Efficient Algorithms for Computing Random Walk Centrality

Random walk centrality is a fundamental metric in graph mining for quantifying node importance and influence, defined as the weighted average of hitting times to a node from all other nodes. Despite its ability to capture rich graph structural information and its wide range of applications, computing this measure for large networks remains impractical due to the computational demands of existing methods. In this paper, we present a novel formulation of random walk centrality, underpinning two scalable algorithms: one leveraging approximate Cholesky factorization and sparse inverse estimation, while the other sampling rooted spanning trees. Both algorithms operate in near-linear time and provide strong approximation guarantees. Extensive experiments on large real-world networks, including one with over 10 million nodes, demonstrate the efficiency and approximation quality of the proposed algorithms.

Extensions of Robbins-Siegmund Theorem with Applications in Reinforcement Learning

The Robbins-Siegmund theorem establishes the convergence of stochastic processes that are almost supermartingales and is foundational for analyzing a wide range of stochastic iterative algorithms in stochastic approximation and reinforcement learning (RL). However, its original form has a significant limitation as it requires the zero-order term to be summable. In many important RL applications, this summable condition, however, cannot be met. This limitation motivates us to extend the Robbins-Siegmund theorem for almost supermartingales where the zero-order term is not summable but only square summable. Particularly, we introduce a novel and mild assumption on the increments of the stochastic processes. This together with the square summable condition enables an almost sure convergence to a bounded set. Additionally, we further provide almost sure convergence rates, high probability concentration bounds, and $L^p$ convergence rates. We then apply the new results in stochastic approximation and RL. Notably, we obtain the first almost sure convergence rate, the first high probability concentration bound, and the first $L^p$ convergence rate for $Q$-learning with linear function approximation.

Finite Sample Analysis of Linear Temporal Difference Learning with Arbitrary Features

Linear TD($\lambda$) is one of the most fundamental reinforcement learning algorithms for policy evaluation. Previously, convergence rates are typically established under the assumption of linearly independent features, which does not hold in many practical scenarios. This paper instead establishes the first $L^2$ convergence rates for linear TD($\lambda$) operating under arbitrary features, without making any algorithmic modification or additional assumptions. Our results apply to both the discounted and average-reward settings. To address the potential non-uniqueness of solutions resulting from arbitrary features, we develop a novel stochastic approximation result featuring convergence rates to the solution set instead of a single point.

Linear $Q$-Learning Does Not Diverge: Convergence Rates to a Bounded Set

$Q$-learning is one of the most fundamental reinforcement learning algorithms. Previously, it is widely believed that $Q$-learning with linear function approximation (i.e., linear $Q$-learning) suffers from possible divergence. This paper instead establishes the first $L^2$ convergence rate of linear $Q$-learning to a bounded set. Notably, we do not make any modification to the original linear $Q$-learning algorithm, do not make any Bellman completeness assumption, and do not make any near-optimality assumption on the behavior policy. All we need is an $\epsilon$-softmax behavior policy with an adaptive temperature. The key to our analysis is the general result of stochastic approximations under Markovian noise with fast-changing transition functions. As a side product, we also use this general result to establish the $L^2$ convergence rate of tabular $Q$-learning with an $\epsilon$-softmax behavior policy, for which we rely on a novel pseudo-contraction property of the weighted Bellman optimality operator.

Almost Sure Convergence Rates and Concentration of Stochastic Approximation and Reinforcement Learning with Markovian Noise

This paper establishes the first almost sure convergence rate and the first maximal concentration bound with exponential tails for general contractive stochastic approximation algorithms with Markovian noise. As a corollary, we also obtain convergence rates in $L^p$. Key to our successes is a novel discretization of the mean ODE of stochastic approximation algorithms using intervals with diminishing (instead of constant) length. As applications, we provide the first almost sure convergence rate for $Q$-learning with Markovian samples without count-based learning rates. We also provide the first concentration bound for off-policy temporal difference learning with Markovian samples.

OpenSlot: Mixed Open-set Recognition with Object-centric Learning

Existing open-set recognition (OSR) studies typically assume that each image contains only one class label, and the unknown test set (negative) has a disjoint label space from the known test set (positive), a scenario termed full-label shift. This paper introduces the mixed OSR problem, where test images contain multiple class semantics, with known and unknown classes co-occurring in negatives, leading to a more challenging super-label shift. Addressing the mixed OSR requires classification models to accurately distinguish different class semantics within images and measure their "knowness". In this study, we propose the OpenSlot framework, built upon object-centric learning. OpenSlot utilizes slot features to represent diverse class semantics and produce class predictions. Through our proposed anti-noise-slot (ANS) technique, we mitigate the impact of noise (invalid and background) slots during classification training, effectively addressing the semantic misalignment between class predictions and the ground truth. We conduct extensive experiments with OpenSlot on mixed & conventional OSR benchmarks. Without elaborate designs, OpenSlot not only exceeds existing OSR studies in detecting super-label shifts across single & multi-label mixed OSR tasks but also achieves state-of-the-art performance on conventional benchmarks. Remarkably, our method can localize class objects without using bounding boxes during training. The competitive performance in open-set object detection demonstrates OpenSlot's ability to explicitly explain label shifts and benefits in computational efficiency and generalization.

2L3: Lifting Imperfect Generated 2D Images into Accurate 3D

Reconstructing 3D objects from a single image is an intriguing but challenging problem. One promising solution is to utilize multi-view (MV) 3D reconstruction to fuse generated MV images into consistent 3D objects. However, the generated images usually suffer from inconsistent lighting, misaligned geometry, and sparse views, leading to poor reconstruction quality. To cope with these problems, we present a novel 3D reconstruction framework that leverages intrinsic decomposition guidance, transient-mono prior guidance, and view augmentation to cope with the three issues, respectively. Specifically, we first leverage to decouple the shading information from the generated images to reduce the impact of inconsistent lighting; then, we introduce mono prior with view-dependent transient encoding to enhance the reconstructed normal; and finally, we design a view augmentation fusion strategy that minimizes pixel-level loss in generated sparse views and semantic loss in augmented random views, resulting in view-consistent geometry and detailed textures. Our approach, therefore, enables the integration of a pre-trained MV image generator and a neural network-based volumetric signed distance function (SDF) representation for a single image to 3D object reconstruction. We evaluate our framework on various datasets and demonstrate its superior performance in both quantitative and qualitative assessments, signifying a significant advancement in 3D object reconstruction. Compared with the latest state-of-the-art method Syncdreamer~\cite{liu2023syncdreamer}, we reduce the Chamfer Distance error by about 36\% and improve PSNR by about 30\% .

Holistic Inverse Rendering of Complex Facade via Aerial 3D Scanning

In this work, we use multi-view aerial images to reconstruct the geometry, lighting, and material of facades using neural signed distance fields (SDFs). Without the requirement of complex equipment, our method only takes simple RGB images captured by a drone as inputs to enable physically based and photorealistic novel-view rendering, relighting, and editing. However, a real-world facade usually has complex appearances ranging from diffuse rocks with subtle details to large-area glass windows with specular reflections, making it hard to attend to everything. As a result, previous methods can preserve the geometry details but fail to reconstruct smooth glass windows or verse vise. In order to address this challenge, we introduce three spatial- and semantic-adaptive optimization strategies, including a semantic regularization approach based on zero-shot segmentation techniques to improve material consistency, a frequency-aware geometry regularization to balance surface smoothness and details in different surfaces, and a visibility probe-based scheme to enable efficient modeling of the local lighting in large-scale outdoor environments. In addition, we capture a real-world facade aerial 3D scanning image set and corresponding point clouds for training and benchmarking. The experiment demonstrates the superior quality of our method on facade holistic inverse rendering, novel view synthesis, and scene editing compared to state-of-the-art baselines.