Related papers: Closed-form Continuous-time Neural Models

Deep-predictive-coding networks (DPCNs) are hierarchical, generative models. They rely on feed-forward and feed-back connections to modulate latent feature representations of stimuli in a dynamic and context-sensitive manner. A crucial…

The main challenge of large-scale numerical simulation of radiation transport is the high memory and computation time requirements of discretization methods for kinetic equations. In this work, we derive and investigate a neural…

Recurrent neural networks (RNNs) trained on neuroscience-inspired tasks offer powerful models of brain computation. However, typical training paradigms rely on open-loop, supervised settings, whereas real-world learning unfolds in…

Closed-loop neurotechnology requires the capability to predict the state evolution and its regulation under (possibly) partial measurements. There is evidence that neurophysiological dynamics can be modeled by fractional-order dynamical…

Ordinary Differential Equations (ODE) based models have become popular as foundation models for solving many time series problems. Combining neural ODEs with traditional RNN models has provided the best representation for irregular time…

Neural ordinary differential equations (NODE) have been proposed as a continuous depth generalization to popular deep learning models such as Residual networks (ResNets). They provide parameter efficiency and automate the model selection…

Feedforward neural networks offer a promising approach for solving differential equations. However, the reliability and accuracy of the approximation still represent delicate issues that are not fully resolved in the current literature.…

I introduce a unified framework for finding a closed-form interpretation of any single neuron in an artificial neural network. Using this framework I demonstrate how to interpret neural network classifiers to reveal closed-form expressions…

Conditional Neural Processes (CNPs; Garnelo et al., 2018a) are meta-learning models which leverage the flexibility of deep learning to produce well-calibrated predictions and naturally handle off-the-grid and missing data. CNPs scale to…

Many time series are effectively generated by a combination of deterministic continuous flows along with discrete jumps sparked by stochastic events. However, we usually do not have the equation of motion describing the flows, or how they…

Irregularly measured time series are common in many of the applied settings in which time series modelling is a key statistical tool, including medicine. This provides challenges in model choice, often necessitating imputation or similar…

Neural networks have been identified as powerful tools for the study of complex systems. A noteworthy example is the neural network differential equation (NN DE) solver, which can provide functional approximations to the solutions of a wide…

Graph Neural Networks (GNNs) have demonstrated remarkable success in modeling complex relationships in graph-structured data. A recent innovation in this field is the family of Differential Equation-Inspired Graph Neural Networks (DE-GNNs),…

We investigate neural ordinary and stochastic differential equations (neural ODEs and SDEs) to model stochastic dynamics in fully and partially observed environments within a model-based reinforcement learning (RL) framework. Through a…

Control of complex systems involves both system identification and controller design. Deep neural networks have proven to be successful in many identification tasks, however, from model-based control perspective, these networks are…

Learning interpretable representations of neural dynamics at a population level is a crucial first step to understanding how observed neural activity relates to perception and behavior. Models of neural dynamics often focus on either…

Deep Neural networks are efficient and flexible models that perform well for a variety of tasks such as image, speech recognition and natural language understanding. In particular, convolutional neural networks (CNN) generate a keen…

Stochastic dynamics govern many important processes in cellular biology, and an underlying theoretical approach describing these dynamics is desirable to address a wealth of questions in biology and medicine. Mathematical tools exist for…

Continuous-depth neural networks, such as Neural ODEs, have refashioned the understanding of residual neural networks in terms of non-linear vector-valued optimal control problems. The common solution is to use the adjoint sensitivity…

Neural ODEs (NODEs) have emerged as powerful tools for modeling time series data, offering the flexibility to adapt to varying input scales and capture complex dynamics. However, they face significant challenges: first, their reliance on…