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WEI-KAI CHANG

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2 papers

1 author row

NeurIPS Conference 2025 Conference Paper

A Unified Stability Analysis of SAM vs SGD: Role of Data Coherence and Emergence of Simplicity Bias

WEI-KAI CHANG
Rajiv Khanna

Understanding the dynamics of optimization algorithms in deep learning has become increasingly critical, especially as models grow in scale and complexity. Despite the empirical success of stochastic gradient descent (SGD) and its variants in finding solutions that generalize well, the precise mechanisms underlying this generalization remain poorly understood. A particularly intriguing aspect of this phenomenon is the bias of optimization algorithms towards certain types of minima—often flatter or simpler—especially in overparameterized regimes. While prior works have associated flatness of the loss landscape with better generalization, tools to mechanistically connect data, optimization algorithms, and the nature of the resulting minima are still limited. For instance, methods like Sharpness-Aware Minimization (SAM) have shown practical gains by explicitly promoting flatness, but lack a unified theoretical framework explaining their influence across different data structures and model architectures. In this work, we introduce a comprehensive linear stability analysis framework to dissect the behavior of optimization algorithms—SGD, random perturbations, and SAM—in neural networks, focusing particularly on two-layer ReLU models. Our approach is built upon a novel coherence measure that captures the interaction between data geometry and gradient similarity, providing new insights into why and how certain solutions are favored.

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NeurIPS Conference 2025 Conference Paper

Stable Coresets via Posterior Sampling: Aligning Induced and Full Loss Landscapes

WEI-KAI CHANG
Rajiv Khanna

As deep learning models continue to scale, the growing computational demands have amplified the need for effective coreset selection techniques. Coreset selection aims to accelerate training by identifying small, representative subsets of data that approximate the performance of the full dataset. Among various approaches, gradient-based methods stand out due to their strong theoretical underpinnings and practical benefits, particularly under limited data budgets. However, these methods face challenges such as naïve stochastic gradient descent (SGD) acting as a surprisingly strong baseline and the breakdown of representativeness due to loss curvature mismatches over time. In this work, we propose a novel framework that addresses these limitations. First, we establish a connection between posterior sampling and loss landscapes, enabling robust coreset selection even in high-data-corruption scenarios. Second, we introduce a smoothed loss function based on posterior sampling onto the model weights, enhancing stability and generalization while maintaining computational efficiency. We also present a novel convergence analysis for our sampling-based coreset selection method. Finally, through extensive experiments, we demonstrate how our approach achieves faster training and enhanced generalization across diverse datasets than the current state of the art.

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