An efficient algorithm for tensor learning

We present a new algorithm for recovering paths from their third-order signature tensors, an inverse problem in rough analysis that can be formalized through the group orbit of a special core tensor. Our algorithm provides an exact solution to this learning problem and improves upon existing Gröbner-based approaches by an order of magnitude.

In this talk, we begin with the low-dimensional regime, where generic transformations can be read directly from the tensor. We then proceed to the general setting and formulate our algorithm, relying on normal forms and stabilizers of group actions via matrix-tensor congruence. Throughout the talk, we present several running examples and benchmarks using our implementation in the computer algebra system OSCAR.