Log-Polar-Mapping | Laurent Perrinet

Illusions visuelles

Cydonia Mensae (1976) Viking Orbiter image

Illusions visuelles : Paréidolie

Illusions visuelles : Paréidolie

Illusions visuelles : Paréidolie

Victor Vasarely (1971) Gare Montparnasse

La perception comme processus émergent

La perception comme processus émergent

François Morrelet (1962) Mönchengladbach, Sphère - trames

La perception comme processus émergent

Étienne Rey, Trames

C’est dans ce cadre que nous avons expérimenté avec Étienne Rey sur des trames, qui crée ces interférences. Émergence de nouvelles formes — hexagones comme utilisés à l’Alhambra — espaces tridimensionnels.

Je reviendrai sur le fait que vous pouvez transformer l’image en bougeant les yeux.

La perception comme processus émergent

Étienne Rey (2025) Variable Density, série Delaunay

---

La vibration des apparences

Paul Cézanne, Montagne Sainte-Victoire, 1904

le muset Granet est le musée de Cézanne

le titre de l’exposition fait référence…

La vibration des apparences

Merleau-Ponty, Sens et non-sens

Étienne Rey (2019) Horizon faille - Densité flou - Sans gravité - une poétique de l’air à Ardenome Avignon https://www.enrevenantdelexpo.com

La vibration des apparences

Étienne Rey (2025) Polaire

La vibration des apparences


def retino_grid(cr, N_rho=34, N_phi=233, N_H, N_V, offset,
 size_mag, ecc_max, alpha, c1, c2, power):
 # https://laurentperrinet.github.io/sciblog/posts/2020-04-16-creating-an-hexagonal-grid.html
 phi_v, rho_v = np.meshgrid(np.linspace(0, 2*np.pi, N_phi, endpoint=False),
 np.linspace(0, ecc_max, N_rho+1, endpoint=True)[1:], sparse=False, indexing='xy')
 phi_v[::2, :] += np.pi/N_phi

 offsets, colors = [-offset, offset], [c1, c2]
 for offset_, color in zip(offsets, colors):
 # convert to cartesian coordinates
 X, Y = (rho_v * np.sin(phi_v) + offset_+1)/2, (rho_v * np.cos(phi_v)+1)/2
 R = size_mag * rho_v**power / N_rho

 for x, y, r in zip(X.ravel(), Y.ravel(), R.ravel()):
 circle(cr, x, y, r)
 cr.set_source_rgba(*hue_to_rgba(color, alpha))
 cr.fill()
 return cr
c_blue, dc = 240, 60
opts = dict(N_rho=N_rho, N_phi=N_phi, N_H=N_H, N_V=N_V,
 offset=0.07, size_mag=0.3, ecc_max=0.8, alpha=0.80,
 c1=c_blue-dc, c2=c_blue+dc)
@disp
def draw(cr, N_H=N_H, N_V=N_V): cr = retino_grid(cr, **opts)

## À quoi sert la vision ?

Ilya Repin (1884) An Unexpected Visitor

Nous avons vu que la vision est un processus qui essaie de faire du sens — même s’il n’y en a pas forcément. Ce processus assemble différentes parties ensemble. On connaît le processus « comment », mais on peut se poser la question « pourquoi » : à quoi ça sert, la vision ?

C’est là qu’intervient Yarbus et cette peinture d’Ilya Repin : un soldat rentrant à la maison, tension liée à la surprise évoquée par le titre de la peinture.

À quoi sert la vision ?

Yarbus (1965) An Unexpected Visitor

À quoi sert la vision ?

Yarbus (1965) An Unexpected Visitor How long?

À quoi sert la vision ?

Yarbus (1965) An Unexpected Visitor - Age?

À quoi sert la vision : rétinotopie fovéale

À quoi sert la vision : rétinotopie fovéale

À quoi sert la vision : rétinotopie fovéale

E Rey et LP (2026) Formes & perception

À quoi sert la vision : rétinotopie fovéale

À quoi sert la vision : rétinotopie fovéale

Étienne Rey, Spectre audiographique

Illusions visuelles

Rotating Snakes Akiyoshi KITAOKA

Art & Sciences révèlent la vision en action

Art & Sciences révèlent la vision en action

Carlos Cruz-Diez (2013) Chromosaturation

Felice Varini.

Art & Sciences révèlent la vision en action : Tropique

Étienne Rey, Tropique

Art & Sciences révèlent la vision en action : Tropique

---

Art & Sciences révèlent la vision en action : Tropique

Étienne Rey, TRAME ÉLASTICITÉ

Autre collaboration de taille:

DIMENSIONS : 3 M DE HAUT 5 M DE LARGE INOX POLI MIROIR / ALUMINIUM / ACIER / MOTEURS / PROGRAMME TEMPS RÉEL À la Fondation Vasarely à Aix-en-Provence, Étienne Rey a choisi d’installer dans la salle des Intégrations architectoniques un ballet visuel hypnotique. Composé d’une succession de lames de miroirs, verticales et rotatives, l’installation Trame se joue des reflets et de la démultiplication de l’espace, offrant au spectateur une multiplicité de points de vue dans lesquels il peut se perdre à loisir. Par un effet de « porosité » recherché par l’artiste, le dispositif dialogue intensément avec les Intégrations.

Art & Sciences révèlent la vision en action : TRAME ÉLASTICITÉ

Art & Sciences révèlent la vision en action

Ede Rancz, Role of neuromodulators in active perception

Art & Sciences révèlent la vision en action

Ede Rancz, Role of neuromodulators in active perception

L’intelligence du regard

Laurent Perrinet

Forum des Sciences Cognitives 2026

[2026-04-11]

Art-Sciences / Contact me @ laurent.perrinet@univ-amu.fr

---

Diapositives supplémentaires

Victor Vasarely

Victor Vasarely (1962) Mönchengladbach, Sphère - trames

Victor Vasarely

Victor Vasarely (1977)Outdoor Vasarely artwork at the church of Pálos in Pécs.

Victor Vasarely

Victor Vasarely (1962) Supernovae

Victor Vasarely

Victor Vasarely (1976) Fondation Vasarely, Aix-en-Provence

Étienne Rey, Cristal n2

La vibration des apparences

Foveated Retinotopy Improves Classification and Localization in CNNs

Mon, 23 Feb 2026 00:00:00 +0000

Foveated Retinotopy in CNNs. We represent Left an input image and how it is transformed by foveated retinotopy. We show below a representative reconstruction showing that it also acts as a cortical zoom on the image around the point of fixation. The transformed image is then fed to the ResNet deep learning architecture.

From falcons spotting prey to humans recognizing faces, the ability to rapidly process visual information depends on a foveated retinal organization that provides high-acuity central vision while preserving low-resolution peripheral vision. This organization is conserved along early visual pathways, yet remains under-explored in machine learning. Here, we examine the impact of embedding a foveated retinotopic transformation as a preprocessing layer on convolutional neural networks (CNNs) for image classification. By applying a log-polar mapping to off-the-shelf models and retraining them, we achieve comparable accuracy while improving robustness to scale and rotation. We demonstrate that this architecture is highly sensitive to shifts in the fixation point and that this sensitivity provides an effective proxy for defining saliency maps that facilitate object localization. Our results demonstrate that foveated retinotopy encodes prior geometric knowledge, providing a solution for visual searches and a meaningful classification robustness and localization trade-off. These findings provides a proof of concept in order to connect principles of biological vision with artificial networks, suggesting new, robust and efficient approaches for computer vision systems.

Foveated Retinotopy simulated by a log-polar map. We represent Left an input image with some geometrical objects and how it is transformed by the log-polar representation that implements foveated retinotopy. This shows that a rotation amounts to a translation on the polar axis (abscissa) and a zoom to a translation on the ordinates. We show right a representative reconstructionshowing that it also acts as a cortical zoom on the image around the point of fixation.

Lab Tour for Art - Perception Collaboration

Thu, 01 Jan 2026 00:00:00 +0000

👁️ Very glad to present our Art/Perception collaboration with Étienne Rey today!

🔗 https://laurentperrinet.github.io/talk/2026-01-19-art-and-science

This session is part of the France: perception en Provence: French art and science course from the Rhode Island School of Design, organized by Catherine Huang with Nick Tolley.

What happens today:

We will discuss with Etienne about the emergence of our collaboration
To discover the fantastic world of neuroAI, I will give a * scientific talk* about computational neuroscience and neuroAI - in line with:
Laurent U Perrinet (2025). A New Look for Convolutional Deep Networks. Montreal AI and Neuroscience conference, Dec 11-13th, 2025.
Cite MAIN Slides YouTube

Laurent U Perrinet (2025). La vibration des apparences. Journées d’Ouverture Scientifique (JOS).
Cite Project Project Slides URL
We will see and discuss some actual works that emerged from that collaboration and notably this art exhibit:

Étienne Rey, Laurent U Perrinet (2024). La vibration des apparences.

Project Code

#DeepLearning #ComputerVision #AI #Research #NeuralNetworks #NeuroAI #OpenScience #artScience

The work of Étienne Rey links natural and physical phenomena with our perception. His works reveal themselves and become concrete in the personal experience of viewers. Light, the central element of his approach, activates these experiences, revealing the interactions between the material and the immaterial.

Since 2011, Étienne Rey has been collaborating with Dr. Laurent Perrinet of the Timone Institute of Neuroscience. Together, they explore the domain of perception at the intersection of their respective disciplines, combining science and art to develop new perceptual approaches. Selected works: Tropiques (2013) & Space Odyssey (2015‑2024), Trame Eslasticité 2016, Turbulences 2018, Instabilités et Delaunay (2019), La vibration des apparences (2025), Azur (2028).

A New Look for Convolutional Deep Networks

Fri, 12 Dec 2025 00:00:00 +0000

🔬 Excited to present our latest research at the #MAIN2025 conference today!

🔗 https://www.main2025.org/

👁️ What if CNNs could see like humans? Our new work shows how foveated vision—concentrating processing at gaze center—makes networks more robust to perturbations & great at localization. Inspired by human vision’s architecture (high-resolution foveal center, low-resolution periphery), we embedded this retinotopic transformation into CNN architectures, allowing to actively scan the image. This gives literally a new look to #ConvNets !

📄 Paper:

Jean-Nicolas Jérémie, Emmanuel Daucé, Laurent U Perrinet (2026). Foveated Retinotopy Improves Classification and Localization in CNNs. Vision.

PDF Cite DOI URL arXiv

#DeepLearning #ComputerVision #AI #Research #NeuralNetworks #NeuroAI #OpenScience I love #Montreal

Media storm - share if you like :

A New Look for Convolutional Deep Networks

Tue, 02 Dec 2025 00:00:00 +0000

Foveal Retinotopy and Dual Pathways: A Computational Model for Active Visual Search

Fri, 10 Oct 2025 00:00:00 +0000

Abstract

This thesis investigates visual search through the lens of the dual visual pathways found in biological systems : the ventral (“what”) pathway, involved in object recognition, and the dorsal (“where”) pathway, responsible for spatial localisation and saccadic planning. Drawing from both neuroscience and computer vision, we propose a computational framework that integrates deep convolutional neural networks (DCNNs) within a biologically inspired architecture grounded in foveal retinotopy. As a proof of concept, prior work has demonstrated that incorporating saccadic planning improves digit categorisation performance in a controlled environment. Building upon this foundation, the primary objective of this thesis is to extend the computational framework to natural images in more ecologically valid settings. Our contributions are as follows : (1) We introduce a novel framework for training and evaluating DCNNs using semantically grounded, task-specific labels ; (2) We bridge the gap between artificial models and biological substrates by emphasizing the role of foveal retinotopy in robust object categorisation and precise localisation ; (3) We disentangle the interplay between categorisation and localisation by proposing a novel “localisation-frame” dataset, aimed at guiding the design of a biologically plausible dorsal stream model ; and (4) We present an initial model of the dorsal pathway, leveraging the new dataset to develop interpretable and efficient active vision systems—where interpretability is achieved through modular and spatially structured representations, and efficiency is reflected in reduced computational cost during inference with saccade planning. Overall, this thesis extends the dual-stream computational paradigm for visual search, contributes tools for explainable active vision, and offers a platform to explore hypotheses about functional specialisation in the human visual cortex.

Keywords

Visual search, Dual visual pathways, Deep Convolutional Neuronal, Network, Foveal retinotopy, Active vision

Résumé

Cette thèse étudie la recherche visuelle à travers le prisme des deux voies visuelles identifiées dans les systèmes biologiques : la voie ventrale, impliquée dans la reconnaissance des objets, et la voie dorsale, responsable de la localisation spatiale et de la planification des saccades. S’inspirant à la fois des neurosciences et de la vision artificielle, nous proposons un cadre computationnel intégrant des réseaux neuronal convolutifs profonds (DCNN) dans une architecture biologiquement plausible, fondée sur la rétinotopie fovéale. Des travaux antérieurs ont démontré que l’intégration de la planification des saccades améliorait les performances de catégorisation de chiffres dans un environnement contrôlé. S’appuyant sur cette base, l’objectif principal de cette thèse est d’étendre ce cadre théorique à des images naturelles dans des contextes plus écologiquement valides. Nos contributions sont les suivantes : (1) Nous proposons un nouveau cadre de travail pour l’entraînement et l’évaluation des DCNN, basé sur la sémantique sous-jacente aux labels initialement définis dans la communauté de la recherche computationnelle, ce qui permet de définir des tâches écologiques spécifiques ; (2) nous rapprochons les modèles artificiels des substrats biologiques en soulignant le rôle crucial de la retinotopie fovéales pour une catégorisation robuste et une localisation précise. (3) Nous approfondissons la connaissance de l’interaction entre la catégorisation et la localisation en proposant un ensemble de résultats structuré autour de cette relation, afin de guider la conception d’un modèle plausible de la voie dorsale ; (4) Enfin, en nous appuyant sur ces résultats, nous proposons une première modélisation de la voie dorsale visant à développer des systèmes de vision active à la fois interprétables, grâce à des représentations modulables et spatialement structurées, et efficaces, grâce à la planification de saccades permettant de réduire les coûts de calcul liés à l’inférence. Dans l’ensemble, cette thèse apporte plusieurs éléments : elle enrichit le modèle de vision artificielle des deux voies majeures impliquées dans la recherche visuelle, elle permet de développer des outils de vision active interprétables et elle fournit un cadre pour étudier les hypothèses biologiques relatives à la spécialisation fonctionnelle des aires cérébrales dédiées à la vision chez l’être humain.

Mots-clés

Recherche visuelle, Voie visuel ventrale, Voie visuel dorsale, Réseau neuronal convolutifs profonds, Rétinotopie fovéale, Vision active

Jean-Nicolas Jérémie (2025). Soutenance de Jean-Nicolas Jérémie "Foveal Retinotopy and Dual Pathways: A Computational Model for Active Visual Search".

Soutenance de Jean-Nicolas Jérémie "Foveal Retinotopy and Dual Pathways: A Computational Model for Active Visual Search"

Fri, 10 Oct 2025 00:00:00 +0000

Jean-Nicolas Jérémie soutiendra publiquement ses travaux de thèse intitulés: Foveal Retinotopy and Dual Pathways: A Computational Model for Active Visual Search

dirigés par Monsieur Laurent PERRINET et Monsieur Emmanuel DAUCE

Date: le vendredi 10 octobre 2025 à 13h30
Lieu : Faculté de Médecine de la Timone 27 Boulevard Jean Moulin, 13005 Marseille 5ème
Salle : Amphithéâtre CERIMED

Jean-Nicolas Jérémie (2025). Foveal Retinotopy and Dual Pathways: A Computational Model for Active Visual Search.

Cite

Composition du jury proposé

Name	Affiliation	Role
M. Ronan SICRE	IRIT (UMR 5505) – Université de Toulouse III	Rapporteur
M. Jean‑Julien AUCOUTURIER	FEMTO‑ST (UMR 6174) – Université de Bourgogne Franche‑Comté	Rapporteur
Mme Teresa SERRANO‑GOTARREDONA	IMSE‑CNM‑CSIC – Universidad de Sevilla	Examinatrice
M. Franck RUFFIER	Lab‑STICC (UMR 6285) – ENSTA\|IP Paris	Examinateur
M. Matthieu GILSON	INT (UMR 7289) – Aix Marseille Université	Président
M. Laurent PERRINET	INT (UMR 7289) – Aix Marseille Université	Directeur de thèse
M. Emmanuel DAUCÉ	Centrale Méditerranée	Co‑directeur de thèse

Résumé

Abstract

2025-02-14-supaero

Fri, 14 Feb 2025 00:00:00 +0000

Qu'est-ce que les Neurosciences peuvent apporter à l'Intelligence Artificielle ?
[2025-02-14] Airbus Helicopters Laurent Perrinet ― https://laurentperrinet.github.io

outline =

Bonjour. Je suis Laurent Perrinet, directeur de recherche CNRS en neurosciences computationnelles à l’Institut des neurosciences de la Timone à Marseille. Je vous remercie pour cette invitation à participer à cette journée conviviale.

Mais que fait un neuroscientifique à Airbus Helictopters?

Je suis moi-même un passionné d’aéronautique et de spatial, ce qui m’a amené à suivre l’école d’aéronautique SUPAERO. Puis vers l’imagerie satellitaire, qui dépendait déjà de l’IA sous la forme des réseaux de neurones. C’est à partir de là, grâce à la rencontre avec mon professeur de mathématiques Manuel Samuelides, que j’ai découvert les neurosciences computationnelles et les pouvoirs qu’elles peuvent offrir pour mieux comprendre le cerveau et pour créer de nouveaux systèmes d’intelligence artificielle. Voici un

Le jury était consistué (de gauche à droite) de Jeanny Hérault (Rapporteur), Michel Imbert (Président), Yves Burnod (Rapporteur, absent de la photo), Manuel Samuelides (Directeur de thèse) et Simon Thorpe (Co-directeur de thèse).

Depuis ce temps là, je développe des réseaux de neurones concus comme des algorithmes / processus d’optimisation numérique, que j’applique pour le traitement automatisé des images. une optique nouvelle n’est pas simplement d’utiliser l’inspiration neuro-mimétique mais de faire des aller retours avec l’expérimentation

mais d’abord quid AI ?

L’intelligence artificielle est-elle “intelligente” ?

L’intelligence artificielle (IA) est-elle “intelligente” ?

L’IA est une science multi-disciplinaire qui vise à créer des machines capables d’exécuter des tâches intelligentes, similaires à celles effectuées par l’être humain.
années 1950-1970 : approches logiques et symboliques
années 1980-2010 : machine learning (apprentissage automatique)
années 2010-2020 : deep learning
années 2020-… : la révolution des transformers
L’intelligence artificielle, plus précisément l’apprentissage profond, a fait d’énormes progrès ces dernières années. Toutefois, deux obstacles majeurs subsistent pour son adoption dans les systèmes embarqués ou la robotique.

perceptron de Rosenblatt (1957) et le néocognitron de Fukushima (1980)
- Je suis convaincu que nous sommes au tournant d’une nouvelle ère dans le développement des systèmes embarqués, où l’intelligence artificielle a le potentiel de créer des innovations disruptives à la hauteur des performances de l’intelligence naturelle et pour lesquelles il est essentiel de s’inspirer des neurosciences biologiques.

L’intelligence artificielle est-elle “intelligente” ?

Sommet de l’IA de 2025

Enjeux de l’IA embarquée : latence de réponse

Visual latencies [Grimaldi et al, 2022]

Tout d’abord, les systèmes sensoriels biologiques sont composés de séquences de traitement qui possèdent des délais de traitement. Je décris ici la chaîne de traitement d’une image visuelle, ici pour un enfant jouant à un jeu et devant cliquer sur le bon bouton, et qui illustre les différentes latences du traitement de l’information de la vision à l’action.

Si les délais dans un système embarqué sont plus rapides, il reste que les informations dans les différentes étapes de traitement peuvent être décalées et nécessitent un traitement adapté afin de répondre de la façon la plus immédiate possible. Je pense notamment à la détection d’objets en mouvement très rapide dans le cadre spatial.

Tout d’abord, la plupart de ces systèmes traitent des données statiques. Ils ignorent notamment l’aspect dynamique, comme la nécessité de pouvoir répondre à tout moment ou de compenser les délais de traitement. Dans un premier temps, je présenterai un nouveau type de caméra, inspirée du fonctionnement de la rétine et du codage neural par potentiels d’actions ou « spikes ». Ces caméras permettent de capturer l’information sous forme d’événements et nécessitent d’adapter les algorithmes de traitement de l’information, qui sont plus proches de ceux utilisés par le cerveau.

Enjeux de l’IA embarquée : budget énergétique

## "L'irraisonnable efficacité de la vision"

Comment la vision a évolué… [Perrinet, 2024]

Illusions visuelles

Rotating Snakes Akiyoshi KITAOKA

Illusions visuelles

Ilusions of brightness or lightness Akiyoshi KITAOKA

Illusions visuelles

Illusions visuelles

Cydonia Mensae (1976) Viking Orbiter image

Illusions visuelles : Paréidolie

Illusions visuelles : Paréidolie

Illusions visuelles : Paréidolie

## Neurosciences computationnelles de la vision

[Sejnowski, Koch & Churchland (1998)]

Anatomie du système visuel humain

Cortex visuel primaire

[Hubel & Wiesel, 1962]

Cortex visuel primaire

[Hubel & Wiesel, 1962]

Modèles hybrides d’IA

Using goal-driven deep learning models to understand sensory cortex [Yamins & DiCarlo, 2016]

Levier #1: Réseaux de neurones impulsionnels (SNNs)

From frame-based to event-based cameras.

Nouvelles caméras : basées sur la même technologie qu’un CMOS, mais au lieu de récolter à intervalles réguliers l’ensemble des valeurs de luminance sur tous les pixels, chaque pixel est indépendant.

le mode de représentation de l’information est différent : le signal consiste à émettre un événement si et seulement si un changement a été observé par ce pixel, ce qui est représenté ici par ces flux d’événements.

Levier #1: Réseaux de neurones impulsionnels (SNNs)

Sensor	Range	Framerate	Resolution	Power
Human eye	60 (?) dB	300 (?) fps	100 (?) Mpx	10 mW
DSLR	44.6 dB	120 fps	2–20 Mpx	30 W
Ultra-high speed	64 dB	10^4 fps	0.3–4 Mpx	300 W
Event-based	120 dB	10^6 fps	0.1–2 Mpx	30 mW

Les caméras événementielles présentent plusieurs propriétés qui les rendent remarquables. Tout d’abord, la précision temporelle des événements est de l’ordre de la microseconde, ce qui permet d’atteindre une cadence théorique de l’ordre du million d’images par seconde. On peut la comparer à celle d’une caméra classique, qui est de l’ordre de la centaine d’images par seconde, ou à celle d’une caméra à grande vitesse, qui peut atteindre 10 000 images par seconde. Il est difficile d’estimer la fréquence d’échantillonnage de la perception humaine, car si 25 images par seconde sont souvent suffisantes pour visionner un film, il a été démontré que l’œil humain peut distinguer des détails temporels jusqu’à la milliseconde.

Une autre caractéristique importante de ces caméras est leur capacité à détecter une très large gamme de luminosité, dépassant de loin celle des caméras conventionnelles à 120 dB (un facteur d’un million, comparé au facteur de un sur mille de l’œil humain entre la pleine lune et le soleil),

Il convient de noter que la « résolution spatiale » de ces caméras est souvent relativement modeste, de l’ordre du mégapixel. Cependant, il ne s’agit pas d’une limitation technique, mais plutôt d’une conséquence des applications technologiques dans lesquelles ces caméras sont couramment utilisées.

Par rapport aux caméras classiques, qui consomment plusieurs watts, les caméras événementielles consomment très peu d’énergie électrique, de l’ordre de 10 milliwatts, soit une consommation équivalente à celle de l’œil humain. https://en.wikipedia.org/wiki/Event_camera#Functional_description

Levier #1: Réseaux de neurones impulsionnels (SNNs)

[Grimaldi et al, 2023, Precise Spiking Motifs]

Levier #1: Réseaux de neurones impulsionnels (SNNs)

Loihi 2

Levier #1: Réseaux de neurones impulsionnels (SNNs)

The HD-SNN neural network [Grimaldi et al, 2023]

Ces caméras ne présentent que des avantages, mais alors, comment traiter cette nouvelle représentation des données ? En effet, les neurosciences montrent que les neurones ne manipulent pas des données continues (comme ceux du deep learning), mais communiquent exactement de la même manière en échangeant de brèves impulsions prototypiques, les potentiels d’action (spikes).
Notre solution : une architecture similaire au deep learning, mais chaque neurone (brique élémentaire) est un modèle simplifié de neurone biologique impulsionnel. Cependant, nous nous retrouvons avec un problème par rapport à l’établissement que nous avons réussi à résoudre théoriquement. Un avantage supplémentaire est que ce genre de calcul est actuellement développé sur des puces embarquées (comme les pixels de la caméra évanementielle).
notre architecture fonctionne ainsi directement sur cette même représentation. Un autre avantage : le « always on computing ».

Quels résultats ? Peut-on les évaluer avant d’avoir ces puces ?

Levier #1: Réseaux de neurones impulsionnels (SNNs)

The HD-SNN neural network [Grimaldi et al, 2023]

Levier #1: Réseaux de neurones impulsionnels (SNNs)

The HD-SNN neural network [Grimaldi et al, 2023]

Levier #1: Réseaux de neurones impulsionnels (SNNs)

The HD-SNN neural network [Grimaldi et al, 2023]

Time-to-Contact maps [Nunes et al, 2023]

2 MINUTES

Nos simulations montrent ainsi une très grande efficacité (ici pour catégoriser un type de flux optique, ce qui peut guider la navigation).
un aspect innovant de notre technologie réside dans notre capacité à utiliser autant de neurones, mais moins de connexions. Nous avons par ailleurs montré que l’efficacité restait acceptable. Par rapport à une technologie classique (en orange) qui montre une baisse rapide, nos résultats montrent une bonne efficacité avec une demi-valeur critique donnée pour un gain de 700x (noter l’axe log). C’est ce qu’on appelle le « frugal computing » et nous œuvrons maintenant à son implémentation dans un PEPR IA.
c’est une étape importante, mais on peut aller plus loin, et je vais vous présenter un deuxième levier : éviter de tout traiter pour ne traiter que ce qui est nécessaire.

Levier #2: Vision active / Active Vision

Levier #2: Vision active / Active Vision

[Kremkow et al, 2018]

Levier #2: Vision active / Active Vision

— ## Levier #2: Vision active / Active Vision

Levier #2: Vision active / Active Vision

Levier #2: Vision active / Active Vision

Levier #2: Vision active / Active Vision

From: https://pressbooks.umn.edu/sensationandperception/chapter/columns-and-hypercolumns-in-v1/

Qu'est-ce que les Neurosciences peuvent apporter à l'Intelligence Artificielle ?
[2025-02-14] Airbus Helicopters Laurent Perrinet ― https://laurentperrinet.github.io

2025-02-11-neuromath

Tue, 11 Feb 2025 00:00:00 +0000

[2025-02-11] When Cortical Neurons Talk Sideways: Beyond Feedforward Visual Processing

Laurent Perrinet - https://laurentperrinet.github.io Séminaire Neuromathématiques, Collège de France

Hi, thanks for the introduction! I am Laurent Perrinet, a researcher in computational neuroscience and currently a research director at CNRS at the Institute of Neuroscience of la Timone in Marseille. Thank you for inviting me to participate in this “NeuroMathematics” seminar at the intersection of mathematics and neuroscience.

As an engineer by training, I could have pursued a career in aeronautics rather than becoming a neuroscientist. It is thanks to my mathematics professor Manuel Samuelides that I discovered the beauty of neural networks at the end of my engineering studies. This developped a curiosity, and thanks to him, I was also able to study in a mastere of cognitive sciences (now called CogMaster) in 1998. This is where I particularly want to acknowledge Jean Petitot - for his course I discovered how natural image statistics could link to principles in the central nervous system. This was a vivid revelation, and I’m grateful for his guidance in my academic path. Today’s seminar represents a return to these roots, as I’ll present my research progress since my mastere thesis on this very topic.

Today, I will address our current knowledge about horizontal connectivity rules in V1. Why is this important? As a matter of fact, one main function of sensory systems, such as the pivotal role of the primary visual cortex for vision, is to bind together the different visual features to help ultimately build a global perception.

Paysage catalan (Le Chasseur), Joan Miró (1924)

Trames (Étienne Rey)

Contour detection and the Association Field

[Field et al, 1993]

Contour detection and the Association Field

[Field et al, 1993]

Contour detection and the Association Field

[Field et al, 1993]

Natural Images : Edges are on a common circle

[Sigman et al, 2001]

A significant contribution to understanding the association field came from studying edge co-occurrences in natural images by Sigman et al. (2001). They quantified the probability density function of edge co-occurrences based on their relative positions and orientations. The figure demonstrates this by showing the spatial distribution patterns for edges relative to a reference edge at different orientations. For iso-oriented edges (a), the co-occurrence pattern shows clear structure. As the relative orientation increases through 22.5° (b), 45° (c), 67.5° (d), to 90° (e), distinct spatial patterns emerge.

A key finding was that for any given relative orientation between edges, the angle of maximal interaction occurs at the bisector between the orientations. This suggests that co-occurring edges tend to lie on a common circle - a property known as cocircularity. Panel (f) illustrates this geometrical principle: given two edges at angles w (red, 20°) and c (blue, 40°), the cocircularity solutions (green lines at 30° and 120°) represent the possible orientations of connecting circular arcs. This mathematical relationship provides insights into how the visual system might leverage statistical regularities in natural scenes for contour integration. We will go back into the details of this a bit further in the talk.

This association field concept provided a compelling framework for understanding how the visual system may implement contour integration through neural connectivity patterns. but before going there we should go back to the basic anatomy of the visual cortex.

Contour detection and the Association Field

[Field et al, 1993]

Dynamics of vision

Human Visual system (Grimaldi et al 2022)

Anatomy of the Human Visual system

Human Visual system (Grimaldi et al 2022)

Thalamic, short- & long-range lateral, inter-areal

A key feature of primary visual cortex is its layered organization, which is shared across cortical areas. The main thalamic input arrives in layer 4, which connects to a dense network of vertical connections across layers. These columns can then communicate via horizontal connections within layers. Hubel and Wiesel also proposed the ice-cube model that every point in the visual field produces a response in a 2 mm x 2 mm area of the cortex. Such an area can contain two complete groups of ocular dominance columns, 16 blobs and interblobs that may contain more than two times all of the orientations possible across 180 degrees. This region of the cortex, which Hubel and Wiesel called a hypercolumn (or, more generally, a cortical module) seems both necessary and sufficient for analyzing the image of a point in visual space. Because the cortex is a continuous cellular layer and because it is very hard to establish the boundaries of these modules physically, their existence from a functional standpoint is still the subject of debate. https://thebrain.mcgill.ca/flash/a/a_02/a_02_cl/a_02_cl_vis/a_02_cl_vis.html

Figure 9.2. Hypercolumn Diagram. Ocular dominance columns are segregated into left and right eye inputs. Orientation columns are neurons that get excited at different orientations and a cluster of these is called a pinwheel. Blobs are color selective and for every pinwheel there is a blob. (Credit: McGill: The Brain from Top to Bottom, Figure of hypercolumns, Copyleft https://copyleft.org/, https://thebrain.mcgill.ca/flash/a/a_02/a_02_cl/a_02_cl_vis/a_02_cl_vis.html. No modifications.)

Thalamic, short- & long-range lateral, inter-areal

[Markov et al 2011]

Anatomy of the Primary Visual Cortex

[Kaschube et al (2010)]

V1 is central to these pathways and shows distinctive anatomical and functional properties along with a complex topographical organization.

This figure from Kaschube et al. (2010) illustrates the organization of orientation preference maps in primary visual cortex (V1). Individual V1 neurons exhibit selective responses to oriented visual stimuli (as denoted by varying hues Colors code preferred ORs as indicated by the bars in (C)), with their spatial arrangement following highly structured patterns across the cortical surface. Panel B shows Synthetic orientation-maps of equal column spacing Λ but widely different pinwheel densities ρ. Left to right: solutions of different models: (13–16).. (C) High (blue frame) and low (orange frame) pinwheel density regions in tree shrew visual cortex. (D to F), Optically recorded orientation-maps in tree shrew (D), galago (E), and ferret (F) visual cortex. Regions shown in (C) are marked in (D). White arrows in (F) mark selected pinwheel centers. Framed regions in (C) and (F) are magnified. In many mammals including cats, monkeys and ferrets, orientation preference is organized in a quasi-periodic manner, forming what are known as orientation preference maps. These maps show remarkable consistency in their geometric properties across species, particularly in the spatial organization of pinwheel centers where orientation preferences converge.

However, this organization shows important species-specific variations. Most notably, while primates and carnivores display orderly orientation maps with smooth transitions between preferred orientations, rodents lack such maps and instead show a “salt-and-pepper” arrangement where neighboring neurons have seemingly random orientation preferences. This organizational diversity raises interesting questions about the computational advantages of these different architectures and their relationship to visual processing requirements and behavioral needs across species.

Horizontal connectivity links different hypercolumns

[Bosking et al, 1997]

This figure shows landmark results by Bosking et al. (1997) combining orientation preference maps with retrograde tracers. After injecting tracers (white arrow), they found labeled synapses (black dots) primarily connecting neurons of similar orientation preference, leading to the influential “like-to-like” connectivity hypothesis. However, later studies by Hunt, Goodhill and others revealed significant diversity in these connection patterns across cortical regions and species, suggesting more complex connectivity rules than initially proposed. This nuanced understanding has important implications for how we think about the functional organization of horizontal connections in V1.

Contour detection and the Association Field

[Field et al, 1993]

The like-to-like hypothesis

[Field et al, 2013]

The resemblance between what was shown by Bosking and the structure of the association field that we saw above is such that it is tempting to align both and state that the function of horizontal connections is to bind neurons with a selectivity to *similar orientations over long distances. This like-to-like hypothesis has been influential in understanding horizontal connectivity patterns.

However, we should be cautious about overstating these relationships. While horizontal connections show some orientation specificity, recent evidence indicates the connectivity patterns are more complex and heterogeneous than initially proposed. The functional role of this diverse connectivity remains an active area of investigation.

During the remainder of this talk**, I will try to shed light on our current knowledege on horizontal connectivities.

Supplementary: the HMAX model

[Serre and Poggio, 2007]

Supplementary: Convolutional Neural Nets (CNN)

[Chavane, LP and Rankin, 2022]

Supplementary: Orientation selectivity in V1

[Hubel & Wiesel, 1962]

Supplementary: Orientation selectivity in V1

[Hubel & Wiesel, 1962]

Supplementary: Marr’s three levels of analysis

Marr, 1982

cut in different levels: Marr (+ Poggio)
arbitrary, but useful division of labor= computational / algorithm / hardware
here:
anatomy
algorithm / model
function

First: What is the anatomy of horizontal connections?

<!--

[Marr, 1982]]

-->

Challenging the like-to-like hypothesis

Challenging the like-to-like hypothesis

Revisiting Horizontal Connectivity Rules in V1: From like-to-like towards like-to-All [Chavane, LP and Rankin, 2022]

This figure illustrates different hypothetical connectivity rules for horizontal connections in V1. The target neuron (large circle on left) has a specific orientation preference indicated by its color. Following the classical like-to-like hypothesis (shown in panel A), this neuron would preferentially connect to other neurons with matching orientation preference (similar colors) across multiple hypercolumns, as indicated by the vertical red arrows. The radial spread of connections spans approximately three hypercolumns, consistent with anatomical observations. Each hypercolumn contains a complete set of orientation preferences, represented by the different colored neurons.

This first schematic (noted A) represents one of the like-to-like connectivity rules, where horizontal connections strictly follow orientation similarity.

Challenging the like-to-like hypothesis

Revisiting Horizontal Connectivity Rules in V1: From like-to-like towards like-to-All [Chavane, LP and Rankin, 2022]

Challenging the like-to-like hypothesis

Revisiting Horizontal Connectivity Rules in V1: From like-to-like towards like-to-All [Chavane, LP and Rankin, 2022]

Challenging the like-to-like hypothesis

Revisiting Horizontal Connectivity Rules in V1: From like-to-like towards like-to-All [Chavane, LP and Rankin, 2022]

Challenging the like-to-like hypothesis

Let’s first shows some functional evidence.

This video shows voltage-sensitive dye imaging (VSDI) data from cat primary visual cortex (area 17) in response to a local oriented grating stimulus. The visualization reveals two key aspects:

The broader activation pattern shown by overall fluorescence changes (gray)
The more restricted orientation-selective response pattern (colored regions)

Two contours are overlaid: a red line marking the boundary of significant activation, and a white line delineating regions with statistically significant orientation selectivity. The orientation selectivity is encoded by color hue.

The bottom plots quantify the spatiotemporal dynamics by showing:

Left: The total activated cortical area over time
Right: The extent of orientation-selective regions over time

Together, these measurements demonstrate how orientation-selective signals propagate laterally beyond the classical feedforward input zone through horizontal connections, while maintaining some degree of feature selectivity.

Challenging the like-to-like hypothesis

Revisiting Horizontal Connectivity Rules in V1: From like-to-like towards like-to-All [Chavane, LP and Rankin, 2022]

This figure shows spatial and temporal dynamics of orientation selectivity in cat V1 analyzed from voltage-sensitive dye imaging data. Panel A displays a cortical orientation map averaged over the final 145ms of the response, where hue indicates preferred orientation and brightness shows orientation tuning strength. The dotted red line delineates the expected retinotopic boundary of feedforward input based on Albus (2004).

The inset quantitatively compares the spatial extent of:

Total cortical activation (grey contour)
Orientation-selective activation (black contour)
Theoretical feedforward input boundary (red contour)

This data demonstrates that orientation-selective responses propagate laterally beyond the classical feedforward input zone through horizontal connections, while maintaining some degree of feature selectivity. The systematic comparison between total activation and selective activation provides direct evidence for how horizontal connectivity shapes the spatiotemporal dynamics of orientation processing in V1.

Challenging the like-to-like hypothesis

Revisiting Horizontal Connectivity Rules in V1: From like-to-like towards like-to-All [Chavane, LP and Rankin, 2022]

Challenging the like-to-like hypothesis

Revisiting Horizontal Connectivity Rules in V1: From like-to-like towards like-to-All [Chavane, LP and Rankin, 2022]

Panel C displays intracellular recordings of subthreshold responses visualized as a visuotopic orientation polar map. The color hue represents preferred orientation while brightness indicates the strength of orientation tuning in the membrane potential. White contours outline regions showing statistically significant responses based on both amplitude and orientation selectivity criteria. The middle plots show averaged subthreshold responses to four different oriented stimuli (color-coded) at specific recording locations (marked by circle, triangle and square symbols), with scale bars indicating 50 ms and 1 mV. On the right, normalized orientation tuning curves are shown, computed by integrating responses within a fixed temporal window (shaded region in middle panel). The black circle marks the spontaneous activity level for the depolarizing integral measurement.

These shows a direct functional evidence for a diversity of tuning profile in th horizontal connectivity.

Challenging the like-to-like hypothesis

[Voges and LP, 2012]

Challenging the like-to-like hypothesis

Revisiting Horizontal Connectivity Rules in V1: From like-to-like towards like-to-All [Chavane, LP and Rankin, 2022]

Figure 4 illustrates a neural field model that bridges anatomical structure with functional observations in V1, as developed by Rankin and Chavane (2017).

Panel A depicts radial connectivity profiles with Gaussian-decaying inhibition and distance-dependent excitation that peaks periodically at multiples of distance L. The Ring Width (RW) parameter controls the spread of these excitatory peaks.

Panel B shows how local orientation preference maps influence lateral connectivity patterns under different orientation bias (BR) values in the recurrent connections.

Panel C quantifies the orientation tuning that emerges from these connectivity patterns. While orientations are uniformly represented globally, the local excitatory component shows strong bias around -60°. As BR increases above 0.5, the lateral connection orientation bias strengthens, reaching values around k=1 (consistent with Buzás et al. 2006).

Challenging the like-to-like hypothesis

Revisiting Horizontal Connectivity Rules in V1: From like-to-like towards like-to-All [Chavane, LP and Rankin, 2022]

Challenging the like-to-like hypothesis

Revisiting Horizontal Connectivity Rules in V1: From like-to-like towards like-to-All [Chavane, LP and Rankin, 2022]

Panel F maps the normalized selective area (relative to the feedforward footprint) across Ring Width (RW) and orientation bias (BR) parameters. White contours delineate anatomically plausible ranges where k values fall between 0.7-1.2, consistent with experimental measurements. The green region indicates parameter combinations that additionally satisfy constraints on both orientation preference and the observed radial decay of selectivity.

The neural field model effectively connects anatomical connectivity patterns with functional observations of orientation selectivity propagation in V1. The resulting connectivity structure exhibits similarities with “association field” patterns, suggesting potential optimization for encoding natural image statistics. This framework provides a quantitative basis for investigating computational principles underlying horizontal connectivity in visual cortex.

Challenging the like-to-like hypothesis

Revisiting Horizontal Connectivity Rules in V1: From like-to-like towards like-to-All [Chavane, LP and Rankin, 2022]

Modelling the Association field

[Field et al, 2013]

Edge co-occurences in natural images

Revisiting Horizontal Connectivity Rules in V1: From like-to-like towards like-to-All [Chavane, LP and Rankin, 2022]

Panel A illustrates the groundbreaking approach developed by Geisler et al. (2001) for analyzing edge statistics in natural images. The method involves:

Detecting oriented edge elements in natural images (shown as red segments)
For each edge pair, measuring:
- Their relative orientation difference (𝜃)
- The relative position angle (𝜙)
- Center-to-center distance (d)
- Azimuth difference (φ)
- Co-circularity parameter ψ = φ - θ/2

This quantitative analysis reveals two key distributions:

A strong bias for parallel edge arrangements, evident in the orientation difference histogram
A marked preference for co-circular alignments, shown in the relative position histogram

These statistics vary significantly across image databases. For example, images containing animals exhibit enhanced co-circularity compared to general natural scenes. This suggests that rather than implementing a single fixed association field, the visual system may need to handle diverse statistical regularities present in natural inputs.

The next section will examine how these statistical regularities inform computational models of the association field.

Edge co-occurences in natural images

[Geisler, 2001]

Edge co-occurences in natural images

Edge co-occurrences can account for rapid categorization of natural versus animal images [LP and Bednar, 2015]

The probability distribution function p(ψ,θ) represents the distribution of the different geometrical arrangements of edges’ angles, which we call a “chevron map”. We show here the histogram for non-animal natural images, illustrating the preference for co-linear edge configurations. For each chevron configuration, deeper and deeper red circles indicate configurations that are more and more likely with respect to a uniform prior, with an average maximum of about 3 times more likely, and deeper and deeper blue circles indicate configurations less likely than a flat prior (with a minimum of about 0.8 times as likely). Conveniently, this “chevron map” shows in one graph that non-animal natural images have on average a preference for co-linear and parallel edges, (the horizontal middle axis) and orthogonal angles (the top and bottom rows), along with a slight preference for co-circular configurations (for ψ =0 and ψ = ± π/2, just above and below the central row).

Edge co-occurences in natural images

Edge co-occurrences can account for rapid categorization of natural versus animal images [LP and Bednar, 2015]

Edge co-occurences in natural images

Edge co-occurrences can account for rapid categorization of natural versus animal images [LP and Bednar, 2015]

This figure shows classification performance across image categories using different statistical features. We used an SVM classifier with three feature sets: first-order orientation statistics (FO), the reduced 2D “chevron map” (CM), and full 4D second-order statistics (SO). The classification accuracy (F1 score) was tested for distinguishing between image categories. Results show strong performance in separating man-made from natural images, as expected. More notably, the classifier achieved ~80% accuracy in discriminating animal vs non-animal natural images, matching human performance levels reported by Serre et al. This suggests that relatively simple edge co-occurrence statistics contain sufficient information for basic image categorization tasks, without requiring higher-level semantic processing.

We also found that our model made the same errors as humans do: if an image without an animal contains more co-circular edges, it is more likely to be falsely categorized as containing an animal.

Edge co-occurences in natural images

Edge co-occurrences can account for rapid categorization of natural versus animal images [LP and Bednar, 2015]

Can we explain the diversity ?

[Bosking et al, 1997]

Indeed, this diversity is revealed in the anatomical data: V1 horizontal connectivity exhibits more complexity than suggested by the classical like-to-like hypothesis. While orientation-specific connections exist, they coexist with non-selective connections that link neurons irrespective of their tuning preferences. This diversity likely serves multiple computational functions:

Specific connections could support contour integration and feature binding
Non-selective connections may enable broad contextual modulation
Mixed connectivity patterns could help maintain network stability while preserving functional specificity

This anatomical heterogeneity aligns with V1’s role in both specialized feature detection and broader contextual processing. Understanding how these distinct connectivity patterns interact remains an active area of research in visual neuroscience.

Predictive processing

To understand the diversity in horizontal connectivity patterns, we developed a biologically plausible hierarchical model based on Convolutional Neural Networks (CNNs) backbone. The model processes natural images through multiple convolutional layers organized in a hierarchical structure:.

Natural image as input

Local receptive fields via convolution operations

Hierarchical processing through multiple layers

Predictive processing

To bridge the gap between anatomical observations and functional requirements of visual processing, We added two key ingredients in the sparse deep predictive coding (SDPC) model :

Sparse connectivity patterns:

Enforcing regularization of the activity map using L1 penalty

Activity computed via recurrent local connectivity

Similar to biological observations

Feedback from efferent layers:

Predicts activity of afferent layer

Only residual prediction error is processed

Defines long-range inter-areal connectivity

Specific influence demonstrated in Neural Computation paper

By defining a cost on minimizing the prediction error in each layer, everything stays derivable, such that we can use a classical gradient descent. These additions should allow us to better understand how feedback shapes visual processing in biological neural networks.

Predictive processing

Predictive processing

More specifically in the context of our focus today, we can look at the co-occurence

llustration of the procedure to generate interaction map. In this illustrative example we consider a V1 representation with only 4 feature maps (represented in the upper-left box). Step 1 is to extract a neighborhood (of size 3x3 in the illustration only) around the most strongly activated neuron (represented with a red square in the illustration) for a given central preferred orientation (denoted ✓ c ). Step 2 is to normalize the neural activity in the extracted neighborhood using the marginal activity (see Eq.8). Step 3 is to compute the resulting orientation and activity at every position of the neighborhood using a circular mean (see Eq. 11 and Eq. 12 respectively). To keep a concise figure we have illustrated the computation of the central edge of the interaction map only. For simplification, the illustration shows only 1 neighborhood extraction whereas the interaction maps shown in the paper are computed by averaging neighborhoods centered on the 10 most strongly activated neurons

Predictive processing

Predictive processing

Predictive processing with pooling

[Boutin et al, 2022]

## Challenging the like-to-like hypothesis

[Bosking et al, 1997]

Challenging the like-to-like hypothesis

Revisiting Horizontal Connectivity Rules in V1: From like-to-like towards like-to-All [Chavane, LP and Rankin, 2022]

To conclude, our review of horizontal connectivity in V1 reveals patterns more complex than initially theorized. The classical like-to-like hypothesis, while valuable, doesn’t fully capture the diversity of observed connectivity patterns.

Mathematical modeling has proven essential in bridging theory and biology. Our predictive processing framework shows how simple computational principles can explain the emergence of these complex connectivity patterns. The model demonstrates how feedback influences lateral interactions and reproduces key experimental observations.

However, important questions remain unanswered. We need to better understand how precise timing information is encoded in these circuits, how temporal dynamics shape processing, and whether similar principles apply across other cortical areas.

These fundamental questions will guide future experimental and theoretical work as we continue to unravel the computational principles of cortical processing.

[2025-02-11] When Cortical Neurons Talk Sideways: Beyond Feedforward Visual Processing

Laurent Perrinet - https://laurentperrinet.github.io Séminaire Neuromathématiques, Collège de France

Dynamics of vision

[Marr, 1982]

Dynamics of vision

Visual latencies (see review).

Dynamics of vision

Sensorimotor delays (Perrinet & Friston 2014)

Dynamics of vision

Sensorimotor delays (Perrinet & Friston, 2014)

Dynamics of vision

Diagonal markov model (Khoei et al, 2017).

Dynamics of vision

Flash-lag effect: MBP (Khoei et al, 2017)

Dynamics of vision

[Marr, 1982]

Dynamics of vision: Neural modeling

Spiking Neural Networks: Spiking motifs

[Grimaldi et al, 2023, Precise Spiking Motifs]

Spiking Neural Networks: Spiking motifs

Review on Precise Spiking Motifs.

Spiking Neural Networks: Spiking motifs

Review on Precise Spiking Motifs.

Spiking Neural Networks: HD-SNN

2 MINUTE

We then used a neural network with a classical architecture, which we enhanced by using an impulse representation that takes into account different possible synaptic delays. In this figure, we have represented the input in the left grid, which represents the occurrence of spikes of positive or negative polarity. Then we have represented different processing channels denoted by the colors green and orange, which are applied to this input to produce membrane activity. As illustrated above, this activity will produce output pulses, notably in synaptic connection nuclei, with heterogeneous delays corresponding to the detection of precise spatio-temporal patterns.

Spiking Neural Networks: HD-SNN

2 MINUTE

One advantage of this network is that it is differentiable, enabling us to apply classical machine learning methods, notably supervised learning. We then see the emergence of different convolution kernels, and here I represent a subset of its kernels for different directions, as denoted by the red arrows on the left of the graph. It shows the kernels obtained on the spatial representation according to the different columns, and each row represents the different delays from a delay of one on the right to a delay of 12 time steps on the left. Detectors that follow the motion emerge. For example, for the top line from top to bottom. These kernels integrate both positive neurons in red and negative polarity inputs in blue. Such spatio-temporal filtering is observed in neurobiology, but to my knowledge had never been observed in a model of spiking neurons trained under natural conditions.

Spiking Neural Networks: HD-SNN

Spiking Neural Networks: HD-SNN

Spiking Neural Networks: HD-SNN