Divide and conquer networks

Alex Nowak, David Folqué, Joan Bruna

Research output: Contribution to conferencePaper

Abstract

We consider the learning of algorithmic tasks by mere observation of input-output pairs. Rather than studying this as a black-box discrete regression problem with no assumption whatsoever on the input-output mapping, we concentrate on tasks that are amenable to the principle of divide and conquer, and study what are its implications in terms of learning. This principle creates a powerful inductive bias that we leverage with neural architectures that are defined recursively and dynamically, by learning two scale-invariant atomic operations: how to split a given input into smaller sets, and how to merge two partially solved tasks into a larger partial solution. Our model can be trained in weakly supervised environments, namely by just observing input-output pairs, and in even weaker environments, using a non-differentiable reward signal. Moreover, thanks to the dynamic aspect of our architecture, we can incorporate the computational complexity as a regularization term that can be optimized by backpropagation. We demonstrate the flexibility and efficiency of the Divide- and-Conquer Network on several combinatorial and geometric tasks: convex hull, clustering, knapsack and euclidean TSP. Thanks to the dynamic programming nature of our model, we show significant improvements in terms of generalization error and computational complexity.

Original languageEnglish (US)
StatePublished - Jan 1 2018
Event6th International Conference on Learning Representations, ICLR 2018 - Vancouver, Canada
Duration: Apr 30 2018May 3 2018

Conference

Conference6th International Conference on Learning Representations, ICLR 2018
CountryCanada
CityVancouver
Period4/30/185/3/18

ASJC Scopus subject areas

  • Language and Linguistics
  • Education
  • Computer Science Applications
  • Linguistics and Language

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    Nowak, A., Folqué, D., & Bruna, J. (2018). Divide and conquer networks. Paper presented at 6th International Conference on Learning Representations, ICLR 2018, Vancouver, Canada.