Summary Exactly Solvable Statistical Physics Models for Large Neuronal Populations arxiv.org
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One Line
Researchers have developed statistical physics models that can be solved and focus on capturing collective behavior in large neuronal populations.
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Key Points
- Researchers have developed solvable statistical physics models for large neuronal populations.
- The undersampled regime poses a challenge in choosing which observables to constrain in the maximum entropy construction.
- The researchers focus on correlations among pairs of neurons that form a tree structure to tackle this problem.
- They apply this method to analyze data from experiments on populations of around 1500 neurons in the mouse hippocampus.
- The resulting model captures the distribution of synchronous activity in the network.
- Maximum entropy methods connect neural activity data to statistical physics models.
- The number of samples collected in experiments does not typically increase proportionally with the number of degrees of freedom.
- The minimax entropy principle suggests finding the tree that minimizes entropy while obeying constraints.
Summaries
17 word summary
Researchers create solvable statistical physics models for large neuronal populations, focusing on correlations to capture collective behavior.
64 word summary
Researchers have developed solvable statistical physics models for large neuronal populations. By focusing on correlations among pairs of neurons, they construct models that capture collective behavior. Applying this method to data from experiments on 1500 neurons in the mouse hippocampus, they demonstrate that the resulting model captures synchronous activity distribution. The minimax entropy principle and efficient algorithms offer promise for studying larger neural networks.
125 word summary
Researchers have developed exactly solvable statistical physics models for large neuronal populations. By focusing on correlations among pairs of neurons that form a tree structure, they are able to efficiently construct models that capture essential features of the collective behavior in the network. The researchers apply this method to analyze data from experiments on populations of around 1500 neurons in the mouse hippocampus and demonstrate that the resulting model captures the distribution of synchronous activity in the network. The minimax entropy principle and the efficient algorithms used in this framework offer a promising approach for studying larger neural networks. The researchers also investigate how the maximally informative correlations scale with population size, finding that the minimax entropy framework becomes more effective as population size increases.
470 word summary
Researchers have developed exactly solvable statistical physics models for large neuronal populations. These models connect neural activity measurements to statistical physics and have been successful for populations of around 100 neurons. However, as the number of neurons increases, the undersampled regime poses a challenge in choosing which observables to constrain in the maximum entropy construction.
To tackle this problem, the researchers focus on correlations among pairs of neurons that form a tree structure. This approach allows for efficient computation of the best tree and exact solutions to the statistical physics models. The researchers apply this method to analyze data from experiments on populations of around 1500 neurons in the mouse hippocampus and demonstrate that the resulting model captures the distribution of synchronous activity in the network.
The maximum entropy approach takes into account the limited number of observables and requires that the expectation values predicted by the model match those measured in experiments. The probability distribution over the microscopic degrees of freedom can be written in terms of observables or operators, and the maximum entropy distribution is chosen to have the least possible structure while satisfying the constraints.
In the case of large neuronal populations, it is not feasible to constrain all pairwise correlations due to limited connectivity and the undersampled regime. To overcome this challenge, the researchers restrict the class of observables to pairwise correlations among neurons that form a tree structure. The minimax entropy principle suggests finding the tree that minimizes the entropy while obeying the constraints. This problem is solved by finding the tree with the largest total mutual information between pairs of neurons.
The researchers analyze data from experiments on populations of around 1500 neurons in the mouse hippocampus. The distribution of mutual information between pairs of neurons is heavy-tailed, with a small number of correlations containing orders of magnitude more information than average. The optimal tree captures most of this information and predicts enhancements in the probability of synchronous activity involving a large number of neurons.
The researchers investigate how the maximally informative correlations scale with population size. They construct populations of increasing size by starting from a single neuron and expanding to include neighboring neurons. The fractional reduction in entropy achieved by the optimal tree increases slowly with population size, suggesting that the minimax entropy framework becomes more effective as population size increases.
In conclusion, the researchers have developed exactly solvable statistical physics models for large neuronal populations. By focusing on pairwise correlations that form a tree structure, they are able to efficiently construct models that capture essential features of the collective behavior in the network. These models provide insights into the distribution of synchronous activity and the strength of interactions between neurons. The minimax entropy principle and the efficient algorithms used in this framework offer a promising approach for studying larger neural networks.
711 word summary
Researchers have developed exactly solvable statistical physics models for large neuronal populations. These models connect measurements of neural activity to statistical physics and have been successful for populations of around 100 neurons. However, as the number of neurons increases, the undersampled regime poses a challenge in choosing which observables to constrain in the maximum entropy construction. The principle of "minimax entropy" suggests choosing observables that provide the greatest reduction in entropy. To tackle this problem, the researchers focus on correlations among pairs of neurons that form a tree structure. This approach allows for efficient computation of the best tree and exact solutions to the statistical physics models. The researchers apply this method to analyze data from experiments on populations of around 1500 neurons in the mouse hippocampus and demonstrate that the resulting model captures the distribution of synchronous activity in the network.
The hope of describing neural networks using concepts from statistical physics has been revolutionized by techniques that enable the recording of electrical activity from thousands of individual neurons simultaneously. Maximum entropy methods have been used to connect these data to statistical physics models, which have provided successful predictions for various features of neural activity patterns. These models have also been applied in other contexts, such as the evolution of protein families and ordering in flocks of birds. However, as experiments investigate systems with more degrees of freedom, the number of samples collected typically does not increase proportionally.
The maximum entropy approach takes into account the limited number of observables and requires that the expectation values predicted by the model match those measured in experiments. The probability distribution over the microscopic degrees of freedom can be written in terms of observables or operators, and the maximum entropy distribution is chosen to have the least possible structure while satisfying the constraints. The optimization problem to find this distribution is solved by finding the distribution that generates samples that are as random as possible while still obeying the constraints. The solution is given by an exponential function with coupling constants that need to be chosen to satisfy the constraints.
In the case of large neuronal populations, it is not feasible to constrain all pairwise correlations due to limited connectivity and the undersampled regime. To overcome this challenge, the researchers restrict the class of observables to pairwise correlations among neurons that form a tree structure. The minimax entropy principle suggests finding the tree that minimizes the entropy while obeying the constraints. This problem is solved by finding the tree with the largest total mutual information between pairs of neurons. Efficient algorithms, such as Prim's algorithm, can be used to construct the optimal tree. The resulting statistical physics models are exactly solvable and provide explicit expressions for the fields and couplings.
The researchers analyze data from experiments on populations of around 1500 neurons in the mouse hippocampus. The distribution of mutual information between pairs of neurons is heavy-tailed, with a small number of correlations containing orders of magnitude more information than average. The optimal tree captures most of this information and predicts enhancements in the probability of synchronous activity involving a large number of neurons. The interactions in the optimal tree are predominantly positive, indicating a backbone of ferromagnetic interactions in the network. The model also correctly predicts deviations from the Gaussian distribution expected for independent neurons in the distribution of simultaneously active neurons.
The researchers investigate how the maximally informative correlations scale with population size. They construct populations of increasing size by starting from a single neuron and expanding to include neighboring neurons. The fractional reduction in entropy achieved by the optimal tree increases slowly with population size, while for random trees, this fraction decays rapidly toward zero. This suggests that the minimax entropy framework becomes more effective as population size increases.
In conclusion, the researchers have developed exactly solvable statistical physics models for large neuronal populations. By focusing on pairwise correlations that form a tree structure, they are able to efficiently construct models that capture essential features of the collective behavior in the network. These models provide insights into the distribution of synchronous activity and the strength of interactions between neurons. The minimax entropy principle and the efficient algorithms used in this framework offer a promising approach for studying larger neural networks.