Clustering in neural configuration space improves inference of synaptic connectivity

PAOLO DEL GIUDICE; GABRIEL BAGLIETTO; GUIDO GIGANTE

Copenague

Congreso; FENS Forum of Neuroscience; 2016

Simultaneous recordings from N electrodes generate N-dimensional time series that pose a challenge in devising efficient representations to expose relevant aspects of the underlying dynamics.Binning the time series defines a sequence of neural activity vectors, that populate the N-dimensional space as a density distribution, especially informative when the neural dynamics proceeds as a noisy path through metastable states (often a case of interest in neuroscience); this makes clustering in the N-dimensional space a natural choice. We develop a variant of the `mean-shift' algorithm to perform such clustering, and validate it on an Hopfield network working above pure retrieval. We next successfully test the flexibility of the approach on a multi-modular attractor spiking network, with spike-frequency adaptation; the latter induces an history dependence of the landscape of metastable states.Inter-module synaptic connectivity implementing a prescribed attractor structure is determined through a new procedure similar to Boltzmann learning, but applicable beyond the usual domain of Ising models inference.We next show that clustering allows to greatly improve inference of the synaptic couplings, through a parametrization of the synaptic matrix as a weighted sum of Hopfield-like terms where the `patterns' are the neural configurations identified as clusters? centroids.Going back to the multi-dimensional dynamics, we cast it in the form of stochastic transitions in the discrete space of clusters' centroids, and obtain a compact representation of memory effects by comparing the Lempel-Ziv complexity of the reduced dynamics to the one of Markov processes generated by the same transition probabilities between centroids.