Overparameterization from Computational Constraints

TL;DR

This paper investigates how computational constraints influence the size of models needed for learning and robustness, showing bounded learners require more parameters than ideal information-theoretic models, especially in robust settings.

Contribution

It demonstrates that computational limitations can significantly increase the model size needed for learning and robustness, extending recent theoretical results to computational regimes.

Findings

Bounded learners need more parameters than information-theoretic ones.

Robust learning under computational constraints requires even larger models.

Restricting adversaries to be computationally bounded can reduce model size requirements.

Abstract

Overparameterized models with millions of parameters have been hugely successful. In this work, we ask: can the need for large models be, at least in part, due to the \emph{computational} limitations of the learner? Additionally, we ask, is this situation exacerbated for \emph{robust} learning? We show that this indeed could be the case. We show learning tasks for which computationally bounded learners need \emph{significantly more} model parameters than what information-theoretic learners need. Furthermore, we show that even more model parameters could be necessary for robust learning. In particular, for computationally bounded learners, we extend the recent result of Bubeck and Sellke [NeurIPS'2021] which shows that robust models might need more parameters, to the computational regime and show that bounded learners could provably need an even larger number of parameters. Then, we address the following related question: can we hope to remedy the situation for robust computationally bounded learning by restricting \emph{adversaries} to also be computationally bounded for sake of obtaining models with fewer parameters? Here again, we show that this could be possible. Specifically, building on the work of Garg, Jha, Mahloujifar, and Mahmoody [ALT'2020], we demonstrate a learning task that can be learned efficiently and robustly against a computationally bounded attacker, while to be robust against an information-theoretic attacker requires the learner to utilize significantly more parameters.