将海马体神经活动建模为双曲几何，提升记忆容量与解码精度。
Hyperbolic Neural Population Geometry Benefits Computation
- 基于统计构造海马体调谐曲线，自然诱导双曲结构。
- 证明现代霍普菲尔德网络可实现最小均方误差估计。
- 新双曲关联记忆模型容量显著优于现有主流模型。
神经种群几何结构决定下游计算性能。最新神经生物学实证发现海马体种群活动具有双曲结构。本文提出理论框架：首先，构造一种可统计诱导双曲几何的海马体调谐曲线；其次，建立神经解码与关联记忆的联系，证明现代霍普菲尔德网络更新规则等价于最小均方误差（MMSE）估计器；最后，提出一种定义在双曲空间的新型关联记忆模型，其容量显著高于现有领先模型。结果表明，动物可能以潜在的双曲认知地图编码空间信息，从而同时提升记忆容量与解码准确性。
原文摘要 · Abstract (English)
Neural population geometry shapes downstream computation. Recent empirical findings in neurobiology suggest that a hyperbolic structure underlies population activity in the hippocampus. Here we provide a theoretical framework for this phenomenon. First, we propose a plausible construction of hippocampal tuning curves that statistically induces hyperbolic geometry. Next, we establish a connection between neural decoding and associative memory by demonstrating that the Modern Hopfield Network update rule computes the minimum mean-squared-error (MMSE) estimator. Finally, we introduce a novel associative memory model defined in hyperbolic space that yields significantly larger capacity than leading models. Our results suggest that animals encode spatial information as a latent hyperbolic cognitive map, improving both memory capacity and decoding accuracy.
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