overparameterization and sparsity

It is a mystery how overparameterized models behave and why. It is especially intriguing why overparameterized models can generalize well despite the excessive capacity, and why highly sparse neural networks can still achieve comparable performance to the dense networks (as suggested in the lottery ticket hypothesis).

Over the past few months, I have been intrigued by the possible relationship between model generalization and sparsity. The slide below shows a brief review of several related works and the questions that I cared about. Luckily I am able to answer a few of them with my own research now (see sparse double descent).

References

2022

Sparse double descent: Where network pruning aggravates overfitting

Zheng He, Zeke Xie, Quanzhi Zhu, and Zengchang Qin

In International Conference on Machine Learning, ICML, 2022

Abs arXiv Poster Code

People usually believe that network pruning not only reduces the computational cost of deep networks, but also prevents overfitting by decreasing model capacity. However, our work surprisingly discovers that network pruning sometimes even aggravates overfitting. We report an unexpected sparse double descent phenomenon that, as we increase model sparsity via network pruning, test performance first gets worse (due to overfitting), then gets better (due to relieved overfitting), and gets worse at last (due to forgetting useful information). While recent studies focused on the deep double descent with respect to model overparameterization, they failed to recognize that sparsity may also cause double descent. In this paper, we have three main contributions. First, we report the novel sparse double descent phenomenon through extensive experiments. Second, for this phenomenon, we propose a novel learning distance interpretation that the curve of l2 learning distance of sparse models (from initialized parameters to final parameters) may correlate with the sparse double descent curve well and reflect generalization better than minima flatness. Third, in the context of sparse double descent, a winning ticket in the lottery ticket hypothesis surprisingly may not always win.

References

2022

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