Neural Information Processing Systems http://nips.cc/

Solving statistical learning problems often involves nonconvex optimization. Despite the empirical success of nonconvex statistical optimization methods, their global dynamics, especially convergence to the desirable local minima, remain less well understood in theory. In this paper, we propose a new analytic paradigm based on diffusion processes to characterize the global dynamics of nonconvex statistical optimization. As a concrete example, we study stochastic gradient descent (SGD) for the tensor decomposition formulation of independent component analysis. In particular, we cast different phases of SGD into diffusion processes, i.e., solutions to stochastic differential equations.

Business Process Simulation (BPS) is a critical tool for analyzing and improving organizational processes by estimating the impact of process changes. A key component of BPS is the case-arrival model, which determines the pattern of new case entries into a process. Although accurate case-arrival modeling is essential for reliable simulations--as it influences waiting and overall cycle times--existing approaches often rely on oversimplified static distributions of inter-arrival times. These approaches fail to capture the dynamic and temporal complexities inherent in organizational environments, leading to less accurate and reliable outcomes. To address this limitation, we propose Auto Time Kernel Density Estimation (AT-KDE), a divide-and-conquer approach that models arrival times of processes by incorporating global dynamics, day-of-week variations, and intraday distributional changes, ensuring both precision and scalability. Experiments conducted across 20 diverse processes demonstrate that AT-KDE is far more accurate and robust than existing approaches while maintaining sensible execution time efficiency.

In recent years, deep learning with Convolutional Neural Networks (CNNs) has achieved remarkable results in the field of HMER (Handwritten Mathematical Expression Recognition). However, it remains challenging to improve performance with limited labeled training data. This paper presents, for the first time, a simple yet effective semi-supervised HMER framework by introducing dual-branch semi-supervised learning. Specifically, we simplify the conventional deep co-training from consistency regularization to cross-supervised learning, where the prediction of one branch is used as a pseudo-label to supervise the other branch directly end-to-end. Considering that the learning of the two branches tends to converge in the later stages of model optimization, we also incorporate a weak-to-strong strategy by applying different levels of augmentation to each branch, which behaves like expanding the training data and improving the quality of network training. Meanwhile, We propose a novel module, Global Dynamic Counting Module(GDCM), to enhance the performance of the HMER decoder, which alleviates recognition inaccuracies in long-distance formula recognition and the occurrence of repeated characters. We release our code at https://github.com/chenkehua/SemiHMER.

This paper aims to study the global dynamics of nonconvex statistical optimization based on diffusion processes. As an example of non-convex problems, this paper discusses in details the SGD applied on the tensor decomposition formulation of independent component analysis (ICA). An interesting finding in this paper is a three-phases phenomenon of the global dynamics of SGD to capture the transition of SGD solution from unstable initialization to finally stable local minimum. Overall, this paper is well written and it addresses a very challenge problem. This paper serves as a first step in the theoretical understanding of global dynamics of SGD, and is believed to stimulate many work on the global dynamic of non-convex optimizations. Q1: Discuss how to generalize it other non-convex models?

Solving statistical learning problems often involves nonconvex optimization. Despite the empirical success of nonconvex statistical optimization methods, their global dynamics, especially convergence to the desirable local minima, remain less well understood in theory. In this paper, we propose a new analytic paradigm based on diffusion processes to characterize the global dynamics of nonconvex statistical optimization. As a concrete example, we study stochastic gradient descent (SGD) for the tensor decomposition formulation of independent component analysis. In particular, we cast different phases of SGD into diffusion processes, i.e., solutions to stochastic differential equations.

Accurate modeling of system dynamics holds intriguing potential in broad scientific fields including cytodynamics and fluid mechanics. This task often presents significant challenges when (i) observations are limited to cross-sectional samples (where individual trajectories are inaccessible for learning), and moreover, (ii) the behaviors of individual particles are heterogeneous (especially in biological systems due to biodiversity). To address them, we introduce a novel framework dubbed correlational Lagrangian Schr\"odinger bridge (CLSB), aiming to seek for the evolution "bridging" among cross-sectional observations, while regularized for the minimal population "cost". In contrast to prior methods relying on \textit{individual}-level regularizers for all particles \textit{homogeneously} (e.g. restraining individual motions), CLSB operates at the population level admitting the heterogeneity nature, resulting in a more generalizable modeling in practice. To this end, our contributions include (1) a new class of population regularizers capturing the temporal variations in multivariate relations, with the tractable formulation derived, (2) three domain-informed instantiations based on genetic co-expression stability, and (3) an integration of population regularizers into data-driven generative models as constrained optimization, and a numerical solution, with further extension to conditional generative models. Empirically, we demonstrate the superiority of CLSB in single-cell sequencing data analyses such as simulating cell development over time and predicting cellular responses to drugs of varied doses.

A recently released Temporal Graph Benchmark is analyzed in the context of Dynamic Link Property Prediction. We outline our observations and propose a trivial optimization-free baseline of "recently popular nodes" outperforming other methods on medium and large-size datasets in the Temporal Graph Benchmark. We propose two measures based on Wasserstein distance which can quantify the strength of short-term and long-term global dynamics of datasets. By analyzing our unexpectedly strong baseline, we show how standard negative sampling evaluation can be unsuitable for datasets with strong temporal dynamics. We also show how simple negative-sampling can lead to model degeneration during training, resulting in impossible to rank, fully saturated predictions of temporal graph networks. We propose improved negative sampling schemes for both training and evaluation and prove their usefulness. We conduct a comparison with a model trained non-contrastively without negative sampling. Our results provide a challenging baseline and indicate that temporal graph network architectures need deep rethinking for usage in problems with significant global dynamics, such as social media, cryptocurrency markets or e-commerce. We open-source the code for baselines, measures and proposed negative sampling schemes.

This paper proposes an integration of surrogate modeling and topology to significantly reduce the amount of data required to describe the underlying global dynamics of robot controllers, including closed-box ones. A Gaussian Process (GP), trained with randomized short trajectories over the state-space, acts as a surrogate model for the underlying dynamical system. Then, a combinatorial representation is built and used to describe the dynamics in the form of a directed acyclic graph, known as {\it Morse graph}. The Morse graph is able to describe the system's attractors and their corresponding regions of attraction (\roa). Furthermore, a pointwise confidence level of the global dynamics estimation over the entire state space is provided. In contrast to alternatives, the framework does not require estimation of Lyapunov functions, alleviating the need for high prediction accuracy of the GP. The framework is suitable for data-driven controllers that do not expose an analytical model as long as Lipschitz-continuity is satisfied. The method is compared against established analytical and recent machine learning alternatives for estimating \roa s, outperforming them in data efficiency without sacrificing accuracy. Link to code: https://go.rutgers.edu/49hy35en

Understanding the global dynamics of a robot controller, such as identifying attractors and their regions of attraction (RoA), is important for safe deployment and synthesizing more effective hybrid controllers. This paper proposes a topological framework to analyze the global dynamics of robot controllers, even data-driven ones, in an effective and explainable way. It builds a combinatorial representation representing the underlying system's state space and non-linear dynamics, which is summarized in a directed acyclic graph, the Morse graph. The approach only probes the dynamics locally by forward propagating short trajectories over a state-space discretization, which needs to be a Lipschitz-continuous function. The framework is evaluated given either numerical or data-driven controllers for classical robotic benchmarks. It is compared against established analytical and recent machine learning alternatives for estimating the RoAs of such controllers. It is shown to outperform them in accuracy and efficiency. It also provides deeper insights as it describes the global dynamics up to the discretization's resolution. This allows to use the Morse graph to identify how to synthesize controllers to form improved hybrid solutions or how to identify the physical limitations of a robotic system.