Resource-Efficient Invariant Networks: Exponential Gains by Unrolled Optimization

TL;DR

This paper introduces a novel optimization-based approach for building invariant networks that significantly improves efficiency over traditional sampling methods, demonstrated through theoretical analysis and practical experiments.

Contribution

It proposes a new primitive for invariant networks based on optimization, overcoming the exponential scaling of sampling methods in high-dimensional transformation spaces.

Findings

Optimization-based invariance is more efficient than sampling in high dimensions.

The method achieves exponential gains in resource efficiency.

Empirical validation on a hierarchical object detection task.

Abstract

Achieving invariance to nuisance transformations is a fundamental challenge in the construction of robust and reliable vision systems. Existing approaches to invariance scale exponentially with the dimension of the family of transformations, making them unable to cope with natural variabilities in visual data such as changes in pose and perspective. We identify a common limitation of these approaches--they rely on sampling to traverse the high-dimensional space of transformations--and propose a new computational primitive for building invariant networks based instead on optimization, which in many scenarios provides a provably more efficient method for high-dimensional exploration than sampling. We provide empirical and theoretical corroboration of the efficiency gains and soundness of our proposed method, and demonstrate its utility in constructing an efficient invariant network for a simple hierarchical object detection task when combined with unrolled optimization. Code for our networks and experiments is available at https://github.com/sdbuch/refine.