Related papers: Gauge invariant input to neural network for path o…
The transmission switching problem aims to determine the optimal network topology that minimizes the operating costs of a power system. This problem is typically formulated as a mixed-integer optimization model, which involves big-M…
Using a gauge covariant operator technique we deduce the path integral for a charged particle in a stationary magnetic field, verifying the "midpoint rule" for the discrete form of the interaction term with the vector potential.
We address the problem of improving the performance and in particular the sample complexity of deep neural networks by enforcing and guaranteeing invariances to symmetry transformations rather than learning them from data. Group-equivariant…
Optimizing a network of maps among a collection of objects/domains (or map synchronization) is a central problem across computer vision and many other relevant fields. Compared to optimizing pairwise maps in isolation, the benefit of map…
Efficient signal representation is essential for the functioning of living and artificial systems operating under resource constraints. A widely recognized framework for deriving such representations is the information bottleneck method,…
The concept of gauge invariance is one of the most subtle and useful concepts in modern theoretical physics. It is one of the Standard Model cornerstones. The main benefit due to the gauge invariance is that it can permit the comprehension…
Given a graph $G$, the maximal induced subgraphs problem asks to enumerate all maximal induced subgraphs of $G$ that belong to a certain hereditary graph class. While its optimization version, known as the minimum vertex deletion problem in…
Quantum computing is currently strongly limited by the impact of noise, in particular introduced by the application of two-qubit gates. For this reason, reducing the number of two-qubit gates is of paramount importance on noisy…
Given a graph $G=(V,E)$, the longest induced path problem asks for a maximum cardinality node subset $W\subseteq V$ such that the graph induced by $W$ is a path. It is a long established problem with applications, e.g., in network analysis.…
Logic optimization is an NP-hard problem commonly approached through hand-engineered heuristics. We propose to combine graph convolutional networks with reinforcement learning and a novel, scalable node embedding method to learn which local…
This paper presents the input convex neural network architecture. These are scalar-valued (potentially deep) neural networks with constraints on the network parameters such that the output of the network is a convex function of (some of)…
Recently, message-passing graph neural networks (MPNNs) have shown potential for solving combinatorial and continuous optimization problems due to their ability to capture variable-constraint interactions. While existing approaches leverage…
We present a novel neural architecture to solve graph optimization problems where the solution consists of arbitrary node labels, allowing us to solve hard problems like graph coloring. We train our model using reinforcement learning,…
Recently, a new class of non-convex optimization problems motivated by the statistical problem of learning an acyclic directed graphical model from data has attracted significant interest. While existing work uses standard first-order…
Local gauge symmetry underlies fundamental interactions and strongly correlated quantum matter, yet existing machine-learning approaches lack a general, principled framework for learning under site-dependent symmetries, particularly for…
Packet networks need to maintain state in the form of forwarding tables at each switch. The cost of this state increases as networks support ever more sophisticated per-flow routing, traffic engineering, and service chaining. Per-flow or…
In computational physics, machine learning has now emerged as a powerful complementary tool to explore efficiently candidate designs in engineering studies. Outputs in such supervised problems are signals defined on meshes, and a natural…
In this paper, we consider the scenario-based two-stage stochastic DC optimal power flow (OPF) problem for optimal and reliable dispatch when the load is facing uncertainty. Although this problem is a linear program, it remains…
We present an algorithm for steering the output of a linear system from a feasible initial condition to a desired target position, while satisfying input constraints and non-convex output constraints. The system input is generated by a…
Graph node embedding aims at learning a vector representation for all nodes given a graph. It is a central problem in many machine learning tasks (e.g., node classification, recommendation, community detection). The key problem in graph…