[论文解读] Self-Supervised Learning of Representations for Space Generates Multi-Modular Grid Cells

Rylan Schaeffer, Mikail Khona+4 more|arXiv (Cornell University)|Nov 4, 2023

Single-cell and spatial transcriptomics被引用 26

一句话总结

本文提出一个自监督学习框架，称为 SIC，它在速度输入上训练一个递归网络以学习空间表征，产生多个网格单元样的模块，而无需监督位置信息。涌现的表征可以推广到更大的环境，呈现网格状的、模块化结构。

ABSTRACT

To solve the spatial problems of mapping, localization and navigation, the mammalian lineage has developed striking spatial representations. One important spatial representation is the Nobel-prize winning grid cells: neurons that represent self-location, a local and aperiodic quantity, with seemingly bizarre non-local and spatially periodic activity patterns of a few discrete periods. Why has the mammalian lineage learnt this peculiar grid representation? Mathematical analysis suggests that this multi-periodic representation has excellent properties as an algebraic code with high capacity and intrinsic error-correction, but to date, there is no satisfactory synthesis of core principles that lead to multi-modular grid cells in deep recurrent neural networks. In this work, we begin by identifying key insights from four families of approaches to answering the grid cell question: coding theory, dynamical systems, function optimization and supervised deep learning. We then leverage our insights to propose a new approach that combines the strengths of all four approaches. Our approach is a self-supervised learning (SSL) framework - including data, data augmentations, loss functions and a network architecture - motivated from a normative perspective, without access to supervised position information or engineering of particular readout representations as needed in previous approaches. We show that multiple grid cell modules can emerge in networks trained on our SSL framework and that the networks and emergent representations generalize well outside their training distribution. This work contains insights for neuroscientists interested in the origins of grid cells as well as machine learning researchers interested in novel SSL frameworks.

研究动机与目标

• 阐明为什么在结合编码理论、动力学和优化的规范性原则下会出现网格状、多模态的表征。
• 提出一个纯粹的自监督学习框架，从速度序列中学习空间表征，而无需显式位置监督。
• 证明通过 SSL 训练的网络会发展出多个网格模块，并且能够超越训练分布进行泛化。
• 表征涌现的神经表征，并通过消融分析评估每个损失分量的作用。

提出的方法

• 从速度序列构造 SSL 训练数据，使用随机排列以创建轨迹交叉。
• 使用一个带有速度条件的交互矩阵 W(v) = MLP(v) 的RNN，动力学为 g_t = Norm(ReLU(W(v_t) g_{t-1})).
• 在表征上强制非负性和单位范数约束，以避免塌缩。
• 定义四个 SSL 损失：L_Sep（分离）、L_Inv（路径不变性）、L_Cap（容量）、L_ConIso（共形等距）。
• 将损失组合为 L = λ_Sep L_Sep + λ_Inv L_Inv + λ_Cap L_Cap + λ_ConIso L_ConIso，构成 SIC 框架。

实验结果

研究问题

• RQ1 在没有监督空间目标的情况下，SSL 框架是否能在深度递归网络中产生多模块网格细胞表征？
• RQ2 哪些数据、增强和损失的组合足以产生网格状的模块化编码和路径积分动力学？
• RQ3 涌现的表征如何推广到更大的场地和不同的轨迹统计？
• RQ4 每个损失项在生成和保持网格模块中起到怎样的作用？

主要发现

• 使用 SIC 框架训练的网络发展出具有空间周期性调谐和离散多网格模块的神经元。
• 涌现的网格细胞表征可以推广到比训练时更大的环境和多样化的速度统计。
• 群体分析揭示涌现表征中的圆环状吸引子流形和六边形晶格样结构。
• 消融研究表明，移除容量损失或其他损失会破坏模块化的网格状结构，有时会产生称为 place-cell 的编码或丧失空间调谐。
• 该框架产生三组共模网格群，其周期和取向不同，类似生物网格细胞的模态性。