Continuous-time neural networks are a class of machine learning systems that can tackle representation learning on spatiotemporal decision-making tasks. These models are typically represented by continuous differential equations. However, their expressive power when they are deployed on computers is bottlenecked by numerical differential equation solvers. This limitation has notably slowed down the scaling and understanding of numerous natural physical phenomena such as the dynamics of nervous systems. Ideally, we would circumvent this bottleneck by solving the given dynamical system in closed form. This is known to be intractable in general. Here, we show that it is possible to closely approximate the interaction between neurons and synapses—the building blocks of natural and artificial neural networks—constructed by liquid time-constant networks efficiently in closed form. To this end, we compute a tightly bounded approximation of the solution of an integral appearing in liquid time-constant dynamics that has had no known closed-form solution so far. This closed-form solution impacts the design of continuous-time and continuous-depth neural models. For instance, since time appears explicitly in closed form, the formulation relaxes the need for complex numerical solvers. Consequently, we obtain models that are between one and five orders of magnitude faster in training and inference compared with differential equation-based counterparts. More importantly, in contrast to ordinary differential equation-based continuous networks, closed-form networks can scale remarkably well compared with other deep learning instances. Lastly, as these models are derived from liquid networks, they show good performance in time-series modelling compared with advanced recurrent neural network models.

Autonomous robots can learn to perform visual navigation tasks from offline human demonstrations and generalize well to online and unseen scenarios within the same environment they have been trained on. It is challenging for these agents to take a step further and robustly generalize to new environments with drastic scenery changes that they have never encountered. Here, we present a method to create robust flight navigation agents that successfully perform vision-based fly-to-target tasks beyond their training environment under drastic distribution shifts. To this end, we designed an imitation learning framework using liquid neural networks, a brain-inspired class of continuous-time neural models that are causal and adapt to changing conditions. We observed that liquid agents learn to distill the task they are given from visual inputs and drop irrelevant features. Thus, their learned navigation skills transferred to new environments. When compared with several other state-of-the-art deep agents, experiments showed that this level of robustness in decision-making is exclusive to liquid networks, both in their differential equation and closed-form representations.

The adoption of powerful software tools and computational methods from the software industry by the scientific research community has resulted in a renewed interest in integrative, large-scale biological simulations. These typically involve the development of computational platforms to combine diverse, process-specific models into a coherent whole. The OpenWorm Foundation is an independent research organization working towards an integrative simulation of the nematode Caenorhabditis elegans , with the aim of providing a powerful new tool to understand how the organism's behaviour arises from its fundamental biology. In this perspective, we give an overview of the history and philosophy of OpenWorm, descriptions of the constituent sub-projects and corresponding open-science management practices, and discuss current achievements of the project and future directions. This article is part of a discussion meeting issue ‘Connectome to behaviour: modelling C. elegans at cellular resolution’.

The OpenWorm project has the ambitious goal of producing a highly detailed in silico model of the nematode Caenorhabditis elegans . A crucial part of this work will be a model of the nervous system encompassing all known cell types and connections. The appropriate level of biophysical detail required in the neuronal model to reproduce observed high-level behaviours in the worm has yet to be determined. For this reason, we have developed a framework, c302, that allows different instances of neuronal networks to be generated incorporating varying levels of anatomical and physiological detail, which can be investigated and refined independently or linked to other tools developed in the OpenWorm modelling toolchain. This article is part of a discussion meeting issue ‘Connectome to behaviour: modelling C. elegans at cellular resolution’.