While the phenomenon of grokking, i.e., delayed generalization, has been studied extensively, it remains an open problem whether there is a mathematical framework that characterizes what kind of features will emerge, how and in which conditions it happens, and is closely related to the gradient dynamics of the training, for complex structured inputs. We propose a novel framework, named $\mathbf{Li}_2$, that captures three key stages for the grokking behavior of 2-layer nonlinear networks: (I) Lazy learning, (II) independent feature learning and (III) interactive feature learning. At the lazy learning stage, top layer overfits to random hidden representation and the model appears to memorize, and at the same time, the backpropagated gradient $G_F$ from the top layer now carries information about the target label, with a specific structure that enables each hidden node to learn their representation independently. Interestingly, the independent dynamics follows exactly the gradient ascent of an energy function $E$, and its local maxima are precisely the emerging features. We study whether these local-optima induced features are generalizable, their representation power, and how they change on sample size, in group arithmetic tasks. When hidden nodes start to interact in the later stage of learning, we provably show how $G_F$ changes to focus on missing features that need to be learned. Our study sheds lights on roles played by key hyperparameters such as weight decay, learning rate and sample sizes in grokking, leads to provable scaling laws of feature emergence, memorization and generalization, and reveals why recent optimizers such as Muon can be effective, from the first principles of gradient dynamics. Our analysis can be extended to multi-layers. The code is available at https://github.com/yuandong-tian/understanding/tree/main/ssl/real-dataset/cogo.

Hand gesture classification using high-quality structured data such as videos, images, and hand skeletons is a well-explored problem in computer vision. Leveraging low-power, cost-effective biosignals, e.g. surface electromyography (sEMG), allows for continuous gesture prediction on wearables. In this paper, we demonstrate that learning representations from weak-modality data that are aligned with those from structured, high-quality data can improve representation quality and enables zero-shot classification. Specifically, we propose a Contrastive Pose-EMG Pre-training (CPEP) framework to align EMG and pose representations, where we learn an EMG encoder that produces high-quality and pose-informative representations. We assess the gesture classification performance of our model through linear probing and zero-shot setups. Our model outperforms emg2pose benchmark models by up to 21% on in-distribution gesture classification and 72% on unseen (out-of-distribution) gesture classification.

The ubiquity of missing data in urban intelligence systems, attributable to adverse environmental conditions and equipment failures, poses a significant challenge to the efficacy of downstream applications, notably in the realms of traffic forecasting and energy consumption prediction. Therefore, it is imperative to develop a robust spatio-temporal learning methodology capable of extracting meaningful insights from incomplete datasets. Despite the existence of methodologies for spatio-temporal graph forecasting in the presence of missing values, unresolved issues persist. Primarily, the majority of extant research is predicated on time-series analysis, thereby neglecting the dynamic spatial correlations inherent in sensor networks. Junbo Zhang is the corresponding author. This research was done when the first author was an intern at JD Intelligent Cities Research & JD iCity under the supervision of the fifth author. The model is comprised of three principal components: an input preprocessing module, an attention-based spatio-temporal forecasting network (STAFN), and an auxiliary learning task, which draws inspiration from Masking AutoEncoders to enhance the robustness of spatio-temporal representation learning. Empirical evaluations on real-world datasets demonstrate that GeoMAE significantly outperforms existing benchmarks, achieving up to 13.20% relative improvement over the best baseline models. Introduction Spatio-temporal representation learning has emerged as a pivotal research area, underpinning various intelligent applications in smart cities that play crucial roles across multiple domains. For instance, precise weather forecasting can significantly mitigate the detrimental impacts of natural disasters through early prevention; advanced traffic prediction systems help optimize traffic flow and substantially reduce congestion; environmental monitoring enables rapid identification of pollution hotspots within urban environments.

In this work, we introduce a new information-theoretic perspective on Multiple Instance Learning (MIL) for parameter estimation with i.i.d. data, and show that MIL can outperform single-instance learners in low-signal regimes. Prior work [Nachman and Thaler, 2021] argued that single-instance methods are often sufficient, but this conclusion presumes enough single-instance signal to train near-optimal classifiers. We demonstrate that even state-of-the-art single-instance models can fail to reach optimal classifier performance in challenging low-signal regimes, whereas MIL can mitigate this sub-optimality. As a concrete application, we constrain Wilson coefficients of the Standard Model Effective Field Theory (SMEFT) using kinematic information from subatomic particle collision events at the Large Hadron Collider (LHC). In experiments, we observe that under specific modeling and weak signal conditions, pooling instances can increase the effective Fisher information compared to single-instance approaches.

Many users and contributors of large open-source projects report software defects or enhancement requests (known as bug reports) to the issue-tracking systems. However, they sometimes report issues that have already been reported. First, they may not have time to do sufficient research on existing bug reports. Second, they may not possess the right expertise in that specific area to realize that an existing bug report is essentially elaborating on the same matter, perhaps with a different wording. In this paper, we propose a novel approach based on machine learning methods that can automatically detect duplicate bug reports in an open bug repository based on the textual data in the reports. We present six alternative methods: Topic modeling, Gaussian Naive Bayes, deep learning, time-based organization, clustering, and summarization using a generative pre-trained transformer large language model. Additionally, we introduce a novel threshold-based approach for duplicate identification, in contrast to the conventional top-k selection method that has been widely used in the literature. Our approach demonstrates promising results across all the proposed methods, achieving accuracy rates ranging from the high 70%'s to the low 90%'s. We evaluated our methods on a public dataset of issues belonging to an Eclipse open-source project.

The intrinsic alignments (IA) of galaxies, a key contaminant in weak lensing analyses, arise from correlations in galaxy shapes driven by tidal interactions and galaxy formation processes. Accurate IA modeling is essential for robust cosmological inference, but current approaches rely on perturbative methods that break down on nonlinear scales or on expensive simulations. We introduce IAEmu, a neural network-based emulator that predicts the galaxy position-position ($ξ$), position-orientation ($ω$), and orientation-orientation ($η$) correlation functions and their uncertainties using mock catalogs based on the halo occupation distribution (HOD) framework. Compared to simulations, IAEmu achieves ~3% average error for $ξ$ and ~5% for $ω$, while capturing the stochasticity of $η$ without overfitting. The emulator provides both aleatoric and epistemic uncertainties, helping identify regions where predictions may be less reliable. We also demonstrate generalization to non-HOD alignment signals by fitting to IllustrisTNG hydrodynamical simulation data. As a fully differentiable neural network, IAEmu enables $\sim$10,000$\times$ speed-ups in mapping HOD parameters to correlation functions on GPUs, compared to CPU-based simulations. This acceleration facilitates inverse modeling via gradient-based sampling, making IAEmu a powerful surrogate model for galaxy bias and IA studies with direct applications to Stage IV weak lensing surveys.

3D Gaussian Splatting (3DGS) has demonstrated remarkable effectiveness in 3D reconstruction, achieving high-quality results with real-time radiance field rendering. However, a key challenge is the substantial storage cost: reconstructing a single scene typically requires millions of Gaussian splats, each represented by 59 floating-point parameters, resulting in approximately 1 GB of memory. To address this challenge, we propose a compression method by building separate attribute codebooks and storing only discrete code indices. Specifically, we employ noise-substituted vector quantization technique to jointly train the codebooks and model features, ensuring consistency between gradient descent optimization and parameter discretization. Our method reduces the memory consumption efficiently (around $45\times$) while maintaining competitive reconstruction quality on standard 3D benchmark scenes. Experiments on different codebook sizes show the trade-off between compression ratio and image quality. Furthermore, the trained compressed model remains fully compatible with popular 3DGS viewers and enables faster rendering speed, making it well-suited for practical applications.

This chapter opens with a review of classic tools for regression, a subset of machine learning that seeks to find relationships between variables. With the advent of scientific machine learning this field has moved from a purely data-driven (statistical) formalism to a constrained or ``physics-informed'' formalism, which integrates physical knowledge and methods from traditional computational engineering. In the first part, we introduce the general concepts and the statistical flavor of regression versus other forms of curve fitting. We then move to an overview of traditional methods from machine learning and their classification and ways to link these to traditional computational science. Finally, we close with a note on methods to combine machine learning and numerical methods for physics

In this paper, we investigate a second-order stochastic algorithm for solving large-scale binary classification problems. We propose to make use of a new hybrid stochastic Newton algorithm that includes two weighted components in the Hessian matrix estimation: the first one coming from the natural Hessian estimate and the second associated with the stochastic gradient information. Our motivation comes from the fact that both parts evaluated at the true parameter of logistic regression, are equal to the Hessian matrix. This new formulation has several advantages and it enables us to prove the almost sure convergence of our stochastic algorithm to the true parameter. Moreover, we significantly improve the almost sure rate of convergence to the Hessian matrix. Furthermore, we establish the central limit theorem for our hybrid stochastic Newton algorithm. Finally, we show a surprising result on the almost sure convergence of the cumulative excess risk.

Bipartite networks are widely used to encode the ecological interactions. Being able to compare the organization of bipartite networks is a first step toward a better understanding of how environmental factors shape community structure and resilience. Yet current methods for structure detection in bipartite networks overlook shared patterns across collections of networks. We introduce the \emph{colBiSBM}, a family of probabilistic models for collections of bipartite networks that extends the classical Latent Block Model (LBM). The proposed framework assumes that networks are independent realizations of a shared mesoscale structure, encoded through common inter-block connectivity parameters. We establish identifiability conditions for the different variants of \emph{colBiSBM} and develop a variational EM algorithm for parameter estimation, coupled with an adaptation of the Integrated Classification Likelihood (ICL) criterion for model selection. We demonstrate how our approach can be used to classify networks based on their topology or organization. Simulation studies highlight the ability of \emph{colBiSBM} to recover common structures, improve clustering performance, and enhance link prediction by borrowing strength across networks. An application to plant--pollinator networks highlights how the method uncovers shared ecological roles and partitions networks into sub-collections with similar connectivity patterns. These results illustrate the methodological and practical advantages of joint modeling over separate network analyses in the study of bipartite systems.