B. The global error signal is sent directly to each layer. Backprop is not, however, the only way to train deep feedforward networks.

We agree "biological plausibility" is subjective, but we did try to address some of your points and we'll elaborate

We'll assume that information about the labels,

Robust information representation and its persistent maintenance are fundamental for higher cognitive functions. Existing models employ distinct neural mechanisms to separately address noise-resistant processing or information maintenance, yet a unified framework integrating both operations remains elusive -- a critical gap in understanding cortical computation. Here, we introduce a recurrent neural circuit that combines divisive normalization with self-excitation to achieve both robust encoding and stable retention of normalized inputs. Mathematical analysis shows that, for suitable parameter regimes, the system forms a continuous attractor with two key properties: (1) input-proportional stabilization during stimulus presentation; and (2) self-sustained memory states persisting after stimulus offset. We demonstrate the model's versatility in two canonical tasks: (a) noise-robust encoding in a random-dot kinematogram (RDK) paradigm; and (b) approximate Bayesian belief updating in a probabilistic Wisconsin Card Sorting Test (pWCST). This work establishes a unified mathematical framework that bridges noise suppression, working memory, and approximate Bayesian inference within a single cortical microcircuit, offering fresh insights into the brain's canonical computation and guiding the design of biologically plausible artificial neural architectures.

Stability in recurrent neural models poses a significant challenge, particularly in developing biologically plausible neurodynamical models that can be seamlessly trained. Traditional cortical circuit models are notoriously difficult to train due to expansive nonlinearities in the dynamical system, leading to an optimization problem with nonlinear stability constraints that are difficult to impose. Conversely, recurrent neural networks (RNNs) excel in tasks involving sequential data but lack biological plausibility and interpretability. In this work, we address these challenges by linking dynamic divisive normalization (DN) to the stability of "oscillatory recurrent gated neural integrator circuits'' (ORGaNICs), a biologically plausible recurrent cortical circuit model that dynamically achieves DN and that has been shown to simulate a wide range of neurophysiological phenomena. By using the indirect method of Lyapunov, we prove the remarkable property of unconditional local stability for an arbitrary-dimensional ORGaNICs circuit when the recurrent weight matrix is the identity.

Autonomous driving is a challenging scenario for image segmentation due to the presence of uncontrolled environmental conditions and the eventually catastrophic consequences of failures. Previous work suggested that a biologically motivated computation, the so-called Divisive Normalization, could be useful to deal with image variability, but its effects have not been systematically studied over different data sources and environmental factors. Here we put segmentation U-nets augmented with Divisive Normalization to work far from training conditions to find where this adaptation is more critical. We categorize the scenes according to their radiance level and dynamic range (day/night), and according to their achromatic/chromatic contrasts. We also consider video game (synthetic) images to broaden the range of environments. We check the performance in the extreme percentiles of such categorization. Then, we push the limits further by artificially modifying the images in perceptually/environmentally relevant dimensions: luminance, contrasts and spectral radiance. Results show that neural networks with Divisive Normalization get better results in all the scenarios and their performance remains more stable with regard to the considered environmental factors and nature of the source. Finally, we explain the improvements in segmentation performance in two ways: (1) by quantifying the invariance of the responses that incorporate Divisive Normalization, and (2) by illustrating the adaptive nonlinearity of the different layers that depends on the local activity.

Components estimated by independent component analysis and related methods are typically not independent in real data. A very common form of nonlinear dependency between the components is correlations in their variances or energies. Here, we propose a principled probabilistic model to model the energycorrelations between the latent variables. Our two-stage model includes a linear mixing of latent signals into the observed ones like in ICA. The main new feature is a model of the energy-correlations based on the structural equation model (SEM), in particular, a Linear Non-Gaussian SEM. The SEM is closely related to divisive normalization which effectively reduces energy correlation. Our new twostage model enables estimation of both the linear mixing and the interactions related to energy-correlations, without resorting to approximations of the likelihood function or other non-principled approaches. We demonstrate the applicability of our method with synthetic dataset, natural images and brain signals.