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Kangjie Zhou

Kangjie Zhou contributes to research discovery and scholarly infrastructure.

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Robotics Machine Learning math.ST Artificial Intelligence math.NA math.OC Numerical Analysis Statistics Theory

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preprint2026arXiv

CoINS: Counterfactual Interactive Navigation via Skill-Aware VLM

Recent Vision-Language Models (VLMs) have demonstrated significant potential in robotic planning. However, they typically function as semantic reasoners, lacking an intrinsic understanding of the specific robot's physical capabilities. This limitation is particularly critical in interactive navigation, where robots must actively modify cluttered environments to create traversable paths. Existing VLM-based navigators are predominantly confined to passive obstacle avoidance, failing to reason about when and how to interact with objects to clear blocked paths. To bridge this gap, we propose Counterfactual Interactive Navigation via Skill-aware VLM (CoINS), a hierarchical framework that integrates skill-aware reasoning and robust low-level execution. Specifically, we fine-tune a VLM, named InterNav-VLM, which incorporates skill affordance and concrete constraint parameters into the input context and grounds them into a metric-scale environmental representation. By internalizing the logic of counterfactual reasoning through fine-tuning on the proposed InterNav dataset, the model learns to implicitly evaluate the causal effects of object removal on navigation connectivity, thereby determining interaction necessity and target selection. To execute the generated high-level plans, we develop a comprehensive skill library through reinforcement learning, specifically introducing traversability-oriented strategies to manipulate diverse objects for path clearance. A systematic benchmark in Isaac Sim is proposed to evaluate both the reasoning and execution aspects of interactive navigation. Extensive simulations and real-world experiments demonstrate that CoINS significantly outperforms representative baselines, achieving a 17\% higher overall success rate and over 80\% improvement in complex long-horizon scenarios compared to the best-performing baseline

preprint2026arXiv

When Does Model Collapse Occur in Structured Interactive Learning?

The proliferation of generative artificial intelligence has given rise to an interactive learning environment, where model parameters are continuously updated using not only data generated by natural processes, but also synthetic outputs produced by other models. This paradigm introduces two major challenges: (1) training data are no longer drawn exclusively from the target population, undermining a core assumption of classical statistical learning, and (2) model training processes become inherently correlated, as models interact with one another through repeated exposure to each other's synthetic outputs in a potentially complex manner. Establishing reliable statistical inference in such structured interactive learning environments therefore remains an important open problem. In particular, there is growing concern about model collapse, a phenomenon in which the performance of generative models progressively degrades as they are trained on synthetic data produced by earlier model generations. Prior work on model collapse primarily focuses on a single model trained on its own output, failing to capture model performance in multi-model interactive settings. In this work, we fill this gap by investigating the performance of generative models in an interactive learning environment with general interaction patterns. In particular, we formalize model interactions using directed graphs and show that the occurrence of model collapse depends critically on the topology of the interaction graph. We further derive an explicit necessary and sufficient condition characterizing when model collapse occurs, and establish finite-sample results for linear regression and asymptotic guarantees for general M-estimators. We support our theoretical findings through extensive numerical experiments.

preprint2025arXiv

AINav: Large Language Model-Based Adaptive Interactive Navigation

Robotic navigation in complex environments remains a critical research challenge. Traditional navigation methods focus on optimal trajectory generation within fixed free workspace, therefore struggling in environments lacking viable paths to the goal, such as disaster zones or cluttered warehouses. To address this problem, we propose AINav, an adaptive interactive navigation approach that proactively interacts with environments to create feasible paths to achieve originally unreachable goals. Specifically, we present a primitive skill tree for task planning with large language models (LLMs), facilitating effective reasoning to determine interaction objects and sequences. To ensure robust subtask execution, we adopt reinforcement learning to pre-train a comprehensive skill library containing versatile locomotion and interaction behaviors for motion planning. Furthermore, we introduce an adaptive replanning approach featuring two LLM-based modules: an advisor serving as a flexible replanning trigger and an arborist for autonomous plan adjustment. Integrated with the tree structure, the replanning mechanism allows for convenient node addition and pruning, enabling rapid plan adaptation in a priori unknown environments. Comprehensive simulations and experiments have demonstrated AINav's effectiveness and adaptivity in diverse scenarios. The supplementary video is available at: https://youtu.be/CjXm5KFx9AI.

preprint2025arXiv

Basic Inequalities for First-Order Optimization with Applications to Statistical Risk Analysis

We introduce \textit{basic inequalities} for first-order iterative optimization algorithms, forming a simple and versatile framework that connects implicit and explicit regularization. While related inequalities appear in the literature, we isolate and highlight a specific form and develop it as a well-rounded tool for statistical analysis. Let $f$ denote the objective function to be optimized. Given a first-order iterative algorithm initialized at $θ_0$ with current iterate $θ_T$, the basic inequality upper bounds $f(θ_T)-f(z)$ for any reference point $z$ in terms of the accumulated step sizes and the distances between $θ_0$, $θ_T$, and $z$. The bound translates the number of iterations into an effective regularization coefficient in the loss function. We demonstrate this framework through analyses of training dynamics and prediction risk bounds. In addition to revisiting and refining known results on gradient descent, we provide new results for mirror descent with Bregman divergence projection, for generalized linear models trained by gradient descent and exponentiated gradient descent, and for randomized predictors. We illustrate and supplement these theoretical findings with experiments on generalized linear models.

preprint2025arXiv

ReSPIRe: Informative and Reusable Belief Tree Search for Robot Probabilistic Search and Tracking in Unknown Environments

Target search and tracking (SAT) is a fundamental problem for various robotic applications such as search and rescue and environmental exploration. This paper proposes an informative trajectory planning approach, namely ReSPIRe, for SAT in unknown cluttered environments under considerably inaccurate prior target information and limited sensing field of view. We first develop a novel sigma point-based approximation approach to fast and accurately estimate mutual information reward under non-Gaussian belief distributions, utilizing informative sampling in state and observation spaces to mitigate the computational intractability of integral calculation. To tackle significant uncertainty associated with inadequate prior target information, we propose the hierarchical particle structure in ReSPIRe, which not only extracts critical particles for global route guidance, but also adjusts the particle number adaptively for planning efficiency. Building upon the hierarchical structure, we develop the reusable belief tree search approach to build a policy tree for online trajectory planning under uncertainty, which reuses rollout evaluation to improve planning efficiency. Extensive simulations and real-world experiments demonstrate that ReSPIRe outperforms representative benchmark methods with smaller MI approximation error, higher search efficiency, and more stable tracking performance, while maintaining outstanding computational efficiency.

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