# Searching for collective behavior in a network of real neurons

arXiv: https://arxiv.org/abs/1306.3061 · HTML: https://mlsanity.com/paper/1306.3061/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Jun 2013.

## Built on by (most cited first, 9 of 9)

- [On the Sample Complexity of Quantum Boltzmann Machine Learning](https://mlsanity.com/paper/2306.14969/) (2023)
- [Inferring effective couplings with Restricted Boltzmann Machines](https://mlsanity.com/paper/2309.02292/) (2023)
- [Explosive neural networks via higher-order interactions in curved statistical manifolds](https://mlsanity.com/paper/2408.02326/) (2024)
- [Biases in Inverse Ising Estimates of Near-Critical Behaviour](https://mlsanity.com/paper/2301.05556/) (2023)
- [Leader-Follower Neural Networks with Local Error Signals Inspired by Complex Collectives](https://mlsanity.com/paper/2310.07885/) (2023)
- [Signal Processing in the Retina: Interpretable Graph Classifier to Predict Ganglion Cell Responses](https://mlsanity.com/paper/2401.01813/) (2024)
- [Understanding temperature tuning in energy-based models](https://mlsanity.com/paper/2512.09152/) (2025)
- [Inference of stochastic time series with missing data](https://mlsanity.com/paper/2101.11816/) (2021)
- [Exploring Biological Neuronal Correlations with Quantum Generative Models](https://mlsanity.com/paper/2409.09125/) (2024)

## Abstract (arXiv)

Maximum entropy models are the least structured probability distributions that exactly reproduce a chosen set of statistics measured in an interacting network. Here we use this principle to construct probabilistic models which describe the correlated spiking activity of populations of up to 120 neurons in the salamander retina as it responds to natural movies. Already in groups as small as 10 neurons, interactions between spikes can no longer be regarded as small perturbations in an otherwise independent system; for 40 or more neurons pairwise interactions need to be supplemented by a global interaction that controls the distribution of synchrony in the population. Here we show that such "K-pairwise" models--being systematic extensions of the previously used pairwise Ising models--provide an excellent account of the data. We explore the properties of the neural vocabulary by: 1) estimating its entropy, which constrains the population's capacity to represent visual information; 2) classifying activity patterns into a small set of metastable collective modes; 3) showing that the neural codeword ensembles are extremely inhomogenous; 4) demonstrating that the state of individual neurons is highly predictable from the rest of the population, allowing the capacity for error correction.