Random initialisations performing above chance and how to find them
This addresses the understanding of neural network optimization and generalization for researchers, showing incremental insights into solution diversity across architectures.
The paper tackled the problem of whether neural networks trained from different random initializations find functionally similar solutions, providing empirical evidence that fully connected networks already reside in the same loss valley at initialization, with permuted initializations averaging to perform significantly above chance, while convolutional networks do not hold this hypothesis, especially with large learning rates.
Neural networks trained with stochastic gradient descent (SGD) starting from different random initialisations typically find functionally very similar solutions, raising the question of whether there are meaningful differences between different SGD solutions. Entezari et al.\ recently conjectured that despite different initialisations, the solutions found by SGD lie in the same loss valley after taking into account the permutation invariance of neural networks. Concretely, they hypothesise that any two solutions found by SGD can be permuted such that the linear interpolation between their parameters forms a path without significant increases in loss. Here, we use a simple but powerful algorithm to find such permutations that allows us to obtain direct empirical evidence that the hypothesis is true in fully connected networks. Strikingly, we find that two networks already live in the same loss valley at the time of initialisation and averaging their random, but suitably permuted initialisation performs significantly above chance. In contrast, for convolutional architectures, our evidence suggests that the hypothesis does not hold. Especially in a large learning rate regime, SGD seems to discover diverse modes.