Exact Combinatorial Optimization with Graph Convolutional Neural Networks

Combinatorial optimization problems are typically tackled by the branch-and-bound paradigm. We propose a new graph convolutional neural network model for learning branch-and-bound variable selection policies, which leverages the natural variable-constraint bipartite graph representation of mixed-integer linear programs. We train our model via imitation learning from the strong branching expert rule, and demonstrate on a series of hard problems that our approach produces policies that improve upon state-of-the-art machine-learning methods for branching and generalize to instances significantly larger than seen during training. Moreover, we improve for the first time over expert-designed branching rules implemented in a state-of-the-art solver on large problems. Code for reproducing all the experiments can be found at https://github.com/ds4dm/learn2branch.Comment: Accepted paper at the NeurIPS 2019 conferenc

Going in circles is the way forward: the role of recurrence in visual inference

Biological visual systems exhibit abundant recurrent connectivity. State-of-the-art neural network models for visual recognition, by contrast, rely heavily or exclusively on feedforward computation. Any finite-time recurrent neural network (RNN) can be unrolled along time to yield an equivalent feedforward neural network (FNN). This important insight suggests that computational neuroscientists may not need to engage recurrent computation, and that computer-vision engineers may be limiting themselves to a special case of FNN if they build recurrent models. Here we argue, to the contrary, that FNNs are a special case of RNNs and that computational neuroscientists and engineers should engage recurrence to understand how brains and machines can (1) achieve greater and more flexible computational depth, (2) compress complex computations into limited hardware, (3) integrate priors and priorities into visual inference through expectation and attention, (4) exploit sequential dependencies in their data for better inference and prediction, and (5) leverage the power of iterative computation

Selective algorithms for large-scale classification and structured learning

The desired output in many machine learning tasks is a structured object, such as tree, clustering, or sequence. Learning accurate prediction models for such problems requires training on large amounts of data, making use of expressive features and performing global inference that simultaneously assigns values to all interrelated nodes in the structure. All these contribute to significant scalability problems. In this thesis, we describe a collection of results that address several aspects of these problems – by carefully selecting and caching samples, structures, or latent items. Our results lead to efficient learning algorithms for large-scale binary classification models, structured prediction models and for online clustering models which, in turn, support reduction in problem size, improvements in training and evaluation speed and improved performance. We have used our algorithms to learn expressive models from large amounts of annotated data and achieve state-of-the art performance on several natural language processing tasks