InputDSA: Demixing then Comparing Recurrent and Externally Driven Dynamics

2025-10-29

AI Summary

Existing dynamical systems similarity analysis (DSA) relies solely on intrinsic recurrent dynamics, neglecting external input effects and thus mischaracterizing non-autonomous systems. This work introduces InputDSA—the first framework to explicitly decouple and jointly compare input-driven dynamics with intrinsic recurrent dynamics, supporting surrogate input signals when true inputs are unknown. Methodologically, InputDSA extends the DSA framework using controlled dynamic mode decomposition (DMDc) and subspace identification to jointly estimate and contrast the input-response operator and the intrinsic dynamics operator within a unified similarity metric. Evaluated on reinforcement learning-trained RNNs and in vivo rat neural recordings, InputDSA accurately identifies shared dynamical structures across high-performing policies and quantifies the transition from input-dependent processing to intrinsic decision-making. The approach significantly enhances modeling fidelity and cross-system comparability for non-autonomous dynamical systems.

Technology Category

• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Intelligent Robots: State Estimation
• Humans and AI: Human-Aware Planning and Behavior Prediction

Application Category

• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Web Mining and Content Analysis: Machine learning and data science for the Web

Abstract

In control problems and basic scientific modeling, it is important to compare observations with dynamical simulations. For example, comparing two neural systems can shed light on the nature of emergent computations in the brain and deep neural networks. Recently, Ostrow et al. (2023) introduced Dynamical Similarity Analysis (DSA), a method to measure the similarity of two systems based on their recurrent dynamics rather than geometry or topology. However, DSA does not consider how inputs affect the dynamics, meaning that two similar systems, if driven differently, may be classified as different. Because real-world dynamical systems are rarely autonomous, it is important to account for the effects of input drive. To this end, we introduce a novel metric for comparing both intrinsic (recurrent) and input-driven dynamics, called InputDSA (iDSA). InputDSA extends the DSA framework by estimating and comparing both input and intrinsic dynamic operators using a variant of Dynamic Mode Decomposition with control (DMDc) based on subspace identification. We demonstrate that InputDSA can successfully compare partially observed, input-driven systems from noisy data. We show that when the true inputs are unknown, surrogate inputs can be substituted without a major deterioration in similarity estimates. We apply InputDSA on Recurrent Neural Networks (RNNs) trained with Deep Reinforcement Learning, identifying that high-performing networks are dynamically similar to one another, while low-performing networks are more diverse. Lastly, we apply InputDSA to neural data recorded from rats performing a cognitive task, demonstrating that it identifies a transition from input-driven evidence accumulation to intrinsically-driven decision-making. Our work demonstrates that InputDSA is a robust and efficient method for comparing intrinsic dynamics and the effect of external input on dynamical systems.

Problem

• Compares intrinsic and input-driven dynamics in systems
• Extends DSA to handle externally driven dynamical systems
• Measures similarity of partially observed noisy systems

Innovation

• Extends DSA with input-driven dynamics comparison
• Uses DMDc for input and intrinsic operator estimation
• Applies to noisy data with surrogate input capability