Learning Computational Structure for Sample-Efficient Prediction

Hangyu Zhou, Constantine Dovrolis, Stephen Mussmann

Statistical learning in high dimensions suffers from the curse of dimensionality. Fortunately, many functions of practical interest are compositionally sparse, meaning they admit a composition of local functions, each depending on only a few variables, allowing sample complexity to depend on local arity rather than ambient dimension. Yet realizing this benefit requires exploiting hidden compositional structure, which theory does not establish for practical gradient-based training. We study this gap with CSFRBench, a controlled benchmark that hides the target's compositional computation during training but retains it for diagnosis, and find that dense networks and sparsity-based baselines leave much of that benefit unrealized. Inspired by the spatial organization of biological neural circuits, we introduce Learned Wiring (LeWi): each neuron has a learned low-dimensional embedding, only nearby neurons connect, and embeddings and weights are trained jointly. LeWi improves sample efficiency on targets with hierarchical structure, intermediate reuse, or independent modules. Across 32 additional targets generated by independently sampled computation graphs, LeWi is the most…