Generating functionals for computational intelligence: the Fisher information as an objective function for self-limiting Hebbian learning rules
This work addresses the challenge of stable and adaptive synaptic plasticity in neural networks for computational intelligence, though it appears incremental as it builds on existing Hebbian and Fisher information concepts.
The authors tackled the problem of deriving self-limiting Hebbian learning rules for neural networks by proposing a new objective function based on minimizing Fisher information, resulting in rules that enable stable online learning, align synaptic weights with principal input directions, and show robust performance with full homeostatic adaptation.
Generating functionals may guide the evolution of a dynamical system and constitute a possible route for handling the complexity of neural networks as relevant for computational intelligence. We propose and explore a new objective function, which allows to obtain plasticity rules for the afferent synaptic weights. The adaption rules are Hebbian, self-limiting, and result from the minimization of the Fisher information with respect to the synaptic flux. We perform a series of simulations examining the behavior of the new learning rules in various circumstances. The vector of synaptic weights aligns with the principal direction of input activities, whenever one is present. A linear discrimination is performed when there are two or more principal directions; directions having bimodal firing-rate distributions, being characterized by a negative excess kurtosis, are preferred. We find robust performance and full homeostatic adaption of the synaptic weights results as a by-product of the synaptic flux minimization. This self-limiting behavior allows for stable online learning for arbitrary durations. The neuron acquires new information when the statistics of input activities is changed at a certain point of the simulation, showing however, a distinct resilience to unlearn previously acquired knowledge. Learning is fast when starting with randomly drawn synaptic weights and substantially slower when the synaptic weights are already fully adapted.