Hyperbolic neural population geometry benefits computation

Neural population geometry shapes downstream inference. Recent findings in neurobiology suggest that a hyperbolic structure underlies population activity. However, a theoretical framework for this phenomenon is still lacking. Here, we propose a plausible construction of hippocampal tuning curves that statistically induce hyperbolic geometry. Next, we establish a connection between neural decoding and associative memory by demonstrating that the Modern Hopfield Network update rule computes the optimal squared loss estimator under hyperbolic geometry. Furthermore, we introduce a novel associative memory model defined in hyperbolic space that yields significantly larger capacity than existing models. Our results suggest that animals encode spatial information as a latent hyperbolic cognitive map, which enhances both memory capacity and decoding accuracy.