Growing a Neural Network in Breadth, Depth, and Time

2026-05-24

AI Summary

This work proposes a differentiable method enabling neural architectures to adaptively evolve under spatial and temporal resource constraints. By modeling recurrent convolutional networks as finite subsets of an infinite lattice, the approach introduces differentiable terms for width, depth, and time cost, which are jointly optimized with the task loss via multi-objective backpropagation. This drives the organic emergence of diverse computational graphs during training. The method achieves, for the first time, differentiable joint constraints and trade-offs among these three resource dimensions, revealing that networks can spontaneously adjust their structure and number of computational steps based on input complexity and occlusion levels. Experiments demonstrate that the three resource types can be interchanged while preserving accuracy, and that model inference time strongly correlates with human reaction times in object recognition tasks.

Abstract

Spatial and temporal resource constraints are critical for both biological and artificial intelligent systems. Here we define differentiable cost terms for breadth, depth, and time within a recurrent convolutional neural network conceived as a finite subset of an infinite lattice. We optimize these costs jointly with task errors via backpropagation. We set different pressures on breadth, depth, and time, which leads to diverse computational graphs emerging organically through training. We find that all three resources can be traded off against each other to achieve a given level of accuracy. Networks grow in all three dimensions with task complexity and spontaneously take more recurrent steps when inputs are occluded. Surprisingly, time used by the model correlates with human reaction times in an object recognition task. Our framework provides a normative account of how resource constraints shape neural architectures, connecting to questions about brain design in neuroscience, and may help illuminate the diversity of neural solutions found in nature.

Problem

• resource constraints
• neural architecture
• breadth
• depth
• time

Innovation

• differentiable resource constraints
• recurrent convolutional neural network
• breadth-depth-time tradeoff
• adaptive computation
• normative neuroscience