# Understanding Deep Architectures using a Recursive Convolutional Network

arXiv: https://arxiv.org/abs/1312.1847 · HTML: https://mlsanity.com/paper/1312.1847/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Dec 2013.

## Built on by (most cited first, 11 of 11)

- [Relaxed Recursive Transformers: Effective Parameter Sharing with Layer-wise LoRA](https://mlsanity.com/paper/2410.20672/) (2024)
- [Non-deep Networks](https://mlsanity.com/paper/2110.07641/) (2021)
- [The Uncanny Similarity of Recurrence and Depth](https://mlsanity.com/paper/2102.11011/) (2021)
- [Latent Iterative Refinement for Modular Source Separation](https://mlsanity.com/paper/2211.11917/) (2022)
- [Adaptive recurrent vision performs zero-shot computation scaling to unseen difficulty levels](https://mlsanity.com/paper/2311.06964/) (2023)
- [Zero Token-Driven Deep Thinking in LLMs: Unlocking the Full Potential of Existing Parameters via Cyclic Refinement](https://mlsanity.com/paper/2502.12214/) (2025)
- [VSpSR: Explorable Super-Resolution via Variational Sparse Representation](https://mlsanity.com/paper/2104.08575/) (2021)
- [Learning to Stop Overthinking at Test Time](https://mlsanity.com/paper/2502.10954/) (2025)
- [Beyond the Black Box: Do More Complex Deep Learning Models Provide Superior XAI Explanations?](https://mlsanity.com/paper/2405.08658/) (2024)
- [Traveling Waves Integrate Spatial Information Through Time](https://mlsanity.com/paper/2502.06034/) (2025)
- [Scaling Vision Models Does Not Consistently Improve Localisation-Based Explanation Quality](https://mlsanity.com/paper/2605.10142/) (2026)

## Abstract (arXiv)

A key challenge in designing convolutional network models is sizing them appropriately. Many factors are involved in these decisions, including number of layers, feature maps, kernel sizes, etc. Complicating this further is the fact that each of these influence not only the numbers and dimensions of the activation units, but also the total number of parameters. In this paper we focus on assessing the independent contributions of three of these linked variables: The numbers of layers, feature maps, and parameters. To accomplish this, we employ a recursive convolutional network whose weights are tied between layers; this allows us to vary each of the three factors in a controlled setting. We find that while increasing the numbers of layers and parameters each have clear benefit, the number of feature maps (and hence dimensionality of the representation) appears ancillary, and finds most of its benefit through the introduction of more weights. Our results (i) empirically confirm the notion that adding layers alone increases computational power, within the context of convolutional layers, and (ii) suggest that precise sizing of convolutional feature map dimensions is itself of little concern; more attention should be paid to the number of parameters in these layers instead.