arXiv subjects

Tao Tang

Publications and source records attributed to Tao Tang.

At least 19 recordsLinked to original sources

arXiv2026

GeoThinker-$F$: Endogenous Predictive World Representations for Fast Spatial Intelligence

Existing geometry-aware Multimodal Large Language Models (MLLMs) increasingly rely on external 3D encoders to provide structural priors, but executing these additional encoder paths at inference introduces substantial latency and computational overhead. We propose GeoThinker-$F$, an efficient framework that internalizes spatiotemporal perception by transforming causal MLLM hidden states into predictive latent world representations. Our key insight is that intermediate semantic representations contain sufficient information to predict useful representations of current geometry and future semantics, without requiring an exact reproduction of features from a dedicated 3D encoder. To realize this idea, GeoThinker-$F$ adopts a decoupled two-stage training strategy. In the first stage, the MLLM backbone is frozen while lightweight Latent Frame Prediction (LFP) heads learn from an offline 3D geometry expert and next-frame semantic targets. In the second stage, the external expert is removed, and the model is jointly optimized to generate and selectively integrate its self-predicted priors through a specialized Spatial-Grounded Temporal (SGT) Fusion module. Extensive evaluations show that GeoThinker-$F$ eliminates runtime dependence on external 3D geometry encoders while maintaining competitive performance across diverse spatial intelligence benchmarks. It achieves up to a $3.6\times$ inference speedup, reducing latency from $1.45\,\mathrm{s}$ to $0.40\,\mathrm{s}$ while retaining strong spatial reasoning performance.

cs.CV↗

arXiv2026

Taylor-Approximation-Based Repair of High Floating-Point Errors

Numerical libraries can still lose many bits of accuracy on localized ill-conditioned inputs, such as roots, poles, cancellation points, and branch boundaries. This paper presents NPTaylor, a Taylor-approximation-based framework for repairing localized high floating-point errors in numerical C routines. Given a high-error input, a localized repair domain, a high-precision oracle, and an error threshold, NPTaylor searches over Taylor degree, expansion center, segmentation, and floating-point evaluation strategy. It emits guarded C patches that use a generated Taylor evaluator inside the repair domain and fall back to the original routine outside it. Candidate patches are accepted only after validating the emitted C code on recorded local samples, guard endpoints, and the pre-repair peak input. The generated evaluator uses coefficient splitting and compensated Horner evaluation to reduce rounding error introduced by the patch itself. We evaluate NPTaylor on GSL benchmark workloads. On 38 one-input functions, both NPTaylor and AutoRNP repair all 114 configurations across three accuracy thresholds. NPTaylor is 3.33x faster by geometric-mean offline repair time and emits 0.162x as many C bytes. In the strictest setting, its median repair time is 3.74s versus 81.97s for AutoRNP. NPTaylor also repairs localized multi-input benchmark cases beyond AutoRNP's implemented one-input workflow. These results show that Taylor-based guarded patches can provide compact, efficient local repairs, while the claims remain validation-relative rather than full-domain proofs.

cs.SE↗

arXiv2026

Adaptive Bayesian Regression on Data with Low Intrinsic Dimensionality

We study how the posterior contraction rate under a Gaussian process (GP) prior depends on the intrinsic dimension of the predictors and the smoothness of the regression function. An open question is whether a generic GP prior that does not incorporate knowledge of the intrinsic lower-dimensional structure of the predictors can attain an adaptive rate for a broad class of such structures. We show that this is indeed the case, establishing conditions under which the posterior contraction rates become adaptive to the intrinsic dimension in terms of the covering number of the data domain (the Minkowski dimension) and prove the nonparametric posterior contraction rate, up to a logarithmic factor. When the domain is a compact manifold, we prove the RKHS approximation to intrinsically defined Hölder functions on the manifold of any order of smoothness by a novel analysis, leading to the optimal adaptive posterior contraction rate. We propose an empirical Bayes prior on the kernel bandwidth using kernel affinity and $k$-nearest neighbor statistics, bypassing explicit estimation of the intrinsic dimension. The efficiency of the proposed Bayesian regression approach is demonstrated in various numerical experiments.

math.ST↗

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↗

arXiv2026

ProMeta: Few-shot PROTAC-targeted degradation prediction across E3 ligases

Proteolysis-targeting chimeras (PROTACs) have emerged as a transformative therapeutic strategy that selectively degrades historically ''undruggable'' targets via the ubiquitin-proteasome system. Despite growing efforts to develop computational predictors of PROTAC degradation activity, existing supervised approaches remain severely challenged by data scarcity and imbalance across E3 ligases, limiting their ability to generalize beyond well-studied ligase contexts. In practice, labeled data are heavily concentrated on a few ligases (e.g., CRBN and VHL), while the majority of E3 ligases remain underexplored yet are critical for expanding the design space of targeted degraders. Developing methods that enable robust cross-ligase generalization with minimal labeled data is therefore essential for improving the practical utility of computational PROTAC discovery. We reformulate PROTAC degradation activity prediction across E3 ligases as a few-shot meta-learning problem and present ProMeta, a prototype-based graph neural network trained through episodic meta-learning on source-E3 tasks and evaluated on held-out target-E3 tasks through support-conditioned inference. ProMeta performs inference without updating the encoder by dynamically estimating class prototypes from minimal target-ligase support samples. On the CRBN-to-VHL benchmark, ProMeta achieves AUROC values of 0.796 under K=2, Q=3 and 0.883 under K=2, Q=5, improving by 19.9% and 6.8%, respectively, over the corresponding supervised GNN baseline. Reverse VHL-to-CRBN transfer under the same protocol yielded AUROC values of 0.702 (K=2, Q=3) and 0.821 (K=2, Q=5), confirming bidirectional applicability while revealing direction and data-regime dependence. Together, these results support ProMeta as a practical framework for cross-ligase few-shot prediction under the evaluated support/query protocols.

cs.LG↗

arXiv2026

AtomicVLA: Unlocking the Potential of Atomic Skill Learning in Robots

Recent advances in Visual-Language-Action (VLA) models have shown promising potential for robotic manipulation tasks. However, real-world robotic tasks often involve long-horizon, multi-step problem-solving and require generalization for continual skill acquisition, extending beyond single actions or skills. These challenges present significant barriers for existing VLA models, which use monolithic action decoders trained on aggregated data, resulting in poor scalability. To address these challenges, we propose AtomicVLA, a unified planning-and-execution framework that jointly generates task-level plans, atomic skill abstractions, and fine-grained actions. AtomicVLA constructs a scalable atomic skill library through a Skill-Guided Mixture-of-Experts (SG-MoE), where each expert specializes in mastering generic yet precise atomic skills. Furthermore, we introduce a flexible routing encoder that automatically assigns dedicated atomic experts to new skills, enabling continual learning. We validate our approach through extensive experiments. In simulation, AtomicVLA outperforms $π_{0}$ by 2.4\% on LIBERO, 10\% on LIBERO-LONG, and outperforms $π_{0}$ and $π_{0.5}$ by 0.22 and 0.25 in average task length on CALVIN. Additionally, our AtomicVLA consistently surpasses baselines by 18.3\% and 21\% in real-world long-horizon tasks and continual learning. These results highlight the effectiveness of atomic skill abstraction and dynamic expert composition for long-horizon and lifelong robotic tasks. The project page is \href{https://zhanglk9.github.io/atomicvla-web/}{here}.

cs.RO↗

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

Intend, Reflect, Refine: An Adaptive Multimodal Reflection Framework for Autonomous Driving

Recent Vision-Language-Action (VLA) models have advanced end-to-end autonomous driving by incorporating reasoning for better interpretability and planning quality. However, most existing approaches directly generate the final trajectory without explicitly examining its future consequences, which limits their reliability in complex and dynamic environments. To address this limitation, we propose IRR-Drive (Intend, Reflect, Refine), an adaptive multimodal reflection framework for autonomous driving. Specifically, to tightly couple high-level reasoning with physical constraints, IRR-Drive first generates a preliminary textual intention and anticipates potential interactions by predicting future semantic bird's-eye view (BEV) representations. This dual-modality (Text + BEV) reflection space explicitly models anticipated scene evolution, enabling the model to rigorously self-correct and refine its initial intent before generating the final trajectory. Furthermore, to balance planning performance and computational efficiency, we construct reflection-oriented training data and design an adaptive reflection reward, enabling the model to adaptively select its reasoning mode according to scene complexity. Instead of using reasoning primarily as an auxiliary interpretation, IRR-Drive directly integrates an adaptive reflection mechanism into the planning framework, enabling grounded, decision-aware trajectory correction that is driven by scene complexity. Our method achieves state-of-the-art performance on the NAVSIM benchmark in both PDMS and EPDMS. Extensive experiments demonstrate the effectiveness of our multimodal reflection framework and validate the efficacy of the proposed adaptive reflection strategy.

cs.CV↗

arXiv2026

A second-order product-type implicit-explicit Runge-Kutta method preserving unit length and energy dissipation structures for gradient flows of vector fields

Gradient flows of unit vector fields arise in a wide range of physical models such as harmonic map heat flows, nematic liquid crystals, and magnetization dynamics. Designing numerical schemes that simultaneously preserve the unit length constraint and dissipate energy is essential for reliable simulations of such systems. Although projection methods can effectively enforce the unit length constraint, ensuring energy dissipation under projection, especially in high-order schemes, remains challenging. Unlike traditional implicit-explicit Runge-Kutta (IMEX-RK) methods, in this work we propose a general methodology for constructing product-type IMEX-RK schemes that offers greater adaptability to various models with the goal of designing structure-preserving numerical schemes. For gradient flows of unit vector fields with Dirichlet energy, we design a linear and second-order numerical scheme that simultaneously preserves energy dissipation and the unit length constraint by using product-type IMEX-RK methods and projection techniques. Numerical experiments verify the accuracy, stability, and structure-preserving properties of the scheme. According to our best knowledge, this is the first second-order linear scheme that can preserve both the unit length and the original Dirichlet energy for harmonic map heat flows.

math.NA↗

arXiv2026

Thinking with Geometry: Active Geometry Integration for Spatial Reasoning

Recent progress in spatial reasoning with Multimodal Large Language Models (MLLMs) increasingly leverages geometric priors from 3D encoders. However, most existing integration strategies remain passive: geometry is exposed as a global stream and fused in an indiscriminate manner, which often induces semantic-geometry misalignment and redundant signals. We propose GeoThinker, a framework that shifts the paradigm from passive fusion to active perception. Instead of feature mixing, GeoThinker enables the model to selectively retrieve geometric evidence conditioned on its internal reasoning demands. GeoThinker achieves this through Spatial-Grounded Fusion applied at carefully selected VLM layers, where semantic visual priors selectively query and integrate task-relevant geometry via frame-strict cross-attention, further calibrated by Importance Gating that biases per-frame attention toward task-relevant structures. Comprehensive evaluation results show that GeoThinker sets a new state-of-the-art in spatial intelligence, achieving a peak score of 72.6 on the VSI-Bench. Furthermore, GeoThinker demonstrates robust generalization and significantly improved spatial perception across complex downstream scenarios, including embodied referring and autonomous driving. Our results indicate that the ability to actively integrate spatial structures is essential for next-generation spatial intelligence. Code can be found at https://github.com/Li-Hao-yuan/GeoThinker.

cs.CV↗

arXiv2026

MoPO: Incorporating Motion Prior for Occluded Human Mesh Recovery

Although recent studies have made remarkable progress in human mesh recovery, they still exhibit limited robustness to occlusions and often produce inaccurate poses and severe motion jitter due to the insufficient spatial features for occluded body parts. Inspired by the rapid advancements in human motion prediction, we discover that compared to occluded image features, pose sequence inherently contains reliable motion prior for estimating occluded body parts. In this paper, we incorporate Motion Prior for Occluded human mesh recovery, called MoPO. Our MoPO mainly consists of two components: 1) The motion de-occlusion module, where we propose a spatial-temporal occlusion detector to detect joint visibility, and then we propose a lightweight motion predictor to complete the occluded body parts by predicting the most plausible joint positions based on history poses. 2) The motion-aware fusion and refinement module, which fuses the completed joint sequence with image features to estimate human shape and initial human pose. Moreover, the completed joint sequence is further used to refine the final human pose through inverse kinematics, which provides the occlusion-free motion prior for regressing human poses. Extensive experiments demonstrate that MoPO achieves state-of-the-art performance on both occlusion-specific and standard benchmarks, significantly enhancing the accuracy and temporal consistency of occluded human mesh recovery. Our code and demo can be found in the supplementary material.

cs.CV↗

arXiv2026

Diff-KD: Diffusion-based Knowledge Distillation for Collaborative Perception under Corruptions

Multi-agent collaborative perception enables autonomous systems to overcome individual sensing limits through collective intelligence. However, real-world sensor and communication corruptions severely undermine this advantage. Crucially, existing approaches treat corruptions as static perturbations or passively conform to corrupted inputs, failing to actively recover the underlying clean semantics. To address this limitation, we introduce Diff-KD, a framework that integrates diffusion-based generative refinement into teacher-student knowledge distillation for robust collaborative perception. Diff-KD features two core components: (i) Progressive Knowledge Distillation (PKD), which treats local feature restoration as a conditional diffusion process to recover global semantics from corrupted observations; and (ii) Adaptive Gated Fusion (AGF), which dynamically weights neighbors based on ego reliability during fusion. Evaluated on OPV2V and DAIR-V2X under seven corruption types, Diff-KD achieves state-of-the-art performance in both detection accuracy and calibration robustness.

cs.AI↗

arXiv2026

MolLangBench: A Comprehensive Benchmark for Language-Prompted Molecular Structure Recognition, Editing, and Generation

Precise recognition, editing, and generation of molecules are essential prerequisites for both chemists and AI systems tackling various chemical tasks. We present MolLangBench, a comprehensive benchmark designed to evaluate fundamental molecule-language interface tasks: language-prompted molecular structure recognition, editing, and generation. To ensure high-quality, unambiguous, and deterministic outputs, we construct the recognition tasks using automated cheminformatics tools, and curate editing and generation tasks through rigorous expert annotation and validation. MolLangBench supports the evaluation of models that interface language with different molecular representations, including linear strings, molecular images, and molecular graphs. Evaluations of state-of-the-art models reveal significant limitations: the strongest model (GPT-5) achieves $86.2\%$ and $85.5\%$ accuracy on recognition and editing tasks, which are intuitively simple for humans, and performs even worse on the generation task, reaching only $43.0\%$ accuracy. These results highlight the shortcomings of current AI systems in handling even preliminary molecular recognition and manipulation tasks. We hope MolLangBench will catalyze further research toward more effective and reliable AI systems for chemical applications.The dataset and code can be accessed at https://huggingface.co/datasets/ChemFM/MolLangBench and https://github.com/TheLuoFengLab/MolLangBench, respectively.

cs.CL↗

arXiv2026

Energy Dissipation Preserving Feature-based DNN Galerkin Methods for Gradient Flows

In recent years, deep learning methods, exemplified by Physics-Informed Neural Networks (PINNs), have been widely applied to the numerical solution of differential equations. However, these methods may suffer from limited accuracy, high training costs, and lack of robustness, particularly their inability to preserve the intrinsic physical structures of continuous PDE models, such as the energy dissipation property in gradient flow systems. To address these challenges, we propose a feature-based Deep Neural Network Galerkin (DNN-G) framework designed for structure-preserving simulations of gradient flows. Instead of treating neural networks merely as optimization-driven solvers, we employ them as adaptive feature generators that define nonlinear trial spaces within a Galerkin projection formulation.This formulation guarantees semi-discrete energy dissipation and can be naturally combined with energy stable time integration schemes. Several strategies for constructing neural basis functions are investigated, including random features, structured initialization, and problem-informed pre-training. Numerical experiments demonstrate that the proposed method preserves robust energy stability in high-dimensional settings and accurately captures complex topological transitions. With equivalent degrees of freedom, the DNN-G framework achieves higher accuracy than classical spectral methods, highlighting the effectiveness of neural feature representations for the numerical solution of partial differential equations.

math.NA↗

arXiv2026

AD-R1: Closed-Loop Reinforcement Learning for End-to-End Autonomous Driving with Impartial World Models

End-to-end models for autonomous driving hold the promise of learning complex behaviors directly from sensor data, but face critical challenges in safety and handling long-tail events. Reinforcement Learning (RL) offers a promising path to overcome these limitations, yet its success in autonomous driving has been elusive. We identify a fundamental flaw hindering this progress: a deep seated optimistic bias in the world models used for RL. To address this, we introduce a framework for post-training policy refinement built around an Impartial World Model. Our primary contribution is to teach this model to be honest about danger. We achieve this with a novel data synthesis pipeline, Counterfactual Synthesis, which systematically generates a rich curriculum of plausible collisions and off-road events. This transforms the model from a passive scene completer into a veridical forecaster that remains faithful to the causal link between actions and outcomes. We then integrate this Impartial World Model into our closed-loop RL framework, where it serves as an internal critic. During refinement, the agent queries the critic to ``dream" of the outcomes for candidate actions. We demonstrate through extensive experiments, including on a new Risk Foreseeing Benchmark, that our model significantly outperforms baselines in predicting failures. Consequently, when used as a critic, it enables a substantial reduction in safety violations in challenging simulations, proving that teaching a model to dream of danger is a critical step towards building truly safe and intelligent autonomous agents.

cs.CV↗

arXiv2026

CATNet: Collaborative Alignment and Transformation Network for Cooperative Perception

Cooperative perception significantly enhances scene understanding by integrating complementary information from diverse agents. However, existing research often overlooks critical challenges inherent in real-world multi-source data integration, specifically high temporal latency and multi-source noise. To address these practical limitations, we propose Collaborative Alignment and Transformation Network (CATNet), an adaptive compensation framework that resolves temporal latency and noise interference in multi-agent systems. Our key innovations can be summarized in three aspects. First, we introduce a Spatio-Temporal Recurrent Synchronization (STSync) that aligns asynchronous feature streams via adjacent-frame differential modeling, establishing a temporal-spatially unified representation space. Second, we design a Dual-Branch Wavelet Enhanced Denoiser (WTDen) that suppresses global noise and reconstructs localized feature distortions within aligned representations. Third, we construct an Adaptive Feature Selector (AdpSel) that dynamically focuses on critical perceptual features for robust fusion. Extensive experiments on multiple datasets demonstrate that CATNet consistently outperforms existing methods under complex traffic conditions, proving its superior robustness and adaptability.

cs.CV↗

arXiv2026

DriveCombo: Benchmarking Compositional Traffic Rule Reasoning in Autonomous Driving

Multimodal Large Language Models (MLLMs) are rapidly becoming the intelligence brain of end-to-end autonomous driving systems. A key challenge is to assess whether MLLMs can truly understand and follow complex real-world traffic rules. However, existing benchmarks mainly focus on single-rule scenarios like traffic sign recognition, neglecting the complexity of multi-rule concurrency and conflicts in real driving. Consequently, models perform well on simple tasks but often fail or violate rules in real world complex situations. To bridge this gap, we propose DriveCombo, a text and vision-based benchmark for compositional traffic rule reasoning. Inspired by human drivers' cognitive development, we propose a systematic Five-Level Cognitive Ladder that evaluates reasoning from single-rule understanding to multi-rule integration and conflict resolution, enabling quantitative assessment across cognitive stages. We further propose a Rule2Scene Agent that maps language-based traffic rules to dynamic driving scenes through rule crafting and scene generation, enabling scene-level traffic rule visual reasoning. Evaluations of 14 mainstream MLLMs reveal performance drops as task complexity grows, particularly during rule conflicts. After splitting the dataset and fine-tuning on the training set, we further observe substantial improvements in both traffic rule reasoning and downstream planning capabilities. These results highlight the effectiveness of DriveCombo in advancing compliant and intelligent autonomous driving systems.

cs.CV↗

arXiv2026

Adaptive mesh methods for hyperbolic conservation laws with bound-preserving flux limiters

In this paper, we develop bound-preserving (BP) finite-volume schemes for hyperbolic conservation laws on adaptive moving meshes. For scalar conservative laws, we rewrite the conventional high-order discretization as a convex combination of first-order counterparts on each sub-cell, which is mathematically equivalent to introducing a bound-preserving flux limiter. Such a limiter is inexpensive to evaluate, with a feature that the corresponding BP CFL conditions depend solely on the first-order sub-cell schemes. A mild CFL restriction is derived under which high-order spatial accuracy is retained. The proposed BP schemes are extend to two nonlinear systems, namely, the Euler equations and the five-equation transport model of two-medium flows. Numerical results demonstrate that the present schemes possess high resolution and strong robustness properties.

math.NA↗