Kymn Christopher J, Mazelet Sonia, Thomas Anthony, Kleyko Denis, Frady E Paxon, Sommer Friedrich T, Olshausen Bruno A
Redwood Center for Theoretical Neuroscience, UC Berkeley, Berkeley, USA.
Université Paris-Saclay, ENS Paris-Saclay, Gif-sur-Yvette, France.
ArXiv. 2024 Jun 27:arXiv:2406.18808v1.
We propose a normative model for spatial representation in the hippocampal formation that combines optimality principles, such as maximizing coding range and spatial information per neuron, with an algebraic framework for computing in distributed representation. Spatial position is encoded in a residue number system, with individual residues represented by high-dimensional, complex-valued vectors. These are composed into a single vector representing position by a similarity-preserving, conjunctive vector-binding operation. Self-consistency between the representations of the overall position and of the individual residues is enforced by a modular attractor network whose modules correspond to the grid cell modules in entorhinal cortex. The vector binding operation can also associate different contexts to spatial representations, yielding a model for entorhinal cortex and hippocampus. We show that the model achieves normative desiderata including superlinear scaling of patterns with dimension, robust error correction, and hexagonal, carry-free encoding of spatial position. These properties in turn enable robust path integration and association with sensory inputs. More generally, the model formalizes how compositional computations could occur in the hippocampal formation and leads to testable experimental predictions.
我们提出了一种海马结构中空间表征的规范模型，该模型将最优性原理（如最大化每个神经元的编码范围和空间信息）与分布式表征中的代数计算框架相结合。空间位置在余数系统中编码，单个余数由高维复值向量表示。通过相似性保持的联合向量绑定操作，将这些向量组合成一个表示位置的单个向量。整体位置和单个余数的表征之间的自一致性由模块化吸引子网络强制执行，其模块对应于内嗅皮层中的网格细胞模块。向量绑定操作还可以将不同的上下文与空间表征相关联，从而产生一个内嗅皮层和海马体的模型。我们表明，该模型实现了规范要求，包括模式随维度的超线性缩放、强大的纠错能力以及空间位置的六边形无进位编码。这些特性进而实现了强大的路径整合以及与感觉输入的关联。更一般地说，该模型形式化了海马结构中组合计算如何发生，并导致可测试的实验预测。
