Manifold Metric: A Loss Landscape Approach for Predicting Model Performance

Abstract

Determining the optimal model for a given task often requires training multiple models from scratch, which becomes impractical as dataset and model sizes grow. A more efficient alternative is to expand smaller pre-trained models, but this approach is underutilized due to a limited understanding of its impact on the training dynamics. Existing methods for quantifying this impact have notable limitations, including computation cost. To address this, we introduce a new perspective based on the loss landscape, which has been shown to contain a manifold of linearly connected minima. Specifically, we propose a metric that estimates the size of this manifold to study the impact of model expansion. Our experiments reveal a strong correlation between performance gains and our manifold metric, enabling more informed model comparison and offering a first step toward a geometry-driven approach for reliable model expansion. Notably, our metric outperforms other baselines, even when different types of expansion with equivalent number of parameters are applied to a model.