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Pairwise maximum-entropy models have been used in recent neuroscientificliterature to predict the activity of neuronal populations, given only thetime-averaged correlations of the neuron activities. This paper providesevidence that the pairwise model, applied to experimental recordings, predictsa bimodal distribution for the population-averaged activity, and for somepopulation sizes the second mode peaks at high activities, with 90% of theneuron population active within time-windows of few milliseconds. Thisbimodality has several undesirable consequences: 1. The presence of two modesis unrealistic in view of observed neuronal activity. 2. The prediction of ahigh-activity mode is unrealistic on neurobiological grounds. 3. Boltzmannlearning becomes non-ergodic, hence the pairwise model found by this method isnot the maximum entropy distribution; similarly, solving the inverse problem bycommon variants of mean-field approximations has the same problem. 4. TheGlauber dynamics associated with the model is either unrealistically bistable,or does not reflect the distribution of the pairwise model. This bimodality isfirst demonstrated for an experimental dataset comprising 159 neuron activitiesrecorded from the motor cortex of macaque monkey. Using a reducedmaximum-entropy model, evidence is then provided that this bimodality affectstypical neural recordings of population sizes of a couple of hundreds or moreneurons. As a way to eliminate the bimodality and its ensuing problems, amodified pairwise model is presented, which -- most important -- has anassociated pairwise Glauber dynamics. This model avoids bimodality thanks to aminimal asymmetric inhibition. It can be interpreted as aminimum-relative-entropy model with a particular prior, or as a maximum-entropymodel with an additional constraint.

Pairwise maximum-entropy models and their Glauber dynamics: bimodality, bistability, non-ergodicity problems, and their elimination via inhibition