Meta-learning leading to homeostatic plasticity stabilizes synaptic weights together with predictable activity levels

Stabilizing synaptic plasticity together with the neurons activity has remained a central challenge in theoretical neuroscience since the introduction of Hebbian learning principles. Classical Hebbian learning rules typically lead to unbounded synaptic growth, motivating the development of stabilization mechanisms such as normalization methods, BCM-type learning, synaptic scaling and others. While these approaches can prevent divergence, they can also exhibit different limitations e.g. resulting in too-sparse synaptic configurations or leading to poor scalability with increasing network size. A recently introduced meta-plasticity mechanism, termed annealed linear learning (ALL), dynamically reduces the learning rate as neuronal output increases, thereby preserving stable and interpretable fixed-point behavior of the output. However, the original formulation leads to an irreversible decay of the learning rate, preventing adaptation to changing environmental conditions. To address this, in the present study, we balance learning rate reduction at large outputs with recovery at small outputs and in addition introduce forgetting that gradually reduces synaptic weights. These extensions allow the system to discard outdated representations and adapt to novel input conditions. Analytical investigations demonstrate that the favorable output fixed-point properties of the original ALL framework are preserved under the extended rule. Furthermore, simulations with an artificial agent show that the proposed mechanism enables robust and fast re-learning and adaptation in changing environments.