Recent advances in mathematical neuroscience: cortically inspired models for vision and synaptic plasticity

Tuesday, June 15 at 02:15am (PDT)
Tuesday, June 15 at 10:15am (BST)
Tuesday, June 15 06:15pm (KST)

SMB2021 SMB2021 Follow Monday (Tuesday) during the "MS05" time block.
Note: this minisymposia has multiple sessions. The second session is MS17-NEUR (click here).

Share this


Luca Calatroni (Laboratoire I3S, CNRS, UCA & Inria Sophia Antipolis Méditerranée, France), Mathieu Desroches (MathNeuro Project-Team, Inria Sophia Antipolis Méditerranée & Université Côté d’Azur, France), Valentina Franceschi (Dipartimento di Matematica, Università degli Studidi Padova, Italy), Dario Prandi (Université Paris-Saclay, CNRS, CentraleSupélec, L2S, France)


The purpose of this symposium is to gather together experts working in the field of mathematical neuroscience, with a focus on those working on cortical inspired models for vision and synaptic plasticity. In particular the speakers will present recent results on variational and differential approaches to the understanding of the primary visual cortex as well as more recent models based on neural networks and predictive coding.

Laurent Perrinet

(INT, CNRS - Aix-Marseille Université, France)
"Pooling in a predictive model of V1 explains functional and structural diversity across species"
Neurons in the primary visual cortex are selective to orientation with various degrees of selectivity to the spatial phase, from high selectivity in simple cells to low selectivity in complex cells. Various computational models have suggested a possible link between the presence of phase invariant cells and the existence of cortical orientation maps in higher mammals’ V1. These models, however, do not explain the emergence of complex cells in animals that do not show orientation maps. In this study, we build a model of V1 based on a convolutional network called Sparse Deep Predictive Coding (SDPC) and show that a single computational mechanism, pooling, allows the SDPC model to account for the emergence of complex cells as well as cortical orientation maps in V1, as observed in distinct species of mammals. By using different pooling functions, our model developed complex cells in networks that exhibit orientation maps (e.g., like in carnivores and primates) or not (e.g., rodents and lagomorphs). The SDPC can therefore be viewed as a unifying framework that explains the diversity of structural and functional phenomena observed in V1. In particular, we show that orientation maps emerge naturally as the most cost-efficient structure to generate complex cells under the predictive coding principle.

Rufin Van Rullen

(CerCo, CNRS and ANITI, Universite de Toulouse, France)
"Deep predictive coding for more robust and human-like vision"
I will report on a series of experiments with deep convolutional neural networks augmented with feedback connections. The dynamics of the network are governed by predictive coding objectives, similar to those that have been proposed to explain neural activity in the brain. Compared to the standard feed-forward networks, these predictive coding networks can be more robust to noise and against certain adversarial attacks. They also respond to visual illusions (in particular, illusory contours from Kanisza shapes) in a way that is more similar to biological perception.

Yuri Elias Rodrigues

(INRIA/IPMC/Université Côte d'Azur, France)
"Modelling the experimental heterogeneity of synaptic plasticity"
Discovering the rules of synaptic plasticity is an important step for understanding brain learning. Existing plasticity models are either 1) top-down and interpretable, but not flexible enough to account for experimental data, or 2) bottom-up and biologically realistic, but too intricate to interpret and hard to fit data. We fill the gap between these approaches by uncovering a new plasticity rule based on a geometrical readout mechanism that flexibly maps synaptic enzyme dynamics to plasticity outcomes. We apply this readout to a multi-timescale model of hippocampal synaptic plasticity induction that includes electrical dynamics, calcium, CaMKII and Calcineurin, and accurate representation of intrinsic noise sources. Using a single set of model parameters, we demonstrate the robustness of this plasticity rule by reproducing nine published ex vivo experiments covering various spike-timing and frequency-dependent plasticity induction protocols, animal ages, and experimental conditions. Our model should facilitate experimental design since each variable identify a biological counterpart bridging experiment and simulation.

Halgurd Taher

(Inria Sophia Antipolis-Méditerranée Research Centre, France)
"Bursting in a next generation neural mass model with synaptic dynamics: a slow-fast approach"
We report a detailed analysis on the emergence of bursting in a recently developed neural mass model, that takes short-term synaptic plasticity into account. Neural mass models are capable of mimicking the collective dynamics of large scale neuronal populations in terms of a few macroscopic variables like mean membrane potential and firing rate. The one being used here particularly important, as it represents an exact meanfield limit of synaptically coupled quadratic integrate & fire neurons, a canonical model for type I excitability. In absence of synaptic dynamics, a periodic external current with a slow frequency ϵ can lead to burst-like dynamics. The firing patterns can be understood using techniques of singular perturbation theory, specifically slow-fast dissection. In the model with synaptic dynamics the separation of timescales leads to a variety of slow-fast phenomena and their role for bursting is rendered inordinately more intricate. Canards are one of the main slow-fast elements on the route to bursting. They describe trajectories evolving nearby otherwise repelling invariant sets of the system and are found in the transition region from subthreshold dynamics to bursting. For values of the timescale separation nearby the singular limit ϵ → 0, we report peculiar jump-on canards, which block a continuous transition to bursting. In the biologically more plausible regime this transition becomes continuous and bursts emerge via consecutive spike-adding. The onset of bursting is of complex nature and involves mixed-type like torus canards, that form the very first spikes of the burst and revolve nearby repelling limit cycles. We provide numerical evidence for the same mechanisms to be responsible for the emergence of bursting in the quadratic & fire network with plastic synapses. The main conclusions apply for the network, thanks to the exactness of the meanfield limit.

Hosted by SMB2021 Follow
Virtual conference of the Society for Mathematical Biology, 2021.