# The Propensity for Density in Feed-forward Models

arXiv: https://arxiv.org/abs/2410.14461 · HTML: https://mlsanity.com/paper/2410.14461/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 33 references that are in the map.
- First posted on arXiv 18 Oct 2024.

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

- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [OPT: Open Pre-trained Transformer Language Models](https://mlsanity.com/paper/2205.01068/) (2022)
- [The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networks](https://mlsanity.com/paper/1803.03635/) (2018)
- [Knowledge Distillation: A Survey](https://mlsanity.com/paper/2006.05525/) (2020)
- [Toy Models of Superposition](https://mlsanity.com/paper/2209.10652/) (2022)
- [Towards Automated Circuit Discovery for Mechanistic Interpretability](https://mlsanity.com/paper/2304.14997/) (2023)
- [Deep Double Descent: Where Bigger Models and More Data Hurt](https://mlsanity.com/paper/1912.02292/) (2019)
- [Grokking: Generalization Beyond Overfitting on Small Algorithmic Datasets](https://mlsanity.com/paper/2201.02177/) (2022)
- [What is the State of Neural Network Pruning?](https://mlsanity.com/paper/2003.03033/) (2020)
- [What's Hidden in a Randomly Weighted Neural Network?](https://mlsanity.com/paper/1911.13299/) (2019)
- [Proving the Lottery Ticket Hypothesis: Pruning is All You Need](https://mlsanity.com/paper/2002.00585/) (2020)
- [Deep learning generalizes because the parameter-function map is biased towards simple functions](https://mlsanity.com/paper/1805.08522/) (2018)
- [Multifaceted Feature Visualization: Uncovering the Different Types of Features Learned By Each Neuron in Deep Neural Networks](https://mlsanity.com/paper/1602.03616/) (2016)
- [On the importance of single directions for generalization](https://mlsanity.com/paper/1803.06959/) (2018)
- [The Emergence of Essential Sparsity in Large Pre-trained Models: The Weights that Matter](https://mlsanity.com/paper/2306.03805/) (2023)
- [Frivolous Units: Wider Networks Are Not Really That Wide](https://mlsanity.com/paper/1912.04783/) (2019)

## Abstract (arXiv)

Does the process of training a neural network to solve a task tend to use all of the available weights even when the task could be solved with fewer weights? To address this question we study the effects of pruning fully connected, convolutional and residual models while varying their widths. We find that the proportion of weights that can be pruned without degrading performance is largely invariant to model size. Increasing the width of a model has little effect on the density of the pruned model relative to the increase in absolute size of the pruned network. In particular, we find substantial prunability across a large range of model sizes, where our biggest model is 50 times as wide as our smallest model. We explore three hypotheses that could explain these findings.