# Growing a Neural Network in Breadth, Depth, and Time

arXiv: https://arxiv.org/abs/2605.25174 · HTML: https://mlsanity.com/paper/2605.25174/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 41 references that are in the map.
- First posted on arXiv 24 May 2026.

## Builds on (most cited first, 17 of 17)

- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Deep Compression: Compressing Deep Neural Networks with Pruning, Trained Quantization and Huffman Coding](https://mlsanity.com/paper/1510.00149/) (2015)
- [Visualizing and Understanding Convolutional Networks](https://mlsanity.com/paper/1311.2901/) (2013)
- [The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networks](https://mlsanity.com/paper/1803.03635/) (2018)
- [Learning both Weights and Connections for Efficient Neural Networks](https://mlsanity.com/paper/1506.02626/) (2015)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [DARTS: Differentiable Architecture Search](https://mlsanity.com/paper/1806.09055/) (2018)
- [Pruning Filters for Efficient ConvNets](https://mlsanity.com/paper/1608.08710/) (2016)
- [Learning Efficient Convolutional Networks through Network Slimming](https://mlsanity.com/paper/1708.06519/) (2017)
- [Adaptive Computation Time for Recurrent Neural Networks](https://mlsanity.com/paper/1603.08983/) (2016)
- [Progressive Neural Architecture Search](https://mlsanity.com/paper/1712.00559/) (2017)
- [Human uncertainty makes classification more robust](https://mlsanity.com/paper/1908.07086/) (2019)
- [Beyond accuracy: quantifying trial-by-trial behaviour of CNNs and humans by measuring error consistency](https://mlsanity.com/paper/2006.16736/) (2020)
- [Recurrence is required to capture the representational dynamics of the human visual system](https://mlsanity.com/paper/1903.05946/) (2019)
- [People construct simplified mental representations to plan](https://mlsanity.com/paper/2105.06948/) (2021)
- [A Unified Theory of Early Visual Representations from Retina to Cortex through Anatomically Constrained Deep CNNs](https://mlsanity.com/paper/1901.00945/) (2019)

## Built on by (most cited first, 1 of 1)

- [Retrieval-Centric Deep Learning in Growing Nonparametric Neural Networks](https://mlsanity.com/paper/2610.03858/) (2026)

## Abstract (arXiv)

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.