Symmetry and nonlinear-readout criteria for orientation-tuning dynamics in a cortical neural field

Gain changes and tuning-shape changes are difficult to separate in studies of recurrent and feedback modulation in primary visual cortex (V1). We analyze this distinction in a translation-invariant neural-field model with fast isotropic and slower anisotropic recurrent components. At fixed spatial and temporal frequency, any rotationally symmetric recurrent kernel multiplies the linear response by an angle-independent complex gain and therefore preserves every metric of the normalized orientation profile. Weak anisotropy breaks this scalar-gain symmetry at first order, producing delayed sharpening and preferred-orientation drift described by a phasor-sum relation. We then classify nonlinear readouts. An untuned divisive-normalization pool preserves gain-only invariance, whereas a weakly tuned pool changes the effective modulation according to eff (C) = [1 - {beta}{kappa}C/({sigma} +{kappa} C)]: same-orientation pools broaden tuning and cross-orientation pools sharpen it as gain increases. Pointwise supralinear readouts provide a distinct route to shape change, with a leading distortion controlled by response amplitude, background drive, and nonlinearity exponent. The framework yields experimentally separable signatures for scalar gain, feature-specific recurrence, and nonlinear readout effects, and provides a compact null model for interpreting contrast and feedback perturbations in V1.