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.

翻译：空间和时间资源约束对生物与人工智能系统均至关重要。本文将循环卷积神经网络视为无限格点阵的有限子集，为其定义了广度、深度与时间的可微成本项。通过反向传播，我们联合优化这些成本与任务误差。通过设置不同的广度、深度与时间压力，训练过程中可有机涌现出多样化的计算图。研究发现，这三类资源可相互权衡以达成指定精度水平。网络会随任务复杂度在三个维度上同步增长，并在输入被遮挡时自发增加循环步数。令人惊讶的是，模型消耗的时间与人类在物体识别任务中的反应时间存在相关性。本框架为资源约束如何塑造神经架构提供了规范性解释，可与神经科学中的大脑设计问题形成关联，并可能为理解自然界中神经解的多样性提供新视角。