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Curies principle states that when effects show certain asymmetry, this asymmetry must be found in the causes that gave rise to them. We demonstrate that symmetry equivariant neural networks uphold Curies principle and can be used to articulate many symmetry-relevant scientific questions into simple optimization problems. We prove these properties mathematically and demonstrate them numerically by training a Euclidean symmetry equivariant neural network to learn symmetry-breaking input to deform a square into a rectangle and to generate octahedra tilting patterns in perovskites.
We introduce an exactly integrable version of the well-known leaky integrate-and-fire (LIF) model, with continuous membrane potential at the spiking event, the c-LIF. We investigate the dynamical regimes of a fully connected network of excitatory c-L
Machine learning has demonstrated great power in materials design, discovery, and property prediction. However, despite the success of machine learning in predicting discrete properties, challenges remain for continuous property prediction. The chall
Floquet symmetry protected topological (FSPT) phases are non-equilibrium topological phases enabled by time-periodic driving. FSPT phases of 1d chains of bosons, spins, or qubits host dynamically protected edge states that can store quantum informati
In this paper we investigate the family of functions representable by deep neural networks (DNN) with rectified linear units (ReLU). We give an algorithm to train a ReLU DNN with one hidden layer to *global optimality* with runtime polynomial in the
We demonstrate how graph neural networks can be used to solve combinatorial optimization problems. Our approach is broadly applicable to canonical NP-hard problems in the form of quadratic unconstrained binary optimization problems, such as maximum c