Higher-Order Spatial Information for Self-Supervised Place Cell Learning

TL;DR

The paper addresses how multiple place cells encode space under self-supervision by extending spatial information beyond single neurons. It derives a joint spatial information rate for two place cells, builds a population-level information matrix J, and optimizes the leading eigenvalue λ₁ via the higher-order loss E_higher-order(P) = -|λ₁| to induce multi-cell place representations. Empirically, RNNs trained with this measure yield place-cell-like receptive fields that support high-accuracy spatial decoding, and exhibit path invariance and uniform firing fields, outperforming models trained with Skaggs' single-neuron information. This work links advanced information-theoretic concepts to neuroscience-inspired navigation, enabling robust artificial place-cell representations in novel environments without external location signals.

Abstract

Mammals navigate novel environments and exhibit resilience to sparse environmental sensory cues via place and grid cells, which encode position in space. While the efficiency of grid cell coding has been extensively studied, the computational role of place cells is less well understood. This gap arises partially because spatial information measures have, until now, been limited to single place cells. We derive and implement a higher-order spatial information measure, allowing for the study of the emergence of multiple place cells in a self-supervised manner. We show that emergent place cells have many desirable features, including high-accuracy spatial decoding. This is the first work in which higher-order spatial information measures that depend solely on place cells' firing rates have been derived and which focuses on the emergence of multiple place cells via self-supervised learning. By quantifying the spatial information of multiple place cells, we enhance our understanding of place cell formation and capabilities in recurrent neural networks, thereby improving the potential navigation capabilities of artificial systems in novel environments without objective location information.

Figures (9)

• Figure 1: (a) Place cells recorded in hippocampal subarea CA3. Firing locations are shown as red dots on the path of a rat (black). (b) Activity maps of the cells. Red is high firing rate, and blue is no firing. (c) Diagram of the process of path integration. The agent integrates four velocities to determine its current location via the integrated path (red). (a-b) adapted from stensola2016grid.
• Figure 2: A diagram of RNN architecture used to perform self-supervised learning. As training progresses (right), the neuron's firing fields become more place cell-like.
• Figure 3: (a) Activation maps of top 64 learned place cells from a model trained with higher-order spatial information, normalized to be between 0 and 1, and sorted by place cell score (Equation \ref{['place cell score']}). Fig. \ref{['fig:all_activations']} shows all 128 place cell activation maps from this model. (b) Original and trained place cell score box plots and histograms. Place cell scores are recorded across 50 total models for each loss function with varying place cell sizes. (c) Mean ($\pm$ standard deviation) sparsity, smoothness, binarity ($\epsilon = 0.1$), and spatial information rate (Equations (\ref{['smoothness']}- \ref{['arena spatial information']}) of trained place cells as the number of place cells increases.
• Figure 4: Comparison of decoding capabilities of binarized neurons before and after training. (a) Simulated and predicted trajectories leave-one-out classification with 128 neurons. (b) Skaggs vs higher-order leave-one-out decoding mean square error (MSE) as the number of trained place cells increases. The mean ($\pm$ standard deviation) of MSE across experiments is shown. (c) Correctly (orange) and incorrectly (grey) classified activations from a support vector machine (SVM) for quadrant classification using 16 neurons. (d) Skaggs vs higher-order quadrant classification accuracy. The mean $(\pm$ standard deviation) of accuracy across experiments is shown.
• Figure 5: (a) Two trajectories formed by shuffling the order of velocities. Since both trajectories end at the same location, neural representations at the final position should be identical despite different paths to get there. (b) Histogram of path invariance discrepancy across 1000 trajectories from all pre-trained models, models trained with Skaggs' spatial information, and models trained with higher-order spatial information.

Theorems & Definitions (7)

• Definition 2.1
• Definition 2.2
• Lemma D.2: No-firing term provides no information
• proof
• Theorem D.3: Spatial Information Properties
• proof
• Remark D.4: Eigenvalues of Spatial Information Matrix