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InputDSA: Demixing, then comparing recurrent and externally driven dynamics

ICLR 2026 Conference SubmissionAnonymous Authors
OpenReview Score: 6.5Download Report PDF
dynamical systemsrecurrent neural networksneural dynamicssimilarity metricscomputational neuroscience
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.

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This report is AI-GENERATED using Large Language Models and WisPaper (A scholar search engine). It analyzes academic papers' tasks and contributions against retrieved prior work. While this system identifies POTENTIAL overlaps and novel directions, ITS COVERAGE IS NOT EXHAUSTIVE AND JUDGMENTS ARE APPROXIMATE. These results are intended to assist human reviewers and SHOULD NOT be relied upon as a definitive verdict on novelty.
NOTE that some papers exist in multiple, slightly different versions (e.g., with different titles or URLs). The system may retrieve several versions of the same underlying work. The current automated pipeline does not reliably align or distinguish these cases, so human reviewers will need to disambiguate them manually.
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Overview

Overall Novelty Assessment

The paper introduces InputDSA, a metric for comparing both intrinsic and input-driven dynamics across systems, extending the DSA framework by incorporating external forcing. It resides in the 'Dynamical Similarity Analysis and Comparison Metrics' leaf, which contains only two papers total. This is a notably sparse research direction within the broader taxonomy of 50 papers across 22 leaf nodes. The sibling paper focuses on modeling intrinsic and input dynamics rather than comparison metrics, suggesting that quantitative similarity measurement for input-driven systems remains an underexplored niche despite the field's broader interest in decomposition and identification methods.

The taxonomy reveals that neighboring leaves are densely populated with decomposition techniques: Koopman operator methods (4 papers), latent dynamics architectures (4 papers), and statistical approaches (2 papers). These adjacent directions emphasize separating or modeling intrinsic versus input-driven components, whereas InputDSA's leaf focuses on comparison after decomposition. The scope notes clarify that decomposition methods aim to identify components, while the comparison metrics category addresses quantifying similarity across systems. This structural positioning suggests InputDSA bridges a gap between decomposition-heavy approaches and the need for cross-system evaluation, occupying a distinct methodological space.

Among 30 candidates examined, the core InputDSA metric contribution shows no clear refutation (10 candidates examined, 0 refutable). However, the Subspace DMDc variant and the fast optimization algorithm each face one refutable candidate among 10 examined. The limited search scope means these statistics reflect top-30 semantic matches rather than exhaustive coverage. The metric itself appears more novel than its algorithmic components, which may overlap with existing DMDc or optimization literature. The contribution-level analysis suggests the conceptual framework for comparing input-driven dynamics is less anticipated by prior work than the technical implementation details.

Based on the limited 30-candidate search, InputDSA occupies a sparse research direction with minimal direct competition in its specific comparison-focused niche. The taxonomy structure and sibling paper context suggest the work addresses an underserved need, though the algorithmic contributions show some overlap with existing techniques. The analysis does not cover exhaustive DMDc or optimization literature, so the novelty assessment remains provisional and tied to the semantic search scope employed.

Taxonomy

Core-task Taxonomy Papers
50
3
Claimed Contributions
30
Contribution Candidate Papers Compared
2
Refutable Paper

Research Landscape Overview

Core task: comparing intrinsic and input-driven dynamics of dynamical systems. This field addresses a fundamental challenge in understanding complex systems—distinguishing between behavior arising from a system's internal structure versus behavior shaped by external forcing. The taxonomy reflects a multifaceted landscape organized around five major branches. Decomposition and Identification Methods focus on algorithmic and statistical techniques for separating autonomous dynamics from input effects, often leveraging tools like Koopman operators (Adaptive Koopman Embedding[2], Koopman Partial Observation[11]) and data-driven linearization approaches (Data-Driven Linearization[49]). Neuroscience Applications examine how neural circuits balance intrinsic oscillations with sensory or task-driven inputs (Motor Cortex Input-driven[32], Cortical Attractor Geometry[14]), while Biological and Ecological Systems Dynamics explore similar questions in population models and ecological interactions (Fear-induced Group Defense[18]). Theoretical Foundations provide the mathematical underpinnings—manifold theory, non-autonomous system analysis (Non-autonomous to Autonomous[39], Augmented Manifolds Nonautonomous[34])—and Engineering and Control Applications translate these insights into practical control strategies (Learning Interpretable Control[4], Adaptive Koopman Control[7]). A particularly active line of work centers on developing metrics and frameworks to quantify dynamical similarity when inputs are present, contrasting with classical autonomous system analysis. Some studies emphasize disentangling intrinsic versus extrinsic contributions through explicit decomposition (Separating Intrinsic Extrinsic[13], Disentanglement Intrinsic Input[16]), while others focus on learning latent representations that capture both modes (Latent Dynamics Networks[5], Learning Dynamical Systems[3]). InputDSA[0] sits within the Dynamical Similarity Analysis cluster, closely aligned with Modeling Intrinsic Input Dynamics[1], and addresses the challenge of comparing systems when traditional autonomous metrics fail. Unlike approaches that primarily model or control input-driven systems, InputDSA[0] emphasizes comparison and similarity measurement, offering a complementary perspective to decomposition-focused methods like BRAID[15] or control-oriented frameworks. This positioning highlights an ongoing tension in the field: whether to isolate components or to develop holistic metrics that respect the interplay between intrinsic and driven dynamics.

Claimed Contributions

InputDSA: a novel metric for comparing intrinsic and input-driven dynamics

The authors propose InputDSA, which extends the Dynamical Similarity Analysis framework to account for external inputs by estimating and comparing both input and intrinsic dynamic operators. This enables quantitative comparison of how inputs affect dynamics in addition to recurrent dynamics.

10 retrieved papers
Subspace DMDc: a variant of DMD with control for partially observed systems

The authors develop Subspace DMDc, a novel variant of Dynamic Mode Decomposition with control based on subspace identification. This method addresses the failure mode of standard DMDc in partially observed systems where inputs affect both observed and unobserved components.

10 retrieved papers
Can Refute
Fast optimization algorithm for InputDSA metric computation

The authors introduce an optimization algorithm that solves the InputDSA metric via Procrustes alignment rather than iterative optimization, providing exponential acceleration compared to prior methods while maintaining theoretical grounding.

10 retrieved papers
Can Refute

Core Task Comparisons

Comparisons with papers in the same taxonomy category

Contribution Analysis

Detailed comparisons for each claimed contribution

Contribution

InputDSA: a novel metric for comparing intrinsic and input-driven dynamics

The authors propose InputDSA, which extends the Dynamical Similarity Analysis framework to account for external inputs by estimating and comparing both input and intrinsic dynamic operators. This enables quantitative comparison of how inputs affect dynamics in addition to recurrent dynamics.

Contribution

Subspace DMDc: a variant of DMD with control for partially observed systems

The authors develop Subspace DMDc, a novel variant of Dynamic Mode Decomposition with control based on subspace identification. This method addresses the failure mode of standard DMDc in partially observed systems where inputs affect both observed and unobserved components.

Contribution

Fast optimization algorithm for InputDSA metric computation

The authors introduce an optimization algorithm that solves the InputDSA metric via Procrustes alignment rather than iterative optimization, providing exponential acceleration compared to prior methods while maintaining theoretical grounding.

Table of Contents