# Neural Sculpting: Uncovering hierarchically modular task structure in neural networks through pruning and network analysis

arXiv: https://arxiv.org/abs/2305.18402 · HTML: https://mlsanity.com/paper/2305.18402/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 31 of its 58 references that are in the map.
- First posted on arXiv 28 May 2023.

## Builds on (most cited first, 30 of 31)

- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [Learning without Forgetting](https://mlsanity.com/paper/1606.09282/) (2016)
- [Learning both Weights and Connections for Efficient Neural Networks](https://mlsanity.com/paper/1506.02626/) (2015)
- [Progressive Neural Networks](https://mlsanity.com/paper/1606.04671/) (2016)
- [Interpretability in the Wild: a Circuit for Indirect Object Identification in GPT-2 small](https://mlsanity.com/paper/2211.00593/) (2022)
- [In-context Learning and Induction Heads](https://mlsanity.com/paper/2209.11895/) (2022)
- [SNIP: Single-shot Network Pruning based on Connection Sensitivity](https://mlsanity.com/paper/1810.02340/) (2018)
- [Cyclical Learning Rates for Training Neural Networks](https://mlsanity.com/paper/1506.01186/) (2015)
- [Pruning neural networks without any data by iteratively conserving synaptic flow](https://mlsanity.com/paper/2006.05467/) (2020)
- [Picking Winning Tickets Before Training by Preserving Gradient Flow](https://mlsanity.com/paper/2002.07376/) (2020)
- [Compositionality decomposed: how do neural networks generalise?](https://mlsanity.com/paper/1908.08351/) (2019)
- [Comparing Rewinding and Fine-tuning in Neural Network Pruning](https://mlsanity.com/paper/2003.02389/) (2020)
- [Network Trimming: A Data-Driven Neuron Pruning Approach towards Efficient Deep Architectures](https://mlsanity.com/paper/1607.03250/) (2016)
- [Towards Explaining the Regularization Effect of Initial Large Learning Rate in Training Neural Networks](https://mlsanity.com/paper/1907.04595/) (2019)
- [Data-free parameter pruning for Deep Neural Networks](https://mlsanity.com/paper/1507.06149/) (2015)
- [Are Neural Nets Modular? Inspecting Functional Modularity Through Differentiable Weight Masks](https://mlsanity.com/paper/2010.02066/) (2020)
- [Efficient Continual Learning with Modular Networks and Task-Driven Priors](https://mlsanity.com/paper/2012.12631/) (2020)
- [Continual Learning via Local Module Composition](https://mlsanity.com/paper/2111.07736/) (2021)
- [Lookahead: A Far-Sighted Alternative of Magnitude-based Pruning](https://mlsanity.com/paper/2002.04809/) (2020)
- [On the Maximum Hessian Eigenvalue and Generalization](https://mlsanity.com/paper/2206.10654/) (2022)
- [The Generalization-Stability Tradeoff In Neural Network Pruning](https://mlsanity.com/paper/1906.03728/) (2019)
- [Stiffness: A New Perspective on Generalization in Neural Networks](https://mlsanity.com/paper/1901.09491/) (2019)
- [Lifelong Learning of Compositional Structures](https://mlsanity.com/paper/2007.07732/) (2020)
- [Pruning's Effect on Generalization Through the Lens of Training and Regularization](https://mlsanity.com/paper/2210.13738/) (2022)
- [Clusterability in Neural Networks](https://mlsanity.com/paper/2103.03386/) (2021)
- [PHEW: Constructing Sparse Networks that Learn Fast and Generalize Well without Training Data](https://mlsanity.com/paper/2010.11354/) (2020)
- [Modular Representation of Layered Neural Networks](https://mlsanity.com/paper/1703.00168/) (2017)
- [Interpreting Layered Neural Networks via Hierarchical Modular Representation](https://mlsanity.com/paper/1810.01588/) (2018)
- [Clustering units in neural networks: upstream vs downstream information](https://mlsanity.com/paper/2203.11815/) (2022)
- [The evolutionary origins of hierarchy](https://mlsanity.com/paper/1505.06353/) (2015)

## Abstract (arXiv)

Natural target functions and tasks typically exhibit hierarchical modularity -- they can be broken down into simpler sub-functions that are organized in a hierarchy. Such sub-functions have two important features: they have a distinct set of inputs (input-separability) and they are reused as inputs higher in the hierarchy (reusability). Previous studies have established that hierarchically modular neural networks, which are inherently sparse, offer benefits such as learning efficiency, generalization, multi-task learning, and transfer. However, identifying the underlying sub-functions and their hierarchical structure for a given task can be challenging. The high-level question in this work is: if we learn a task using a sufficiently deep neural network, how can we uncover the underlying hierarchy of sub-functions in that task? As a starting point, we examine the domain of Boolean functions, where it is easier to determine whether a task is hierarchically modular. We propose an approach based on iterative unit and edge pruning (during training), combined with network analysis for module detection and hierarchy inference. Finally, we demonstrate that this method can uncover the hierarchical modularity of a wide range of Boolean functions and two vision tasks based on the MNIST digits dataset.