arXiv subjects

Tao Zhang

Publications and source records attributed to Tao Zhang.

At least 37 records · Page 2Linked to original sources

arXiv2026

VLMs are Native Action Models: Unleashing the Manipulation Capabilities of VLMs with Explicit Action-Space Grounding

Pretrained vision-language models (VLMs) already exhibit strong visual, spatial and reasoning capabilities relevant to robotic manipulation. The key challenge in turning pretrained VLMs into generalist manipulation policies is to expose these capabilities through an appropriate action interface. Vision-language-action (VLA) models provide a unified trainable policy, but typically introduce learned action tokens, action heads, or action experts whose semantics must be learned from robot data pretraining. In contrast, modular foundation-model-based manipulation methods can exploit pretrained VLM capabilities for zero-shot manipulation, but rely on external planning and control scaffolds that are not end-to-end trainable as a unified continuous-action policy. In this work, we introduce EASG, an Explicit Action-Space Grounding framework that bridges these two paradigms. By projecting a tool center point (TCP)-centered action frame into the wrist camera observation and expressing actions in the form of VLM's native textual generation interface, EASG makes the semantics of a continuous robot action space directly observable in the VLM's perceptual context. This allows pretrained VLMs to directly generate executable robot actions using their existing visual-spatial reasoning capabilities, without robot-action pretraining or additional action modules. Besides, the same action interface supports direct fine-tuning with robot trajectories, allowing the models to continuously improve beyond their manipulation capabilities unleashed by EASG. Overall, EASG enables zero-shot manipulation and generalization across object positions, categories, and robot embodiments, while supporting effective fine-tuning in the same continuous action space. These results demonstrate that, given an appropriate action interface, pretrained VLMs can themselves serve as native action models for robotic manipulation.

cs.RO↗

arXiv2026

Dual-Stream Memory for Vision-Language-Action Policies

Memory-dependent manipulation requires a policy to track execution state and recover visual evidence that is no longer observable. We propose dual-stream memory for vision-language-action policies, assigning these requirements to complementary representations. A task-agnostic Gated DeltaNet compresses history into one temporal token, supervised by progress prediction and action-conditioned feature reconstruction. A task-conditioned retriever retains frames above a fixed relevance threshold; linear multi-scale fusion encodes each frame into sixteen spatial tokens. We then freeze the temporal compressor and jointly optimize retrieval and policy learning. Across sixteen RoboMME tasks, the complete model achieves 49.22% mean success versus 44.51% for the published FrameSamp+Modul reference, improving fourteen tasks and all four suite means. On four real-robot tasks, mean success reaches 62.5% versus 37.5%, with the largest gains on repeated actions requiring execution-stage discrimination. These results support combining execution context with selective visual access, while failures under cup swaps expose persistent identity tracking as an unresolved requirement.

cs.RO↗

arXiv2026

Quantum Simulation of a Hyperbolically Driven Quantum System with Superconducting Circuits

Hyperbolic geometry hosts a plethora of exotic quantum phenomena ranging from holographic duality to novel topological phases. However, investigating these effects experimentally remains challenging due to the Euclidean constraints of natural crystalline materials. While recent synthetic lattices have achieved static realizations, they often lack the dynamical tunability required to explore the full geometric landscape. Here, we overcome these limitations by implementing a quantum simulation of hyperbolic geometry within the parameter space of a superconducting quantum circuit. We construct a Hyperbolically Driven Quantum System (HDQS) by mapping the hyperbolic properties onto the dynamically controllable Hamiltonian parameters. By probing the systems' response under geometric quantum driving, we elucidate how the intrinsic geometry of the parameter space dictates observable physical quantities. Furthermore, we extend the theoretical framework to realize ensemble simulation. This generalization enables us to harness the fast coherent control of superconducting qubits to capture essential geometric characteristics, establishing a versatile platform for exploring quantum dynamics on hyperbolic manifolds.

quant-ph↗

arXiv2026

Extending Structures for $n$-Lie Algebras

Motivated by the Casas-Loday-Pirashvili maps concerning representations of $n$-Leibniz algebras, we give an intrinsic characterization of the cohomology of $n$-Lie algebras with coefficient in a representation space $V$. We investigated the cohomology theory of $n$-Lie algebras in three different ways: cohomology theory of Leibniz algebras, infinitesimal deformation and abelian extension. In the main part of this paper, we solve the extending problems for $n$-Lie algebras. A necessary and sufficient unified-product criterion is obtained. The case of crossed products, sparse non-abelian extensions, matched pairs are studied as special cases. We also investigate the factorizations, deformation maps, and complements problem for $n$-Lie algebras. An appendix removes the general non-reduced unified product with all intermediate mixed components.

math.RA↗

arXiv2026

Faber-Krahn inequality for the first Dirichlet eigenvalues of the logarithmic Hardy operator

The purpose of this paper is to study Faber--Krahn inequality of Dirichlet eigenvalues $\{ λ^{\ln,μ}_{k}(Ω)\}_{k\in \N}$ for the logarithmic Hardy operator \[ \mathcal{L}_μ=(-Δ)^{\ln}+2μ\log\frac{1}{|x|} \] on a bounded Lipschitz domain $Ω\subset\mathbb{R}^{N}$ containing the origin, with $μ>-1$. We establish a Faber--Krahn inequality for $μ\in(-1,0)$, the ball centered at the origin minimizes the first eigenvalue at fixed volume, with equality only for that ball. Finally, we show this inequality fails for $μ>0$ via an explicit two-ball-and-tube construction.

math.AP↗

arXiv2026

Feature Information Dynamics in Diffusion

Diffusion models generate data through a continuum of denoising problems, and are widely observed to reveal coarse structure before fine detail. Yet, this intuition is mostly empirical and qualitative. We introduce feature information dynamics, an information-theoretic framework for localizing when a feature is generated during diffusion. Using the I-MMSE identity, we connect the rate of feature mutual information change to a gap between optimal unconditional and feature-conditional denoising losses, yielding practical estimators for feature information density. We further develop a chained decomposition that separates shared from incremental information in a feature hierarchy. We use this framework first to quantitatively confirm spectral autoregression in pixel diffusion, and then to extend the analysis beyond frequency: under a class $\to$ mask $\to$ Canny conditioning chain, the per-feature information densities differ across pixel, SDVAE, VAVAE, and RAE, exposing fundamental differences between these representations and suggesting that ordered generation could be beneficial for training diffusion models. Our code is available at https://github.com/AI4Science-WestlakeU/feature-information-dynamics.

stat.ML↗

arXiv2026

Execution-Aligned Progressive Noise for Consistent Asynchronous Replanning in Generative Robot Policies

Continuous asynchronous replanning is essential for real-time generative robot policies, but independent stochastic initialization can cause mode switching and inconsistent continuation across action chunks. We propose Execution-Aligned Progressive Noise (EAPN), which introduces structured stochasticity at both inter-chunk and intra-chunk levels. Across replanning steps, EAPN propagates a shared noise trajectory and aligns it with the actual execution displacement, establishing execution-aligned inter-chunk correlation. Within each action chunk, it models temporal correlation along action time. The aligned stochastic history is further combined with committed action context to condition subsequent generation, allowing new chunks to continue from execution-consistent generative states rather than restart from independent noise. We evaluate EAPN on D3IL, Kinetix, LIBERO, and real-world manipulation tasks. EAPN improves multimodal behavior consistency on D3IL and achieves an average success rate of 88.59% on Kinetix. On LIBERO, it remains robust and maintains strong task performance even under long inference delays. Real-robot experiments further achieve 90.0% success on Object Storage and 96.7% on bimanual Cloth Folding, demonstrating reliable continuous execution under asynchronous replanning.

cs.RO↗

arXiv2026

Conditional Trajectory Peaks: Single-Pass Multimodal Policies over Action Chunks

Multimodal imitation learning requires diverse executable futures under the same observation and consistent behavior across replanning cycles. We present Conditional Trajectory Peaks (CTP), a single-pass policy framework that jointly predicts complete action-chunk candidates, probability masses, and trajectory scales. Distribution-Aware Peak Specialization (DAPS) specializes trajectory peaks using trajectory-level posterior responsibilities and mass- and scale-modulated overlap constraints. Evidence-Gated Trajectory Belief Transport (ETBT) maintains cross-chunk consistency through geometric correspondence between exchangeable candidate sets, while allowing current policy evidence to override historical constraints. CTP achieves a coverage score of 91.40% on Push-T; success rates of 100.0%, 79.72%, and 84.44% on D3IL Avoiding, Aligning, and Sorting-2, respectively. On LIBERO, CTP achieves an average success rate of 97.25%. In real-world dual-arm experiments, CTP preserves both placement modes in a two-plate task, succeeding in all 50 trials. On bottle uprighting and pen placement into a holder, it maintains success rates comparable to $π_{0.5}$ while reducing policy inference latency from 218.24 ms to 75.80 ms. These results demonstrate that single-pass trajectory modeling can combine multimodal behavior, closed-loop consistency, and efficient inference.

cs.RO↗

arXiv2026

Toward Real-Time VLAs: Stage-Aware Two-Step Flow Denoising and System-Level Evaluation

Vision-language-action (VLA) models face a timing gap between low-rate inference and high-rate robot execution. We characterize this gap through end-to-end latency measurements of model inference and the robot execution chain. Repeated Flow Matching denoising contributes substantially to inference cost, while robot-side delays mainly arise from perception acquisition, communication scheduling, and physical response. Analysis of the velocity field shows relatively stable magnitude and direction in early integration, followed by stronger directional correction near the terminal steps. Based on this stage heterogeneity, we propose two-stage non-uniform denoising, reducing the number of steps from 10 to 2 and model-inference time from 61.557 ms to 21.956 ms. We also develop a distributed real-time VLA framework with independent inference, action-publication, and robot-control rates, modular observation acquisition, and action-provenance logging. Using π0.5 as the baseline, we evaluate six real-time execution methods on a long-horizon physical garment-folding task. Legato performs best overall among training-based methods, while Temporal Smoothing leads among training-free methods; both perform strongly in task success, completion time, action continuity, and acceleration smoothness. Combining two-step denoising with representative execution methods substantially reduces inference cost with a small reduction in task performance. These results motivate joint optimization of model-inference efficiency and robot-system timing.

cs.RO↗

arXiv2026

Magic-W0: A Structured World-Action Foundation Model for Physical Intelligence

World-action models (WAMs) augment robot policies with action-conditioned environment dynamics, yet existing approaches largely rely on future observation reconstruction or generic latent prediction and lack structured, control-oriented world representations tightly coupled with action generation. We introduce Magic-W0, a world-action foundation model that jointly models structured physical state evolution and continuous actions. Magic-W0 represents interaction as a Structured World Transition consisting of Current State, Transition, and Future State. Current State combines vision-language context with Current 3D Geometry; Transition is represented by 3D Motion capturing action-induced three-dimensional changes; and Future State is represented by Future Semantics describing task-relevant outcomes. To couple prediction and control, we propose a layer-aligned world-action interaction architecture in which evolving action hypotheses condition world-transition prediction, while predicted world representations continuously inform action generation. Magic-W0 is pre-trained on large-scale egocentric human manipulation, UMI, real-robot, and simulation data, with latent supervision for geometry, 3D motion, and future semantics from pre-trained visual models. Inference-time interventions show that structured world representations respond systematically to changes in candidate actions and that action-related information propagates through shared 3D representations into future semantic predictions. On RoboDojo-Sim, Magic-W0 achieves an average Score of 27.10, the highest among the compared WAMs. Across multiple real-robot tasks, it also demonstrates strong downstream performance after fine-tuning with limited downstream data, supporting generalization and rapid adaptation.

cs.RO↗

arXiv2026

Exact Clifford Optimality for Two-Sided Locally Randomized Classical Shadows

Entangling measurements can reduce the statistical cost of learning many-body correlations. We study Pauli strings with full support on a specified $k$-qubit region using classical shadows with two independent, uniformly random product single-qubit Clifford layers around a controllable unitary acting on that region, followed by computational-basis readout. In this architecture, we prove that a circuit $U_*$ of two collective Pauli rotations attains the exact minimum squared shadow norm over all Clifford choices of the controllable unitary for every $k\geq1$, namely $C_k^{\rm opt}=4\cdot 9^k/(3\cdot 5^k+3^k-6)$ for odd $k$ and $C_k^{\rm opt}=4\cdot 9^k/(3\cdot 5^k-3^k+2)$ for even $k$. The asymptotic optimum $(4/3)\cdot(9/5)^k$ establishes Wu et al.'s exponential base as optimal and improves their prefactor from $2$ to $4/3$. For $1\leq k\leq6$, exact rational certificates prove that the same optimum holds over the entire unitary group $\mathrm U(2^k)$, including all non-Clifford unitaries, within the same measurement architecture. These finite-size results motivate the conjecture that $U_*$ is optimal over all unitaries for arbitrary $k$ within this architecture.

quant-ph↗

arXiv2026

Neural Correlation Learning for Quantum-Enhanced Sensing with Time-Independently Driven Rydberg Atom Arrays

Quantum-enhanced sensing typically relies on preparing specific entangled states. However, engineering these states in scalable many-body systems remains challenging due to the difficulty of designing robust preparation protocols and accounting for realistic noise. We show that evolving a simple product state under native time-independent Hamiltonian dynamics in Rydberg atom arrays generates complex many-body correlations that can potentially enable quantum-enhanced parameter estimation reaching the Heisenberg limit (HL). The key challenge is then shifted to extracting the metrological information encoded in spatial correlations of measurement patterns. We introduce a neural correlation learning framework that combines Bayesian inference with neural networks trained on calibration data. Operating in a two-stage calibration-and-sensing protocol, we numerically demonstrate that this framework effectively extracts many-body correlations to saturate the Cramér--Rao bound dictated by the classical Fisher information. Consequently, it achieves quantum-enhanced sensitivity surpassing the standard quantum limit (SQL). Furthermore, the learned estimator is robust to realistic noise, and remains accurate in the absence of rare measurement patterns. Our results establish a hardware-efficient and scalable paradigm for quantum sensing in interacting many-body systems without requiring engineered entangled states.

quant-ph↗

arXiv2026

Protecting Sensitive Data in Image Synthesis via PAC-Private Adaptation for Diffusion Models

Synthetic data are increasingly used as an alternative to sharing sensitive records. However, synthetic data generation does not guarantee privacy, as diffusion models trained or adapted on sensitive data remain susceptible to reconstruction attacks. Moreover, while approaches that use differential privacy (DP), such as DP-SGD, achieve provably private diffusion model training, the repeated gradient clipping and noise injection they require result in significant utility loss. An important limitation of DP-based privacy is that, although it has a provable relationship to reconstruction privacy (RP), that relationship is indirect. RP is defined in terms of limiting how much an adversary's posterior distribution over sensitive data differs from the prior, whereas DP provides guarantees by bounding the sensitivity of outputs to changes in individual records. This indirection is an important source of the utility loss. To address this, we propose a PAC-private diffusion model adaptation to achieve reconstruction privacy. Since PAC-privacy is defined directly with respect to posterior advantage over the prior, it directly implicates RP. To obtain scalable PAC privatization in high dimensions, we first learn a compact data-dependent diffusion model component using LoRA or Textual Inversion, and then calibrate anisotropic Gaussian noise from the covariance of repeated mechanism outputs. Unlike DP-SGD, our method perturbs the learned component only once after optimization, thereby avoiding privacy composition across gradient updates. We evaluate the framework on few-shot concept personalization and full-dataset image synthesis, and show that the proposed approach better preserves subject identity, generation quality, and downstream classification accuracy than DP while achieving the same reconstruction privacy.

cs.LG↗

arXiv2026

Wells exact sequences for $n$-Lie algebras

We study derivations and automorphisms of arbitrary non-abelian extensions of $n$-Lie algebras through their full crossed-product data. Their relative center is a canonical coefficient module, and a third cohomology class obstructs completion of data satisfying the mixed Filippov identities. When this class vanishes, a relative second cohomology space classifies the remaining extension data. We prove a non-abelian good criterion, construct the Lie algebra and group of compatible pairs, and obtain derivation and automorphism Wells sequences with explicit lifting equations. The derivation obstruction is a Lie algebra $1$-cocycle; the additive automorphism obstruction is a crossed homomorphism. We distinguish the ordinary center from the relative center, and outer derivations of the kernel from the mixed action required. Sparse crossed products are treated, including the representation class of their second mixed operation and the additional equations governing changes of sparse sections.

math.RA↗

arXiv2026

DAMP: Decay-Aware Mixed-Precision Recurrent-State Quantization

Complex reasoning and agentic applications increasingly rely on long-context inference, where growing KV caches increase both memory usage and decoding overhead. Hybrid models reduce these costs by combining Softmax Attention with Gated DeltaNet (GDN) or Kimi Delta Attention (KDA), which maintain fixed-size recurrent states. These states are commonly stored in FP32 and consume substantial GPU memory, while their updates are limited by memory bandwidth. Quantization can reduce both storage footprint and memory traffic, but we find that uniform INT8 and FP8 degrade complex reasoning accuracy, while INT4 and NVFP4 collapse it to near zero. To our knowledge, this is the first study of post-training recurrent-state quantization for GDN and KDA. Our analysis reveals that outliers in GDN and KDA states are concentrated in particular key channels and value dimensions. Learned decay influences how much quantization error is retained. We find that largely the same GDN heads and KDA key channels exhibit slow decay across tasks. Based on these insights, we propose DAMP, which jointly considers quantization error and decay-based error retention to select high-risk key channels offline. Under a fixed storage budget, it retains these channels in FP16 and stores the remainder in INT8. We evaluate DAMP on Qwen3.6-35B, Kimi-Linear-48B and Kimi-K3 across six reasoning and code generation benchmarks. At 9.9 bits per state value, DAMP maintains average accuracy close to FP32. In SGLang, DAMP reduces recurrent-state storage by 69.1%, accelerates the recurrent-state update kernel by up to 2.59x , and lowers full-model time per output token by up to 19.0%.

cs.LG↗

arXiv2026

QuantMLA: Function-Aligned Dual-Path Quantization for Low-Bit MLA KV Caching

Multi-Head Latent Attention (MLA) enables expressive multi-head attention with compact caches for its content and decoupled RoPE paths, yet cache memory still scales linearly with context length and batch size. In this work, we establish a systematic model of MLA's dual-path quantization errors, characterizing their distinct effects on attention-output distortion and explaining the pronounced amplification of RoPE-path errors. Guided by this analysis, we introduce QuantMLA, a function-aligned framework for low-bit dual-path quantization. We derive path-specific transformation spaces that preserve full-precision computation while remaining fully fusible into model parameters offline, eliminating online transformation overhead. Within these spaces, QuantMLA learns path-specific transformations with function-aligned objectives: attention-output reconstruction captures the content path's coupled matching and aggregation errors, while positional QK reconstruction preserves the RoPE-induced component of the attention logits and admits a theoretical bound on output distortion. Across four MLA model families, QuantMLA enables, to our knowledge, the first reported joint INT4 caching of the content and RoPE caches with minimal accuracy degradation. Further compressing the content cache to INT2 while retaining the RoPE key cache at INT4 maintains competitive performance on challenging reasoning and code benchmarks. We develop a native low-bit MLA attention kernel that integrates unpacking and dequantization directly into attention computation. The physical cache layout provides 3.59x compression at 128K context, while a cache-pressure serving workload achieves 5.168x higher whole-job output throughput than BF16. The code will be released upon acceptance.

cs.LG↗

arXiv2026

Soliton resolution conjecture for the Calogero--Moser derivative nonlinear Schrödinger equation in the scaling-critical space

We prove the soliton resolution conjecture for the Calogero--Moser derivative nonlinear Schrödinger equation in the scaling-critical space $L^2_+(\mathbb R)$. For a natural class of initial data including a broad spectral Dini---moment class, global flow--Lax admissible solutions decompose into finitely many explicit modulated solitons plus a dispersive radiation, while finite-time blow-up solutions resolve into quantized zero-carrier $R$-bubbles and a strongly convergent endpoint remainder. This work extends soliton resolution to the optimal critical regularity. Previous results had required weighted $H^{1,1}$ initial data, and in the global case the solution was additionally required to remain in $H^{1,1}$ for all time, which amounts to an extra spatial decay assumption. One key ingredient in our argument is a new modular operator-theoretic framework that separates the discrete and continuous spectral channels and identifies the radiation profile through the distorted Fourier transform. A second ingredient is the development of several independent rigidity criteria for the discrete soliton profiles, which avoids inverse scattering and handles embedded eigenvalues. Our framework also yields a unified description of both global and finite-time asymptotics, with exact mass partition and mass-defect quantization.

math.AP↗

arXiv2026

Mean Field Games and Control on Large Expander Graphs

This paper investigates mean field games on sparse networks. In the case of large expander graphs, the limit topologies are analyzed using the graphexon framework, which characterizes sparse connections. We prove that the associated sequence of discrete averaging operators converges strongly to a continuous operator and this is illustrated in the development of infinite limits of Gabber-Galil-Margulis expander graphs \cite{gabber1981explicit}. These properties enable the formulation and existence proof of equilibria for linear-quadratic mean field games in which each agent is identified by a spatial network label $α\in X$ and only interacts with the neighborhood average characterized by the operator $\mathcal{G}$, i.e., the average state of a limited number of connected neighbors in a large expander graph. Furthermore, algebraic conditions induced by the spectral gap of $\mathcal{G}$ for the global asymptotic stability of the closed-loop system are established, and parameter thresholds that give rise to a Turing-type topological instability are established.

math.OC↗