Beyond Activation Alignment: The Geometry of Neural Sensitivity

Activation-alignment measures such as Representational Similarity Analysis (RSA), Canonical Correlation Analysis (CCA), and Centered Kernel Alignment (CKA) are widely used to compare biological and artificial neural representations. Recent theoretical work interprets many of these methods as assessing agreement between optimal linear readouts over broad families of global tasks. However, agreement at the level of global readouts does not determine how a system uses local stimulus evidence. Specifically, representations may align in activation space yet differ in their sensitivity to small perturbations. To address this challenge, we introduce a complementary framework based on local decodable information, which focuses on a representation's ability, under noise, to discriminate small perturbations within a specified stimulus-coordinate subspace. Building on Fisher information and local representation geometry, we summarize each representation using the expected projected pullback/Fisher metric over that subspace. This formulation induces a second-moment family of local discrimination tasks, for which the resulting operator provides a minimal, complete dataset-level summary of expected discriminability. We compare these regularized signatures using a log-spectral distance on the manifold of symmetric positive definite (SPD) matrices, yielding the Spectral Riemannian Alignment Score (S-RAS) and a uniform multiplicative certificate over the corresponding family of lifted task values. Empirically, this framework enables the recovery of corresponding layers across independently trained artificial neural networks, supports transferable class-conditional probes, reveals controlled dissociations between standard and robust training, and uncovers stimulus-coordinate family effects across mouse visual cortex using the Allen Brain Observatory static gratings dataset.

Robust Tracking and Behavioral Modeling of Movements of Biological Collectives from Ordinary Video Recordings

We propose a novel computational method to extract information about interactions among individuals with different behavioral states in a biological collective from ordinary video recordings. Assuming that individuals are acting as finite state machines, our method first detects discrete behavioral states of those individuals and then constructs a model of their state transitions, taking into account the positions and states of other individuals in the vicinity. We have tested the proposed method through applications to two real-world biological collectives: termites in an experimental setting and human pedestrians in a university campus. For each application, a robust tracking system was developed in-house, utilizing interactive human intervention (for termite tracking) or online agent-based simulation (for pedestrian tracking). In both cases, significant interactions were detected between nearby individuals with different states, demonstrating the effectiveness of the proposed method.