Chemical reaction networks and opportunities for machine learning
Chemical reaction networks (CRNs), defined by sets of species and possible reactions
between them, are widely used to interrogate chemical systems. To capture increasingly …
between them, are widely used to interrogate chemical systems. To capture increasingly …
On neural differential equations
P Kidger - arXiv preprint arXiv:2202.02435, 2022 - arxiv.org
The conjoining of dynamical systems and deep learning has become a topic of great
interest. In particular, neural differential equations (NDEs) demonstrate that neural networks …
interest. In particular, neural differential equations (NDEs) demonstrate that neural networks …
Denoising diffusion implicit models
Denoising diffusion probabilistic models (DDPMs) have achieved high quality image
generation without adversarial training, yet they require simulating a Markov chain for many …
generation without adversarial training, yet they require simulating a Markov chain for many …
Beltrami flow and neural diffusion on graphs
B Chamberlain, J Rowbottom… - Advances in …, 2021 - proceedings.neurips.cc
We propose a novel class of graph neural networks based on the discretized Beltrami flow, a
non-Euclidean diffusion PDE. In our model, node features are supplemented with positional …
non-Euclidean diffusion PDE. In our model, node features are supplemented with positional …
Effectively modeling time series with simple discrete state spaces
Time series modeling is a well-established problem, which often requires that methods (1)
expressively represent complicated dependencies,(2) forecast long horizons, and (3) …
expressively represent complicated dependencies,(2) forecast long horizons, and (3) …
A framework for machine learning of model error in dynamical systems
The development of data-informed predictive models for dynamical systems is of
widespread interest in many disciplines. We present a unifying framework for blending …
widespread interest in many disciplines. We present a unifying framework for blending …
Generalization bounds for neural ordinary differential equations and deep residual networks
P Marion - Advances in Neural Information Processing …, 2024 - proceedings.neurips.cc
Neural ordinary differential equations (neural ODEs) are a popular family of continuous-
depth deep learning models. In this work, we consider a large family of parameterized ODEs …
depth deep learning models. In this work, we consider a large family of parameterized ODEs …
On numerical integration in neural ordinary differential equations
The combination of ordinary differential equations and neural networks, ie, neural ordinary
differential equations (Neural ODE), has been widely studied from various angles. However …
differential equations (Neural ODE), has been widely studied from various angles. However …
Noisy recurrent neural networks
We provide a general framework for studying recurrent neural networks (RNNs) trained by
injecting noise into hidden states. Specifically, we consider RNNs that can be viewed as …
injecting noise into hidden states. Specifically, we consider RNNs that can be viewed as …
Understanding self-attention mechanism via dynamical system perspective
The self-attention mechanism (SAM) is widely used in various fields of artificial intelligence
and has successfully boosted the performance of different models. However, current …
and has successfully boosted the performance of different models. However, current …