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Neuroscience

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

Zhaotian Gu, Jie Su, Weiwei Wang, Chang Liu, Tianyi Qian, Dahui Wang

Featured August 6, 2026

Original Paper

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Simply

By using a brain-inspired divisive normalization trick, the new network learns to smoothly hold onto continuous memories, like a car staying on a smooth road, instead of jumping between bumpy spots like older methods.

In depth
The paper introduces the Recurrent Divisive Normalization Network (RDNN), a biologically inspired model that uses dynamic division to learn robust, low-rank slow manifolds for continuous working memory. This mechanism overcomes the fragility of classical continuous attractor networks and the state space discretization issues of standard recurrent neural networks, by introducing an activity-dependent local gradient scaling that effectively compresses the network's effective rank.

Key Takeaways

  • 1
    The Recurrent Divisive Normalization Network (RDNN) learns robust, high-fidelity continuous working memory representations, outperforming standard RNNs that tend to discretize state space.
  • 2
    Divisive normalization induces emergent low-rank dynamics by scaling gradients during training, leading to a self-compression of the network's effective rank without requiring explicit low-rank factorization.
  • 3
    Unlike subtractive inhibition, divisive normalization is mathematically essential for preventing manifold shattering under time-varying inputs, thereby maintaining continuous representations.

Conceptual Flow

HIGH LEVEL
1
Methodology: Smooth Memory with Division

The new network uses a special 'division' rule to keep its internal memory smooth and stable, like a smart calculator.

Input Signal
Memory State
Divide & Update
Smooth Memory
2
Results: Stable Continuous Tracking

This new network keeps memories flowing smoothly, unlike old networks that make memories jumpy and hard to update.

Old Network Memory
New Network Memory
Compare Smoothness
Smooth Memory Wins