# Preserving Bilinear Weight Spectra with a Signed and Shrunk Quadratic Activation Function

arXiv: https://arxiv.org/abs/2509.01874 · HTML: https://mlsanity.com/paper/2509.01874/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 17 references that are in the map.
- First posted on arXiv 2 Sep 2025.

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

- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [GLU Variants Improve Transformer](https://mlsanity.com/paper/2002.05202/) (2020)
- [Sparse Autoencoders Find Highly Interpretable Features in Language Models](https://mlsanity.com/paper/2309.08600/) (2023)
- [Language Modeling with Gated Convolutional Networks](https://mlsanity.com/paper/1612.08083/) (2016)
- [Scaling and evaluating sparse autoencoders](https://mlsanity.com/paper/2406.04093/) (2024)
- [TinyStories: How Small Can Language Models Be and Still Speak Coherent English?](https://mlsanity.com/paper/2305.07759/) (2023)
- [Modular Networks: Learning to Decompose Neural Computation](https://mlsanity.com/paper/1811.05249/) (2018)
- [Interpreting Attention Layer Outputs with Sparse Autoencoders](https://mlsanity.com/paper/2406.17759/) (2024)
- [Gradient Routing: Masking Gradients to Localize Computation in Neural Networks](https://mlsanity.com/paper/2410.04332/) (2024)
- [Bilinear MLPs enable weight-based mechanistic interpretability](https://mlsanity.com/paper/2410.08417/) (2024)
- [A technical note on bilinear layers for interpretability](https://mlsanity.com/paper/2305.03452/) (2023)

## Abstract (arXiv)

Understanding the inner workings of machine learning models is critical for ensuring their reliability and robustness. Whilst many techniques in mechanistic interpretability focus on activation driven analyses, being able to derive meaningful features directly from the weights of a neural network would provide greater guarantees and more computational efficiency. Existing techniques for analyzing model features through weights suffer from drawbacks such as reduced performance and data inefficiency. In this paper, we introduce Signed Quadratic Shrink (SQS), an activation function designed to allow Gated Linear Units (GLUs) to learn interpretable features without these drawbacks. Our experimental results show that SQS achieves performance competitive with state-of-the-art activation functions whilst enabling weight-based interpretability