# Weight Tying Biases Token Embeddings Towards the Output Space

arXiv: https://arxiv.org/abs/2603.26663 · HTML: https://mlsanity.com/paper/2603.26663/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 51 references that are in the map.
- First posted on arXiv 27 Mar 2026.

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

- [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)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [HellaSwag: Can a Machine Really Finish Your Sentence?](https://mlsanity.com/paper/1905.07830/) (2019)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [PIQA: Reasoning about Physical Commonsense in Natural Language](https://mlsanity.com/paper/1911.11641/) (2019)
- [The Pile: An 800GB Dataset of Diverse Text for Language Modeling](https://mlsanity.com/paper/2101.00027/) (2020)
- [BoolQ: Exploring the Surprising Difficulty of Natural Yes/No Questions](https://mlsanity.com/paper/1905.10044/) (2019)
- [Can a Suit of Armor Conduct Electricity? A New Dataset for Open Book Question Answering](https://mlsanity.com/paper/1809.02789/) (2018)
- [How Contextual are Contextualized Word Representations? Comparing the Geometry of BERT, ELMo, and GPT-2 Embeddings](https://mlsanity.com/paper/1909.00512/) (2019)
- [XTREME: A Massively Multilingual Multi-task Benchmark for Evaluating Cross-lingual Generalization](https://mlsanity.com/paper/2003.11080/) (2020)
- [Eliciting Latent Predictions from Transformers with the Tuned Lens](https://mlsanity.com/paper/2303.08112/) (2023)
- [BLiMP: The Benchmark of Linguistic Minimal Pairs for English](https://mlsanity.com/paper/1912.00582/) (2019)
- [Dolma: an Open Corpus of Three Trillion Tokens for Language Model Pretraining Research](https://mlsanity.com/paper/2402.00159/) (2024)
- [Using the Output Embedding to Improve Language Models](https://mlsanity.com/paper/1608.05859/) (2016)
- [Representation Degeneration Problem in Training Natural Language Generation Models](https://mlsanity.com/paper/1907.12009/) (2019)
- [Exploiting Similarities among Languages for Machine Translation](https://mlsanity.com/paper/1309.4168/) (2013)
- [Emerging Cross-lingual Structure in Pretrained Language Models](https://mlsanity.com/paper/1911.01464/) (2019)
- [Towards a Cleaner Document-Oriented Multilingual Crawled Corpus](https://mlsanity.com/paper/2201.06642/) (2022)
- [Rethinking embedding coupling in pre-trained language models](https://mlsanity.com/paper/2010.12821/) (2020)
- [Tying Word Vectors and Word Classifiers: A Loss Framework for Language Modeling](https://mlsanity.com/paper/1611.01462/) (2016)
- [Improving Neural Language Modeling via Adversarial Training](https://mlsanity.com/paper/1906.03805/) (2019)
- [An Isotropy Analysis in the Multilingual BERT Embedding Space](https://mlsanity.com/paper/2110.04504/) (2021)
- [Comparing Foundation Models using Data Kernels](https://mlsanity.com/paper/2305.05126/) (2023)
- [Better Embeddings with Coupled Adam](https://mlsanity.com/paper/2502.08441/) (2025)

## Built on by (most cited first, 3 of 3)

- [Kronecker Embeddings: Byte-Level Structured Token Representations for Parameter-Efficient Language Models](https://mlsanity.com/paper/2605.29459/) (2026)
- [Reading Without a Reader: Large Language Models Collapse Reading and Writing into a Single Entangled Code](https://mlsanity.com/paper/2607.24797/) (2026)
- [Tracing Morphology, Semantics, and Divergence in Language Acquisition](https://mlsanity.com/paper/2610.19041/) (2026)

## Abstract (arXiv)

Weight tying, i.e. sharing parameters between input and output embedding matrices, is common practice in language model design, yet its impact on the learned embedding space remains poorly understood. In this paper, we show that tied embedding matrices align more closely with output (unembedding) matrices than with input embeddings of comparable untied models, indicating that the shared matrix is shaped primarily for output prediction rather than input representation. This unembedding bias arises because output gradients dominate early in training. Using tuned lens analysis, we show this negatively affects early-layer computations, which contribute less effectively to the residual stream. Scaling input gradients during training reduces this bias, providing causal evidence for the role of gradient imbalance. This is mechanistic evidence that weight tying optimizes the embedding matrix for output prediction, compromising its role in input representation. These results help explain why weight tying can harm performance at scale and have implications for training smaller LLMs, where the embedding matrix contributes substantially to total parameter count.