LLMs demonstrate significant inference capacities in complicated machine learning tasks, using the Transformer model as its backbone. Motivated by the limited understanding of such models on the unsupervised learning problems, we study the learning guarantees of Transformers in performing multi-class clustering of the Gaussian Mixture Models. We develop a theory drawing strong connections between the Softmax Attention layers and the workflow of the EM algorithm on clustering the mixture of Gaussians. Our theory provides approximation bounds for the Expectation and Maximization steps by proving the universal approximation abilities of multivariate mappings by Softmax functions. In addition to the approximation guarantees, we also show that with a sufficient number of pre-training samples and an initialization, Transformers can achieve the minimax optimal rate for the problem considered. Our extensive simulations empirically verified our theory by revealing the strong learning capacities of Transformers even beyond the assumptions in the theory, shedding light on the powerful inference capacities of LLMs.

High-voltage transmission lines are located far from the road, resulting in inconvenient inspection work and rising maintenance costs. Intelligent inspection of power transmission lines has become increasingly important. However, subsequent intelligent inspection relies on accurately detecting various key components. Due to the low detection accuracy of key components in transmission line image inspection, this paper proposed an improved object detection model based on the YOLOv5s (You Only Look Once Version 5 Small) model to improve the detection accuracy of key components of transmission lines. According to the characteristics of the power grid inspection image, we first modify the distance measurement in the k-means clustering to improve the anchor matching of the YOLOv5s model. Then, we add the convolutional block attention module (CBAM) attention mechanism to the backbone network to improve accuracy. Finally, we apply the focal loss function to reduce the impact of class imbalance. Our improved method's mAP (mean average precision) reached 98.1%, the precision reached 97.5%, the recall reached 94.4%, and the detection rate reached 84.8 FPS (frames per second). The experimental results show that our improved model improves detection accuracy and has performance advantages over other models.

Understanding disease progression at the molecular pathway level usually requires capturing both structural dependencies between pathways and the temporal dynamics of disease evolution. In this work, we solve the former challenge by developing a biologically informed graph-forming method to efficiently construct pathway graphs for subjects from our newly curated JR5558 mouse transcriptomics dataset. We then develop Graph-level Pseudotime Analysis (GPA) to infer graph-level trajectories that reveal how disease progresses at the population level, rather than in individual subjects. Based on the trajectories estimated by GPA, we identify the most sensitive pathways that drive disease stage transitions. In addition, we measure changes in pathway features using neural stochastic differential equations (SDEs), which enables us to formally define and compute pathway stability and disease bifurcation points (points of no return), two fundamental problems in disease progression research. We further extend our theory to the case when pathways can interact with each other, enabling a more comprehensive and multi-faceted characterization of disease phenotypes. The comprehensive experimental results demonstrate the effectiveness of our framework in reconstructing the dynamics of the pathway, identifying critical transitions, and providing novel insights into the mechanistic understanding of disease evolution.

Effective self-supervised learning (SSL) techniques have been key to unlocking large datasets for representation learning. While many promising methods have been developed using online corpora and captioned photographs, their application to scientific domains, where data encodes highly specialized knowledge, remains in its early stages. We present a self-supervised masked modeling framework for 3D particle trajectory analysis in Time Projection Chambers (TPCs). These detectors produce globally sparse (<1% occupancy) but locally dense point clouds, capturing meter-scale particle trajectories at millimeter resolution. Starting with PointMAE, this work proposes volumetric tokenization to group sparse ionization points into resolution-agnostic patches, as well as an auxiliary energy infilling task to improve trajectory semantics. This approach -- which we call Point-based Liquid Argon Masked Autoencoder (PoLAr-MAE) -- achieves 99.4% track and 97.7% shower classification F-scores, matching that of supervised baselines without any labeled data. While the model learns rich particle trajectory representations, it struggles with sub-token phenomena like overlapping or short-lived particle trajectories. To support further research, we release PILArNet-M -- the largest open LArTPC dataset (1M+ events, 5.2B labeled points) -- to advance SSL in high energy physics (HEP). Project site: https://youngsm.com/polarmae/

Discriminative dictionary learning (DL) has been widely studied in various pattern classification problems. Most of the existing DL methods aim to learn a synthesis dictionary to represent the input signal while enforcing the representation coefficients and/or representation residual to be discriminative.

We present a general framework for graph clustering where a label is observed to each pair of nodes. This allows a very rich encoding of various types of pairwise interactions between nodes. We propose a new tractable approach to this problem based on maximum likelihood estimator and convex optimization. We analyze our algorithm under a general generative model, and provide both necessary and sufficient conditions for successful recovery of the underlying clusters. Our theoretical results cover and subsume a wide range of existing graph clustering results including planted partition, weighted clustering and partially observed graphs. Furthermore, the result is applicable to novel settings including time-varying graphs such that new insights can be gained on solving these problems. Our theoretical findings are further supported by empirical results on both synthetic and real data.

The problem of drawing samples from a discrete distribution can be converted into a discrete optimization problem [1, 2, 3, 4]. In this work, we show how sampling from a continuous distribution can be converted into an optimization problem over continuous space. Central to the method is a stochastic process recently described in mathematical statistics that we call the Gumbel process.

Distributed learning of probabilistic models from multiple data repositories with minimum communication is increasingly important. We study a simple communication-efficient learning framework that first calculates the local maximum likelihood estimates (MLE) based on the data subsets, and then combines the local MLEs to achieve the best possible approximation to the global MLE given the whole dataset. We study this framework's statistical properties, showing that the efficiency loss compared to the global setting relates to how much the underlying distribution families deviate from full exponential families, drawing connection to the theory of information loss by Fisher, Rao and Efron. We show that the "full-exponential-family-ness" represents the lower bound of the error rate of arbitrary combinations of local MLEs, and is achieved by a KL-divergence-based combination method but not by a more common linear combination method. We also study the empirical properties of both methods, showing that the KL method significantly outperforms linear combination in practical settings with issues such as model misspecification, non-convexity, and heterogeneous data partitions.

The global Markov property for Gaussian graphical models ensures graph separation implies conditional independence.

Gaussian process regression can be accelerated by constructing a small pseudodataset to summarize the observed data. This idea sits at the heart of many approximation schemes, but such an approach requires the number of pseudo-datapoints to be scaled with the range of the input space if the accuracy of the approximation is to be maintained. This presents problems in time-series settings or in spatial datasets where large numbers of pseudo-datapoints are required since computation typically scales quadratically with the pseudo-dataset size. In this paper we devise an approximation whose complexity grows linearly with the number of pseudo-datapoints. This is achieved by imposing a tree or chain structure on the pseudo-datapoints and calibrating the approximation using a Kullback-Leibler (KL) minimization. Inference and learning can then be performed efficiently using the Gaussian belief propagation algorithm. We demonstrate the validity of our approach on a set of challenging regression tasks including missing data imputation for audio and spatial datasets. We trace out the speed-accuracy trade-off for the new method and show that the frontier dominates those obtained from a large number of existing approximation techniques.