On the Learning Dynamics of Two-layer Linear Networks with Label Noise SGD

One crucial factor behind the success of deep learning lies in the implicit bias induced by noise inherent in gradient-based training algorithms. Motivated by empirical observations that training with noisy labels improves model generalization, we delve into the underlying mechanisms behind stochastic gradient descent (SGD) with label noise. Focusing on a two-layer over-parameterized linear network, we analyze the learning dynamics of label noise SGD, unveiling a two-phase learning behavior. In \emph{Phase I}, the magnitudes of model weights progressively diminish, and the model escapes the lazy regime; enters the rich regime. In \emph{Phase II}, the alignment between model weights and the ground-truth interpolator increases, and the model eventually converges. Our analysis highlights the critical role of label noise in driving the transition from the lazy to the rich regime and minimally explains its empirical success. Furthermore, we extend these insights to Sharpness-Aware Minimization (SAM), showing that the principles governing label noise SGD also apply to broader optimization algorithms. Extensive experiments, conducted under both synthetic and real-world setups, strongly support our theory. Our code is released at https://github.com/a-usually/Label-Noise-SGD.

Physics-Driven 3D Gaussian Rendering for Zero-Shot MRI Super-Resolution

High-resolution Magnetic Resonance Imaging (MRI) is vital for clinical diagnosis but limited by long acquisition times and motion artifacts. Super-resolution (SR) reconstructs low-resolution scans into high-resolution images, yet existing methods are mutually constrained: paired-data methods achieve efficiency only by relying on costly aligned datasets, while implicit neural representation approaches avoid such data needs at the expense of heavy computation. We propose a zero-shot MRI SR framework using explicit Gaussian representation to balance data requirements and efficiency. MRI-tailored Gaussian parameters embed tissue physical properties, reducing learnable parameters while preserving MR signal fidelity. A physics-grounded volume rendering strategy models MRI signal formation via normalized Gaussian aggregation. Additionally, a brick-based order-independent rasterization scheme enables highly parallel 3D computation, lowering training and inference costs. Experiments on two public MRI datasets show superior reconstruction quality and efficiency, demonstrating the method's potential for clinical MRI SR.

Solution to the 10th ABAW Expression Recognition Challenge: A Robust Multimodal Framework with Safe Cross-Attention and Modality Dropout

Emotion recognition in real-world environments is hindered by partial occlusions, missing modalities, and severe class imbalance. To address these issues, particularly for the Affective Behavior Analysis in-the-wild (ABAW) Expression challenge, we propose a multimodal framework that dynamically fuses visual and audio representations. Our approach uses a dual-branch Transformer architecture featuring a safe cross-attention mechanism and a modality dropout strategy. This design allows the network to rely on audio-based predictions when visual cues are absent. To mitigate the long-tail distribution of the Aff-Wild2 dataset, we apply focal loss optimization, combined with a sliding-window soft voting strategy to capture dynamic emotional transitions and reduce frame-level classification jitter. Experiments demonstrate that our framework effectively handles missing modalities and complex spatiotemporal dependencies, achieving an accuracy of 60.79% and an F1-score of 0.5029 on the Aff-Wild2 validation set.

S2O: Enhancing Adversarial Training with Second-Order Statistics of Weights

Adversarial training has emerged as a highly effective way to improve the robustness of deep neural networks (DNNs). It is typically conceptualized as a min-max optimization problem over model weights and adversarial perturbations, where the weights are optimized using gradient descent methods, such as SGD. In this paper, we propose a novel approach by treating model weights as random variables, which paves the way for enhancing adversarial training through \textbf{S}econd-Order \textbf{S}tatistics \textbf{O}ptimization (S$^2$O) over model weights. We challenge and relax a prevalent, yet often unrealistic, assumption in prior PAC-Bayesian frameworks: the statistical independence of weights. From this relaxation, we derive an improved PAC-Bayesian robust generalization bound. Our theoretical developments suggest that optimizing the second-order statistics of weights can substantially tighten this bound. We complement this theoretical insight by conducting an extensive set of experiments that demonstrate that S$^2$O not only enhances the robustness and generalization of neural networks when used in isolation, but also seamlessly augments other state-of-the-art adversarial training techniques. The code is available at https://github.com/Alexkael/S2O.

Joint Optimization of Flexible Antenna Array Shape and Beamforming for Secure Communication

Flexible antenna arrays (FAAs) can physically reshape their geometry to add new spatial degrees of freedom, whereas transmit beamforming adjusts the complex element weights to electronically steer and shape the array's radiation pattern, thereby significantly improving communication performance. This paper is the first to explore the integration of FAA geometry control and beamforming for physical layer security enhancement, where a base station equipped with an FAA communicates with a legitimate user in the presence of passive eavesdroppers. To safeguard confidential transmissions, we formulate a new secrecy rate maximization problem that jointly optimizes the transmit beamforming vector and a continuous FAA shape control parameter. Due to the non convex nature of the problem, an alternating optimization algorithm is developed to decompose the joint design into tractable subproblems, which are solved iteratively to refine both the FAA geometry and beamforming strategy. Simulation results confirm that the proposed joint optimization framework significantly outperforms conventional fixed shape or beamforming only schemes, demonstrating the potential of FAA enabled reconfigurability for secure wireless communications.

Flow Matching from Viewpoint of Proximal Operators

We reformulate Optimal Transport Conditional Flow Matching (OT-CFM), a class of dynamical generative models, showing that it admits an exact proximal formulation via an extended Brenier potential, without assuming that the target distribution has a density. In particular, the mapping to recover the target point is exactly given by a proximal operator, which yields an explicit proximal expression of the vector field. We also discuss the convergence of minibatch OT-CFM to the population formulation as the batch size increases. Finally, using second epi-derivatives of convex potentials, we prove that, for manifold-supported targets, OT-CFM is terminally normally hyperbolic: after time rescaling, the dynamics contracts exponentially in directions normal to the data manifold while remaining neutral along tangential directions.

Proximal Action Replacement for Behavior Cloning Actor-Critic in Offline Reinforcement Learning

Offline reinforcement learning (RL) optimizes policies from a previously collected static dataset and is an important branch of RL. A popular and promising approach is to regularize actor-critic methods with behavior cloning (BC), which yields realistic policies and mitigates bias from out-of-distribution actions, but can impose an often-overlooked performance ceiling: when dataset actions are suboptimal, indiscriminate imitation structurally prevents the actor from fully exploiting high-value regions suggested by the critic, especially in later training when imitation is already dominant. We formally analyzed this limitation by investigating convergence properties of BC-regularized actor-critic optimization and verified it on a controlled continuous bandit task. To break this ceiling, we propose proximal action replacement (PAR), a plug-and-play training sample replacer that progressively replaces low-value actions with high-value actions generated by a stable actor, broadening the action exploration space while reducing the impact of low-value data. PAR is compatible with multiple BC regularization paradigms. Extensive experiments across offline RL benchmarks show that PAR consistently improves performance and approaches state-of-the-art when combined with the basic TD3+BC.

Small Shifts, Large Gains: Unlocking Traditional TSP Heuristic Guided-Sampling via Unsupervised Neural Instance Modification

The Traveling Salesman Problem (TSP) is one of the most representative NP-hard problems in route planning and a long-standing benchmark in combinatorial optimization. Traditional heuristic tour constructors, such as Farthest or Nearest Insertion, are computationally efficient and highly practical, but their deterministic behavior limits exploration and often leads to local optima. In contrast, neural-based heuristic tour constructors alleviate this issue through guided-sampling and typically achieve superior solution quality, but at the cost of extensive training and reliance on ground-truth supervision, hindering their practical use. To bridge this gap, we propose TSP-MDF, a novel instance modification framework that equips traditional deterministic heuristic tour constructors with guided-sampling capability. Specifically, TSP-MDF introduces a neural-based instance modifier that strategically shifts node coordinates to sample multiple modified instances, on which the base traditional heuristic tour constructor constructs tours that are mapped back to the original instance, allowing traditional tour constructors to explore higher-quality tours and escape local optima. At the same time, benefiting from our instance modification formulation, the neural-based instance modifier can be trained efficiently without any ground-truth supervision, ensuring the framework maintains practicality. Extensive experiments on large-scale TSP benchmarks and real-world benchmarks demonstrate that TSP-MDF significantly improves the performance of traditional heuristics tour constructors, achieving solution quality comparable to neural-based heuristic tour constructors, but with an extremely short training time.

Spectral Gradient Descent Mitigates Anisotropy-Driven Misalignment: A Case Study in Phase Retrieval

Spectral gradient methods, such as the Muon optimizer, modify gradient updates by preserving directional information while discarding scale, and have shown strong empirical performance in deep learning. We investigate the mechanisms underlying these gains through a dynamical analysis of a nonlinear phase retrieval model with anisotropic Gaussian inputs, equivalent to training a two-layer neural network with the quadratic activation and fixed second-layer weights. Focusing on a spiked covariance setting where the dominant variance direction is orthogonal to the signal, we show that gradient descent (GD) suffers from a variance-induced misalignment: during the early escaping stage, the high-variance but uninformative spike direction is multiplicatively amplified, degrading alignment with the true signal under strong anisotropy. In contrast, spectral gradient descent (SpecGD) removes this spike amplification effect, leading to stable alignment and accelerated noise contraction. Numerical experiments confirm the theory and show that these phenomena persist under broader anisotropic covariances.

LLM-AutoDP: Automatic Data Processing via LLM Agents for Model Fine-tuning

Large Language Models (LLMs) can be fine-tuned on domain-specific data to enhance their performance in specialized fields. However, such data often contains numerous low-quality samples, necessitating effective data processing (DP). In practice, DP strategies are typically developed through iterative manual analysis and trial-and-error adjustment. These processes inevitably incur high labor costs and may lead to privacy issues in high-privacy domains like healthcare due to direct human access to sensitive data. Thus, achieving automated data processing without exposing the raw data has become a critical challenge. To address this challenge, we propose LLM-AutoDP, a novel framework that leverages LLMs as agents to automatically generate and optimize data processing strategies. Our method generates multiple candidate strategies and iteratively refines them using feedback signals and comparative evaluations. This iterative in-context learning mechanism enables the agent to converge toward high-quality processing pipelines without requiring direct human intervention or access to the underlying data. To further accelerate strategy search, we introduce three key techniques: Distribution Preserving Sampling, which reduces data volume while maintaining distributional integrity; Processing Target Selection, which uses a binary classifier to identify low-quality samples for focused processing; Cache-and-Reuse Mechanism}, which minimizes redundant computations by reusing prior processing results. Results show that models trained on data processed by our framework achieve over 80% win rates against models trained on unprocessed data. Compared to AutoML baselines based on LLM agents, LLM-AutoDP achieves approximately a 65% win rate. Moreover, our acceleration techniques reduce the total searching time by up to 10 times, demonstrating both effectiveness and efficiency.