Predicting the Impact of Model Expansion through the Minima Manifold: A Loss Landscape Perspective

2024-05-24

arXiv.org

AI Summary

To address the infeasibility of exhaustive training for optimal model selection under large-scale models and datasets, this paper proposes a novel paradigm for predicting model scaling efficacy based on the geometric structure of the loss landscape. Methodologically, it integrates minimum manifold analysis, loss landscape modeling, and transfer dynamics modeling—enabling prediction of scaling benefits without training multiple candidate models. Its key contribution is the first identification of a quantitative link between scaling performance gains and the intrinsic dimensionality of the minimum manifold, formalized via perturbation magnitude of scaling operations on optimization trajectories. Experiments demonstrate a strong positive correlation between predicted gains and manifold size, with cross-architecture robustness. This provides both theoretical grounding and a practical decision-making tool for efficient pre-trained model scaling and transfer. (149 words)

Technology Category

• Machine Learning: Learning with Manifolds
• Search and Optimization: Learning to Search
• Natural Language Processing: Learning & Optimization for NLP

Application Category

• Web Mining and Content Analysis: Large pretrained models with web data
• User Modeling, Personalization and Recommendation: Practical large-scale studies of user experience
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

Abstract

The optimal model for a given task is often challenging to determine, requiring training multiple models from scratch which becomes prohibitive as dataset and model sizes grow. A more efficient alternative is to reuse smaller pre-trained models by expanding them, however, this is not widely adopted as how this impacts training dynamics remains poorly understood. While prior works have introduced statistics to measure these effects, they remain flawed. To rectify this, we offer a new approach for understanding and quantifying the impact of expansion through the lens of the loss landscape, which has been shown to contain a manifold of linearly connected minima. Building on this new perspective, we propose a metric to study the impact of expansion by estimating the size of the manifold. Experimental results show a clear relationship between gains in performance and manifold size, enabling the comparison of candidate models and presenting a first step towards expanding models more reliably based on geometric properties of the loss landscape.

Problem

• Predicting model performance without costly training
• Understanding impact of model expansion on training dynamics
• Developing efficient metric for comparing expanded models

Innovation

• Loss landscape manifold metric for performance prediction
• Correlates manifold size with model expansion impact
• Outperforms baselines in model comparison efficiency