# Dense Structural Compression of Transformers via Gauge-Correct Channel Removal

arXiv: https://arxiv.org/abs/2609.07264 · HTML: https://mlsanity.com/paper/2609.07264/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 26 of its 28 references that are in the map.
- First posted on arXiv 7 Sep 2026.

## Builds on (most cited first, 26 of 26)

- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [DistilBERT, a distilled version of BERT: smaller, faster, cheaper and lighter](https://mlsanity.com/paper/1910.01108/) (2019)
- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [The Lottery Ticket Hypothesis: Finding Sparse, Trainable Neural Networks](https://mlsanity.com/paper/1803.03635/) (2018)
- [Learning both Weights and Connections for Efficient Neural Networks](https://mlsanity.com/paper/1506.02626/) (2015)
- [GLU Variants Improve Transformer](https://mlsanity.com/paper/2002.05202/) (2020)
- [DARTS: Differentiable Architecture Search](https://mlsanity.com/paper/1806.09055/) (2018)
- [Neural Architecture Search with Reinforcement Learning](https://mlsanity.com/paper/1611.01578/) (2016)
- [TinyBERT: Distilling BERT for Natural Language Understanding](https://mlsanity.com/paper/1909.10351/) (2019)
- [Pruning Filters for Efficient ConvNets](https://mlsanity.com/paper/1608.08710/) (2016)
- [Are Sixteen Heads Really Better than One?](https://mlsanity.com/paper/1905.10650/) (2019)
- [Compressive Transformers for Long-Range Sequence Modelling](https://mlsanity.com/paper/1911.05507/) (2019)
- [To prune, or not to prune: exploring the efficacy of pruning for model compression](https://mlsanity.com/paper/1710.01878/) (2017)
- [Learning Structured Sparsity in Deep Neural Networks](https://mlsanity.com/paper/1608.03665/) (2016)
- [Importance Estimation for Neural Network Pruning](https://mlsanity.com/paper/1906.10771/) (2019)
- [Sharp Minima Can Generalize For Deep Nets](https://mlsanity.com/paper/1703.04933/) (2017)
- [Reducing Transformer Depth on Demand with Structured Dropout](https://mlsanity.com/paper/1909.11556/) (2019)
- [Sheared LLaMA: Accelerating Language Model Pre-training via Structured Pruning](https://mlsanity.com/paper/2310.06694/) (2023)
- [Movement Pruning: Adaptive Sparsity by Fine-Tuning](https://mlsanity.com/paper/2005.07683/) (2020)
- [SliceGPT: Compress Large Language Models by Deleting Rows and Columns](https://mlsanity.com/paper/2401.15024/) (2024)
- [Norm-Based Capacity Control in Neural Networks](https://mlsanity.com/paper/1503.00036/) (2015)
- [DynaBERT: Dynamic BERT with Adaptive Width and Depth](https://mlsanity.com/paper/2004.04037/) (2020)
- [Structured Pruning Learns Compact and Accurate Models](https://mlsanity.com/paper/2204.00408/) (2022)
- [On the Effect of Dropping Layers of Pre-trained Transformer Models](https://mlsanity.com/paper/2004.03844/) (2020)
- [Equi-normalization of Neural Networks](https://mlsanity.com/paper/1902.10416/) (2019)

## Abstract (arXiv)

Inference energy per token drives the cost and carbon footprint of deployed transformers. It is dominated by dense matrix products that incur fused multiply-accumulate (FMA) operations and memory traffic. To reduce these computations while retaining dense tensors for high GPU throughput, we develop a methodology from first principles to adapt structural complexity during training to maximize inference utility per unit compute. Channel penalties drive entire tensor slices to zero to enable physical removal while preserving density and the network function. The natural approach, penalizing the norm of operator components acting through each channel, is provably destabilized by gauge freedom. We resolve this pathology with GaugeLasso: additive symmetric group-lasso penalties that recover a monotone function of product-norms when the network converges to gauge balance. Our equilibrium analysis enables per-channel calibration to correctly suppress slices that under-perform in inference utility per unit compute. Under adaptive pressure, the network reorganizes into depth-dependent structural profiles that can be far smaller than the architecture required to learn the task. On polynomial long division over mathbbF31, compute compresses from 148 to 255 times with perfect accuracy. On character-level language modeling, compressed models outperform the hand-designed baseline at equal FMA. On masked autoencoding, a compression trial exposes which axes were over-provisioned and which saturated, guiding a better second design. Compaction also accelerates training monotonically as the model progresses. Post-hoc pruning with the same utility ranking cannot reach these structures, showing that sustained pressure is central to discovery of efficient models. Retraining a discovered architecture recovers baseline quality on our statistical tasks, but fails on our exact algorithmic task.