# End-to-End Efficient Representation Learning via Cascading Combinatorial Optimization

## TL;DR

This paper introduces a hierarchical quantization method for embedding representations that achieves state-of-the-art search accuracy and significantly faster inference speeds by optimizing sparse hash codes via flow networks.

## Contribution

It proposes a novel hierarchical quantization approach combined with combinatorial optimization for efficient, accurate similarity search, enabling end-to-end training with polynomial-time algorithms.

## Key findings

- State-of-the-art search accuracy on Cifar100 and ImageNet
- Several orders of magnitude speedup in inference
- Efficient end-to-end training via flow network optimization

## Abstract

We develop hierarchically quantized efficient embedding representations for similarity-based search and show that this representation provides not only the state of the art performance on the search accuracy but also provides several orders of speed up during inference. The idea is to hierarchically quantize the representation so that the quantization granularity is greatly increased while maintaining the accuracy and keeping the computational complexity low. We also show that the problem of finding the optimal sparse compound hash code respecting the hierarchical structure can be optimized in polynomial time via minimum cost flow in an equivalent flow network. This allows us to train the method end-to-end in a mini-batch stochastic gradient descent setting. Our experiments on Cifar100 and ImageNet datasets show the state of the art search accuracy while providing several orders of magnitude search speedup respectively over exhaustive linear search over the dataset.