# Transformer Normalisation Layers and the Independence of Semantic Subspaces

arXiv: https://arxiv.org/abs/2406.17837 · HTML: https://mlsanity.com/paper/2406.17837/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 47 of its 68 references that are in the map.
- First posted on arXiv 25 Jun 2024.

## Builds on (most cited first, 30 of 47)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Efficient Estimation of Word Representations in Vector Space](https://mlsanity.com/paper/1301.3781/) (2013)
- [Distributed Representations of Words and Phrases and their Compositionality](https://mlsanity.com/paper/1310.4546/) (2013)
- [Locating and Editing Factual Associations in GPT](https://mlsanity.com/paper/2202.05262/) (2022)
- [Sparks of Artificial General Intelligence: Early experiments with GPT-4](https://mlsanity.com/paper/2303.12712/) (2023)
- [Root Mean Square Layer Normalization](https://mlsanity.com/paper/1910.07467/) (2019)
- [Interpretability in the Wild: a Circuit for Indirect Object Identification in GPT-2 small](https://mlsanity.com/paper/2211.00593/) (2022)
- [Toy Models of Superposition](https://mlsanity.com/paper/2209.10652/) (2022)
- [On Layer Normalization in the Transformer Architecture](https://mlsanity.com/paper/2002.04745/) (2020)
- [Probing Classifiers: Promises, Shortcomings, and Advances](https://mlsanity.com/paper/2102.12452/) (2021)
- [A Primer in BERTology: What we know about how BERT works](https://mlsanity.com/paper/2002.12327/) (2020)
- [How Contextual are Contextualized Word Representations? Comparing the Geometry of BERT, ELMo, and GPT-2 Embeddings](https://mlsanity.com/paper/1909.00512/) (2019)
- [The Linear Representation Hypothesis and the Geometry of Large Language Models](https://mlsanity.com/paper/2311.03658/) (2023)
- [Scaling Vision Transformers to 22 Billion Parameters](https://mlsanity.com/paper/2302.05442/) (2023)
- [Attention is Not All You Need: Pure Attention Loses Rank Doubly Exponentially with Depth](https://mlsanity.com/paper/2103.03404/) (2021)
- [Query-Key Normalization for Transformers](https://mlsanity.com/paper/2010.04245/) (2020)
- [Transformers Learn Shortcuts to Automata](https://mlsanity.com/paper/2210.10749/) (2022)
- [Understanding and Improving Layer Normalization](https://mlsanity.com/paper/1911.07013/) (2019)
- [Visualizing and Measuring the Geometry of BERT](https://mlsanity.com/paper/1906.02715/) (2019)
- [Finding Alignments Between Interpretable Causal Variables and Distributed Neural Representations](https://mlsanity.com/paper/2303.02536/) (2023)
- [Linearity of Relation Decoding in Transformer Language Models](https://mlsanity.com/paper/2308.09124/) (2023)
- [Localizing Model Behavior with Path Patching](https://mlsanity.com/paper/2304.05969/) (2023)
- [Small-scale proxies for large-scale Transformer training instabilities](https://mlsanity.com/paper/2309.14322/) (2023)
- [Linear Algebraic Structure of Word Senses, with Applications to Polysemy](https://mlsanity.com/paper/1601.03764/) (2016)
- [Transformers without Tears: Improving the Normalization of Self-Attention](https://mlsanity.com/paper/1910.05895/) (2019)
- [Finding Universal Grammatical Relations in Multilingual BERT](https://mlsanity.com/paper/2005.04511/) (2020)
- [Information Flow Routes: Automatically Interpreting Language Models at Scale](https://mlsanity.com/paper/2403.00824/) (2024)
- [A Mechanistic Interpretation of Arithmetic Reasoning in Language Models using Causal Mediation Analysis](https://mlsanity.com/paper/2305.15054/) (2023)
- [What needs to go right for an induction head? A mechanistic study of in-context learning circuits and their formation](https://mlsanity.com/paper/2404.07129/) (2024)

## Built on by (most cited first, 6 of 6)

- [HybridNorm: Towards Stable and Efficient Transformer Training via Hybrid Normalization](https://mlsanity.com/paper/2503.04598/) (2025)
- [Methods of improving LLM training stability](https://mlsanity.com/paper/2410.16682/) (2024)
- [Looking Locally: Object-Centric Vision Transformers as Foundation Models for Efficient Segmentation](https://mlsanity.com/paper/2502.02763/) (2025)
- [GeoNorm: Unify Pre-Norm and Post-Norm with Geodesic Optimization](https://mlsanity.com/paper/2601.22095/) (2026)
- [FlashNorm: Fast Normalization for Transformers](https://mlsanity.com/paper/2407.09577/) (2024)
- [Three-Phase Transformer](https://mlsanity.com/paper/2604.14430/) (2026)

## Abstract (arXiv)

Recent works have shown that transformers can solve contextual reasoning tasks by internally executing computational graphs called circuits. Circuits often use attention to logically match information from subspaces of the representation, e.g. using position-in-sequence to identify the previous token. In this work, we consider a semantic subspace to be any independent subspace of the latent representation that can fully determine an attention distribution. We show that Pre-Norm, the placement of normalisation layer used by state-of-the-art transformers, violates this ability unless the model learns a strict representation structure of orthogonal spheres. This is because it causes linear subspaces to interfere through their common normalisation factor. Theoretically, we analyse circuit stability by modelling this interference as random noise on the L2-norms of the query/key/value vectors, predicting a phenomenon of circuit collapse when sparse-attention shifts to a different token. Empirically, we investigate the sensitivity of real-world models trained for mathematical addition, observing a 1% rate of circuit collapse when the norms are artificially perturbed by lesssim10%. We contrast Pre-Norm with QKV-Norm, which places normalisation after the attention head's linear operators. Theoretically this relaxes the representational constraints. Empirically we observe comparable in-distribution but worse out-of-distribution performance.