Rethinking Parameter Counting in Deep Models: Effective Dimensionality Revisited

By Wesley J. Maddox, Gregory W. Benton, Andrew Gordon Wilson. 2020

68 citations recorded by the source corpus.

Neural networks appear to have mysterious generalization properties when using parameter counting as a proxy for complexity. Indeed, neural networks often have many more parameters than there are data points, yet still provide good generalization performance. Moreover, when we measure generalization as a function of parameters, we see double descent behaviour, where the test error decreases, increases, and then again decreases. We show that many of these properties become understandable when viewed through the lens of effective dimensionality, which measures the dimensionality of the parameter space determined by the data. We relate effective dimensionality to posterior contraction in Bayesian deep learning, model selection, width-depth tradeoffs, double descent, and functional diversity in loss surfaces, leading to a richer understanding of the interplay between parameters and functions in deep models. We also show that effective dimensionality compares favourably to alternative norm- and flatness- based generalization measures.

Subfields: Artificial Intelligence, Computer Vision and Pattern Recognition, Statistical and Nonlinear Physics, Scaling & Learning Theory

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Citations in the corpus

GShard: Scaling Giant Models with Conditional Computation and Automatic Sharding (2020, positive): “Lastly, our experimental results empirically support that, mere parameter counting does not always correlate with the effective capacity of the models at scale [85, 86].”