6 papers
On Universality of Deep Equivariant Networks
Marco Pacini, Mircea Petrache, Bruno Lepri +2
Universality results for equivariant neural networks remain rare. Those that do exist typically hold only in restrictive settings: either they rely on regular or higher-order tenso…
Recurrent Equivariant Constraint Modulation: Learning Per-Layer Symmetry Relaxation from Data
Stefanos Pertigkiozoglou, Mircea Petrache, Shubhendu Trivedi +1
Equivariant neural networks exploit underlying task symmetries to improve generalization, but strict equivariance constraints can induce more complex optimization dynamics that can…
Three iterations of -WL test distinguish non isometric clouds of -dimensional points
Valentino Delle Rose, Alexander Kozachinskiy, Cristóbal Rojas +2
The Weisfeiler--Lehman (WL) test is a fundamental iterative algorithm for checking isomorphism of graphs. It has also been observed that it underlies the design of several graph ne…
Symmetry-Based Structured Matrices for Efficient Approximately Equivariant Networks
Ashwin Samudre, Mircea Petrache, Brian D. Nord +1
There has been much recent interest in designing neural networks (NNs) with relaxed equivariance, which interpolate between exact equivariance and full flexibility for consistent p…
Approximation-Generalization Trade-offs under (Approximate) Group Equivariance
Mircea Petrache, Shubhendu Trivedi
The explicit incorporation of task-specific inductive biases through symmetry has emerged as a general design precept in the development of high-performance machine learning models…
Optimal quantization with branched optimal transport distances
Paul Pegon, Mircea Petrache
We consider the problem of optimal approximation of a target measure by an atomic measure with atoms, in branched optimal transport distance. This is a new branched transport v…