arXiv subjects

Fei Lu

Publications and source records attributed to Fei Lu.

At least 19 recordsLinked to original sources

arXiv2026

ABot-World-0: Infinite Interactive World Rollout on a Single Desktop GPU

We present ABot-World-0, an action-conditioned video world model for real-time, long-horizon closed-loop interaction, supported by a multi-source data infrastructure spanning AAA games, simulation engines, and internet videos to learn controllable world dynamics. WorldExplorer performs agent-driven collection guided by training feedback, while a unified pipeline applies 14 deterministic quality checks, VLM-based assessment, and synchronized action and text annotation. We progressively distill a bidirectional action-conditioned teacher into a causal student through teacher forcing and ODE distillation, and introduce LongForcing to align long student self-rollouts with an extended-horizon teacher, mitigating accumulated distribution shift and autoregressive drift. Raw keyboard actions provide a unified control interface for scene roaming and third-person character interaction, while reference-character memory provides persistent appearance cues for identity consistency during third-person rollouts. For deployment, we co-design a streaming inference stack with a lightweight VAE decoder, efficient attention, memory-aware scheduling, and low-bit DiT inference. Across optimized low-bit configurations, ABot-World-0 streams 720P video at up to 16 FPS on a single NVIDIA RTX 5090 desktop GPU, with 1.2s action-to-first-frame latency and approximately 19GiB peak VRAM. Experiments on WorldRoamBench and extended interactive rollouts demonstrate competitive controllability and coherent long-horizon world evolution.

cs.CV↗

arXiv2026

When Rough Data Helps: A Phase Transition in Convergence Rates for Kernel Recovery in Integral Operators

Learning kernels in operators from data is a fundamental task that arises in nonlocal continuum mechanics, operator learning, and interacting particle systems. A central question is how the roughness of input data impacts the accuracy of kernel recovery. We quantify the roughness of the input data via its spectral decay exponent and analyze how it determines the degree of ill-posedness of the inverse problem and, consequently, the convergence rates of the Tikhonov-regularized estimator in the small-noise limit. Within this framework, we identify a phase transition between an under-rough regime, in which rougher data improves recovery, and an over-rough regime, in which further roughening leads to slower rates. These theoretical findings are supported by numerical experiments ranging from idealized settings to more realistic configurations, with quantitative agreement in the former and broad consistency of the main trends in the latter.

math.NA↗

arXiv2026

Learning interacting particle systems from unlabeled data

Learning the potentials of interacting particle systems is a fundamental task across various scientific disciplines. A major challenge is that unlabeled data collected at discrete time points lack trajectory information due to limitations in data collection methods or privacy constraints. We address this challenge by introducing a trajectory-free self-test loss function that leverages the weak-form stochastic evolution equation of the empirical distribution. The loss function is quadratic in potentials, supporting parametric and nonparametric regression algorithms for robust estimation that scale to large, high-dimensional systems with big data. Systematic numerical tests show that our method outperforms baseline methods that regress on trajectories recovered via label matching, tolerating large observation time steps. We establish the convergence of parametric estimators as the sample size increases, providing a theoretical foundation for the proposed approach.

stat.ML↗

arXiv2026

Learning Multi-type heterogeneous interacting particle systems

We propose a framework for the joint inference of network topology, multi-type interaction kernels, and latent type assignments in heterogeneous interacting particle systems from multi-trajectory data. This learning task is a challenging non-convex mixed-integer optimization problem, which we address through a novel three-stage approach. First, we leverage shared structure across agent interactions to recover a low-rank embedding of the system parameters via matrix sensing. Second, we identify discrete interaction types by clustering within the learned embedding. Third, we recover the network weight matrix and kernel coefficients through matrix factorization and a post-processing refinement. We provide theoretical guarantees with estimation error bounds under a Restricted Isometry Property (RIP) assumption and establish conditions for the exact recovery of interaction types based on cluster separability. Numerical experiments on synthetic datasets, including heterogeneous predator-prey systems, demonstrate that our method yields an accurate reconstruction of the underlying dynamics and is robust to noise.

stat.ML↗

arXiv2025

Learning L\'evy density via adaptive RKHS regression with bi-level optimization

We propose a nonparametric method to learn the L\'evy density from probability density data governed by a nonlocal Fokker-Planck equation. We recast the problem as identifying the kernel in a nonlocal integral operator from discrete data, which leads to an ill-posed inverse problem. To regularize it, we construct an adaptive reproducing kernel Hilbert space (RKHS) whose kernel is built directly from the data. Under standard source and spectral decay conditions, we show that the reconstruction error decays in the mesh size at a near optimal rate. Importantly, we develop a generalized singular value decomposition (GSVD)-based bilevel optimization algorithm to choose the regularization parameter, leading to efficient and robust computation of the regularized estimator. Numerical experiments for several L\'evy densities, drift fields and data types (PDE-based densities and sample ensemble-based KDE reconstructions) demonstrate that our bilevel RKHS method outperforms classical L-curve and generalized cross-validation strategies and that the adaptive RKHS norm is more accurate and robust than $L^2_\rho$- and $\ell^2$-based regularization.

math.NA↗

arXiv2025

From Events to Trending: A Multi-Stage Hotspots Detection Method Based on Generative Query Indexing

LLM-based conversational systems have become a popular gateway for information access, yet most existing chatbots struggle to handle news-related trending queries effectively. To improve user experience, an effective trending query detection method is urgently needed to enable differentiated processing of such target traffic. However, current research on trending detection tailored to the dialogue system scenario remains largely unexplored, and methods designed for traditional search engines often underperform in conversational contexts due to radically distinct query distributions and expression patterns. To fill this gap, we propose a multi-stage framework for trending detection, which achieves systematic optimization from both offline generation and online identification perspectives. Specifically, our framework first exploits selected hot events to generate index queries, establishing a key bridge between static events and dynamic user queries. It then employs a retrieval matching mechanism for real-time online detection of trending queries, where we introduce a cascaded recall and ranking architecture to balance detection efficiency and accuracy. Furthermore, to better adapt to the practical application scenario, our framework adopts a single-recall module as a cold-start strategy to collect online data for fine-tuning the reranker. Extensive experiments demonstrate that our framework significantly outperforms baseline methods in both offline evaluations and online A/B tests, and user satisfaction is relatively improved by 27\% in terms of positive-negative feedback ratio.

cs.IR↗

arXiv2025

Minimax Rates for Learning Pairwise Interactions in Attention-Style Models

We study the convergence rate of learning pairwise interactions in single-layer attention-style models, where tokens interact through a weight matrix and a nonlinear activation function. We prove that the minimax rate is $M^{-\frac{2\beta}{2\beta+1}}$, where $M$ is the sample size and $\beta$ is the H\"older smoothness of the activation function. Importantly, this rate is independent of the embedding dimension $d$, the number of tokens $N$, and the rank $r$ of the weight matrix, provided that $rd \le (M/\log M)^{\frac{1}{2\beta+1}}$. These results highlight a fundamental statistical efficiency of attention-style models, even when the weight matrix and activation are not separately identifiable, and provide a theoretical understanding of attention mechanisms and guidance on training.

stat.ML↗

arXiv2025

Automatic reproducing kernel and regularization for learning convolution kernels

Learning convolution kernels in operators from data arises in numerous applications and represents an ill-posed inverse problem of broad interest. With scant prior information, kernel methods offer a natural nonparametric approach with regularization. However, a major challenge is to select a proper reproducing kernel, especially as operators and data vary. We show that the input data and convolution operator themselves induce an automatic, data-adaptive RKHS (DA-RKHS), obviating manual kernel selection. In particular, when the observation data is discrete and finite, there is a finite set of automatic basis functions sufficient to represent the estimators in the DA-RKHS, including the minimal-norm least-squares, Tikhonov, and conjugate-gradient estimators. We develop both Tikhonov and scalable iterative and hybrid algorithms using the automatic basis functions. Numerical experiments on integral, nonlocal, and aggregation operators confirm that our automatic RKHS regularization consistently outperforms standard ridge regression and Gaussian process methods with preselected kernels.

math.NA↗

arXiv2025

Minimax rates for learning kernels in operators

Learning kernels in operators from data lies at the intersection of inverse problems and statistical learning, providing a powerful framework for capturing non-local dependencies in function spaces and high-dimensional settings. In contrast to classical nonparametric regression, where the inverse problem is well-posed, kernel estimation involves a compact normal operator and an ill-posed deconvolution. To address these challenges, we introduce adaptive spectral Sobolev spaces, which unify Sobolev spaces and reproducing kernel Hilbert spaces, automatically discarding non-identifiable components and controlling terms with small eigenvalues. Within this framework, we establish the minimax convergence rates for the mean squared error under both polynomial and exponential spectral decay regimes. Methodologically, we develop a tamed least squares estimator achieving the minimax upper rates via controlling the left-tail probability for eigenvalues of the random normal matrix; and for the minimax lower rates, we resolve challenges from infinite-dimensional measures through their projections.

math.ST↗

arXiv2025

Probabilistic cellular automata with local transition matrices: synchronization, ergodicity, and inference

We introduce a new class of probabilistic cellular automata that are capable of exhibiting rich dynamics such as synchronization and ergodicity and can be easily inferred from data. The system is a finite-state locally interacting Markov chain on a circular graph. Each site's subsequent state is random, with a distribution determined by its neighborhood's empirical distribution multiplied by a local transition matrix. We establish sufficient and necessary conditions on the local transition matrix for synchronization and ergodicity. Also, we introduce novel least squares estimators for inferring the local transition matrix from various types of data, which may consist of either multiple trajectories, a long trajectory, or ensemble sequences without trajectory information. Under suitable identifiability conditions, we show the asymptotic normality of these estimators and provide non-asymptotic bounds for their accuracy.

math.PR↗

arXiv2025

Transformer learns the cross-task prior and regularization for in-context learning

Transformers have shown a remarkable ability for in-context learning (ICL), making predictions based on contextual examples. However, while theoretical analyses have explored this prediction capability, the nature of the inferred context and its utility for downstream predictions remain open questions. This paper aims to address these questions by examining ICL for inverse linear regression (ILR), where context inference can be characterized by unsupervised learning of underlying weight vectors. Focusing on the challenging scenario of rank-deficient inverse problems, where context length is smaller than the number of unknowns in the weight vectors and regularization is necessary, we introduce a linear transformer to learn the inverse mapping from contextual examples to the underlying weight vector. Our findings reveal that the transformer implicitly learns both a prior distribution and an effective regularization strategy, outperforming traditional ridge regression and regularization methods. A key insight is the necessity of low task dimensionality relative to the context length for successful learning. Furthermore, we numerically verify that the error of the transformer estimator scales linearly with the noise level, the ratio of task dimension to context length, and the condition number of the input data. These results not only demonstrate the potential of transformers for solving ill-posed inverse problems, but also provide a new perspective towards understanding the knowledge extraction mechanism within transformers.

cs.LG↗

arXiv2025

Optimal minimax rate of learning nonlocal interaction kernels

Nonparametric estimation of nonlocal interaction kernels is crucial in various applications involving interacting particle systems. The inference challenge, situated at the nexus of statistical learning and inverse problems, arises from the nonlocal dependency. A central question is whether the optimal minimax rate of convergence for this problem aligns with the rate of $M^{-\frac{2β}{2β+1}}$ in classical nonparametric regression, where $M$ is the sample size and $β$ represents the regularity index of the radial kernel. Our study confirms this alignment for systems with a finite number of particles. We introduce a tamed least squares estimator (tLSE) that achieves the optimal convergence rate when $β\geq 1/4$ for a broad class of exchangeable distributions by leveraging random matrix theory and Sobolev embedding. The upper minimax rate relies on fourth-moment bounds for normal vectors and nonasymptotic bounds for the left tail probability of the smallest eigenvalue of the normal matrix. The lower minimax rate is derived using the Fano-Tsybakov hypothesis testing method. Our tLSE method offers a straightforward approach for establishing the optimal minimax rate for models with either local or nonlocal dependency.

math.ST↗

arXiv2025

Energy-Aware Routing Algorithm for Mobile Ground-to-Air Charging

We investigate the problem of energy-constrained planning for a cooperative system of an Unmanned Ground Vehicles (UGV) and an Unmanned Aerial Vehicle (UAV). In scenarios where the UGV serves as a mobile base to ferry the UAV and as a charging station to recharge the UAV, we formulate a novel energy-constrained routing problem. To tackle this problem, we design an energy-aware routing algorithm, aiming to minimize the overall mission duration under the energy limitations of both vehicles. The algorithm first solves a Traveling Salesman Problem (TSP) to generate a guided tour. Then, it employs the Monte-Carlo Tree Search (MCTS) algorithm to refine the tour and generate paths for the two vehicles. We evaluate the performance of our algorithm through extensive simulations and a proof-of-concept experiment. The results show that our algorithm consistently achieves near-optimal mission time and maintains fast running time across a wide range of problem instances.

cs.RO↗

arXiv2024

Self-test loss functions for learning weak-form operators and gradient flows

The construction of loss functions presents a major challenge in data-driven modeling involving weak-form operators in PDEs and gradient flows, particularly due to the need to select test functions appropriately. We address this challenge by introducing self-test loss functions, which employ test functions that depend on the unknown parameters, specifically for cases where the operator depends linearly on the unknowns. The proposed self-test loss function conserves energy for gradient flows and coincides with the expected log-likelihood ratio for stochastic differential equations. Importantly, it is quadratic, facilitating theoretical analysis of identifiability and well-posedness of the inverse problem, while also leading to efficient parametric or nonparametric regression algorithms. It is computationally simple, requiring only low-order derivatives or even being entirely derivative-free, and numerical experiments demonstrate its robustness against noisy and discrete data.

stat.ML↗

arXiv2024

Robust First and Second-Order Differentiation for Regularized Optimal Transport

Applications such as unbalanced and fully shuffled regression can be approached by optimizing regularized optimal transport (OT) distances, such as the entropic OT and Sinkhorn distances. A common approach for this optimization is to use a first-order optimizer, which requires the gradient of the OT distance. For faster convergence, one might also resort to a second-order optimizer, which additionally requires the Hessian. The computations of these derivatives are crucial for efficient and accurate optimization. However, they present significant challenges in terms of memory consumption and numerical instability, especially for large datasets and small regularization strengths. We circumvent these issues by analytically computing the gradients for OT distances and the Hessian for the entropic OT distance, which was not previously used due to intricate tensor-wise calculations and the complex dependency on parameters within the bi-level loss function. Through analytical derivation and spectral analysis, we identify and resolve the numerical instability caused by the singularity and ill-posedness of a key linear system. Consequently, we achieve scalable and stable computation of the Hessian, enabling the implementation of the stochastic gradient descent (SGD)-Newton methods. Tests on shuffled regression examples demonstrate that the second stage of the SGD-Newton method converges orders of magnitude faster than the gradient descent-only method while achieving significantly more accurate parameter estimations.

math.NA↗

arXiv2024

A Data-Adaptive Prior for Bayesian Learning of Kernels in Operators

Kernels are efficient in representing nonlocal dependence and they are widely used to design operators between function spaces. Thus, learning kernels in operators from data is an inverse problem of general interest. Due to the nonlocal dependence, the inverse problem can be severely ill-posed with a data-dependent singular inversion operator. The Bayesian approach overcomes the ill-posedness through a non-degenerate prior. However, a fixed non-degenerate prior leads to a divergent posterior mean when the observation noise becomes small, if the data induces a perturbation in the eigenspace of zero eigenvalues of the inversion operator. We introduce a data-adaptive prior to achieve a stable posterior whose mean always has a small noise limit. The data-adaptive prior's covariance is the inversion operator with a hyper-parameter selected adaptive to data by the L-curve method. Furthermore, we provide a detailed analysis on the computational practice of the data-adaptive prior, and demonstrate it on Toeplitz matrices and integral operators. Numerical tests show that a fixed prior can lead to a divergent posterior mean in the presence of any of the four types of errors: discretization error, model error, partial observation and wrong noise assumption. In contrast, the data-adaptive prior always attains posterior means with small noise limits.

stat.ML↗

arXiv2024

Differential cross-section measurements for neutron-induced $α$ production reactions on carbon across neutron energy range of 6.2 to 76 MeV

Angle-differential cross sections for neutron-induced $α$ production in carbon were determined at thirty discrete neutron energy levels ranging from 6.2 to 76 MeV at the Back-n white neutron source of the China Spallation Neutron Source. Utilizing the $ΔE-E$ telescopes within the Light-charged Particle Detector Array spanning angular measurements from 24.5°to 155.5° in the laboratory frame, the $^{12}C(n,α)x$ reaction cross sections were obtained. These experimental findings exhibit a strong concordance with prior results and have been benchmarked against theoretical estimates from codes such as TALYS, Geant4, and assessments from the ENDF/B-VIII.0 database. Remarkably, distinct resonance-like features were observed at neutron energies of 13.7, 22.4, 29.5, and 61.8 MeV, marking their first-time identification in the literature.Furthermore, a comparative analysis involving the theoretical Distorted Wave Born Approximation was conducted.

nucl-ex↗

arXiv2024

Small noise analysis for Tikhonov and RKHS regularizations

Regularization plays a pivotal role in ill-posed machine learning and inverse problems. However, the fundamental comparative analysis of various regularization norms remains open. We establish a small noise analysis framework to assess the effects of norms in Tikhonov and RKHS regularizations, in the context of ill-posed linear inverse problems with Gaussian noise. This framework studies the convergence rates of regularized estimators in the small noise limit and reveals the potential instability of the conventional L2-regularizer. We solve such instability by proposing an innovative class of adaptive fractional RKHS regularizers, which covers the L2 Tikhonov and RKHS regularizations by adjusting the fractional smoothness parameter. A surprising insight is that over-smoothing via these fractional RKHSs consistently yields optimal convergence rates, but the optimal hyper-parameter may decay too fast to be selected in practice.

stat.ML↗