5 papers
Topological Recursion and Quantum Path Signatures
Inês Aniceto, Thomas Cass, Samuel Crew
We introduce a non-commutative Laplace transform between functionals on path space and formal series in a tensor algebra, under which a natural convolution of path functionals beco…
Random Controlled Differential Equations
Francesco Piatti, Thomas Cass, William F. Turner
We introduce a training-efficient framework for time-series learning that combines random features with controlled differential equations (CDEs). In this approach, large randomly p…
Quantum Path Signatures
Samuel Crew, Cristopher Salvi, William F. Turner +2
We elucidate physical aspects of path signatures by formulating randomised path developments within the framework of matrix models in quantum field theory. Using tools from physics…
Topologies on unparameterised rough path space
Thomas Cass, William F. Turner
The signature of a -weakly geometric rough path summarises a path up to a generalised notion of reparameterisation. The quotient space of equivalence classes on which the signat…
Free probability, path developments and signature kernels as universal scaling limits
Thomas Cass, William F. Turner
Random developments of a path into a matrix Lie group have recently been used to construct signature-based kernels on path space. Two examples include developments into GL$(N…