# All Roads Lead to Rome? Exploring the Invariance of Transformers' Representations

arXiv: https://arxiv.org/abs/2305.14555 · HTML: https://mlsanity.com/paper/2305.14555/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 40 references that are in the map.
- First posted on arXiv 23 May 2023.

## Builds on (most cited first, 29 of 29)

- [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)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [RoBERTa: A Robustly Optimized BERT Pretraining Approach](https://mlsanity.com/paper/1907.11692/) (2019)
- [GLUE: A Multi-Task Benchmark and Analysis Platform for Natural Language Understanding](https://mlsanity.com/paper/1804.07461/) (2018)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [Locating and Editing Factual Associations in GPT](https://mlsanity.com/paper/2202.05262/) (2022)
- [A Broad-Coverage Challenge Corpus for Sentence Understanding through Inference](https://mlsanity.com/paper/1704.05426/) (2017)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [BERT Rediscovers the Classical NLP Pipeline](https://mlsanity.com/paper/1905.05950/) (2019)
- [What Does BERT Look At? An Analysis of BERT's Attention](https://mlsanity.com/paper/1906.04341/) (2019)
- [A Primer in BERTology: What we know about how BERT works](https://mlsanity.com/paper/2002.12327/) (2020)
- [Designing and Interpreting Probes with Control Tasks](https://mlsanity.com/paper/1909.03368/) (2019)
- [Underspecification Presents Challenges for Credibility in Modern Machine Learning](https://mlsanity.com/paper/2011.03395/) (2020)
- [Git Re-Basin: Merging Models modulo Permutation Symmetries](https://mlsanity.com/paper/2209.04836/) (2022)
- [Fine-Tuning Pretrained Language Models: Weight Initializations, Data Orders, and Early Stopping](https://mlsanity.com/paper/2002.06305/) (2020)
- [Revealing the Dark Secrets of BERT](https://mlsanity.com/paper/1908.08593/) (2019)
- [Towards Causal Representation Learning](https://mlsanity.com/paper/2102.11107/) (2021)
- [Emerging Cross-lingual Structure in Pretrained Language Models](https://mlsanity.com/paper/1911.01464/) (2019)
- [What Happens To BERT Embeddings During Fine-tuning?](https://mlsanity.com/paper/2004.14448/) (2020)
- [The MultiBERTs: BERT Reproductions for Robustness Analysis](https://mlsanity.com/paper/2106.16163/) (2021)
- [Similarity and Matching of Neural Network Representations](https://mlsanity.com/paper/2110.14633/) (2021)
- [Counterfactual Interventions Reveal the Causal Effect of Relative Clause Representations on Agreement Prediction](https://mlsanity.com/paper/2105.06965/) (2021)
- [Probing for the Usage of Grammatical Number](https://mlsanity.com/paper/2204.08831/) (2022)
- [Are Larger Pretrained Language Models Uniformly Better? Comparing Performance at the Instance Level](https://mlsanity.com/paper/2105.06020/) (2021)
- [Quantifying the Contextualization of Word Representations with Semantic Class Probing](https://mlsanity.com/paper/2004.12198/) (2020)
- [Correlations between Word Vector Sets](https://mlsanity.com/paper/1910.02902/) (2019)

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

- [Merging Text Transformer Models from Different Initializations](https://mlsanity.com/paper/2403.00986/) (2024)
- [Understanding the Inner Workings of Language Models Through Representation Dissimilarity](https://mlsanity.com/paper/2310.14993/) (2023)
- [Exploring Dark Knowledge under Various Teacher Capacities and Addressing Capacity Mismatch](https://mlsanity.com/paper/2405.13078/) (2024)
- [On Affine Homotopy between Language Encoders](https://mlsanity.com/paper/2406.02329/) (2024)
- [From Embeddings to Equations: Genetic-Programming Surrogates for Interpretable Transformer Classification](https://mlsanity.com/paper/2509.21341/) (2025)
- [Structure Retention in Embedding Spaces as a Predictor of Benchmark Performance](https://mlsanity.com/paper/2605.22202/) (2026)

## Abstract (arXiv)

Transformer models bring propelling advances in various NLP tasks, thus inducing lots of interpretability research on the learned representations of the models. However, we raise a fundamental question regarding the reliability of the representations. Specifically, we investigate whether transformers learn essentially isomorphic representation spaces, or those that are sensitive to the random seeds in their pretraining process. In this work, we formulate the Bijection Hypothesis, which suggests the use of bijective methods to align different models' representation spaces. We propose a model based on invertible neural networks, BERT-INN, to learn the bijection more effectively than other existing bijective methods such as the canonical correlation analysis (CCA). We show the advantage of BERT-INN both theoretically and through extensive experiments, and apply it to align the reproduced BERT embeddings to draw insights that are meaningful to the interpretability research. Our code is at https://github.com/twinkle0331/BERT-similarity.