Learning Computational Structure for Sample-Efficient Prediction

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 gains most on hierarchical targets and those with intermediate reuse. Across 32 additional targets generated by independently sampled computation graphs, LeWi is the most sample-efficient method not given the target graph, with 27% lower mean learning-curve area than dense networks. Gains are smaller for flat low-arity compositions, while dense networks perform better on targets with a single high-arity function. LeWi's representations and connectivity align with the target computation. On 17 world-model prediction tasks spanning control, navigation, and manipulation, LeWi beats the dense baseline on 16 and wins 99/119 baseline comparisons. These results show that jointly learning connectivity and weights can exploit computational structure to improve sample efficiency.