Analytic model for feature maps in the primary visual cortex

Xiaochen Liu; Peter A. Robinson

Home/Archive/arXiv

arXiv · 2103.09954

Analytic model for feature maps in the primary visual cortex

Xiaochen Liu·Peter A. Robinson

View original source ↗Read source document ↗Export metadata ↓

Abstract

A compact analytic model is proposed to describe the combined orientation preference (OP) and ocular dominance (OD) features of simple cells and their layout in the primary visual cortex (V1). This model consists of three parts: (i) an anisotropic Laplacian (AL) operator that represents the local neural sensitivity to the orientation of visual inputs; (ii) a receptive field (RF) operator that models the anisotropic spatial RF that projects to a given V1 cell over scales of a few tenths of a millimeter and combines with the AL operator to give an overall OP operator; and (iii) a map that describes how the parameters of these operators vary approximately periodically across V1. The parameters of the proposed model maximize the neural response at a given OP with an OP tuning curve fitted to experimental results. It is found that the anisotropy of the AL operator does not significantly affect OP selectivity, which is dominated by the RF anisotropy, consistent with Hubel and Wiesel's original conclusions that orientation tuning width of V1 simple cell is inversely related to the elongation of its RF. A simplified OP-OD map is then constructed to describe the approximately periodic OP-OD structure of V1 in a compact form. Specifically, the map is approximated by retaining its dominant spatial Fourier coefficients, which are shown to suffice to reconstruct the overall structure of the OP-OD map. This representation is a suitable form to analyze observed maps compactly and to be used in neural field theory of V1. Application to independently simulated V1 structures shows that observed irregularities in the map correspond to a spread of dominant coefficients in a circle in Fourier space.

Explore related subjects

q-bio.NC physics.bio-ph

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Xiaochen Liu, Peter A. Robinson. 2021-03-17. Analytic model for feature maps in the primary visual cortex. https://arxiv.org/abs/2103.09954

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Identifying Neural State Changes due to Gain versus Off-Manifold Displacement

Memory segmentation is thought to arise from rapid decorrelation in neural activity, often quantified by Euclidean distance or cosine angle. Although these metrics detect a transition, they do not reveal how the new state relates to the repertoire represented by the neural manifold. This matters because neuromodulators that drive state transitions also alter excitability, and learning may repurpose existing representations or create new ones. Here, I introduce a geometric decomposition that separates changes attributable to gain modulation of a nearby manifold state from movement within the manifold and genuine off-manifold displacement. The approach uses the radial axis of neural population activity to partition the normal space of a local manifold region. A central challenge is identifiability: given only a static reference manifold and a single test state, neither the state from which a perturbation began nor its gain magnitude and mechanistic decomposition can generally be recovered uniquely. I therefore formulate identifiability as a cascade of geometric gates specifying when each component can be interpreted. The gates distinguish structural failures, including the absence of a local chart or incorrect intrinsic dimensionality, from estimation error and systematic bias caused by reference sampling, tangent-frame error, gain-axis misalignment, anchor displacement, and poor ratio conditioning. Simulations show that neighborhood size, curvature, sampling density, ambient dimension, and noise act through a small set of geometric quantities. The framework specifies when assignments to gain or novelty are identifiable, how they become biased, and which diagnostics reveal the relevant failure regime. By quantifying the nature rather than only the magnitude of neural state change, it provides a clear, readily interpretable framework for evaluating mechanisms of neural state transitions.

q-bio.NC↗

arXiv2026

Neural Langevin Machine: a local asymmetric learning rule can be creative

Fixed points of recurrent neural networks can be leveraged to store and generate information. These fixed points are captured by the Boltzmann-Gibbs measure, which leads to neural Langevin dynamics that relax to those fixed points for generative learning of a real dataset. We call this type of generative model a neural Langevin machine, which derives an asymmetric and firing-rate-speed-adjusted learning rule requiring only local neural signals, thereby bearing biological relevance in terms of local predictive learning. An out-of-equilibrium regime of the generative process is revealed, together with a memorization-to-generalization transition with increasing training data size. The neuro-inspired machine can also realize a continuous exploration of the phase space for different kinds of generative images and can denoise a corrupted image as well.

q-bio.NC↗

arXiv2026

A Mathematical Model of Motivated Emotional Mind - Cognitive Embodied System

This article presents a mathematical model of the Motivated Emotional Mind cognitive architecture developed for embodied intelligent systems. Such a system learns to maintain its homeostasis through a generalized form of reinforcement learning based on its internal motivations, termed motivated learning (ML). The principal contribution of this article is a rigorous formalization of the re-entrant loop integrating feedforward processing, lateral interactions, and feedback pathways, together with the representational selection mechanisms that govern adaptive system responses. The model specifies how ongoing exteroceptive and interoceptive signals, bodily-motivational context, and memory traces are bound into associative memory structures termed semblions, which compete for access to further processing and top-down reconstruction. The formalization encompasses secondary perception, representational competition, curiosity, procedural gaps, and action selection directed toward limiting allostatic violations. Within this framework, motivated learning is tailored to embodied systems whose dynamics are shaped by needs, affect, and the current regulatory state. Unlike standard reinforcement-learning models, the proposed approach incorporates need thresholds, goal generation and shifting goals, bodily state, resource constraints, and action uncertainty, thereby providing a more adequate account of response selection under regulatory pressure. Global affect functions as a central control signal, modulating the learning rate, representational valence, and the balance between exploration and exploitation. The model presented here is a step toward a more rigorous formalization of cognitive phenomena and may provide a basis for further theoretical analysis, computer simulation, and implementation in artificial-intelligence systems inspired by biological processes.

q-bio.NC↗