# Element-wise Modulation of Random Matrices for Efficient Neural Layers

arXiv: https://arxiv.org/abs/2512.13480 · HTML: https://mlsanity.com/paper/2512.13480/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 23 references that are in the map.
- First posted on arXiv 15 Dec 2025.

## Builds on (most cited first, 11 of 11)

- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer](https://mlsanity.com/paper/1701.06538/) (2017)
- [Cyclical Learning Rates for Training Neural Networks](https://mlsanity.com/paper/1506.01186/) (2015)
- [Deep Learning with Limited Numerical Precision](https://mlsanity.com/paper/1502.02551/) (2015)
- [Exploiting Linear Structure Within Convolutional Networks for Efficient Evaluation](https://mlsanity.com/paper/1404.0736/) (2014)
- [Predicting Parameters in Deep Learning](https://mlsanity.com/paper/1306.0543/) (2013)
- [Structured Transforms for Small-Footprint Deep Learning](https://mlsanity.com/paper/1510.01722/) (2015)
- [Random Projection in Deep Neural Networks](https://mlsanity.com/paper/1812.09489/) (2018)
- [Enhanced Expressive Power and Fast Training of Neural Networks by Random Projections](https://mlsanity.com/paper/1811.09054/) (2018)

## Abstract (arXiv)

Fully connected layers are a primary source of memory and computational overhead in deep neural networks due to their dense, often redundant parameterization. While various compression techniques exist, they frequently introduce complex engineering trade-offs or degrade model performance. We propose the Parametrized Random Projection (PRP) layer, a novel approach that decouples feature mixing from adaptation by utilizing a fixed random matrix modulated by lightweight, learnable element-wise parameters. This architecture drastically reduces the trainable parameter count to a linear scale while retaining reliable accuracy across various benchmarks. The design serves as a stable, computationally efficient solution for architectural scaling and deployment in resource-limited settings.