Constrained Hebbian learning supports efficient representational allocation under structural constraints

Biological systems are constrained by anatomy and metabolism, with synaptic maintenance consuming substantial energy and spatial limitations restricting connectivity. These constraints favor neural codes that compress behaviorally relevant information into low-redundancy patterns. Here, we investigate whether an excitatory competitive Hebbian rule can implement synaptic resource allocation under anatomical and metabolic constraints, and whether the resulting representations occupy a more favorable cost-performance regime than reference learning rules.

Representational cost is operationalized using mutual-information-based quantities derived from the Variational Information Bottleneck objective. Experiments employ three audiovisual benchmarks (AVE, Kinetics-Sounds, and VGGSound100) with fixed upstream audiovisual embeddings as a controlled higher-level sensory regime. We isolate downstream associative plasticity and compare Hebbian learning against biologically inspired local target-propagation (DDTP) and backpropagation (BP) under matched sparsity and architectural constraints.

Hebbian learning yields lower task-information cost CTI than sparse BP- and DDTP-trained networks in the main compressed comparisons, while reaching a CTI range comparable to shallow nonnegativity-constrained BP. Rather than uniformly improving classification performance, Hebbian learning shifts the trade-off between task-relevant information and representational cost, yielding lower CTI at comparable functional performance in several settings.

Overall, the results indicate an explicit cost-performance trade-off rather than uniform accuracy gains, while maintaining functional task performance under the evaluated constraints. For a given level of task-relevant information, less information about the input is retained; task performance remains functional, although it can be slightly reduced on some datasets. These results support a computational-neuroscientific interpretation of Hebbian learning as a local mechanism for synaptic resource allocation, rather than as a general-purpose strategy for maximizing audiovisual classification accuracy.