The Combinatorial Brain Surgeon: Pruning Weights That Cancel One Another in Neural Networks

Neural networks tend to achieve better accuracy with training if they are larger — even if the resulting models are overparameterized. Nevertheless, carefully removing such excess parameters before, during, or after training may also produce models with similar or even improved accuracy. In many cases, that can be curiously achieved by heuristics as simple as … Read more

Scaling Up Exact Neural Network Compression by ReLU Stability

We can compress a neural network while exactly preserving its underlying functionality with respect to a given input domain if some of its neurons are stable. However, current approaches to determine the stability of neurons in networks with Rectified Linear Unit (ReLU) activations require solving or finding a good approximation to multiple discrete optimization problems. … Read more

Lossless Compression of Deep Neural Networks

Deep neural networks have been successful in many predictive modeling tasks, such as image and language recognition, where large neural networks are often used to obtain good accuracy. Consequently, it is challenging to deploy these networks under limited computational resources, such as in mobile devices. In this work, we introduce an algorithm that removes units … Read more

Template-based Minor Embedding for Adiabatic Quantum Optimization

Quantum Annealing (QA) can be used to quickly obtain near-optimal solutions for Quadratic Unconstrained Binary Optimization (QUBO) problems. In QA hardware, each decision variable of a QUBO should be mapped to one or more adjacent qubits in such a way that pairs of variables defining a quadratic term in the objective function are mapped to … Read more

Empirical Bounds on Linear Regions of Deep Rectifier Networks

One form of characterizing the expressiveness of a piecewise linear neural network is by the number of linear regions, or pieces, of the function modeled. We have observed substantial progress in this topic through lower and upper bounds on the maximum number of linear regions and a counting procedure. However, these bounds only account for … Read more

Seamless Multimodal Transportation Scheduling

Ride-hailing services have expanded the role of shared mobility in passenger transportation systems, creating new markets and creative planning solutions for major urban centers. In this paper, we consider their use for last-mile passenger transportation in coordination with a mass transit service to provide a seamless multimodal transportation experience for the user. A system that … Read more

The Integrated Last-Mile Transportation Problem

Last-mile transportation (LMT) refers to any service that moves passengers from a hub of mass transportation (MT), such as air, boat, bus, or train, to destinations, such as a home or an office. In this paper, we introduce the problem of scheduling passengers jointly on MT and LMT services, with passengers sharing a car, van, … Read more

Bounding and Counting Linear Regions of Deep Neural Networks

We investigate the complexity of deep neural networks (DNN) that represent piecewise linear (PWL) functions. In particular, we study the number of linear regions, i.e. pieces, that a PWL function represented by a DNN can attain, both theoretically and empirically. We present (i) tighter upper and lower bounds for the maximum number of linear regions … Read more

Compact Representation of Near-Optimal Integer Programming Solutions

It is often useful in practice to explore near-optimal solutions of an integer programming problem. We show how all solutions within a given tolerance of the optimal value can be efficiently and compactly represented in a weighted decision diagram, once the optimal value is known. The structure of a decision diagram facilitates rapid processing of … Read more