AI summaryⓘ
The authors address how certain types of neural networks struggle to keep smooth, continuous memories over time, often breaking them into separate points. They introduce a new model called the Recurrent Divisive Normalization Network (RDNN), inspired by a brain process called divisive normalization, which helps the network maintain stable, continuous memory states. Their analysis shows this method helps avoid common training problems by keeping the network's activity focused and efficient. They also demonstrate that divisive normalization is necessary to maintain these smooth memories when inputs change over time, unlike simpler inhibition methods. Overall, the authors suggest this brain-inspired computation is key for learning continuous information robustly.
working memorycontinuous attractor networksrecurrent neural networksdivisive normalizationslow manifoldsgradient scalingBackpropagation Through Timelow-dimensional subspacemanifold shatteringsubtractive inhibition
Authors
Zhaotian Gu, Jie Su, Weiwei Wang, Chang Liu, Tianyi Qian, Dahui Wang
Abstract
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.