Discretization of continuous input spaces in the hippocampal autoencoder

TL;DR

The paper shows that sparse autoencoders can develop hippocampal-like place cells and discretize input spaces into non-overlapping receptive fields, even when trained without temporal predictive objectives. This sparse, high-dimensional coding extends to both visual and auditory domains, enabling robust tiling of image and frequency spaces and supporting zero-shot generalization to unseen environments. The work also demonstrates that reinforcement learning agents can utilize these representations effectively, suggesting a modality-independent, episodic-memory–like framework. Collectively, the findings offer a unified account for how sparse, decorrelated, high-dimensional codes can support precise memory formation and visuo-spatial navigation with plausible neural mechanisms and broad implications for AI learning systems.

Abstract

The hippocampus has been associated with both spatial cognition and episodic memory formation, but integrating these functions into a unified framework remains challenging. Here, we demonstrate that forming discrete memories of visual events in sparse autoencoder neurons can produce spatial tuning similar to hippocampal place cells. We then show that the resulting very high-dimensional code enables neurons to discretize and tile the underlying image space with minimal overlap. Additionally, we extend our results to the auditory domain, showing that neurons similarly tile the frequency space in an experience-dependent manner. Lastly, we show that reinforcement learning agents can effectively perform various visuo-spatial cognitive tasks using these sparse, very high-dimensional representations.

Figures (6)

• Figure 1: Hippocampal-like place cells emerge in sparse autoencoders. (a) Autoencoder architecture, featuring the hidden layer or latent space $Z$ (denoted as Fc1) with 1000 neurons. (b) Representative examples of the neurons' spatial ratemaps for sparse and dense autoencoders. (c) Probability distribution of place field number across environments. (d) Average spatial information per neuron across environments. (e) Normalized average distance error of linear decoding of position with the ratemaps' population vectors, across environments. The grey dots represent the expected linear decoding errors after performing 1000 random permutations of the ratemaps' values.
• Figure 2: Sparse autoencoders discretize and tile the image space with interpretable neurons. (a) Images taken in one of the environments ('Cylinder'), encoded with CLIP and further reduced to two dimensions with UMAP. Points of different colors correspond to the images that maximally activate each example neuron (above the 50% threshold of the maximum neuron's recorded activity). Clusters of maximally activated images are extracted with DBSCAN, making up the convex hulls. (b) Convex hulls for all neurons in a sparse autoencoder trained with images from the 'Cylinder' environment. The overlap metric corresponds to the expected overlapping area (in %) of two randomly chosen hulls (see Detailed methods in the Appendix for further details). (c) Average overlap in 2D image space of sparse and dense autoencoders, across tasks and for a range of threshold values of maximal activation. (d) Example interpretable neurons in the sparse autoencoder. The corresponding neuron in latent space $Z$ is set to its maximum recorded value across the dataset, while all other neurons are set to zero. Then, the enforced activity vector $Z$ is deconvolved into an image by passing it through the decoder.
• Figure 3: Population structure in sparse autoencoders is grounded on mixed selectivity. (a) Eigenspectrum decay in latent space representations (first two rows) and images from the environments (third row). Parameter $\alpha$ corresponds to the power law exponent from linear fitting in log-log space. (b) Input-output similarity for sparse and dense autoencoders, with data pooled across environments. Correlation scores correspond to Spearman's rank coefficients, and fitting curves have been generated with a locally weighted scatter-plot smoother (LOWESS) for improved visualization. (c) Pairwise Pearson correlation scores between all neurons' activity in latent space, pooled across environments (left) and pairwise kernel similarity in the decoder weights (layer Fc2), representing the similarity density across "words" in the learned "dictionary" (right).
• Figure 4: Zero-shot place cells in sparse autoencoders. (a) Probability distributions of place field number when testing a model within its training environment (light blue) or across unseen environments (dark blue). (b) Average spatial information per neuron, pooled across models and testing environments. (c) Normalized average distance error of linear decoding of position with the ratemaps' population vectors, across models and testing environments. The grey dots represent the expected linear decoding errors after performing 1000 random permutations of the ratemaps' values.
• Figure 5: Sparse autoencoders discretize and tile the input frequency space in an experience-dependent manner. (a) Data samples are generated by applying a uniformly distributed sliding window to a linearly-varying frequency signal. The samples are fed into a convolutional autoencoder, analogous to the one used for vision (more details can be found in the Detailed Methods section of the Appendix). (b) Unsorted and sorted receptive fields by peak activity location for both sparse and dense autoencoders. Latent space activity $Z$ responding to pure tone test inputs was convolved with a Gaussian kernel (sigma of 0.5 Hz), and then normalized by the maximum per neuron in the sorted plots. Lanczos interpolation was applied to all plots for improved visualization. (c) Decoded output signals after setting the corresponding neuron in latent space to its maximum recorded value across the dataset, while all other neurons were set to zero. (d) Sorted receptive fields in a sparse autoencoder trained with an unbalanced dataset. The data samples were generated with a sliding window that was not uniformly distributed in the frequency space, but whose density followed a Gaussian distribution centered at 45 Hz. Dashed vertical lines denote one standard deviation $\sigma$ from the mean.