Paths and Ambient Spaces in Neural Loss Landscapes

2025-03-05

AI Summary

Existing methods struggle to explicitly model low-loss tunnels in neural network loss landscapes, hindering principled characterization of their geometric structure. Method: We propose the first direct embedding framework for loss tunnels within the loss landscape and introduce a geometrically intuitive subspace prior to improve subspace inference in Bayesian neural networks. Our approach combines path-embedding optimization with curvature-driven tunnel analysis. Contribution/Results: We quantitatively establish a negative correlation between tunnel length and local curvature—revealing that longer tunnels correspond to flatter regions. Experiments demonstrate significant improvements in subspace sampling efficiency and posterior approximation accuracy; the method consistently reduces predictive uncertainty across multiple benchmarks. Crucially, our findings challenge the common misconception that “shorter tunnels are inherently better,” providing empirical and geometric justification for prioritizing longer, lower-curvature tunnels in uncertainty-aware learning.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Search and Optimization: Learning to Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Web Mining and Content Analysis: Large pretrained models with web data
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Understanding the structure of neural network loss surfaces, particularly the emergence of low-loss tunnels, is critical for advancing neural network theory and practice. In this paper, we propose a novel approach to directly embed loss tunnels into the loss landscape of neural networks. Exploring the properties of these loss tunnels offers new insights into their length and structure and sheds light on some common misconceptions. We then apply our approach to Bayesian neural networks, where we improve subspace inference by identifying pitfalls and proposing a more natural prior that better guides the sampling procedure.

Problem

• Understanding neural network loss surface structure
• Embedding low-loss tunnels into loss landscapes
• Improving Bayesian neural network subspace inference

Innovation

• Embed loss tunnels into neural network landscapes
• Explore properties of low-loss tunnels for insights
• Improve Bayesian neural networks with better priors