# On Vanishing Variance in Transformer Length Generalization

arXiv: https://arxiv.org/abs/2504.02827 · HTML: https://mlsanity.com/paper/2504.02827/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 32 references that are in the map.
- First posted on arXiv 3 Apr 2025.

## Builds on (most cited first, 27 of 27)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Scalable Diffusion Models with Transformers](https://mlsanity.com/paper/2212.09748/) (2022)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [Robust Speech Recognition via Large-Scale Weak Supervision](https://mlsanity.com/paper/2212.04356/) (2022)
- [Transformer-XL: Attentive Language Models Beyond a Fixed-Length Context](https://mlsanity.com/paper/1901.02860/) (2019)
- [Show, Attend and Tell: Neural Image Caption Generation with Visual Attention](https://mlsanity.com/paper/1502.03044/) (2015)
- [Self-Attention with Relative Position Representations](https://mlsanity.com/paper/1803.02155/) (2018)
- [Train Short, Test Long: Attention with Linear Biases Enables Input Length Extrapolation](https://mlsanity.com/paper/2108.12409/) (2021)
- [Domain Generalization: A Survey](https://mlsanity.com/paper/2103.02503/) (2021)
- [YaRN: Efficient Context Window Extension of Large Language Models](https://mlsanity.com/paper/2309.00071/) (2023)
- [RETAIN: An Interpretable Predictive Model for Healthcare using Reverse Time Attention Mechanism](https://mlsanity.com/paper/1608.05745/) (2016)
- [From Softmax to Sparsemax: A Sparse Model of Attention and Multi-Label Classification](https://mlsanity.com/paper/1602.02068/) (2016)
- [The Impact of Positional Encoding on Length Generalization in Transformers](https://mlsanity.com/paper/2305.19466/) (2023)
- [Exploring Length Generalization in Large Language Models](https://mlsanity.com/paper/2207.04901/) (2022)
- [What Algorithms can Transformers Learn? A Study in Length Generalization](https://mlsanity.com/paper/2310.16028/) (2023)
- [Adaptively Sparse Transformers](https://mlsanity.com/paper/1909.00015/) (2019)
- [Transformer Language Models without Positional Encodings Still Learn Positional Information](https://mlsanity.com/paper/2203.16634/) (2022)
- [Randomized Positional Encodings Boost Length Generalization of Transformers](https://mlsanity.com/paper/2305.16843/) (2023)
- [The CLRS Algorithmic Reasoning Benchmark](https://mlsanity.com/paper/2205.15659/) (2022)
- [KERPLE: Kernelized Relative Positional Embedding for Length Extrapolation](https://mlsanity.com/paper/2205.09921/) (2022)
- [Transformers Can Achieve Length Generalization But Not Robustly](https://mlsanity.com/paper/2402.09371/) (2024)
- [Softmax is not Enough (for Sharp Size Generalisation)](https://mlsanity.com/paper/2410.01104/) (2024)
- [Scaling Stick-Breaking Attention: An Efficient Implementation and In-depth Study](https://mlsanity.com/paper/2410.17980/) (2024)

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

- [What Happens Next? Anticipating Future Motion by Generating Point Trajectories](https://mlsanity.com/paper/2509.21592/) (2025)
- [Quantitative Bounds for Length Generalization in Transformers](https://mlsanity.com/paper/2510.27015/) (2025)
- [Instruct-Particulate: Scaling Feed-Forward 3D Object Articulation with Kinematic Control](https://mlsanity.com/paper/2606.14699/) (2026)
- [Stabilizing Extrapolation in Looped Transformers via Learned Stochastic Stopping](https://mlsanity.com/paper/2606.29983/) (2026)
- [Can Language Models Actually Retrieve In-Context? Drowning in Documents at Million Token Scale](https://mlsanity.com/paper/2607.01538/) (2026)
- [Refit the Probe: Single-Direction Ablation Is Not a Necessity Test](https://mlsanity.com/paper/2606.00926/) (2026)

## Abstract (arXiv)

It is a widely known issue that Transformers, when trained on shorter sequences, fail to generalize robustly to longer ones at test time. This raises the question of whether Transformer models are real reasoning engines, despite their impressive abilities in mathematical problem solving and code synthesis. In this paper, we offer a vanishing variance perspective on this issue. To the best of our knowledge, we are the first to demonstrate that even for today's frontier models, a longer sequence length results in a decrease in variance in the output of the multi-head attention modules. On the argmax retrieval and dictionary lookup tasks, our experiments show that applying layer normalization after the attention outputs leads to significantly better length generalization. Our analyses attribute this improvement to a reduction-though not a complete elimination-of the distribution shift caused by vanishing variance.