# Weight Pair Encoding: Inducing a Smaller Grammar in Neural Network Weights

arXiv: https://arxiv.org/abs/2609.31564 · HTML: https://mlsanity.com/paper/2609.31564/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 27 references that are in the map.
- First posted on arXiv 25 Sep 2026.

## Builds on (most cited first, 18 of 18)

- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Neural Machine Translation of Rare Words with Subword Units](https://mlsanity.com/paper/1508.07909/) (2015)
- [Deep Compression: Compressing Deep Neural Networks with Pruning, Trained Quantization and Huffman Coding](https://mlsanity.com/paper/1510.00149/) (2015)
- [Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation](https://mlsanity.com/paper/1308.3432/) (2013)
- [Quantization and Training of Neural Networks for Efficient Integer-Arithmetic-Only Inference](https://mlsanity.com/paper/1712.05877/) (2017)
- [Editing Models with Task Arithmetic](https://mlsanity.com/paper/2212.04089/) (2022)
- [Intrinsic Dimensionality Explains the Effectiveness of Language Model Fine-Tuning](https://mlsanity.com/paper/2012.13255/) (2020)
- [How to train your ViT? Data, Augmentation, and Regularization in Vision Transformers](https://mlsanity.com/paper/2106.10270/) (2021)
- [Quantizing deep convolutional networks for efficient inference: A whitepaper](https://mlsanity.com/paper/1806.08342/) (2018)
- [Git Re-Basin: Merging Models modulo Permutation Symmetries](https://mlsanity.com/paper/2209.04836/) (2022)
- [The Role of Permutation Invariance in Linear Mode Connectivity of Neural Networks](https://mlsanity.com/paper/2110.06296/) (2021)
- [Soft Weight-Sharing for Neural Network Compression](https://mlsanity.com/paper/1702.04008/) (2017)
- [Scalable Model Compression by Entropy Penalized Reparameterization](https://mlsanity.com/paper/1906.06624/) (2019)
- [TorchAO: PyTorch-Native Training-to-Serving Model Optimization](https://mlsanity.com/paper/2507.16099/) (2025)
- [Improving Matrix-vector Multiplication via Lossless Grammar-Compressed Matrices](https://mlsanity.com/paper/2203.14540/) (2022)
- [Self-Compressing Neural Networks](https://mlsanity.com/paper/2301.13142/) (2023)
- [Algorithmic Simplification of Neural Networks with Mosaic-of-Motifs](https://mlsanity.com/paper/2602.14896/) (2026)
- [Zero-Shot Quantization via Weight-Space Arithmetic](https://mlsanity.com/paper/2604.03420/) (2026)

## Abstract (arXiv)

We show that neural network weights can be explicilty fintuned to admit a smaller grammar. Weight Pair Encoding (WeightPE) does so by placing a lossy Re-Pair compressor inside a straight-through estimator. The int8 weights of the network are flattened into one string, and near-matching Re-Pair patterns are made exactly equal within a global L2 budget. The network computes with the rewritten weights and trains through them with a straight-through estimator. Unlike a flat codebook of fixed-size entries, a grammar offers variable-length patterns and reuses them hierarchically inside larger ones. On the MLP weights of ViT-B/16 and ViT-L/16 finetuned on CIFAR-10, WeightPE produces a Re-Pair grammar 0.43x and 0.38x the size of the one produced by an equivalent int8 QAT run, at a cost of 1.9 and 1.1 accuracy points. The trend extends to different grammar compressors (LZ78, SEQUITUR), over which the networks has not be finetuned against. To our knowledge, this is the first time grammar size has been used as an explicit training objective for network weights.