Divisive Normalization Shapes Low-Rank Slow Manifolds for Continuous Working Memory

The ability to robustly maintain and update continuous variables is a hallmark of working memory. While classical continuous attractor networks suffer from severe fine-tuning fragility, standard artificial recurrent neural networks (RNNs) like GRUs and LSTMs typically fail to stably learn continuous manifolds, instead shattering the state space into discretized point attractors. To bridge this gap, we draw inspiration from divisive normalization, a canonical neural computation widely observed across cortical circuits, and propose the Recurrent Divisive Normalization Network (RDNN), a minimal and algebraically isolated model of dynamic division. Through dynamical systems analysis on canonical working memory tasks, we demonstrate that this biophysical constraint allows the network to converge to robust, high-fidelity slow manifolds. Furthermore, we analyze the gradient dynamics of divisive normalization during Backpropagation Through Time (BPTT), showing that it introduces an activity-dependent local gradient scaling. This scaling dampens parameter updates in highly active regimes, which empirically aligns with a significant self-compression of the network's effective rank, confining the recurrent dynamics to a tight, low-dimensional subspace while avoiding the optimization pathologies associated with explicit low-rank factorization. Finally, ablations demonstrate that while subtractive inhibition can maintain static memories, divisive normalization is mathematically essential to prevent manifold shattering under time-varying inputs. Our findings identify divisive normalization not merely as a biological artifact, but as a critical computational mechanism for learning high-fidelity continuous representations.

Self-organized MT Direction Maps Emerge from Spatiotemporal Contrastive Optimization

The spatial and functional organization of the primate visual cortex is a fundamental problem in neuroscience. While recent computational frameworks like the Topographic Deep Artificial Neural Network (TDANN) have successfully modeled spatial organization in the ventral stream, the computational origins of the dorsal stream's distinct topographies, such as direction-selective maps in the middle temporal (MT) area, remain largely unresolved. In this work, we present a spatiotemporal TDANN to investigate whether MT topography is governed by the same universal principles. By training a 3D ResNet on naturalistic videos via a Momentum Contrast (MoCo) self-supervised paradigm alongside a biologically inspired spatial loss, we demonstrate the spontaneous emergence of brain-like direction maps and topological pinwheel structures. Crucially, we reveal that MT tuning properties, characterized by strong direction selectivity paired with a residual axial component, arise from a strict optimization trade-off between task-driven discriminative pressure and spatial regularization. The model's representations quantitatively match in vivo macaque MT physiological baselines, including direction selectivity index, circular variance, and pinwheel density. These findings unify the computational origins of the ventral and dorsal streams, establishing a general mechanism for cortical self-organization.