Task: Summarization
Input (English): 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.
Output (English): Dynamic model that learns divide and conquer strategies by weak supervision.