Hyperbolic Neural Population Geometry Benefits Computation

The paper presents a theoretical framework linking hyperbolic geometry to neural population activity in the hippocampus, proposing a construction of tuning curves that induces this geometry. It establishes a connection between neural decoding and associative memory through the Modern Hopfield Network, demonstrating that its update rule computes the minimum mean-squared-error estimator. Additionally, a new associative memory model in hyperbolic space is introduced, which offers significantly larger capacity compared to existing models, suggesting implications for spatial information encoding and memory performance in AI systems.