Neuromodulation-inspired gated associative memory networks:extended memory retrieval and emergent multistability

TL;DR

This work addresses memory retrieval limits in classical autoassociative networks by introducing a neuromodulation-inspired, self-adaptively gated two-layer architecture. The neuronal layer interacts with an activity-dependent neuromodulator layer via multiplicative gating, leading to an extended memory retrieval phase that persists beyond the standard capacity $α_c \simeq 0.13$ and preserves attractor basins. The mechanism stabilizes transient ghost attractors into true fixed points, producing continuous multistability in the memory landscape, a result supported by direct simulations and dynamical mean-field theory (DMFT) in the thermodynamic limit. The findings illuminate how neuromodulation could dramatically expand memory capacity and dynamics in biological circuits and inform gated neuromorphic designs and learning-enabled gated RNNs.

Abstract

Classical autoassociative memory models have been central to understanding emergent computations in recurrent neural circuits across diverse biological contexts. However, they typically neglect neuromodulatory agents that are known to strongly shape memory capacity and stability. Here we introduce a minimal, biophysically motivated associative memory network where neuropeptide-like signals are modeled by a self-adaptive, activity-dependent gating mechanism. Using many-body simulations and dynamical mean-field theory, we show that such gating fundamentally reorganizes the attractor structure: the network bypasses the classical spin-glass transition, maintaining robust, high-overlap retrieval far beyond the standard critical capacity, without shrinking basins of attraction. Mechanistically, the gate stabilizes transient ghost remnants of stored patterns even far above the Hopfield limit, converting them into multistable attractors. These results demonstrate that neuromodulation-like gating alone can dramatically enhance associative memory capacity, eliminate the sharp Hopfield-style catastrophic breakdown, and reshape the memory landscape, providing a simple, general route to richer memory dynamics and computational capabilities in neuromodulated circuits and neuromorphic architectures.

Figures (4)

• Figure 1: Gating enables memory retrieval beyond the traditional capacity threshold without narrowing empirical attractor basins. (a) Ungated benchmark. (Left) Schematic of the standard Amari--Hopfield network ($\gamma=0$). (Right) The steady-state overlap $m_\text{ss}$ plotted as a function of memory load $\alpha$ and initial overlap $m(0)$. Color intensity represents the retrieval quality, ranging from failure (white) to successful retrieval (darkblue). The vertical dashed line marks the standard critical capacity $\alpha_\text{c} \simeq 0.13$ of the ungated network. Notably, catastrophic blackout (the spin-glass transition) is observed for $\alpha> \alpha_\text{c}$. (b) Self-adaptively gated network. (Left) Schematic of the architecture, where an auxiliary neuromodulatory layer $\mathbf{z}$ gates the recurrent neural layer $\mathbf{x}$. (Right) Corresponding phase diagram for the same range of parameters in the binary gating limit ($\gamma \to \infty$). In contrast to (a), catastrophic blackout is not observed. (c) Performance gain. The difference in steady-state overlaps, $\Delta m_\mathrm{ss} = m^{\gamma\to\infty}_\mathrm{ss} - m^{\gamma=0}_\mathrm{ss}$, highlighting the region where gating recovers memories that fail in the ungated network. This demonstrates that the capacity gain is achieved without degrading the size of the attractor basins. Parameters used: $N=1000$, $dt=0.2$, total run time $T=2000$.
• Figure 2: Gating stabilizes retrieval of patterns in regimes beyond critical capacity (a) The temporal evolution of the overlap $m(t)$ in the memory overload regime ($\alpha=0.4 > \alpha_\text{c}$) for various gating steepness parameters $\gamma$. The case $\gamma=0$ corresponds to the standard ungated network, which exhibits a transient high-overlap state that eventually decays. As $\gamma$ increases, the lifetime of this transient extends, eventually leading to a stable retrieval state. Each curve is averaged over 30 independent simulation runs with different realizations of the patterns $\{\bm{\xi}^\mu\}_{\mu=1}^P$, couplings $W_{ij}$, and initial conditions $\mathbf{z}(0)$ and $\mathbf{x}(0)$ (fixed at $m(0)\simeq0.55$). (Inset) Decomposition of the overlap for the binary gated limit ($\gamma\to\infty$) into the closed ($m_{\mathcal{F}_t}(t)$) and active ($m_{\mathcal{A}_t}(t)$) sub-population overlaps. (Bottom) Representative dynamical traces of neuronal activity $\phi(x_i)$ (b) and gating values $\sigma(z_i)$ (c) for the binary gated case, illustrating the dynamical exchange between frozen and active populations before reaching the steady state. Parameters used: $N=1000$ and $dt=0.2$.
• Figure 3: DMFT dynamics and their time-asymptotic solutions. (Top row) Overlap dynamics $m(t)$ of ungated and gated networks for memory load above critical capacity $\alpha = 0.4$ and initial overlap $m(0) \simeq 0.65$ using many-body simulations and DMFT: (a) ungated $\gamma=0$, (b) intermediate gating $\gamma=10.0$, and (c) binary gating $\gamma \to \infty$. Light gray curves correspond to individual many-body simulations while the dashed black curves are their average. Solid red curves show the DMFT predictions. (d) Time-asymptotic DMFT solutions for overlaps in ungated (red dots and dashed lines) and gated (blue dots and dashed lines) networks. The band of steady state overlap values for the gated network is bound by the the maximum and minimum steady state overlap values of the closed neurons $m_{\mathcal{F}_t}^{\text{ss}}$. The maximum and minimum values were obtained from many-body simulations with $m(0)= 1$ and $m(0) = 0.01$, respectively, for a range of memory loads $\alpha$. DMFT curves in the top row were calculated using the numerical parameters : $M=5000, \alpha=0.4, dt=0.02$. In (d), dashed lines were added to guide the eye.
• Figure 4: Gating creates continuous manifolds of fixed points. Flow diagrams in the overlap phase space $\tilde{\mathbf{m}}=(m_+,m_-)$, where $m_\pm=m_1\pm m_2$, for a network storing $P=2$ orthogonal patterns. Arrows represent the flow direction of the vector field, and dark circles indicate stable fixed points reached from various initial conditions. The background heatmap encodes the displacement magnitude $\|{\Delta\mathbf{m}}\|=\|\mathbf{m}(T)-\mathbf{m}(0)\|$ with $\mathbf{m}=(m_{1},m_{2})$, serving as a proxy for the attractor landscape. (a) In the ungated network, the system flows into one of four discrete fixed points (corresponding to the retrieval of $\bm{\xi}^1, \bm{\xi}^2$ or their inverses), determined solely by the initial basin of attraction. (b) In the gated network, the system reaches a continuum of distinct fixed points depending on the specific initial overlap, creating a "cloud" of stable fixed points. For both panels, the realization of patterns $\{\bm{\xi}^1,\bm{\xi}^2\}$, couplings $(W_{ij})$, and initialization $\mathbf{z}(0)$ are identical and fixed; only $\mathbf{x}(0)$ varies. Parameters used: $N=1000$, $dt=0.25$, and $T=2000$.