Communication compression is a common technique in distributed optimization that can alleviate communication overhead by transmitting compressed gradients and model parameters. However, compression can introduce information distortion, which slows down convergence and incurs more communication rounds to achieve desired solutions. Given the trade-off between lower per-round communication costs and additional rounds of communication, it is unclear whether communication compression reduces the total communication cost. This paper explores the conditions under which unbiased compression, a widely used form of compression, can reduce the total communication cost, as well as the extent to which it can do so. To this end, we present the first theoretical formulation for characterizing the total communication cost in distributed optimization with unbiased compressors. We demonstrate that unbiased compression alone does not necessarily save the total communication cost, but this outcome can be achieved if the compressors used by all workers are further assumed independent. We establish lower bounds on the communication rounds required by algorithms using independent unbiased compressors to minimize smooth convex functions and show that these lower bounds are tight by refining the analysis for ADIANA. Our results reveal that using independent unbiased compression can reduce the total communication cost by a factor of up to Θ( p min{n,κ}) when all local smoothness constants are constrained by a common upper bound, where nis the number of workers and κis the condition number of the functions being minimized. These theoretical findings are supported by experimental results.

The relationship between perception and inference, as postulated by Helmholtz in the 19th century, is paralleled in modern machine learning by generative models like Variational Autoencoders (VAEs) and their hierarchical variants. Here, we evaluate the role of hierarchical inference and its alignment with brain function in the domain of motion perception. We first introduce a novel synthetic data framework, Retinal Optic Flow Learning (ROFL), which enables control over motion statistics and their causes. We then present a new hierarchical VAE and test it against alternative models on two downstream tasks: (i) predicting ground truth causes of retinal optic flow (e.g., self-motion); and (ii) predicting the responses of neurons in the motion processing pathway of primates. We manipulate the model architectures (hierarchical versus non-hierarchical), loss functions, and the causal structure of the motion stimuli.

We present a systematic recipe for translating ReLU approximation results to softmax Transformers1. Given a constructive ReLU approximator for a target, we construct an explicit softmax transformer with the same accuracy. The recipe applies to many common approximation targets and yields quantitative resource bounds beyond universal approximation statements. This matters because broad Universal Approximation Properties (UAP) still dominate Transformer approximation theory. For softmax Transformer, many universality results provide explicit constructions and quantitative resource bounds (e.g., parameters, depth, width...etc) [Yun et al., 2020, Kajitsuka and Sato, 2023, Takakura and Suzuki, 2023, Jiang and Li, 2024, Hu et al., 2025,

Nonlinear dynamical systems with regime transitions are typically described by ordinary differential equations with jumping parameters parameters. Traditional methods often treat change-point detection and parameter estimation as separate tasks, ignoring the inherent coupling between them. To address this, we propose residual-loss anomaly analysis of physics-informed neural networks, a unified framework that leverages dynamical consistency within the physics-informed learning paradigm. This approach jointly infers piecewise parameters and transition points under a single set of constraints. The method follows a two-stage strategy: First, local physical residuals are analyzed through overlapping subinterval decomposition. When a subinterval spans a true transition point, the residual exhibits a distinct structural elevation in noise-free conditions, which has a non-zero lower bound, enabling effective localization of potential transition intervals. Second, within our framework, change-point locations and piecewise parameters are integrated into a unified physical loss function for joint optimization, enabling simultaneous identification. Experiments on benchmark nonlinear dynamical systems, including Malthusian and logistic growth models, Van der Pol oscillator, Lotka-Volterra model and Lorenz system, demonstrate that the proposed method outperforms traditional decoupled approaches in both change-point localization and parameter estimation accuracy. This study provides an efficient, unified solution for structurally coupled inverse problems in nonlinear dynamical systems with regime switching.

Sparse Optimal Scoring (SOS) reformulates linear discriminant analysis to enable feature selection through elastic net regularization, making it well-suited for high-dimensional settings where the number of features exceeds observations. Most existing SOS methods use deflation-based strategies that compute discriminant vectors sequentially, which can propagate errors and produce suboptimal solutions. We propose a novel approach that estimates all discriminant vectors simultaneously under an explicit global orthogonality constraint, which we call Deflation-Free Sparse Optimal Scoring (DFSOS). DFSOS combines Bregman iteration with orthogonality-constrained optimization, decomposing the problem into tractable subproblems for scoring vectors, discriminant vectors, and orthogonality enforcement. We establish convergence to stationary points of the augmented Lagrangian under mild conditions. Extensive experiments using synthetic data and real-world time series data demonstrate that DFSOS achieves classification accuracy comparable to or better than existing deflation-based methods. These results indicate that deflation-free approaches offer a robust and effective framework for sparse discriminant analysis in high-dimensional problems.

In the last few decades, Markov chain Monte Carlo (MCMC) methods have been widely applied to Bayesian updating of structural dynamic models in the field of structural health monitoring. Recently, several MCMC algorithms have been developed that incorporate neural networks to enhance their performance for specific Bayesian model updating problems. However, a common challenge with these approaches lies in the fact that the embedded neural networks often necessitate retraining when faced with new tasks, a process that is time-consuming and significantly undermines the competitiveness of these methods. This paper introduces a newly developed adaptive meta-learning stochastic gradient Hamiltonian Monte Carlo (AM-SGHMC) algorithm. The idea behind AM-SGHMC is to optimize the sampling strategy by training adaptive neural networks, and due to the adaptive design of the network inputs and outputs, the trained sampler can be directly applied to various Bayesian updating problems of the same type of structure without further training, thereby achieving meta-learning. Additionally, practical issues for the feasibility of the AM-SGHMC algorithm for structural dynamic model updating are addressed, and two examples involving Bayesian updating of multi-story building models with different model fidelity are used to demonstrate the effectiveness and generalization ability of the proposed method.

Label noise presents a fundamental challenge in modern machine learning, especially when large-scale datasets are generated via automated processes. An increasingly common and important data paradigm, particularly in domains like medical imaging, involves learning from a large dataset with coarse, noisy labels supplemented by a small, expert-verified, clean dataset. This setting constitutes a typical information transfer and fusion problem. However, the significant distribution shift between the noisy and clean data violates the core overall parametric similarity assumptions of existing statistical transfer learning methods, while their reliance on parametric models is ill-suited for complex data like images. To address these limitations, this paper develops a generic model-agnostic nonparametric framework for classification with label noise, which applies to a broad class of classifiers. Our approach leverages the small clean dataset to ``purify'' the large noisy one and carefully manages the remaining ambiguous samples. This framework is underpinned by a rigorous statistical theory. Its empirical performance is demonstrated through simulations and a real-world application to medical image analysis for pneumonia diagnosis.

We introduce camouflaged data poisoning attacks, a new attack vector that arises in the context of machine unlearning and other settings when model retraining may be induced. An adversary first adds a few carefully crafted points to the training dataset such that the impact on the model's predictions is minimal. The adversary subsequently triggers a request to remove a subset of the introduced points at which point the attack is unleashed and the model's predictions are negatively affected. In particular, we consider clean-label targeted attacks (in which the goal is to cause the model to misclassify a specific test point) on datasets including CIFAR-10, Imagenette, and Imagewoof. This attack is realized by constructing camouflage datapoints that mask the effect of a poisoned dataset. We demonstrate the efficacy of our attack when unlearning is performed via retraining from scratch, the idealized setting of machine unlearning which other efficient methods attempt to emulate, as well as against the approximate unlearning approach of Graves et al. [2021].

With the concept of teaching being introduced to the machine learning community, a teacher model start using dynamic loss functions to teach the training of a student model. The dynamic intends to set adaptive loss functions to different phases of student model learning. In existing works, the teacher model 1) merely determines the loss function based on the present states of the student model, i.e., disregards the experience of the teacher; 2) only utilizes the states of the student model, e.g., training iteration number and loss/accuracy from training/validation sets, while ignoring the states of the loss function. In this paper, we first formulate the loss adjustment as a temporal task by designing a teacher model with memory units, and, therefore, enables the student learning to be guided by the experience of the teacher model. Then, with a dynamic loss network, we can additionally use the states of the loss to assist the teacher learning in enhancing the interactions between the teacher and the student model. Extensive experiments demonstrate our approach can enhance student learning and improve the performance of various deep models on real-world tasks, including classification, objective detection, and semantic segmentation scenarios.