Analyzing Monotonic Linear Interpolation in Neural Network Loss Landscapes

2021/04/22 by James Lucas, Juhan Bae, Lucas, James +9 · 1 citation
Computer Science · #Advanced Neural Network Applications #Adversarial Robustness in Machine Learning #Artificial Intelligence (cs.AI) #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Stochastic Gradient Optimization Techniques

paper · pdf · doi:10.48550/arxiv.2104.11044

openalex publication_date 2021/04/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Linear interpolation between initial neural network parameters and converged parameters after training with stochastic gradient descent (SGD) typically leads to a monotonic decrease in the training objective. This Monotonic Linear Interpolation (MLI) property, first observed by Goodfellow et al. (2014) persists in spite of the non-convex objectives and highly non-linear training dynamics of neural networks. Extending this work, we evaluate several hypotheses for this property that, to our knowledge, have not yet been explored. Using tools from differential geometry, we draw connections between the interpolated paths in function space and the monotonicity of the network - providing sufficient conditions for the MLI property under mean squared error. While the MLI property holds under various settings (e.g. network architectures and learning problems), we show in practice that networks violating the MLI property can be produced systematically, by encouraging the weights to move far from initialization. The MLI property raises important questions about the loss landscape geometry of neural networks and highlights the need to further study their global properties.

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Cited by

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