16 papers
Stable and Near-Reversible Diffusion ODE Solvers for Image Editing
Barbora Barancikova, Daniil Shmelev, Cristopher Salvi
The inversion of diffusion models plays a central role in image editing. Algebraically reversible ODE solvers provide an appealing approach to diffusion inversion for text-guided i…
Explicit and Effectively Symmetric Schemes for Neural SDEs on Lie Groups
Daniil Shmelev, Luke Thompson, Cristopher Salvi
Backpropagation through (neural) SDE solvers is traditionally approached in two ways: discretise-then-optimise, which offers accurate gradients but incurs prohibitive memory costs;…
Explicit and Effectively Symmetric Runge-Kutta Methods
Daniil Shmelev, Kurusch Ebrahimi-Fard, Nikolas Tapia +1
Symmetry is a key property of numerical methods. The geometric properties of symmetric schemes make them an attractive option for integrating Hamiltonian systems, whilst their abil…
A path-dependent PDE solver based on signature kernels
Alexandre Pannier, Cristopher Salvi
We develop a kernel-based solver for path-dependent PDEs (PPDEs) along with a convergence theory. Our numerical scheme leverages signature kernels, a recently introduced class of k…
Novelty detection on path space
Ioannis Gasteratos, Antoine Jacquier, Maud Lemercier +2
We frame novelty detection on path space as a hypothesis testing problem with signature-based test statistics. Using transportation-cost inequalities of Gasteratos and Jacquier (20…
Structured Linear CDEs: Maximally Expressive and Parallel-in-Time Sequence Models
Benjamin Walker, Lingyi Yang, Nicola Muca Cirone +2
This work introduces Structured Linear Controlled Differential Equations (SLiCEs), a unifying framework for sequence models with structured, input-dependent state-transition matric…