Neuromatematica

How might one infer circuit properties from neurophysiological data. We address this challenge for the mouse visual system with a novel neural manifold obtained using unsupervised machine learning algorithms. Each point on our manifold is a neuron; nearby neurons respond similarly in time to similar parts of a stimulus ensemble. This ensemble includes drifting gratings and flows, i.e. patterns resembling what a mouse would “see” while running through fields. Our manifold differs from the standard practice in computational neuroscience, of embedding trials in neural coordinates. Importantly, for our manifolds topology matters: from spectral theory we infer that, if the circuit consists of separate components, the manifold is discontinuous (illustrated with retinal data). If there is significant overlap between circuits, the manifold is nearly-continuous (cortical data). To approach real circuits, local neighborhoods on the manifold are identified with actual circuit components. For the retinal data we show these components correspond to distinct ganglion cell types by their mosaic-like receptive field organization, while for cortical data, neighborhoods organize neurons by type (excitatory/inhibitory) and anatomical layer. The manifold topology for deep CNN's will also be developed. Joint research with Luciano Dyballa (Yale), Marija Rudzite (Duke), Michael Styrker (UCSF) and Greg Field (UCLA).

Enabling visually-guided behaviors in artificial agents implies picking-up and organizing appropriate information from the visual signal at multiple levels. The question arises about how to carefully define which feature to extract, or, from a different perspective, which kind of representation to adopt for the visual signal itself. It is well known that receptive fields (RFs) in the early stages of the primary visual cortex behave as band-pass linear filters performing a multichannel representation of the visual signal (cf. the Gabor jets). Typically, visual features are direcly derived, as symbols, from the outputs of such front-end RFs. Here, I want to emphasize the advantages of thinking early visual processes in terms of signal processing, pointing out the key role played by a full harmonic representation of the visual signal and how highly informative properties of the visual signal are efficiently and effectively embedded in the local image phases and their relationships. Accordingly, instead of directly extracting "classic" spatial features (such as edges, corners, etc.) and then looking for correspondences, we can follow a complementary approach: the visual signal is described in frequency bandwidths in terms of local amplitude, phase and orientation, and more complex visual features are derived as "qualities" based on local phase properties e.g., such as phase conguency, phase difference, and phase constancy, for contrast transitions, disparity and motion, respectively. Notably, phase-based interpretation of the visual signal allows direct links between consolidated machine vision computational techniques and the ascertained properties of visual cortical cells. The issue of direct phase-based measurements vs. distributed population coding of visual features will be discussed in relations to motion and stereo perceptual tasks.

Along the last years the technological advancements have been fundamental to improve the recording capability from brain areas and neural populations. For example multi-site recordings can be achieved from thousands of channels (sites) with a good spatial and temporal resolution yielding a good description of the underlying network dynamics. Given that, the brain operates on a single trial basis such recordings are becoming important to understand the neural code. As a first step, multi-site recordings allow to quantify the information flow in the network. The anatomical wiring (i.e. Structural Connectivity, SC) clearly plays a fundamental role to understand how cells communicate among them but it is often not well known neither it can by itself explain the overall network activity. Multi-site recordings can be used to infer statistical dependencies (i.e. Functional Connections, FC) among the recorded units and to track the information flow in the network. On the other hand the Effective Connectivity (EC) denotes the directed causal relationship between the recorded sites. Experimentally, the EC is typically estimated by stimulating one cell and studying the effects on the connected elements. Alternatively the EC can also be studied by using a causal mathematical model between the recorded units data. Importantly, multi-site recordings raise some limitations that need to be evaluated carefully before any further analysis. First, the experimental sessions are often limited in time. Second, the high dimensional data sets involve a set of numerical and mathematical problems that would be hard to face even with long enough recording sessions. These issues are common to different fields and have been coined as “curse of dimensionality”. In order to capture nonlinear interactions between even short and noisy time series, we consider an event- based model. Then, we involve the physiological basis of the signal, which is likely to be mainly nonlinear. Specifically, we suppose that we are able to observe the dynamical behaviours of individual components of a neuronal networks and that few of the components may be causally influencing each other. The variables could be time series from different parts of the brain. In order to introduce our method we have considered a simulated cerebellar granule cell network capturing nonlinear interactions between even short and noisy time series. Although the proposed EC algorithm cannot be applied straightforwardly to the experimental data, our preliminary results are quite promising. This is a joint work with G. Aletti, T. Nieus, and M. Moroni.