50 citations · 159 across the 31 of their papers we have counts for
15 papers · 1 filter
pySigLib -- Fast Signature-Based Computations on CPU and GPU
Daniil Shmelev, Cristopher Salvi
Signature-based methods have recently gained significant traction in machine learning for sequential data. In particular, signature kernels have emerged as powerful discriminators…
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;…
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…
ParallelFlow: Parallelizing Linear Transformers via Flow Discretization
Nicola Muca Cirone, Cristopher Salvi
We present a theoretical framework for analyzing linear attention models through matrix-valued state space models (SSMs). Our approach, Parallel Flows, provides a perspective that…
SigDiffusions: Score-Based Diffusion Models for Time Series via Log-Signature Embeddings
Barbora Barancikova, Zhuoyue Huang, Cristopher Salvi
Score-based diffusion models have recently emerged as state-of-the-art generative models for a variety of data modalities. Nonetheless, it remains unclear how to adapt these models…
Lecture notes on rough paths and applications to machine learning
Thomas Cass, Cristopher Salvi
These notes expound the recent use of the signature transform and rough path theory in data science and machine learning. We develop the core theory of the signature from first pri…
Log-PDE Methods for Rough Signature Kernels
Maud Lemercier, Terry Lyons, Cristopher Salvi
Signature kernels, inner products of path signatures, underpin several machine learning algorithms for multivariate time series analysis. For bounded variation paths, signature ker…
Theoretical Foundations of Deep Selective State-Space Models
Nicola Muca Cirone, Antonio Orvieto, Benjamin Walker +2
Structured state-space models (SSMs) such as S4, stemming from the seminal work of Gu et al., are gaining popularity as effective approaches for modeling sequential data. Deep SSMs…
Signature Kernel Conditional Independence Tests in Causal Discovery for Stochastic Processes
Georg Manten, Cecilia Casolo, Emilio Ferrucci +3
Inferring the causal structure underlying stochastic dynamical systems from observational data holds great promise in domains ranging from science and health to finance. Such proce…
A Neural RDE approach for continuous-time non-Markovian stochastic control problems
Melker Hoglund, Emilio Ferrucci, Camilo Hernandez +4
We propose a novel framework for solving continuous-time non-Markovian stochastic control problems by means of neural rough differential equations (Neural RDEs) introduced in Morri…
New directions in the applications of rough path theory
Adeline Fermanian, Terry Lyons, James Morrill +1
This article provides a concise overview of some of the recent advances in the application of rough path theory to machine learning. Controlled differential equations (CDEs) are di…
Neural Stochastic PDEs: Resolution-Invariant Learning of Continuous Spatiotemporal Dynamics
Cristopher Salvi, Maud Lemercier, Andris Gerasimovics
Stochastic partial differential equations (SPDEs) are the mathematical tool of choice for modelling spatiotemporal PDE-dynamics under the influence of randomness. Based on the noti…
Neural Rough Differential Equations for Long Time Series
James Morrill, Cristopher Salvi, Patrick Kidger +2
Neural controlled differential equations (CDEs) are the continuous-time analogue of recurrent neural networks, as Neural ODEs are to residual networks, and offer a memory-efficient…
Distribution Regression for Sequential Data
Maud Lemercier, Cristopher Salvi, Theodoros Damoulas +2
Distribution regression refers to the supervised learning problem where labels are only available for groups of inputs instead of individual inputs. In this paper, we develop a rig…
Deep Signature Transforms
Patric Bonnier, Patrick Kidger, Imanol Perez Arribas +2
The signature is an infinite graded sequence of statistics known to characterise a stream of data up to a negligible equivalence class. It is a transform which has previously been…