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The combination of new recording techniques in neuroscience and powerfulinference methods recently held the promise to recover useful effective models,at the single neuron or network level, directly from observed data. The valueof a model of course should critically depend on its ability to reproduce thedynamical behavior of the modeled system; however, few attempts have been madeto inquire into the dynamics of inferred models in neuroscience, and none, toour knowledge, at the network level. Here we introduce a principledmodification of a widely used generalized linear model (GLM), and learn itsstructural and dynamic parameters from ex-vivo spiking data. We show that thenew model is able to capture the most prominent features of the highlynon-stationary and non-linear dynamics displayed by the biological network,where the reference GLM largely fails. Two ingredients turn out to be key forsuccess. The first one is a bounded transfer function that makes the singleneuron able to respond to its input in a saturating fashion; beyond itsbiological plausibility such property, by limiting the capacity of the neuronto transfer information, makes the coding more robust in the face of the highlyvariable network activity, and noise. The second ingredient is a super-Poissonspikes generative probabilistic mechanism; this feature, that accounts for thefact that observations largely undersample the network, allows the model neuronto more flexibly incorporate the observed activity fluctuations. Takentogether, the two ingredients, without increasing complexity, allow the modelto capture the key dynamic elements. When left free to generate its spontaneousactivity, the inferred model proved able to reproduce not only thenon-stationary population dynamics of the network, but also part of thefine-grained structure of the dynamics at the single neuron level.

Spontaneous activity emerging from an inferred network model captures complex temporal dynamics of spiking data