solver that performs multimodal reasoning over the generated visual content. All three roles are initialized from the same base model and trained using Group Relative Policy Optimization (GRPO), with carefully designed reward mechanisms that integrate execution feedback, visual verification, and difficulty balancing. Our experiments show that MM-Zero improves VLM reasoning performance across a wide range of multimodal benchmarks. MM-Zero establishes a scalable path toward self-evolving multi-model systems for multimodal models, extending the frontier of self-improvement beyond the conventional two-model paradigm.

cs.CV↗
arXiv2026

GigaBrain-0.5M*: a VLA That Learns From World Model-Based Reinforcement Learning

Vision-language-action (VLA) models that directly predict multi-step action chunks from current observations face inherent limitations due to constrained scene understanding and weak future anticipation capabilities. In contrast, video world models pre-trained on web-scale video corpora exhibit robust spatiotemporal reasoning and accurate future prediction, making them a natural foundation for enhancing VLA learning. Therefore, we propose \textit{GigaBrain-0.5M*}, a VLA model trained via world model-based reinforcement learning. Built upon \textit{GigaBrain-0.5}, which is pre-trained on over 10,000 hours of robotic manipulation data, whose intermediate version currently ranks first on the international RoboChallenge benchmark. \textit{GigaBrain-0.5M*} further integrates world model-based reinforcement learning via \textit{RAMP} (Reinforcement leArning via world Model-conditioned Policy) to enable robust cross-task adaptation. Empirical results demonstrate that \textit{RAMP} achieves substantial performance gains over the RECAP baseline, yielding improvements of approximately 30\% on challenging tasks including \texttt{Laundry Folding}, \texttt{Box Packing}, and \texttt{Espresso Preparation}. Critically, \textit{GigaBrain-0.5M$^*$} exhibits reliable long-horizon execution, consistently accomplishing complex manipulation tasks without failure as validated by real-world deployment videos on our \href{https://gigabrain05m.github.io}{project page}.

cs.CV↗
arXiv2025

GigaBrain-0: A World Model-Powered Vision-Language-Action Model

Training Vision-Language-Action (VLA) models for generalist robots typically requires large-scale real-world robot data, which is expensive and time-consuming to collect. The inefficiency of physical data collection severely limits the scalability, and generalization capacity of current VLA systems. To address this challenge, we introduce GigaBrain-0, a novel VLA foundation model empowered by world model-generated data (e.g., video generation, real2real transfer, human transfer, view transfer, sim2real transfer data). By leveraging world models to generate diverse data at scale, GigaBrain-0 significantly reduces reliance on real robot data while improving cross-task generalization. Our approach further improves policy robustness through RGBD input modeling and embodied Chain-of-Thought (CoT) supervision, enabling the model to reason about spatial geometry, object states, and long-horizon dependencies during task execution. This leads to substantial gains in real-world performance on dexterous, long-horizon, and mobile manipulation tasks. Extensive experiments demonstrate that GigaBrain-0 achieves superior generalization across variations in appearances (e.g., textures, colors), object placements, and camera viewpoints. Additionally, we present GigaBrain-0-Small, an optimized lightweight variant designed to run efficiently on devices such as the NVIDIA Jetson AGX Orin.

cs.RO↗
arXiv2025

Audio Frequency-Time Dual Domain Evaluation on Depression Diagnosis

Depression, as a typical mental disorder, has become a prevalent issue significantly impacting public health. However, the prevention and treatment of depression still face multiple challenges, including complex diagnostic procedures, ambiguous criteria, and low consultation rates, which severely hinder timely assessment and intervention. To address these issues, this study adopts voice as a physiological signal and leverages its frequency-time dual domain multimodal characteristics along with deep learning models to develop an intelligent assessment and diagnostic algorithm for depression. Experimental results demonstrate that the proposed method achieves excellent performance in the classification task for depression diagnosis, offering new insights and approaches for the assessment, screening, and diagnosis of depression.

cs.CV↗
arXiv2025

On the Weight Spectrum of Rate-Compatible Polar Codes

The weight spectrum plays a crucial role in the performance of error-correcting codes. Despite substantial theoretical exploration of polar codes with mother code length, a framework for the weight spectrum of rate-compatible polar codes remains elusive. In this paper, we address this gap by presenting the theoretical results for enumerating the number of minimum-weight codewords for quasi-uniform punctured, Wang-Liu shortened, and bit-reversal shortened decreasing polar codes. Additionally, we propose efficient algorithms for computing the average spectrum of random upper-triangular pre-transformed shortened and punctured polar codes. Notably, our algorithms operate with polynomial complexity relative to the code length. Simulation results affirm that our findings yield a precise estimation of the performance of rate-compatible polar codes.

cs.IT↗
arXiv2025

Humanoid Occupancy: Enabling A Generalized Multimodal Occupancy Perception System on Humanoid Robots

Humanoid robot technology is advancing rapidly, with manufacturers introducing diverse heterogeneous visual perception modules tailored to specific scenarios. Among various perception paradigms, occupancy-based representation has become widely recognized as particularly suitable for humanoid robots, as it provides both rich semantic and 3D geometric information essential for comprehensive environmental understanding. In this work, we present Humanoid Occupancy, a generalized multimodal occupancy perception system that integrates hardware and software components, data acquisition devices, and a dedicated annotation pipeline. Our framework employs advanced multi-modal fusion techniques to generate grid-based occupancy outputs encoding both occupancy status and semantic labels, thereby enabling holistic environmental understanding for downstream tasks such as task planning and navigation. To address the unique challenges of humanoid robots, we overcome issues such as kinematic interference and occlusion, and establish an effective sensor layout strategy. Furthermore, we have developed the first panoramic occupancy dataset specifically for humanoid robots, offering a valuable benchmark and resource for future research and development in this domain. The network architecture incorporates multi-modal feature fusion and temporal information integration to ensure robust perception. Overall, Humanoid Occupancy delivers effective environmental perception for humanoid robots and establishes a technical foundation for standardizing universal visual modules, paving the way for the widespread deployment of humanoid robots in complex real-world scenarios.

cs.RO↗