Ostrow, M. | bioRxiv Science

bioRxiv2026

A metric for comparing complex systems by their dynamics

Comparisons are fundamental to science: experiment against model, one organism against another, a system against itself across time. Because many systems, from brains to climate, are characterized by how they evolve in time, it is a natural goal to compare their dynamics. Dynamical systems comparison is well defined, but has been intractable for nonlinear, high-dimensional, noisy, and partially observed data. As a result, standard comparison methods have focused on the geometry or topology of data. Here we present Dynamical Similarity Analysis (DSA), a class of metrics to compare systems by their temporal evolution. Its foundation is Koopman Operator theory, which recasts nonlinear systems as linear operators. We estimate these operators from data, then compare the operators across systems. The computation is fast, scalable, and robust to noise and partial observation. It is also differentiable. DSA identifies dynamical structure that geometric and topological methods miss. It matches recordings from the head direction circuit to ring attractor models. It shows that macaque motor cortex dynamics for two reaching tasks drift apart across years despite preserved behavior, and that primary motor cortex breaks from premotor cortex as movement begins. As an optimization objective, it induces neural networks to learn never-before hypothesized solutions that run counter to their inductive biases. Thus, DSA transforms the dynamics of a system into an object that can be measured, compared, and optimized.

neuroscience↗

bioRxiv2025

Computation-through-Dynamics Benchmark: Simulated datasets and quality metrics for dynamical models of neural activity

A primary goal of systems neuroscience is to discover how ensembles of neurons transform inputs into goal-directed behavior, a process known as neural computation. A powerful framework for understanding neural computation uses neural dynamics - the rules that govern how neural activity evolves over time - to explain how goal-directed input-output transformations occur. As dynamical rules are not directly observable, we need computational models that can infer neural dynamics from recorded neural activity. We typically validate such models using synthetic datasets with known ground-truth dynamics, but unfortunately existing synthetic datasets dont reflect fundamental features of neural computation and may therefore be poor proxies for neural systems. Further, the field lacks validated metrics for quantifying the accuracy of the dynamics inferred by models. The Computation-through-Dynamics Toolkit (CtDToolkit) addresses these critical gaps by providing: 1) synthetic datasets that reflect computational properties of biological neural circuits, 2) interpretable metrics for quantifying model performance, and 3) a standardized pipeline for training and evaluating models with or without known external inputs. In this manuscript, we demonstrate how CtDToolkit can help guide the development, tuning, and troubleshooting of neural dynamics models. In summary, CtDToolkit provides a necessary framework for model developers to better understand and characterize neural computation through the lens of dynamics. Author SummaryUnderstanding how the brain works requires interpretable accounts of how populations of neurons process information to produce behavior. One powerful approach is to study "neural dynamics", the patterns of how neural activity evolves over time. Scientists develop computational models to infer these dynamics from neural recordings, but it has been challenging to know when the inferred dynamics are trustworthy. Existing datasets often lack key features of biological neural circuits, and current performance metrics can provide an incomplete picture of model quality. We developed the Computation-through-Dynamics Toolkit (CtDToolkit) to solve these problems. Our toolkit provides three key resources: biologically motivated synthetic datasets, improved metrics that provide more holistic accounts of model performance, and a standardized workflow for training and evaluating models. We hope that CtDToolkit enables researchers to rigorously test, improve, and troubleshoot their models before applying them to real brain data. This work establishes a crucial foundation for developing better methods to understand neural computation, ultimately advancing our ability to decode how the brain transforms sensory information into thought and action.

neuroscience↗