# A Novel Sparse Regularizer

arXiv: https://arxiv.org/abs/2301.07285 · HTML: https://mlsanity.com/paper/2301.07285/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 32 references that are in the map.
- First posted on arXiv 18 Jan 2023.

## Builds on (most cited first, 13 of 13)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Switch Transformers: Scaling to Trillion Parameter Models with Simple and Efficient Sparsity](https://mlsanity.com/paper/2101.03961/) (2021)
- [The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networks](https://mlsanity.com/paper/1803.03635/) (2018)
- [Learning Sparse Neural Networks through L0 Regularization](https://mlsanity.com/paper/1712.01312/) (2017)
- [Sparsity in Deep Learning: Pruning and growth for efficient inference and training in neural networks](https://mlsanity.com/paper/2102.00554/) (2021)
- [Ab-Initio Solution of the Many-Electron Schr"odinger Equation with Deep Neural Networks](https://mlsanity.com/paper/1909.02487/) (2019)
- [DeepHoyer: Learning Sparser Neural Network with Differentiable Scale-Invariant Sparsity Measures](https://mlsanity.com/paper/1908.09979/) (2019)
- [Adaptive piecewise polynomial estimation via trend filtering](https://mlsanity.com/paper/1304.2986/) (2013)
- [Controlled Sparsity via Constrained Optimization or: How I Learned to Stop Tuning Penalties and Love Constraints](https://mlsanity.com/paper/2208.04425/) (2022)
- [Learned Threshold Pruning](https://mlsanity.com/paper/2003.00075/) (2020)
- [Principle of Relevant Information for Graph Sparsification](https://mlsanity.com/paper/2206.00118/) (2022)
- [Fiedler Regularization: Learning Neural Networks with Graph Sparsity](https://mlsanity.com/paper/2003.00992/) (2020)
- [Total Variation Optimization Layers for Computer Vision](https://mlsanity.com/paper/2204.03643/) (2022)

## Abstract (arXiv)

Lp-norm regularization schemes such as L0, L1, and L2-norm regularization and Lp-norm-based regularization techniques such as weight decay, LASSO, and elastic net compute a quantity which depends on model weights considered in isolation from one another. This paper introduces a regularizer based on minimizing a novel measure of entropy applied to the model during optimization. In contrast with Lp-norm-based regularization, this regularizer is concerned with the spatial arrangement of weights within a weight matrix. This novel regularizer is an additive term for the loss function and is differentiable, simple and fast to compute, scale-invariant, requires a trivial amount of additional memory, and can easily be parallelized. Empirically this method yields approximately a one order-of-magnitude improvement in the number of nonzero model parameters required to achieve a given level of test accuracy when training LeNet300 on MNIST.