Boundary between noise and information applied to filtering neural network weight matrices
This work addresses the issue of noise in neural network weights for researchers and practitioners dealing with overparametrization and label noise, offering an incremental improvement in filtering techniques.
The paper tackles the problem of distinguishing randomness from learned information in overparametrized neural network weight matrices by identifying a boundary in the singular value spectrum, and introduces a noise filtering algorithm that improves generalization performance significantly for networks trained with label noise.
Deep neural networks have been successfully applied to a broad range of problems where overparametrization yields weight matrices which are partially random. A comparison of weight matrix singular vectors to the Porter-Thomas distribution suggests that there is a boundary between randomness and learned information in the singular value spectrum. Inspired by this finding, we introduce an algorithm for noise filtering, which both removes small singular values and reduces the magnitude of large singular values to counteract the effect of level repulsion between the noise and the information part of the spectrum. For networks trained in the presence of label noise, we indeed find that the generalization performance improves significantly due to noise filtering.