publications

2024

1. 

   The Butterfly Effect: Tiny Perturbations Cause Neural Network Training to Diverge

   Gül Sena Altıntaş, Devin Kwok, and David Rolnick

   In High-dimensional Learning Dynamics 2024: The Emergence of Structure and Reasoning, 2024

   Abs PDF

   Neural network training begins with a chaotic phase in which the network is sensitive to small perturbations, such as those caused by stochastic gradient descent (SGD). This sensitivity can cause identically initialized networks to diverge both in parameter space and functional similarity. However, the exact degree to which networks are sensitive to perturbation, and the sensitivity of networks as they transition out of the chaotic phase, is unclear. To address this uncertainty, we apply a controlled perturbation at a single point in training time and measure its effect on otherwise identical training trajectories. We find that both the Ł^2 distance and the loss barrier (increase in loss on the linear path between two networks) for networks trained in this manner increase with perturbation magnitude and how early the perturbation occurs. Finally, we propose a conjecture relating the sensitivity of a network to how easily it is permuted with respect to another network.

2023

1. 

   Disentangling Linear Mode Connectivity

   Gül Sena Altıntaş, Gregor Bachmann, Lorenzo Noci, and 1 more author

   In UniReps: Unifying Representations in Neural Models at Neurips 2023, Oct 2023

   Abs arXiv PDF

   Linear mode-connectivity (LMC) (or lack thereof) is one of the intriguing characteristics of neural network loss landscapes. While empirically well established, it unfortunately still lacks a proper theoretical understanding. Even worse, although empirical data points are abound, a systematic study of when networks exhibit LMC is largely missing in the literature. In this work we aim to close this gap. We explore how LMC is affected by three factors: (1) architecture (sparsity, weight-sharing), (2) training strategy (optimization setup) as well as (3) the underlying dataset. We place particular emphasis on minimal but non-trivial settings, removing as much unnecessary complexity as possible. We believe that our insights can guide future theoretical works on uncovering the inner workings of LMC.