# Recursive Sketches for Modular Deep Learning

arXiv: https://arxiv.org/abs/1905.12730 · HTML: https://mlsanity.com/paper/1905.12730/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 May 2019.

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

- [A Survey on Hyperdimensional Computing aka Vector Symbolic Architectures, Part II: Applications, Cognitive Models, and Challenges](https://mlsanity.com/paper/2112.15424/) (2021)
- [Vector Symbolic Architectures as a Computing Framework for Emerging Hardware](https://mlsanity.com/paper/2106.05268/) (2021)
- [How to Reuse and Compose Knowledge for a Lifetime of Tasks: A Survey on Continual Learning and Functional Composition](https://mlsanity.com/paper/2207.07730/) (2022)
- [Decomposing Convolutional Neural Networks into Reusable and Replaceable Modules](https://mlsanity.com/paper/2110.07720/) (2021)
- [A Theoretical View on Sparsely Activated Networks](https://mlsanity.com/paper/2208.04461/) (2022)
- [Randomized Algorithms for Scientific Computing (RASC)](https://mlsanity.com/paper/2104.11079/) (2021)
- [Decomposing a Recurrent Neural Network into Modules for Enabling Reusability and Replacement](https://mlsanity.com/paper/2212.05970/) (2022)
- [Modularity in Deep Learning: A Survey](https://mlsanity.com/paper/2310.01154/) (2023)
- [Composing Linear Layers from Irreducibles](https://mlsanity.com/paper/2507.11688/) (2025)
- [Provable Hierarchical Lifelong Learning with a Sketch-based Modular Architecture](https://mlsanity.com/paper/2112.10919/) (2021)
- [Compressive Meta-Learning](https://mlsanity.com/paper/2508.11090/) (2025)

## Abstract (arXiv)

We present a mechanism to compute a sketch (succinct summary) of how a complex modular deep network processes its inputs. The sketch summarizes essential information about the inputs and outputs of the network and can be used to quickly identify key components and summary statistics of the inputs. Furthermore, the sketch is recursive and can be unrolled to identify sub-components of these components and so forth, capturing a potentially complicated DAG structure. These sketches erase gracefully; even if we erase a fraction of the sketch at random, the remainder still retains the `high-weight' information present in the original sketch. The sketches can also be organized in a repository to implicitly form a `knowledge graph'; it is possible to quickly retrieve sketches in the repository that are related to a sketch of interest; arranged in this fashion, the sketches can also be used to learn emerging concepts by looking for new clusters in sketch space. Finally, in the scenario where we want to learn a ground truth deep network, we show that augmenting input/output pairs with these sketches can theoretically make it easier to do so.