Emergent Self-Attention from Astrocyte-Gated Associative Memory Dynamics

We present a biologically detailed extension of the classical Hopfield/Marr auto-associative memory model for CA3, implementing ten populations (two asymmetric pyramidal subtypes, eight GABAergic interneuron classes), forty-seven compartments, multi-rule plasticity (recurrent Hebb, BCM anti-saturation, mossy-fiber short-term, endocannabinoid iLTD, burst-gated Hebb), and a bimodal cholinergic encoding/consolidation cycle. Evaluated on pattern completion across auto-associative, associative, and temporal regimes, and on a controlled inhibitory-proportion manipulation at $N{=}256$, the full architecture exhibits \emph{three qualitative signatures absent from a minimal Hopfield baseline}: (i)~multi-attractor cross-seed behaviour at $K{=}5$ with biologically realistic inhibitory proportions, where two of five seeds converge to positive attractors with margin ${+}0.10{-}0.22$ (Cohen's $d{=}0.71$, one-sided $p{=}0.08$); (ii)~target-selective associative recall in paired $(A, B)$ memory at $K{\geq}5$, where the full model retrieves $B$ from a partial cue of $A$ while the minimal model echoes $A$ (Pearson margin $Δ{=}{+}0.163$ at $K{=}5$); (iii)~reduced cross-seed variance of the full model below the minimal baseline under clean upstream, with ratios $1.0{-}3.0$. These three signatures are architecture-specific: they appear consistently across independent regimes and are absent from the minimal control.

Astrocytes are non-neuronal glial cells that are receiving widespread attention due to their emerging role in neural computation. In this paper, we propose and study dynamical mechanisms by which astrocytes may augment the ability of neural networks to infer context in reinforcement learning (RL) settings. We construct a biologically inspired, two-level dynamical neural-astrocyte network with distinct spatial and temporal organization. We train this model on a hierarchical multi-context task that requires the agent to infer changes in latent task rules based on derived rewards. We find that in this setting, astrocytes enable evidence accumulation of changes in context and subsequent context-specific modulation of neural dynamics. We show that these functions are implemented via two dynamical mechanisms: (i) reward-induced bifurcations that relocate an asymptotically stable attractor into different, context-specific regions of state space, and (ii) the relative shallowness of these attractors, mediated by the entropy of the environment, giving rise to behavioral stickiness. Together, these mechanisms amount to a hybrid automaton, in which uncertainty accumulates until, eventually, the neural dynamics are switched to a new context. This model provides a neuro-dynamic schema, compatible with neural-astrocyte biology and prior empirical observations, for how astrocytes may integrate information from the periphery and drive contextual changes in neural circuits.

Associative memory in the Hopfield network is attractor dynamics in a disordered many-body system, and higher-order and exponential extensions turn its retrieval update into softmax attention. The polynomial and exponential regimes have been analyzed by different methods, with no common architecture in which to ask what fixes the storage scale. In this paper we study the bipartite architecture of Krotov and Hopfield, which we call the class $H$, whose model is fixed by a Lagrangian for each layer, taking the hidden neurons as the order parameter of retrieval. At polynomial load the replica method yields the replica-symmetric phase diagrams and closed-form capacities, and the crosstalk moment is common to Ising and spherical visible neurons, so their differences come from the visible entropy. With a softmax hidden layer the load is exponential, and a copy representation maps the thermodynamics onto random-energy-model counting, with paramagnetic, condensed, and frozen phases. Heating destabilizes retrieval by quantized reassignments of attention, and typical Gaussian patterns remain metastable at every load. The regimes differ in their crosstalk statistics, central-limit at polynomial load and large-deviation at exponential load, and the class $H$ splits retrieval into two roles, the visible Lagrangian fixing stability and the hidden one the storage scale, two axes that may also guide the design of new Lagrangians.