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Lei Zhang

Publications and source records attributed to Lei Zhang.

At least 73 records · Page 4Linked to original sources
arXiv2026

Non-convex optimal control governed by nonlinear elliptic partial differential equation: Analysis, functional-based algorithm and control landscape

Non-convex optimal control arises from various applications but may contain multiple stationary points. Classical solvers usually perform a local search and therefore rely on good initial guesses to reach appropriate local optimal controls. In this work we introduce a novel solution strategy for the non-convex optimal control of an elliptic equation, the main idea of which is to construct the control landscape based on the functional high-index saddle dynamics (FHiSD) method. This method reduces the dependence on prescribed initial guesses by using the information of high-index saddle points, and depicts the macroscopic configuration of the space of the control variable. Then various minima could be systematically computed along transition pathways and the control strategy can then be selected among them. We prove the existence of the optimal control, and then propose and analyze the FHiSD in locating saddle points. Subsequently, the applicability of FHiSD in non-convex optimal control is rigorously justified. Numerical results not only indicate the effectiveness of the proposed method, but reveal unintuitive phenomena (e.g. the non-monotonicity of the values of the cost functional with respect to the Morse indices) that support the necessity of computing multiple solutions of high indices.

math.OC↗
arXiv2026

A High-Accuracy Numerical Homogenization Method for Quasiperiodic Hamilton--Jacobi Equations

In this work, we develop an accurate numerical homogenization method for computing effective Hamiltonians of quasiperiodic Hamilton--Jacobi equations (QHJEs) with convex Hamiltonians of the form $H(x,p) = |p|^k/{k}-f(x), ~k>1$, where $f$ is quasiperiodic. Computing effective Hamiltonians in the quasiperiodic setting requires solving QHJEs posed on the whole space. Their solutions generally possess neither translational symmetry nor decay and may exhibit low regularity. These features pose substantial challenges for numerical computation. To address these difficulties, we introduce a quasiperiodic boundary condition, which allows the original whole-space problem to be treated on a bounded domain while preserving quasiperiodicity at the boundary. We then propose an SL--FPR scheme that combines a semi-Lagrangian (SL) approximation with the finite points recovery (FPR) method and establish stability and error estimates for the resulting scheme. We also extend the quasiperiodic homogenization result from the quadratic case to general $k>1$ and apply the proposed method to accurately approximate the corresponding effective Hamiltonians. Numerical experiments illustrate the convergence and applicability of the method and validate the extended homogenization results.

math.NA↗
arXiv2026

Multivariate quantum signal processing with optimal query complexity

Polynomial transformations of data encoded in quantum operations are a building block of quantum algorithms, and their query complexity measures how often those operations are used. For multiple variables, existing methods either realize restricted polynomial families or implement monomials separately at a query cost exponential in the number of variables. We present a quantum circuit that implements every multivariate trigonometric polynomial up to an explicit normalization. The circuit processes one variable coherently over the frequency components of the remaining variables, allowing all components to share the same signal queries. Each variable is queried exactly as many times as its degree in the polynomial, and we prove that this query complexity is optimal. We further extend the construction to commuting unitaries. The resulting circuit applies the multivariate polynomial simultaneously across their shared eigenbasis, using the minimum numbers of forward and inverse queries to each unitary. We also study trainable rotations with fixed preparation and a local readout of the last input. At query depth at least two, independent uniform initialization gives every active readout gradient a variance lower bound set by its squared branch weight and the inverse square root of the depth, uniformly over data states and dimensions. For supervised squared loss, retaining sample correlations gives an initialization gradient-variance bound in terms of targets and input spectra. This also bounds the expected loss decrease after the first exact gradient step with a specified step size. These results provide a scalable and practical solution for developing multivariate quantum algorithms and quantum learning models.

quant-ph↗
arXiv2026

Guide, Think, Act: Interactive Embodied Reasoning in Vision-Language-Action Models

In this paper, we propose GTA-VLA(Guide, Think, Act), an interactive Vision-Language-Action (VLA) framework that enables spatially steerable embodied reasoning by allowing users to guide robot policies with explicit visual cues. Existing VLA models learn a direct "Sense-to-Act" mapping from multimodal observations to robot actions. While effective within the training distribution, such tightly coupled policies are brittle under out-of-domain (OOD) shifts and difficult to correct when failures occur. Although recent embodied Chain-of-Thought (CoT) approaches expose intermediate reasoning, they still lack a mechanism for incorporating human spatial guidance, limiting their ability to resolve visual ambiguities or recover from mistakes. To address this gap, our framework allows users to optionally guide the policy with spatial priors, such as affordance points, boxes, and traces, which the subsequent reasoning process can directly condition on. Based on these inputs, the model generates a unified spatial-visual Chain-of-Thought that integrates external guidance with internal task planning, aligning human visual intent with autonomous decision-making. For practical deployment, we further couple the reasoning module with a lightweight reactive action head for efficient action execution. Extensive experiments demonstrate the effectiveness of our approach. On the in-domain SimplerEnv WidowX benchmark, our framework achieves a state-of-the-art 81.2% success rate. Under OOD visual shifts and spatial ambiguities, a single visual interaction substantially improves task success over existing methods, highlighting the value of interactive reasoning for failure recovery in embodied control. More details of the project can be found here: https://github.com/FutianLabs/GTA-VLA.

cs.RO↗
arXiv2026

From Energy-Force Weighting to Primal-Dual Optimization of Machine-Learned Interatomic Potentials

Machine-learned interatomic potentials are commonly fitted by weighted-sum scalarization, which combines energy and force errors in a single loss. A nominal weight, however, identifies a potential only relative to the complete fitting protocol. We therefore treat energy--force balancing as a protocol-dependent problem of physical model selection. For fixed-basis atomic cluster expansion models of molten LiCl, liquid H$_2$O, and Si, the resulting scalarization paths contain dominated states at extreme weights. Their nondominated subsets depend on the solver, and the out-of-distribution Si path is nonmonotone. We replace direct weight selection by minimizing the regularized energy objective subject to an upper bound on the normalized force loss. Projected dual ascent adjusts the Lagrange multiplier from the force-constraint residual. A frozen-multiplier limited-memory quasi-Newton refinement then returns the final model. Across the three systems, the constrained procedure reaches the solver-matched low-error region and gives measured speedups of $6.7$--$8.9$ over completed scalarization scans under the stated timing convention. Physical-property calculations show that first-shell geometry is comparatively insensitive to the selected balance, whereas transport and solid-state observables vary more strongly. These results identify the fitted model--protocol pair as the relevant object of energy--force model selection and support force-constrained fitting as an explicit selection rule.

physics.comp-ph↗
arXiv2026

Fyan: A Human--AI Harness with Semantic Auditing for Document-Level Formalization

We present FYAN, a human--AI harness for document-level mathematical formalization. Rather than treating theorems in isolation, FYAN coordinates an end-to-end workflow spanning specification, proof planning, logical review, Lean proof construction, knowledge curation, and validation, with support for independent supervision and human guidance. A central component is evidence-grounded semantic auditing, which assesses whether formal statements faithfully preserve their informal specifications. A language model constructs structured evidence over local correspondences, omissions, scope, and logical relations, while a deterministic validator checks this evidence and produces reproducible judgments. When a substantive but admissible deviation is accepted, FYAN requires an explicit proof-transfer obligation connecting the formal statement back to a source-facing interpretation. With the same model (DeepSeek-V4.1-Flash) in every stage, FYAN proves 86 of 143 FormalTCS theorems under a strict Lean check, against 69 for a general agent harness, and raises the natural-language proof score from 0.501 to 0.851. On ConsistencyCheck, its semantic audit catches more inconsistent statements than a direct LLM judge, both on labels verified against the source (recall 0.777 vs. 0.636) and on the original labels (0.873 vs. 0.820), and localizes each mismatch it reports to a specific hypothesis, conclusion, or scope. FYAN also built ODENumLib, a 9,355-line Lean library for the numerical analysis of ordinary differential equation.

cs.AI↗
arXiv2026

Federated Calibration of Motion Uncertainty for UAV Tracking in Multi-Operator ISAC Systems

In integrated sensing and communication (ISAC) systems involving multiple operators, unmanned aerial vehicle (UAV) tracking can benefit from sensing at multiple base stations, while raw sensing records, channel information, and transmit decisions remain local to each operator. The resulting problem is to obtain a reliable UAV prediction from different track estimates and use it to guide transmission without centralizing their data or control variables. To resolve this, we propose a two-timescale framework comprising slow-timescale motion-uncertainty calibration and online track fusion with predictive beamforming. Local radar innovations calibrate the uncertainty assigned by each tracker to unmodeled UAV motion, with only the resulting parameters shared across operators. During online tracking, covariance intersection (CI) combines local estimates without requiring knowledge of correlations between their estimation errors. The fused prediction then guides each operator's transmission design subject to communication QoS, power, and tracking constraints. We further establish exact rank one recovery for the communication covariances and finite interval bounds on local tracking uncertainty. Simulations show improved consistency of tracking uncertainty under substantial motion model mismatch. CI avoids overconfidence under correlated errors, while using the current fused prediction reduces RMSE by about 31% relative to transmission designed for communication alone, with less than 2% additional power. Ablation further shows that the power difference between current and outdated predictions is driven mainly by predictive covariance rather than predictive mean.

cs.IT↗
arXiv2026

Potential isotriviality of isocrystals and proper covers

We study convergent and overconvergent isocrystals that become trivial after pullback along a proper surjective morphism. On a geometrically unibranch variety over an algebraically closed field, every such object is already trivialized by a finite étale cover. Over a perfect field, this shows that a proper cover giving geometric triviality can be replaced by a finite étale cover over the ground field, and implies finiteness of the geometric monodromy group. For proper geometrically unibranch varieties, finite geometric monodromy is also sufficient. In the overconvergent case, a dominant morphism can replace the given proper cover. A nodal curve shows why the geometrically unibranch hypothesis is needed.

math.AG↗
arXiv2026

On Evaluating Quantum Kernel Robustness for Low-Resource Cross-Corpus Audio Deepfake Detection

Synthetic speech detection is critical for audio security, but performance can degrade when labeled data are scarce and evaluation conditions differ from training. This study examines quantum kernel methods and lightweight neural models for cross-corpus audio deepfake detection under limited training data. We compare a Quantum Support Vector Machine (QSVM), a classical support vector machine (SVM), and a multilayer perceptron (MLP), all trained on frozen wav2vec 2.0 embeddings using a strict budget of 200 training samples. To match the qubit budget of near-term quantum hardware, embeddings are reduced to four dimensions using principal component analysis, and all models use the same reduced features. Experiments on ASVspoof 2019, ASVspoof 5, the ADD 2023 Challenge, and the In-the-Wild dataset show that under severe domain shift from ASVspoof 2019 to ADD 2023, the MLP degrades to near-random performance, with an area under the curve of approximately 50% and an equal error rate of 50.0%. In contrast, the QSVM maintains meaningful discrimination, achieving an area under the curve of 76.0% and an equal error rate of 27.0%. This advantage is not consistent across transfer directions. When trained on ADD 2023, the QSVM falls below chance on two of three transfers, while the MLP performs better. These results suggest that quantum kernel methods can be competitive under severe cross-corpus shifts and strict low-resource constraints, but do not provide a consistent advantage under near-domain transfer. We interpret these findings as an empirical characterization of quantum kernel inductive bias under distribution shift, rather than evidence of quantum advantage, since the four-qubit kernel can be simulated exactly on classical hardware.

cs.SD↗
arXiv2026

Unified-protocol voxel-level pulmonary embolism annotations for three public CT angiography datasets

Reliable clot-volume quantification and subsequent risk assessment in pulmonary embolism depend on precise segmentation of emboli on computed tomography pulmonary angiography. Deep learning models for this task must be trained on accurate voxel-level labels. The three public datasets that provide such labels were annotated under different protocols, and some of their studies contain unlabeled emboli or labels that are discontinuous across slices. This Data Descriptor presents voxel-level pulmonary embolism annotations for 149 of the 166 studies in these datasets. A primary rater drew all annotations under a single protocol. A thoracic radiologist with more than 20 years of experience reviewed and revised them. Three raters at three different centers independently annotated a subset of 15 studies. The subset was selected by source dataset and embolus location. Technical validation quantifies volumetric agreement with the source annotations, changes in within-mask attenuation, and inter-rater agreement on the subset. The dataset is intended to allow segmentation models to be developed and compared under a common reference standard.

eess.IV↗
arXiv2026

LDM-is-AE: Latent Diffusion Model is an Auto-Encoder for End-to-End Image Generation

Latent Diffusion Models (LDMs) typically adopt a two-stage pipeline: an auto-encoder (AE) is first pre-trained to define a latent space, then a diffusion model is trained to perform denoising within it. Such a two-stage design introduces a representation mismatch, as the latent space is optimized for reconstruction rather than adapting the denoising dynamics. We reveal that the LDM itself is an AE, and consequently present LDM-is-AE, an end-to-end one-stage LDM training framework that eliminates the need for a separately trained tokenizer. Our key observation is that the LDM backbone actually performs a latent-to-feature-to-latent transformation at each denoising step, which can be interpreted as an internal decoding--encoding process. Leveraging this structure, we split the DiT backbone into two reciprocal components, DiT-E (i.e., DiT Encoding) and DiT-D (i.e., DiT Decoding), and impose image-space supervision on the intermediate features across all timesteps. Our model encourages the internal representation to align with the image domain throughout denoising, thereby establishing an explicit latent-to-image-to-latent path. At the zero-noise timestep, our model further performs an image-to-latent-to-image mapping, corresponding to an auto-encoding process. As a result, LDM-is-AE jointly learns latent representations and denoising dynamics in an end-to-end manner, yielding a diffusion-native latent space tailored to the generation process. Experiments demonstrate that LDM-is-AE exhibits highly competitive generation performance, achieving an FID of 1.80 and 1.90 on 256x256 and 512x512 class-conditional image generation, respectively.

cs.CV↗
arXiv2026

Global well-posedness and scattering for energy-critical Schrodinger equations with conservative Marcus noise

This work establishes global well-posedness for the three-dimensional defocusing energy-critical nonlinear Schrödinger equation with conservative linear Marcus noise. For arbitrary deterministic energy-space data, we construct a probabilistically strong solution, unique in the critical spacetime class, and prove convergence of finite-activity approximations. The spatial profiles need only be bounded and Lipschitz, while the centered pure-jump Lévy noise is assumed to have finite second moment. If the temporal noise coefficient is square integrable on the half-line, the solution scatters almost surely, with uniform mean-square tail convergence and no smallness restriction. The solution conserves mass and satisfies an exact energy balance. The proof combines deterministic energy-critical stability with Poisson Strichartz estimates; convergence of the interaction-representation martingale gives the critical spacetime control needed for continuation and scattering.

math.AP↗
arXiv2026

Flash EQ-Linear: Accelerating Equivariant Linear Layers via Group-wise Discrete Fourier Transform

Equivariant networks embed geometric symmetries as structural priors through weight sharing, achieving remarkable parameter efficiency across vision tasks. However, this parameter efficiency does not translate into compute efficiency: most existing implementations unroll the structured weights into dense matrices and dispatch them to generic dense kernels, so an equivariant layer costs no fewer MACs than its non-equivariant counterpart. In this paper, we observe that the equivariant linear (EQ-Linear) layer---the most fundamental and frequently used module in modern equivariant architectures---is essentially a circular convolution along the group dimension composed with a linear transform along the channel dimension. Building on this observation, we propose Flash EQ-Linear, an exact acceleration algorithm that reduces the cost to $2(T-1)/T^2$ of the original dense formulation ($T$ is the equivariant group size) by combining the Fourier convolution theorem along the group dimension with the conjugate symmetry of the real DFT. To translate these computational savings into wall-clock speedups, we further develop dedicated CUDA kernels for the $\mathrm{p}4$ group. At the operator level, Flash EQ-Linear achieves up to $2.1\times$ forward speedup over PyTorch's highly optimized F.linear; at the network level, Flash EQ-ViT achieves up to ${1.7\times}$ end-to-end speedup over both equivariant and non-equivariant baselines. As an operator-level acceleration algorithm, Flash EQ-Linear provides plug-and-play acceleration for diverse pretrained equivariant models, including EQ-ViT, EQ-Swin, EQ-VMamba, and EQ-INR, without retraining or architectural changes. Code is available at https://github.com/zhongchenzhao/FlashEQLinear.

cs.CV↗
arXiv2026

PIVOT: Pivot-Aware On Policy Self Distillation for Multi-Turn VLM Agents

Reinforcement learning with verifiable rewards (RLVR) via Group-Relative Policy Optimization (GRPO) is widely used for multi-turn VLM agent training, yet it suffers from zero-gradient silence on uniform failures and coarse episode-level credit assignment. While On-Policy Distillation (OPD) and On-Policy Self-Distillation (OPSD) mitigate sparse rewards using hindsight information, their underlying mechanisms remain poorly understood. Through controlled counterfactual rollback probes across five multi-turn VLM agent benchmarks, we reveal that performance gains in OPSD/OPD are largely driven by physical state rollback at the pivot step, defined as the first unrecoverable action without remaining step budget. However, physical state rollbacks are computationally prohibitive and infeasible in real-world environments. To bridge this gap, we present Pivot-Aware Internalized Visual On-Policy Training (PIVOT), an RL framework that internalizes pivot localization and state restoration directly into token-level parameter updates, eliminating environment rollbacks during RL training and additional skill hints at test time. PIVOT unifies three functional roles within a single architecture: a failure Analyzer non-invasively localizes the pivot step and diagnoses failure modes from visual trajectory collages and action logs; a detached Teacher re-scores failed tokens under this privileged diagnostic context; and a Student optimizes joint GRPO and confidence-gated OPD objectives. At test time, both Teacher and Analyzer branches are stripped. Evaluated on five multi-turn VLM agent tasks across cognitive grid puzzles, 3D embodied control and navigation, and generative reasoning, PIVOT achieves 0.90 overall accuracy on Qwen2.5-VL-3B (+8% over SFT+GRPO baseline and +5% over previous SOTA) and scales to 0.92 on Qwen3-VL-2B (+12% over SFT+GRPO baseline).

cs.CV↗
arXiv2026

LAGO: Language-Guided Adaptive Object-Region Focus for Zero-Shot Visual-Text Alignment

Zero-shot visual recognition often depends on localized parts, attributes, and textures that are diluted in global image representations. Existing training-free localized methods alleviate this limitation by evaluating multiple image regions, but their candidate locations are typically generated before class semantics determine where to look, restricting language to post-hoc scoring of already sampled evidence. We introduce LAGO (LAnguage-Guided adaptive Object-region focus), which reframes localized recognition as language-guided directed region discovery. LAGO first establishes a compact, class-agnostic object-centric visual initialization, then constructs a soft semantic prototype from the intermediate prediction to actively steer subsequent search toward class-relevant evidence during inference. This object-first, language-second design addresses the circular dependence between recognizing a class and locating its supporting evidence, while preserving complementary local, contextual, and global cues. Across standard and distribution-shift benchmarks, LAGO transfers with a single fixed configuration and uses candidate regions more effectively under matched budgets. Controlled experiments further isolate the proposed mechanism, showing that allowing language to alter the search trajectory retrieves more relevant regions and improves recognition over applying the same semantic signal only after candidate generation.

cs.CV↗
arXiv2026

Separating Diagnosis from Disease Representation: Dual-View EEG Learning with Neural-Dynamics-Guided Deformation

Electroencephalography (EEG)-based closed-loop neuromodulation calls for a subject-specific structured state, as opposed to a single disease probability, specifying which brain regions are deviant, at which frequencies, and at which lags. Sensor-space models keep the strongest diagnostic evidence without anatomy, source-space models give anatomy at a loss of predictive signal, and post-hoc attributions stay outside the prediction. We separate the two instead of forcing them into one representation, and propose DMD-EEG (Dual-view Multiscale Deformation for EEG), which keeps a fixed scalp spectral expert for diagnosis and models the source-space disease-related representation as a low-rank, sparse, iterative deformation of a healthy neural-dynamics prior in a $46$-region-of-interest (ROI) $\times$ $5$-frequency $\times$ $4$-lag (autocorrelation-timescale) space. The two experts meet only at a fixed decision level, so the source state is architecturally separate from the scalp expert. Across major depressive disorder (MDD), first-episode psychosis (FEP), and Parkinson's disease (PD), decision-level fusion matches the strongest single expert on MDD and FEP and exceeds the source branch on PD. On FEP the source expert is the strongest branch, the task where the deformation contributes most. The source state is an explicit ROI-frequency-lag attribution defined in a shared source coordinate system across montages, which we treat as an anatomically-coordinated predictive representation whose coordinates are directly readable and hypothesis-generating. The highest-saliency coordinates align with established disease circuitry (fronto-limbic-temporal regions in MDD, motor-cortex beta in PD), and the MDD state transfers by rank to an unseen cohort recorded with a different montage.

cs.AI↗
arXiv2026

Synchronized Solutions for Liouville Systems with Sign-Changing Coefficients

We consider singular Liouville systems on closed Riemann surfaces with a common sign-changing coefficient. Direct continuation from a positive coefficient is obstructed by the unavoidable appearance of degenerate zeroes along such a homotopy. We instead identify an intrinsic ray in the parameter space on which the system admits synchronized solutions and reduces exactly to a scalar sign-changing mean-field equation. Combining this reduction with the variational existence theory of De Marchis--López-Soriano--Ruiz and the nodal singularity compactness theorem of Wu, we obtain existence for every noncritical parameter on this ray. Positive singular sources are allowed on the nodal curve. In particular, when the surface has nonpositive Euler characteristic and every negative component of the coefficient is a disk, the topological hypothesis required by the scalar min--max construction is automatic.

math.AP↗
arXiv2026

Selective Amortization of Full-Budget Counterfactual Reasoning for Visual Token Communication

Generative image communication transmits compact semantic tokens under a limited packet budget, where token selection directly affects the final reconstruction quality after the complete packet is decoded. However, accurately estimating the terminal value of every candidate token requires repeated receiver-side reconstruction, resulting in substantial encoder-side computation. To address this problem, we propose ACV-Gate, an adaptive candidate evaluation framework that learns to approximate full-budget counterfactual evaluation and selectively assigns exact evaluations to the most informative candidates. Specifically, a set-aware student is trained using terminal advantages and regrets to predict candidate rankings directly, while a selective refinement mechanism evaluates only a bounded candidate set containing both Local-MDL and direct actions; cost-based thresholds further enable explicit control of the average evaluation workload. Experiments on CIFAR-10 show that ACV-Gate consistently improves reconstruction quality while substantially reducing candidate evaluations; at 0.20 bpp, the primary adaptive configuration improves PSNR over LocalMDL by 0.636 dB with only 2.13 candidate evaluations per image, corresponding to 27.60% of the calls required by the Exact-Full expert. Matched-candidate comparisons, synchronized GPU measurements, and evaluations on STL-10 and 384 *384 scale transfer further demonstrate consistent quality computation trade-offs, with particularly pronounced gains at low bit rates. These results show that combining terminal-value learning with selective candidate evaluation provides an effective and controllable mechanism for allocating encoder computation in packet-constrained generative image communication.

cs.AI↗