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Found 16 papers, 12 papers with code
On Neural Differential Equations
Topics include: neural ordinary differential equations (e. g. for hybrid neural/mechanistic modelling of physical systems); neural controlled differential equations (e. g. for learning functions of irregular time series); and neural stochastic differential equations (e. g. to produce generative models capable of representing complex stochastic dynamics, or sampling from complex high-dimensional distributions).
Equinox: neural networks in JAX via callable PyTrees and filtered transformations
One: parameterised functions are themselves represented as `PyTrees', which means that the parameterisation of a function is transparent to the JAX framework.
Neural Controlled Differential Equations for Online Prediction Tasks
This is fine when the whole time series is observed in advance, but means that Neural CDEs are not suitable for use in \textit{online prediction tasks}, where predictions need to be made in real-time: a major use case for recurrent networks.
Efficient and Accurate Gradients for Neural SDEs
This reduces computational cost (giving up to a $1. 87\times$ speedup) and removes the numerical truncation errors associated with gradient penalty.
Neural SDEs as Infinite-Dimensional GANs
Stochastic differential equations (SDEs) are a staple of mathematical modelling of temporal dynamics.
"Hey, that's not an ODE'": Faster ODE Adjoints with 12 Lines of Code
Neural differential equations may be trained by backpropagating gradients via the adjoint method, which is another differential equation typically solved using an adaptive-step-size numerical differential equation solver.
Neural SDEs Made Easy: SDEs are Infinite-Dimensional GANs
Several authors have introduced \emph{Neural Stochastic Differential Equations} (Neural SDEs), often involving complex theory with various limitations.
Neural CDEs for Long Time Series via the Log-ODE Method
Neural Controlled Differential Equations (Neural CDEs) are the continuous-time analogue of an RNN, just as Neural ODEs are analogous to ResNets.
"Hey, that's not an ODE": Faster ODE Adjoints via Seminorms
Neural differential equations may be trained by backpropagating gradients via the adjoint method, which is another differential equation typically solved using an adaptive-step-size numerical differential equation solver.
Neural Rough Differential Equations for Long Time Series
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 continuous-time way to model functions of potentially irregular time series.
Ranked #4 on
Time Series Classification
on EigenWorms
A Generalised Signature Method for Multivariate Time Series Feature Extraction
There is a great deal of flexibility as to how this method can be applied.
Generalised Interpretable Shapelets for Irregular Time Series
The shapelet transform is a form of feature extraction for time series, in which a time series is described by its similarity to each of a collection of `shapelets'.
Neural Controlled Differential Equations for Irregular Time Series
The resulting \emph{neural controlled differential equation} model is directly applicable to the general setting of partially-observed irregularly-sampled multivariate time series, and (unlike previous work on this problem) it may utilise memory-efficient adjoint-based backpropagation even across observations.
Signatory: differentiable computations of the signature and logsignature transforms, on both CPU and GPU
Signatory is a library for calculating and performing functionality related to the signature and logsignature transforms.
Deep Signature Transforms
The signature is an infinite graded sequence of statistics known to characterise a stream of data up to a negligible equivalence class.
Universal Approximation with Deep Narrow Networks
The classical Universal Approximation Theorem holds for neural networks of arbitrary width and bounded depth.
