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Zeyu Liu

Publications and source records attributed to Zeyu Liu.

At least 37 records · Page 2Linked to original sources
arXiv2026

Mechanisms of Width Scaling in Normalized Residual Networks: The Effective Alignment Dimension

Existing theories of neural-network width characterize asymptotic limits, but provide limited guidance on whether an expansion direction identified from finite training data remains beneficial on unseen data. We study this problem for function-preserving residual expansion and introduce the effective alignment dimension, a measurable quantity describing the signal-noise geometry of activation gradients. By deriving the exact mean and variance of the inner product between independently estimated training and test gradients, we obtain a finite-sample upper bound on misalignment probability. The bound depends only on the effective alignment dimension and an effective sample size, requiring finite second moments and a nonzero population gradient, without covariance spectral assumptions or prescribed width-growth rates. We integrate this certificate into the train-test residual-expansion framework, yielding a high-probability condition for test-risk improvement. Experiments across width-controlled LLaMA-style Transformers, Pythia, and ResNet-20 show that wider models exhibit larger effective alignment dimensions and lower empirical misalignment. Direct residual interventions confirm that the alignment statistic predicts the sign and magnitude of held-out loss changes.

cs.LG↗
arXiv2026

PathScale-R1: Cross-scale Reasoning for Pathological Image Analysis

Pathological diagnosis is inherently multi-scale, requiring the integration of global tissue architecture at low magnification with cellular morphology at higher magnification. However, existing pathology benchmarks and vision-language models (VLMs) are still largely developed under single-scale settings, limiting their ability to learn clinically meaningful multi-magnification reasoning. Moreover, naively constructed visual question answering (VQA) tasks may be susceptible to text-only or superficial visual shortcuts, leading to unreliable assessments of visual understanding. To address these limitations, we introduce a benchmark and training framework for shortcut-resistant cross-scale pathology reasoning. We design an Adversarial Text-only Screening strategy for semantic reasoning questions and a Structure-controlled Distractor Sampling strategy for visual grounding questions, encouraging models to rely on cross-scale visual evidence. Based on this pipeline, we construct PathScale-VQA, a high-quality cross-scale pathology VQA benchmark with 10,373 multiple-choice questions grounded in 1,368 diagnostic paths across multiple magnification levels. Building on the semantic reasoning set, PathScale-R1 is optimized through Difficulty-driven Reasoning Distillation supervised fine-tuning followed by reinforcement learning with a Scale-aware Reasoning Structure reward, which encourages the use of evidence across magnifications. Extensive experiments demonstrate state-of-the-art performance of PathScale-R1 on cross-scale reasoning tasks and effective transfer to conventional single-scale pathology VQA. Our code is available at https://github.com/iMVR-PL/PathScale-R1.

cs.CV↗
arXiv2026

KineBench: Benchmarking Embodied World Models via IDM-Free Kinematic Grounding

Evaluating the physical consistency of embodied world models(EWMs) is a critical open challenge. While closed-loop evaluation via simulator rollouts offers a more faithful assessment of physical plausibility than open-loop alternatives, existing frameworks almost exclusively rely on Inverse Dynamics Models(IDMs) for action extraction. Due to the intricate mapping from 2D pixel space to 3D kinematic space, the learned IDMs can be brittle to data outside their training distribution, resulting in unreliable action extraction from the generated videos with novel objects and scenarios. This creates an unavoidable attribution ambiguity between world model inaccuracies and extractor errors. To reduce this ambiguity, we present KineBench, an IDM-free closed-loop benchmark for EWMs, built upon an explicit kinematic grounding pipeline. Given a generated video, KineBench employs cascaded visual foundation models to directly extract 6D end-effector poses from individual frames, which are then executed in a physics simulator for closed-loop validation. Beyond execution-based task success, KineBench incorporates two classical 3D kinematic metrics--Spectral Arc Length (SPARC) and the Maruyama Manipulability Index--to characterize trajectory smoothness and kinematic feasibility from a robot-centric perspective. Built on 20 diverse manipulation tasks in ManiSkill3, KineBench evaluates EWMs across four progressive suites: basic execution, task transfer, visual out-of-distribution generalization, and complexity-conditioned scaling. Evaluation across frontier models reveals task-complexity-bounded nonlinear scaling in embodied video generation, providing empirical guidance for future data-scaling strategies.

cs.RO↗
arXiv2026

Learning Agile Navigation in Crowded Environments for Quadruped Robots

Navigating dynamic and crowded environments presents significant challenges for quadruped robots due to severe sensor occlusion and unpredictable human motion. Existing approaches face a trade-off: model-based methods, such as Velocity Obstacles (VO), theoretically guarantee safety but rely on accurate obstacle motion estimates that often fail in dense crowds, while end-to-end learning methods offer robustness but lack motion prediction capability of obstacles, leading to collisions or conservative behaviors. To solve this, we propose VOP-Nav, a novel navigation system that combines the geometric safety of VO with the agile adaptability of end-to-end learning. Using only local onboard observations, our system avoids explicit obstacle detection and tracking pipelines. The VOP-Net processes multi-frame LiDAR data to implicitly encode dynamic constraints and predict a safe velocity region derived from Velocity Obstacle theory. Importantly, the VO predictions serve a dual role: they are used as input to the navigation policy during inference and as a reward signal during training to encourage safe motion. Evaluations in Isaac Gym demonstrate that VOP-Nav achieves higher success rates than all baselines while balancing locomotion speed and collision avoidance. Real-world deployment on a Unitree Go2 quadruped robot further validates the system's robustness and efficiency in complex indoor and outdoor dynamic environments.

cs.RO↗
arXiv2026

Emergence of the Scrooge Ensemble in the Sachdev-Ye-Kitaev Model

The probabilistic nature of quantum measurement provides a direct window into the structure and complexity of many-body wave functions. When only part of a system is measured, the remaining degrees of freedom form an ensemble of post-measurement states whose statistical structure can reveal a stronger form of thermalization, known as deep thermalization. Recent numerical evidence suggests that this phenomenon is characterized by convergence of the projected ensemble to the Scrooge ensemble, a maximally random ensemble compatible with a given density matrix. In this Letter, we use the solvable Sachdev-Ye-Kitaev (SYK) model to unveil the mechanism by which the Scrooge ensemble emerges in many-body systems. By formulating measurement probabilities and post-measurement states in terms of path integrals, we analytically characterize all moments of the projected ensemble and show that they exactly match those of the Scrooge ensemble, even at short evolution times. We further connect this result to the saddle-point structure of the measurement path integral, which naturally generates the replica permutations underlying Scrooge statistics. Our results establish the solvable SYK model as a tractable setting for exploring universal statistics of quantum measurements in chaotic many-body dynamics.

quant-ph↗
arXiv2026

Kairos: A Regret-Aware Native World-Action Model Stack for Physical AI

We introduce \textbf{Kairos}, a regret-aware native world-action model stack for Physical AI. Kairos is motivated by the view that a physical world model should not aim to fully simulate all future pixels, but should learn and maintain the information most relevant to embodiment control: object state, spatial relations, contact conditions, task progress, action consequences, failure boundaries, and deployment uncertainty. Kairos establishes three model-side prerequisites toward this goal. First, it \textbf{learns} control-relevant information through a \textbf{Cross-Embodiment Data Curriculum}, which organizes open-world videos, human behavioral data, and robot interactions into an intervention-strength progression from passive physical observation to intentional behavior and embodied action grounding. Second, it \textbf{maintains} control-sufficient states through a unified \textbf{understanding, generation, and prediction architecture} equipped with \textbf{Hybrid Linear Temporal Attention}, where local, mid-range, and global temporal pathways support multi-timescale state maintenance under efficient inference. Third, it \textbf{deploys} these states through a \textbf{Deployment-Aware System Co-Design}, treating latency, memory footprint, and hardware compatibility as first-order constraints for future observation, action, and feedback loops. Experiments on embodied world-model benchmarks, world-action benchmarks, long-horizon generation, and inference-efficiency evaluation show that Kairos achieves superior performance while offering a favorable efficiency to capability trade-off.

cs.AI↗
arXiv2026

Beyond Entropy: Learning from Token-Level Distributional Deviations for LLM Reasoning

Reinforcement Learning with Verifiable Rewards (RLVR) has significantly advanced Large Language Model (LLM) reasoning; however, it faces a fundamental optimization instability: uniform token updates precipitate entropy collapse, leading to premature convergence to suboptimal strategies, whereas excessive Shannon Entropy maximization can cause entropy explosion, driving blind exploration toward incoherent reasoning chains. To resolve this dichotomy, we introduce the Independent Combinatorial Tokens (ICT) framework, which shifts the optimization focus from scalar uncertainty to the distributional properties of token logits. By leveraging the Jensen-Shannon (JS) divergence between token logits distributions, ICT identifies tokens with distinctive distributional patterns as critical branching points for guiding effective exploration in LLM reasoning. Our theoretical analysis, grounded in both Shannon and second-order Rényi entropy, proves that selectively updating on these tokens regulates policy concentration: it reduces the overall distribution uncertainty measured by Shannon entropy, while controlling probability concentration captured by second-order Rényi entropy. This dual effect prevents over-concentrated token generation from weakening exploration and effectively stabilizes the training landscape. Empirical results demonstrate that updating only the top 10% of unique tokens on Qwen2.5 (0.5B/1.5B/7B) models yields an average pass@4 improvement of 4.58%, with a maximum gain of 14.9%, over GRPO, 20-Entropy, and STAPO baselines across seven benchmarks spanning math, commonsense, and Olympiad-level problems.

cs.AI↗
arXiv2026

Mitigating Bias in Low-SNR Financial Reinforcement Learning via Quantum Representations

The financial market is a typical low signal-to-noise ratio (SNR) setting, which often destabilizes off-policy maximum-entropy methods like Soft Actor-Critic (SAC). Specifically, noisy state representations may produce unreliable Q-value estimates, and bootstrapping amplifies these errors, forming a failure mode we call the "Financial Entropy Trap". In this paper, we propose FPQC-SAC, an efficient and plug-and-play SAC variant that places a compact and bounded Parameterized Quantum Circuit (PQC) before the actor and critic networks to constrain feature propagation at the representation level, rather than filtering raw inputs or regularizing Q-values after bootstrapping. Notably, FPQC-SAC reduces the impact of extreme market fluctuations on Bellman target estimation, while trainable quantum entanglement preserves flexible cross-asset interactions. Empirical evaluations on real-world portfolio management tasks demonstrate that FPQC-SAC substantially enhances out-of-sample stability and cumulative returns by achieving a 66.89% relative gain in cumulative return over standard unconstrained SAC and outperforms the best continuous-control deep reinforcement learning baseline by approximately 27%. Open-source code is available at https://github.com/ZeyuLIU-UST/FPQC-SAC-main.

cs.LG↗
arXiv2026

Curvature-driven revival of charge density waves in non-Euclidean space

Strongly correlated quantum states, such as charge density waves (CDWs), are exquisitely sensitive to Fermi surface topology and lattice symmetry, and are typically quenched by heavy carrier doping. In two-dimensional (2D) systems, however, macroscopic geometric curvature emerges as a novel structural degree of freedom to modulate microscopic quantum coherence. This raises a compelling physical question: can non-Euclidean geometric deformations compete with extreme electronic perturbations to reshape, or even revive, a quenched macroscopic quantum order? Here, by constructing monolayer TiSe$_2$-NbSe$_2$ heterostructure on a BLG/SiC substrate for the first time, we report the curvature-driven revival of a frustrated charge order in a non-Euclidean space. Low-temperature angle-resolved photoemission spectroscopy (ARPES) reveals a massive interfacial charge transfer, which destroys the global Fermi surface nesting and completely suppresses the long-range CDW order in Euclidean flat regions. Strikingly, high-resolution scanning tunneling microscopy (STM) reveals that a novel, non-linear CDW state miraculously survives, remaining strictly localized within morphologically distorted, non-Euclidean nanoscale curved regions. Atomistic simulations unravel the structural origin of this phenomenon, demonstrating that interfacial twist and lattice mismatch spontaneously generate a corrugated superlattice.

cond-mat.mtrl-sci↗
arXiv2026

Linearizing Vision Transformer with Test-Time Training

While linear-complexity attention mechanisms offer a promising alternative to Softmax attention for overcoming the quadratic bottleneck, training such models from scratch remains prohibitively expensive. Inheriting weights from pretrained Transformers provides an appealing shortcut, yet the fundamental representational gap between Softmax and linear attention prevents effective weight transfer. In this work, we address this conversion challenge from two perspectives: architectural alignment and representational alignment. We identify Test-Time Training (TTT) as a linear-complexity architecture whose two-layer dynamic formulation is structurally aligned with Softmax attention, enabling direct inheritance of pretrained attention weights. To further align representational properties, including key shift-invariance and locality, we introduce key instance normalization and a lightweight locality enhancement module. We validate our approach by linearizing Stable Diffusion 3.5 and introduce SD3.5-T$^5$ (Transformer To Test Time Training). With only 1 hour of fine-tuning on 4$\times$H20 GPUs, SD3.5-T$^5$ achieves comparable text-to-image quality to the fine-tuned Softmax model, while accelerating inference by 1.32$\times$ and 1.47$\times$ at 1K and 2K resolutions. Code is available at https://github.com/LeapLabTHU/Transformer-to-TTT.

cs.CV↗
arXiv2026

Local Covariate Selection for Average Causal Effect Estimation without Pretreatment and Causal Sufficiency Assumptions

We study the problem of selecting covariates for unbiased estimation of the total causal effect.Existing approaches typically rely on global causal structure learning over all variables, or on strong assumptions such as causal sufficiency - where observed variables share no latent confounders - or the pretreatment assumption, which limits covariates to those unaffected by the treatment or outcome. These requirements are often unrealistic in practice, and global learning becomes computationally prohibitive in high-dimensional settings.To address these challenges, we propose a novel local learning method for covariate selection in nonparametric causal effect estimation that avoids both the pretreatment and causal sufficiency assumptions. We first characterize a local boundary that contains at least one valid adjustment set whenever one exists for identifying the causal effect, and then develop local identification procedures to efficiently search within this boundary.We prove that the proposed method is sound and complete. Experiments on multiple synthetic datasets and two real-world datasets show that our approach achieves accurate causal effect estimation while substantially improving computational efficiency.

stat.ML↗
arXiv2026

InsightTok: Improving Text and Face Fidelity in Discrete Tokenization for Autoregressive Image Generation

Text and faces are among the most perceptually salient and practically important patterns in visual generation, yet they remain challenging for autoregressive generators built on discrete tokenization. A central bottleneck is the tokenizer: aggressive downsampling and quantization often discard the fine-grained structures needed to preserve readable glyphs and distinctive facial features. We attribute this gap to standard discrete-tokenizer objectives being weakly aligned with text legibility and facial fidelity, as these objectives typically optimize generic reconstruction while compressing diverse content uniformly. To address this, we propose InsightTok, a simple yet effective discrete visual tokenization framework that enhances text and face fidelity through localized, content-aware perceptual losses. With a compact 16k codebook and a 16x downsampling rate, InsightTok significantly outperforms prior tokenizers in text and face reconstruction without compromising general reconstruction quality. These gains consistently transfer to autoregressive image generation in InsightAR, producing images with clearer text and more faithful facial details. Overall, our results highlight the potential of specialized supervision in tokenizer training for advancing discrete image generation.

cs.CV↗
arXiv2026

A $p$-adic Simpson correspondence for singular rigid-analytic varieties

Let $C$ be a complete, algebraically closed non-archimedean extension of $\mathbb{Q}_p$, and $X$ be a proper rigid-analytic variety over $C$. We show that the category of pro-étale vector bundles on $X$ is equivalent to the category of Higgs bundles on the $\eh$-site of $X$, thereby generalizing the work of Faltings and Heuer to arbitrary proper rigid-analytic varieties.

math.AG↗
arXiv2026

Bridging Krylov Complexity and Universal Analog Quantum Simulator

Quantum simulation of complex many-body systems beyond classical computational capabilities provides a promising route toward understanding novel quantum phases and their transitions. In particular, analog quantum simulators with global control fields have attracted considerable attention due to their potential to simulate arbitrary Hamiltonians and perform quantum computing tasks. However, a clear, quantitative measure for the complexity of implementing specific quantum operations in such systems is still lacking. In this Letter, we address this challenge by introducing generalized Krylov complexity, a concept originating from operator growth dynamics, as a direct diagnosis for this synthesis complexity. We construct the block Krylov basis generated by a set of Hamiltonians, which naturally organizes the operator space achievable through the simulator's native interactions and their nested commutators. By analyzing representative systems including Rydberg atom arrays, we demonstrate that the generalized Krylov complexity of a target operation serves as a strong predictor of the minimum time required for its realization. Our results establish Krylov complexity as an intuitive and predictive tool for designing efficient control protocols in analog quantum simulators.

quant-ph↗
arXiv2026

A Qualitative Test-Risk Mechanism for Scaling Behavior in Normalized Residual Networks

The scaling behavior, in which test performance often improves as model size and data increase, is a central empirical phenomenon in modern deep learning, yet its theoretical basis remains incomplete. In this paper, we study depth expansion in normalized residual networks: starting from a trained model in an old hypothesis class, we insert a new residual block at an intermediate layer and ask when such an expansion can yield a provable improvement in test risk. We develop a unified framework that decomposes this question into representational gain, optimization gain, and generalization transfer. First, under a first-order descent condition near zero initialization, we prove that the expanded hypothesis class contains an auxiliary jumpboard model with strictly smaller population risk than the original model. Second, under norm control tailored to post-normalized residual architectures, we establish a norm-based Rademacher complexity bound for the expanded model class. These ingredients lead to two complementary test-risk guarantees: one route passes through population risk and is tighter when a positive population margin is available, while the other works directly at the train/test level, avoids Hoeffding transfer, and is more robust in degenerate regimes. Together, these results provide a theorem-driven mechanism under which residual depth expansion can improve test performance in normalized residual networks. More broadly, they suggest that scaling is inherently joint: depth creates new improving directions, width enhances the finite-sample observability of weak signals, and data determines whether the statistical cost of expansion can be controlled.

cs.LG↗
arXiv2026

Steering Visual Generation in Unified Multimodal Models with Understanding Supervision

Unified multimodal models are envisioned to bridge the gap between understanding and generation. Yet, to achieve competitive performance, state-of-the-art models adopt largely decoupled understanding and generation components. This design, while effective for individual tasks, weakens the connection required for mutual enhancement, leaving the potential synergy empirically uncertain. We propose to explicitly restore this synergy by introducing Understanding-Oriented Post-Training (UNO), a lightweight framework that treats understanding not only as a distinct task, but also a direct supervisory signal to steer generative representations. By incorporating objectives that encode semantic abstraction (captioning) and structural details (visual regression), we enable effective gradient flow from understanding to generation. Extensive experiments on image generation and editing demonstrate that understanding can serve as an effective catalyst for generation.

cs.CV↗
arXiv2026

MambaBack: Bridging Local Features and Global Contexts in Whole Slide Image Analysis

Whole Slide Image (WSI) analysis is pivotal in computational pathology, enabling cancer diagnosis by integrating morphological and architectural cues across magnifications. Multiple Instance Learning (MIL) serves as the standard framework for WSI analysis. Recently, Mamba has become a promising backbone for MIL, overtaking Transformers due to its efficiency and global context modeling capabilities originating from Natural Language Processing (NLP). However, existing Mamba-based MIL approaches face three critical challenges: (1) disruption of 2D spatial locality during 1D sequence flattening; (2) sub-optimal modeling of fine-grained local cellular structures; and (3) high memory peaks during inference on resource-constrained edge devices. Studies like MambaOut reveal that Mamba's SSM component is redundant for local feature extraction, where Gated CNNs suffice. Recognizing that WSI analysis demands both fine-grained local feature extraction akin to natural images, and global context modeling akin to NLP, we propose MambaBack, a novel hybrid architecture that harmonizes the strengths of Mamba and MambaOut. First, we propose the Hilbert sampling strategy to preserve the 2D spatial locality of tiles within 1D sequences, enhancing the model's spatial perception. Second, we design a hierarchical structure comprising a 1D Gated CNN block based on MambaOut to capture local cellular features, and a BiMamba2 block to aggregate global context, jointly enhancing multi-scale representation. Finally, we implement an asymmetric chunking design, allowing parallel processing during training and chunking-streaming accumulation during inference, minimizing peak memory usage for deployment. Experimental results on five datasets demonstrate that MambaBack outperforms seven state-of-the-art methods. Source code and datasets are publicly available.

cs.CV↗
arXiv2026

Geometry-Aware State Space Model: A New Paradigm for Whole-Slide Image Representation

Accurate analysis of histopathological images is critical for disease diagnosis and treatment planning. Whole-slide images (WSIs), which digitize tissue specimens at gigapixel resolution, are fundamental to this process but require aggregating thousands of patches for slide-level predictions. Multiple Instance Learning (MIL) tackles this challenge with a two-stage paradigm, decoupling tile-level embedding and slide-level prediction. However, most existing methods implicitly embed patch representations in homogeneous Euclidean spaces, overlooking the hierarchical organization and regional heterogeneity of pathological tissues. This limits current models' ability to capture global tissue architecture and fine-grained cellular morphology. To address this limitation, we introduce a hybrid hyperbolic-Euclidean representation that embeds WSI features in dual geometric spaces, enabling complementary modeling of hierarchical tissue structures and local morphological details. Building on this formulation, we develop BatMIL, a WSI classification framework that leverages both geometric spaces. To model long-range dependencies among thousands of patches, we employ a structured state space sequence model (S4) backbone that encodes patch sequences with linear computational complexity. Furthermore, to account for regional heterogeneity, we introduce a chunk-level mixture-of-experts (MoE) module that groups patches into regions and dynamically routes them to specialized subnetworks, improving representational capacity while reducing redundant computation. Extensive experiments on seven WSI datasets spanning six cancer types demonstrate that BatMIL consistently outperforms state-of-the-art MIL approaches in slide-level classification tasks. These results indicate that geometry-aware representation learning offers a promising direction for next-generation computational pathology.

cs.CV↗