50 citations · 159 across the 31 of their papers we have counts for
34 papers
Proving LLM-Generated GPU Kernels Correct and Safe: Floating-Point Verification in Lean and VerCors
Archibald Browne, Eugene Lee, Cristopher Salvi
Modern statistical model development begins with a high-level specification in an automatic differentiation framework such as PyTorch, JAX, or TensorFlow, which is then lowered to…
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…
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…
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;…
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…
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…
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…
Rough kernel hedging
Nicola Muca Cirone, Cristopher Salvi
Building on the functional-analytic framework of operator-valued kernels and un-truncated signature kernels, we propose a scalable, provably convergent signature-based algorithm fo…
Sparse Signature Coefficient Recovery via Kernels
Daniil Shmelev, Cristopher Salvi
Central to rough path theory is the signature transform of a path, an infinite series of tensors given by the iterated integrals of the underlying path. The signature poses an effe…
Genus expansion for non-linear random matrix ensembles with applications to neural networks
Nicola Muca Cirone, Jad Hamdan, Cristopher Salvi
We present a unified approach to studying certain non-linear random matrix ensembles and associated random neural networks at initialization. This begins with a novel series expans…
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…
Exact Gradients for Stochastic Spiking Neural Networks Driven by Rough Signals
Christian Holberg, Cristopher Salvi
We introduce a mathematically rigorous framework based on rough path theory to model stochastic spiking neural networks (SSNNs) as stochastic differential equations with event disc…
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…
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…
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…
Non-adversarial training of Neural SDEs with signature kernel scores
Zacharia Issa, Blanka Horvath, Maud Lemercier +1
Neural SDEs are continuous-time generative models for sequential data. State-of-the-art performance for irregular time series generation has been previously obtained by training th…
Optimal Stopping via Distribution Regression: a Higher Rank Signature Approach
Blanka Horvath, Maud Lemercier, Chong Liu +2
Distribution Regression on path-space refers to the task of learning functions mapping the law of a stochastic process to a scalar target. The learning procedure based on the notio…
Neural signature kernels as infinite-width-depth-limits of controlled ResNets
Nicola Muca Cirone, Maud Lemercier, Cristopher Salvi
Motivated by the paradigm of reservoir computing, we consider randomly initialized controlled ResNets defined as Euler-discretizations of neural controlled differential equations (…
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…