Noise-Robust Modes of the Retinal Population Code have the Geometry of "Ridges" and Correspond with Neuronal Communities

Abstract: An appealing new principle for neural population codes is that correlations among neurons organize neural activity patterns into a discrete set of clusters, which can each be viewed as a noise-robust population "codeword". Previous studies assumed that these codewords corresponded geometrically with local peaks in the probability landscape of neural population responses. Here, we analyze multiple datasets of the responses of ~150 retinal ganglion cells and show that local probability peaks are absent under broad, non-repeated stimulus ensembles, which are characteristic of natural behavior. However, we find that neural activity still forms noise-robust clusters in this regime, albeit clusters with a different geometry. We start by defining a soft local maximum, which is a local probability maximum when constrained to a fixed spike count. Next, we show that soft local maxima are robustly present, and can moreover be linked across different spike count levels in the probability landscape to form a "ridge". We found that these ridges are comprised of combinations of spiking and silence in the neural population such that all of the spiking neurons are members of the same neuronal community, a notion from network theory. We argue that a neuronal community shares many of the properties of Donald Hebb's classic cell assembly, and show that a simple, biologically plausible decoding algorithm can recognize the presence of a specific neuronal community.

• The paper demonstrates that retinal neural codes form noise-robust ridge structures rather than traditional local maxima.
• It employs K-Pairwise Maximum Entropy and Tree Hidden Markov models on data from 150 retinal ganglion cells to map soft local maxima across spike counts.
• The identified ridge patterns correlate with neuronal communities, suggesting inherent error correction capabilities in natural neural processing.

Noise-Robust Modes of the Retinal Population Code as Ridges and Neuronal Communities

Introduction

The paper "Noise-Robust Modes of the Retinal Population Code have the Geometry of 'Ridges' and Correspond with Neuronal Communities" (1610.06886) investigates the structure of neural population codes and introduces the notion that neural activity patterns can be organized into discrete clusters or codewords, each acting as a noise-robust population codeword. This work diverges from the traditionally assumed local peaks in the probability landscape, suggesting instead a ridge-based structure correlated with network theory concepts like neuronal communities.

Methods and Models

Experimental Data: The study analyzed datasets from approximately 150 retinal ganglion cells responding to both repeated and non-repeated stimuli, provided by natural movies and white noise checkerboard ensembles. Neural responses were recorded and analyzed to map probability landscapes.

Modeling Approach: The authors employed two principal models to explore neural activity structures: the K-Pairwise Maximum Entropy (MaxEnt) model and the Tree Hidden Markov Model (HMM). These models were chosen to capture the stochastic nature of neural population activity, independent of direct stimulus coding, allowing a focus on intrinsic activity organization.

Key Analytical Techniques:

• Local Maxima and Ridges: Rather than relying solely on the commonly used concept of local maxima, the paper defines "soft local maxima," which are local probability maxima constrained to fixed spike counts. This concept is extended to discover ridges across spike count levels using a novel algorithm linking these maxima.
• Ridge Search Algorithm: A graph-theoretic approach visualizes the connection between soft local maxima across spike levels, presenting them as "ridges" in the neural response landscape.

Results and Findings

Contradictory Findings on Local Maxima: The study finds an absence of local maxima under non-repeated stimuli conditions, refuting earlier hypotheses that had considered them potential candidates for codewords.

Ridge Formation: Using soft local maxima, researchers demonstrate that ridges are prevalent structures in the probability landscape, representing a linked series of high-probability states across spike counts. The ridges derived from the Tree HMM exhibited a close correspondence to statistically derived collective modes.

Neuron Community Dynamics: The ridge structures align closely with the concept of neuronal communities, revealing a non-trivial overlap with Donald Hebb's cell assembly theory, suggesting error correction capabilities intrinsic to these communities.

Figure 1: Schematic illustrating the concept of local maxima and basins.

Discussion

Error Correction and Clustering: The work positions these ridges and the associated neuronal communities as intrinsic codes for handling neural response variability, facilitating error correction via natural clustering.

Stimulus Dependence: The research emphasizes the role of stimulus ensemble properties on the probability landscape and, consequently, the neural coding body's architecture. Specifically, while local maximum structures might manifest with repeated stimuli, ridges accurately depict naturalistic, non-repeated stimulation environments more accurately.

Figure 2: Local maxima results obtained for the dataset using either the K-Pairwise Maximum Entropy model or Tree hidden Markov model as the underlying probability model.

Implications and Future Directions

This paper extends our understanding of neural coding by moving beyond simplistic peak models toward a more inclusive framework accounting for ridge geometries. Practically, these findings suggest that downstream neural decoding algorithms can leverage the robustness of ridge structures. Further exploration into biological plausibility of decoding these structures using simple neuron sets offers a pathway towards developing better artificial neural models that mimic these natural processes.

Figure 3: Experimental design showcasing results for the parametric repeat analysis.

Conclusion

The findings of this study challenge the dominant coding paradigms by promoting ridge structures over local peaks as core components of neural population codes. The connection to neuron community frameworks provides a sophisticated approach to understanding neural information processing, especially in the face of varying natural stimuli. Future work might explore these concepts within other sensory systems, potentially offering broader insights into neural representation across different neural architectures and species.