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Tao Zhou

Publications and source records attributed to Tao Zhou.

At least 19 recordsLinked to original sources
arXiv2026

Overcoming Spectral Bias via Cross-Attention

Neural networks often exhibit spectral bias, a phenomenon where high-frequency components may converge substantially more slowly than low-frequency ones. To address this imbalance, we propose a cross-attention-based network that combines a multiscale random Fourier feature bank with learnable amplitude weighting. The amplitude envelope modulates the Fourier features according to their frequencies, while the cross-attention residual structure provides an input-dependent mechanism to emphasize informative scales. As a result, the proposed design accelerates high-frequency convergence relative to comparison networks built on the same multiscale bank. Moreover, the feature bank can be incrementally enriched with dominant modes identified through discrete Fourier analysis of intermediate approximations, without modifying the hidden-layer architecture. We further extend the framework to PDE learning through a two-network representation in which one subnetwork approximates higher-frequency solution components and the other approximates lower-frequency components, with a learnable or analytically computed mixing coefficient balancing their contributions. Numerical experiments on function approximation, image reconstruction, and representative elliptic PDEs demonstrate the accuracy of the proposed method for problems involving high-frequency, multiscale, and discontinuous features.

math.NA↗
arXiv2026

A semi-generating function approach to the stability of implicit-explicit multistep methods for nonlinear parabolic equations

The rigorous stability analysis of high-order implicit-explicit linear multistep (IELM) methods for nonlinear parabolic equations by using discrete energy arguments is a long standing open issue due to their non-A-stability property. A novel semi-generating function approach combined with a global discrete energy analysis is suggested for the stability and convergence of general IELM methods in solving nonlinear parabolic equations. Inspired from the Grenander-Szegő theorem for Toeplitz matrices, the semi-generating function approach is used to handle the three groups of discrete coefficients via three complex polynomials on the unit circle. A unified theoretical framework is then presented to establish the unconditional stability of IELM methods if the minimum eigenvalue of composite convolution kernels for the implicit part is properly large and the spectral norm bound of composite convolution kernels for the explicit part is properly small. An indicator, called implicit-explicit controllability intensity, is then introduced to evaluate the degree of controllability of the implicit part over the explicit part. Some of the existing IELM methods, up to fifth-order time accuracy, are revisited and compared by computing the associated implicit-explicit controllability intensities such that one can choose an IELM method or proper parameter to maintain the unconditional stability for a specific nonlinear parabolic model. We also propose a new parameterized class of IELM methods, up to the ninth-order time accuracy, which satisfy the a priori settings of our theory and have a large value of the implicit-explicit controllability intensity by choosing a proper parameter so that they would be well suited for a wide class of nonlinear parabolic problems.

math.NA↗
arXiv2026

Generalized principal eigenvalues for nonlocal operators with drift

Nonlocal diffusion operators with a drift term naturally arise in models such as moving coordinate systems induced by climate change. This paper systematically studies several concepts of generalized principal eigenvalues (GPEs) for such operators. We allow the dispersal kernel to be heterogeneous and non-symmetric, and remove the standard global upper bound on the kernel (thereby covering the case of heavy-tailed dispersal kernels). To overcome the analytical difficulties brought by this more general setting, we establish a new Harnack-type inequality for non-compactly supported kernels, and apply homogenization and cut-off approximation techniques to derive two-sided bounds for the domain approximation limit of GPEs. Furthermore, under the almost periodic setting, we prove that the GPEs defined through different admissible test function spaces (e.g., \(C^1\) spaces with bounded derivatives and uniformly continuous function spaces in the viscosity sense) are completely coincident. This characterization reveals a fundamental unification: the limit result of principal eigenvalues under domain approximation by Coville and Hamel coincides exactly with the explicit variational formula by Du, Fang, and Ni, thereby bridging two previously independent theoretical results.

math.AP↗
arXiv2026

Spreading speeds for nonlocal Fisher-KPP equations with time-dependent asymmetric kernels

In this paper, we establish spreading speeds for a nonlocal Fisher-KPP equation with measurable time-dependent asymmetric kernels, without imposing an inequality between growth and diffusion or requiring the kernel to be positive near the origin. The kernel has a time independent upper bound which is thin-tailed. Both the kernel and the linear growth rate have uniform means. Under these assumptions, we determine the exact rightward and leftward spreading speeds and prove convergence to the positive equilibrium inside the spreading interval. The proof is based on comparison arguments and a family of compactly supported subsolutions. Explicit examples show that time-dependent dispersal kernels with the same time average can exhibit different propagation behaviors.

math.AP↗
arXiv2026

The golden cage of science: first-last author prestige gap buys impact over disruption

First and last authors make critical but distinct contributions in the majority of scientific papers. First authors tend to conduct research and analysis, whereas last authors are usually responsible for setting research directions and providing resources and supervision. The first-last author prestige gap (FL gap, $ΔH$) is defined as the H-index difference between the last and first authors prior to the focal paper's publication. The FL gap serves as a measure of the prestige asymmetry between the two dominant collaborators. We find that larger FL gaps in either direction are associated with higher impact and lower disruption. This trade-off is robust across team sizes and intensities of prior collaboration and can not be explained by first and last authors' separate prestige effects or their academic age gap. Further analysis shows that variation in last author prestige is associated with larger differences in both the article's impact and disruption than variation in first author prestige. We refer to this coexistence of higher impact and lower disruption related to the FL gap as the ``golden cage of science'', which reflects a common collaboration structure that statistically produces highly cited but less disruptive work. These findings suggest the first-last author prestige gap as an important indicator for examining how research teams balance senior guidance with exploratory autonomy.

cs.SI↗
arXiv2026

EndoWorld-JEPA: Motion-Guided Global-Local Latent World Modeling for Endoscopic Video Representation Learning

Endoscopic video contains state transitions induced by camera displacement, deformable tissue, and instrument interaction, yet existing pre-training methods treat dynamics implicitly. Inspired by action-conditioned joint-embedding predictive world models and by the observation that endoscopic optical flow contains both shared image-plane displacement and localized residual motion, we reformulate passive endoscopic video pre-training as causal motion-guided latent-state prediction. We present EndoWorld-JEPA, to our knowledge the first latent world-model pre-training framework designed for general-purpose endoscopic video representation learning. In place of recorded actions, calibrated poses, or robot kinematics, the model conditions prediction of the next latent state on motion observed up to the current state. Its Optical Motion-guided module separates dominant displacement from residual motion and converts the resulting evidence into an ordered temporal motion condition and spatial local-motion weights. Complementary global and motion-local predictors use these outputs: the temporal condition modulates both latent transitions, whereas the local weights define an auxiliary motion-local state that extends prediction from scene-level evolution to spatially selective dynamics. Patch-wise motion weighting emphasizes localized change while retaining anatomical context, and past-motion-window dropout randomly withholds the complete motion condition to reduce dependence on unreliable motion. This global--local formulation learns predictable visual--motion dynamics in representation space without reconstructing stochastic appearance artifacts. Evaluation shows that a common pre-trained checkpoint achieves strong transfer across four downstream benchmarks, supporting motion-guided global--local latent prediction as an effective pre-training paradigm for endoscopic video.

cs.CV↗
arXiv2026

SPAR: Stepwise Personalized Autoregressive Recommendation with Prefix-Balanced Semantic IDs

Semantic ID (SID)-based generative recommendation retrieves items through successive token-level decisions, making personalization at each decoding step essential. However, existing methods insufficiently account for prefix-dependent user evidence and imbalanced historical interaction loads among candidate branches. This can cause irreversible branch-selection errors and favor popular paths. We propose SPAR, a generative recommendation framework that jointly improves stepwise personalization and SID construction. Its PATH Decoder retrieves prefix-relevant evidence from compressed long-term user memories and combines it with recent behavior, user profiles, and event context to guide each token decision. Its RQ-PIB module balances historical interaction loads among sibling branches under each parent prefix while preserving semantic structure. Experiments on large-scale Youku production data show an average relative HitRate improvement of 2.66% over the strongest baseline. SPAR also increases target-prefix retention by 5.79 percentage points and reduces the traffic-weighted largest child-branch share by 32.84% across SID levels. In a 7-day online A/B test, SPAR serves 10% of Youku's production traffic and improves average watch time per user by 3.95% and play conversion rate by 3.38%. These results demonstrate more reliable hierarchical decoding, balanced SID branches, and improved user engagement in industrial recommendation.

cs.IR↗
arXiv2026

Quasi-Monte Carlo based meshfree methods for parabolic equations on parameterized Riemannian manifolds

We develop and analyze a randomized path sampling framework for the pointwise approximation of linear parabolic equations on parameterized Riemannian manifolds, treating both closed manifolds and manifolds with Dirichlet boundary. Based on the Feynman-Kac representation, we construct a parameter-coordinate retraction-based discretization, referred to as the p-Ret scheme, for the manifold diffusion generated by the uniformly elliptic operator, and use it to formulate the Monte Carlo (MC) and randomized quasi-Monte Carlo (RQMC) methods. We derive the local weak consistency of the p-Ret transition and first-order weak convergence of the temporal discretization on closed manifolds. For fixed $h$, we show that RQMC sampling yields asymptotically faster variance decay than standard MC. On closed manifolds, the variance is $o(n^{-1})$ and, under additional regularity, satisfies the sharper bound $O(n^{-2+\varepsilon})$ for any $\varepsilon>0$. For Dirichlet problems, despite the discontinuities induced by numerical first exit, nested-uniformly scrambled Sobol' sampling attains $O(n^{-1-1/s+\varepsilon})$ variance for any $\varepsilon>0$ under suitable regularity assumptions, where $s$ denotes the nominal path-space dimension. More notably, we further develop an Array-RQMC strategy based on stepwise low-dimensional randomized point sets and a Hilbert space-filling curve that maps high-dimensional particle states to a one-dimensional ordering, and establish a variance rate of $o(n^{-1})$ under suitable assumptions. Numerical results demonstrate that both RQMC methods reduce variance and root mean square error (RMSE) relative to standard MC and remain effective for manifolds with intrinsic dimension up to $50$.

math.NA↗
arXiv2026

3DTCR: Vortex-following generative reconstruction improves tropical cyclone intensity prediction from global AI weather forecasts

Global numerical weather prediction (NWP) and artificial intelligence (AI) models often underestimate tropical cyclone (TC) intensity, partly because coarse grids underresolve fine-scale three-dimensional inner-core structures that influence TC intensity evolution. Kilometer-scale NWP simulations can better resolve these structures but are too costly for operational use, which also makes high-resolution TC data limited. Here we construct a 3-km, TC-centered dataset for 2018--2024 using the Weather Research and Forecasting (WRF) model and develop 3DTCR, a vortex-following generative framework that reconstructs three-dimensional TC structure from FuXi global forecasts. 3DTCR combines conditional flow matching (CFM) with two-stage training to learn a coarse-to-fine mapping from center-aligned reanalysis simulation pairs and then adapt it to forecast inputs through latent space alignment. Evaluated on 2024 western North Pacific (WNP) forecasts, 3DTCR reduces the root mean square error (RMSE) and the magnitude of the mean bias error (MBE) in maximum 10-m wind speed by 36.5% and 60.7% relative to FuXi, and by 8.9% and 28.2% relative to the European Centre for Medium-Range Weather Forecasts high-resolution system (ECMWF-HRES), respectively. Case studies suggest that reconstructions capture wind gradients between the eye and eyewall, vertical structure of horizontal winds, and vortex asymmetries, while inheriting the FuXi-predicted TC tracks. 3DTCR generates 5-day TC-centered atmospheric fields in approximately 3 minutes on one GPU, whereas a full-basin 3-km WRF simulation takes about 400 hours on 32 CPU cores. These results demonstrate that such a vortex-following generative reconstruction can add localized three-dimensional detail to global forecasts and improve TC intensity prediction without basin-wide kilometer-scale numerical integration.

cs.LG↗
arXiv2026

Universal Incremental Learning: Mitigating Confusion from Inter- and Intra-task Distribution Randomness

Existing incremental learning (IL) methods rely on strong assumptions: incoming tasks either introduce exclusively new classes or new domains (i.e., Class IL and Domain IL), or increment by a fixed scale in a class- and domain-agnostic manner (i.e., Versatile IL, VIL). These assumptions severely limit their applicability in dynamic, unpredictable real-world scenarios. In this work, we investigate Universal Incremental Learning (UIL), a more realistic setting where the model has no prior knowledge of which new classes or domains will appear across sequential tasks, nor the scale of these increments within each task. This uncertainty hinders the model's ability to confidently acquire knowledge across varying task distributions and to learn uniformly from imbalanced intra-task distributions. Consequently, UIL introduces a more general IL scenario, where the model must cope with confusion stemming from both inter-task and intra-task distribution randomness. To mitigate both sources of confusion, we propose MiCo, a simple yet effective framework for UIL. At the inter-task level, we employ a multi-objective learning scheme to enforce accurate and deterministic predictions, further enhanced by a direction recalibration module that alleviates conflicting gradient updates. At the intra-task level, we introduce a magnitude recalibration module to address asymmetrical optimization caused by imbalanced class distributions. Extensive experiments on four benchmarks demonstrate that MiCo significantly outperforms existing state-of-the-art methods in both the proposed UIL and existing VIL scenarios.

cs.CV↗
arXiv2026

Chirally pinned flat bands, helical minibands, and bias-controlled topology of Jackiw-Rebbi states in a periodically modulated Dirac mass texture

Flat bands amplify interactions into correlated phases, and topological bound states are robust by principle; combining the two in a model that is both exactly analyzable and experimentally accessible is therefore especially desirable. Here we show that a square-lattice model with a slowly modulated Dirac mass texture, $m(x)=m+m_0\cos(2πx/L)$ with $L$ up to hundreds of sites, provides such a setting, without engineered geometries, lattice-scale textures, or long-range hoppings. Exact nesting reduces the problem, independently at each transverse momentum $k_y$, to a $1+1$ dimensional Dirac Hamiltonian with a position-dependent mass: every simple zero of $m(x)$ binds Jackiw-Rebbi zero modes, and the two walls of a period form an effective Su-Schrieffer-Heeger ring. The model interpolates between a chirally pinned flat band at large $L$, a helical miniband whose nodes are enforced by a boundary phase of the ring, and a bias-dimerized regime in which the sign of the bias sets a winding number. A central result is that the miniband bandwidth is not a single scale: a max-min measurement conflates three widths of different origin, the helical height $W_{\rm JR}$ exponential in the period, the zone-edge upturn $W_{\rm edge}\propto L^{-2/3}$ dominating at large $L$, and a bias bump exponential in $L$, so the flat band is robust against bias in the thermodynamic limit. We analyze two lattice realizations, a two-orbital model with modulated inter-orbital hybridization and a single-orbital bond-order texture sharing the nodal physics while leaving the van Hove points gapless, and propose experiments on cold-atom superlattices, Kekule-ordered graphene, STM designer lattices, and microwave arrays.

cond-mat.mes-hall↗
arXiv2026

Energy Ring: Stabilizing Feature Energy for Reliable Test-Time Discovery

Test-Time Discovery (TTD) aims to recognize known classes and detect novel ones while the model is already deployed, operating directly on a continual unlabeled test-time stream. Existing TTD methods are overly conservative, making known and unknown features collapse together and difficult to separate during test-time adaptation. In this paper, we revisit TTD from an energy perspective and find that the natural energy gap between known and unknown classes is unstable and easily collapses. We therefore propose Energy Ring to stabilize this gap by anchoring the two types of classes on separate energy rings. A lightweight adapter enlarges the norm-based gap while preserving known-class directions, and a perturbation consistency module forms compact clusters for unknown classes. During testing, energy-guided confidence weighting improves prediction, and a stability-based rectification mechanism corrects unreliable updates. Experimental results show that Energy Ring significantly improves TTD performance against existing TTD methods.

cs.AI↗
arXiv2026

Relational Semantic Grounding for Test-Time Discovery

Test-Time Discovery (TTD) aims to recognize known classes and detect novel ones from a continuous unlabeled test stream after deployment. Existing TTD methods mainly rely on visual clustering or prototype comparison, and can only assign anonymous labels to discovered classes, leaving them difficult to interpret in open-world applications. In this paper, we propose SEGA, a Semantic Grounding with Attributes framework for TTD. SEGA leverages large language models to generate attribute-rich descriptions for known classes and constructs an attribute-anchored visual-semantic space during training. At test time, we introduce Relational Semantic Grounding (RSG), which grounds unknown samples with similar and dissimilar known-class anchors, prompts the LLM to generate candidate concepts, and reranks them in the learned semantic space. The selected concept is further used for confidence-guided test-time semantic stabilization. By coupling attribute-level semantic alignment with relational concept grounding, SEGA transforms anonymous test-time clusters into interpretable semantic concepts. Experiments show that SEGA improves TTD baselines with the promise of semantic grounding for open-world.

cs.AI↗
arXiv2026

CORE-Seg: Reasoning-Driven Segmentation for Complex Lesions via Reinforcement Learning

Medical image segmentation is undergoing a paradigm shift from conventional visual pattern matching to cognitive reasoning analysis. Although Multimodal Large Language Models (MLLMs) have shown promise in integrating linguistic and visual knowledge, significant gaps remain: existing general MLLMs possess broad common sense but lack the specialized visual reasoning required for complex lesions, whereas traditional segmentation models excel at pixel-level segmentation but lack logical interpretability. In this paper, we introduce ComLesion-14K, the first diverse Chain-of-Thought (CoT) benchmark for reasoning-driven complex lesion segmentation. To accomplish this task, we propose CORE-Seg, an end-to-end framework integrating reasoning with segmentation through a Semantic-Guided Prompt Adapter. We design a progressive training strategy from SFT to GRPO, equipped with an adaptive dual-granularity reward mechanism to mitigate reward sparsity. Our Method achieves state-of-the-art results with a mean Dice of 37.06\% (14.89\% higher than the second-best baseline), while reducing the failure rate to 18.42\%. Project Page: https://xyxl024.github.io/CORE-Seg.github.io/

cs.CV↗
arXiv2026

WebRider: Persona-Conditioned Intent Controllers for Live-Web Assistance

Delegating a web task involves more than asking a question; it requires transferring a policy: what to verify, how to handle uncertainty, which preferences matter, and when to stop. Yet, current live-web agents are evaluated solely on the final answer, ignoring the policy constraints that define the delegation. A plausible final answer can conceal violations of that policy. Our full live audit reveals this critical gap: a strong controller completes 99.2% of tasks but honors all policy constraints in only 38.8% of cases. Finishing does not imply fidelity. WebRider bridges this gap by formalizing the delegated policy as an intent contract---an operational record of goals, constraints, evidence obligations, answer form, and task-local persona controls that must hold even as web pages change. WebRider employs a hierarchical architecture: a top-layer controller maintains the contract, a middle layer realizes intentions as guarded executable actions, and a tool layer executes these actions via browser, search, and maps tools. Our benchmark, RiderBench, evaluates this design on 4,096 live-web contracts across 42 public websites, auditing both the internal contract state and the visible user experience to determine if a rollout preserved its policy and if the steps were persona-consistent. The guarded middle interface also serves as a high-quality training signal; an 8B action-policy model trained through this interface outperforms executable-only baselines under a fixed controller. By making the browsing path a first-class object, WebRider enables a system that is auditable, human-judgeable, and learnable without conflating action realization with final-answer decisions. Dataset URL: hf.co/datasets/WebRider/WebRider.

cs.AI↗
arXiv2026

Anchor-driven Multi-modal Multi-scale Expert Selection for Survival Prediction

The integrative analysis of histopathological Whole-Slide Images (WSIs) and transcriptomic profiles holds significant promise for cancer survival prediction. However, existing methods typically project multi-modal features directly into a shared latent space without explicit alignment, leading to the entanglement of mismatched morphological cues and molecular signals. Furthermore, current fusion strategies often treat the extreme spatial heterogeneity of WSIs uniformly, lacking mechanisms to adaptively prioritize clinically relevant tissue scales for individual patients. To address these limitations, we propose an Anchor-driven Multi-modal Multi-scale Expert Selection (AM$^2$ES) framework for survival prediction. Specifically, we present an Anchor-driven Multi-modal Fusion (AMF) module, which introduces learnable semantic anchors as cross-modal mediators to bridge the semantic gap by enforcing a structurally regularized alignment between transcriptomic features and multi-scale pathology representations. Built upon this aligned semantic space, we further design a Hierarchical Mixture-of-Experts (H-MoE) selection module to decouple the hierarchical prognostic selection process. Mimicking the pathologist's diagnostic workflow, H-MoE performs (i) Intra-scale Expert Filtering to discriminatively identify salient tumor regions within each magnification, and (ii) Inter-scale Hierarchy Routing to dynamically weight and select the most informative resolution levels. Extensive experiments on multiple TCGA cancer cohorts demonstrate that our AM$^2$ES achieves state-of-the-art performance while offering fine-grained interpretability by visualizing how specific molecular pathways drive the expert routing decisions across tissue scales. The code will be released at https://github.com/taozh2017/AM2ES.

cs.CV↗
arXiv2026

Decoupled Divergence-Free Neural Networks Basis Method for Incompressible Fluid Problems

We propose a decoupled divergence-free neural networks basis (Decoupled-DFNN) method for solving incompressible flow problems, including the Stokes and Navier-Stokes equations. To ensure the divergence free property exactly, the velocity field is represented as the curl of a stream function in two dimensions and as the curl of a vector potential in three dimensions. Beyond classical stream-function or velocity-vorticity formulations, we further utilize the properties of the curl operator to derive two specific decoupled subproblems for the velocity (through the stream function or vector potential) and the pressure, respectively. The proposed formulations enable a sequential solution strategy, in which the velocity and pressure are solved independently. To resolve the inherent nonlinearity of the Navier-Stokes equations, we employ a Gauss-Newton linearization strategy, transforming the nonlinear velocity subproblem into a sequence of linear subproblems. These decoupled subproblems for velocity and pressure are subsequently solved using the TransNet framework. Compared with existing methods, the proposed approach reduces computational cost while strictly preserving the incompressibility constraint.

math.NA↗
arXiv2026

CI-PINN: Causal Integral Physics-Informed Neural Network for Solving Evolution Equations

Physics-informed neural networks (PINNs) solve partial differential equations (PDEs) by incorporating governing physical laws into the training loss. For evolution equations, however, their conventional pointwise space--time representation does not explicitly encode temporal dependence, which can hinder accurate prediction. To mitigate this limitation, this work proposes a novel neural architecture termed a causal integral neural network (CinNet). The core module of CinNet is a Volterra-type causal integral term, which aggregates historical features to encode temporal dependence, thereby incorporating temporal causality at the architectural level rather than through training-level modifications as in many existing methods. Building on CinNet, we further develop a causal integral physics-informed neural network (CI-PINN) for solving evolution equations. Extensive numerical experiments on benchmark evolution equations demonstrate that the presented method outperforms various baseline PINN variants in terms of solution accuracy, with pronounced superiority under sparse-collocation scenarios. Additional empirical analyses show that CI-PINN exhibits low sensitivity to hyperparameter choices, while ablation studies confirm the effectiveness of the proposed network components.

math.NA↗