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Hypothesis-driven identification of neural algorithms with dynamical structure-preserving manifolds

Poster Session E - Monday, March 9, 2026, 2:30 – 4:30 pm PDT, Fairview/Kitsilano Ballroom
Also presenting in Data Blitz Session 4 - Saturday, March 7, 2026, 10:30 am – 12:00 pm PST, Salon F.

Daniel Calbick¹ (), Jason Kim², Hansem Sohn³, Ilker Yildirim¹; ¹Yale University, ²Cornell University, ³Sungkyunkwan University

Understanding how neural circuits implement complex mental representations remains a central challenge in neuroscience. Existing approaches either lack neural grounding (probabilistic cognitive models) or provide limited algorithmic interpretability (task-optimized deep networks). We present Dynamical Structure-Preserving Manifolds (dSPMs), a framework that enables direct testing of algorithmic hypotheses against neural data by analytically programming physics-based representations into reservoir computers without training. We applied dSPM to identify the algorithm underlying physical prediction in macaque dorsomedial frontal cortex (DMFC). Using high-resolution recordings from 1,889 neurons during a ball interception task, we tested whether DMFC implements structure-preserving physics-based representations versus task-optimized or statistical shortcuts. The dSPM model analytically embeds a 12-dimensional dynamical system encoding Newtonian mechanics—including position, velocity, collision detection, and reflection dynamics—into the connectivity of a reservoir computer by directly computing connectivity weights from symbolic specifications. dSPM reproduced a striking feature of DMFC: rapid endpoint prediction within 250ms of trial onset. More remarkably, dSPM predicted that the entire future ball trajectory, not just the endpoint, should be linearly decodable from this early neural state—a prediction we confirmed in DMFC activity. Representational similarity analysis revealed that dSPM significantly outperformed task-optimized RNNs and subsumed nearly all variance explainable by alternative models through partial correlation analysis. These results suggest DMFC implements interpretable, dynamical, and physics-based manifolds rather than learned statistical representations, and establish dSPM as a powerful tool for hypothesis-driven exploration of neural algorithms underlying complex cognition.

Topic Area: PERCEPTION & ACTION: Vision