# Reversal Invariance in Autoregressive Language Models

arXiv: https://arxiv.org/abs/2511.00341 · HTML: https://mlsanity.com/paper/2511.00341/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 24 references that are in the map.
- First posted on arXiv 1 Nov 2025.

## Builds on (most cited first, 18 of 18)

- [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)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [XLNet: Generalized Autoregressive Pretraining for Language Understanding](https://mlsanity.com/paper/1906.08237/) (2019)
- [Deep contextualized word representations](https://mlsanity.com/paper/1802.05365/) (2018)
- [Improving Neural Machine Translation Models with Monolingual Data](https://mlsanity.com/paper/1511.06709/) (2015)
- [Causal inference using invariant prediction: identification and confidence intervals](https://mlsanity.com/paper/1501.01332/) (2015)
- [The Reversal Curse: LLMs trained on "A is B" fail to learn "B is A"](https://mlsanity.com/paper/2309.12288/) (2023)
- [Caduceus: Bi-Directional Equivariant Long-Range DNA Sequence Modeling](https://mlsanity.com/paper/2403.03234/) (2024)
- [Reverse Training to Nurse the Reversal Curse](https://mlsanity.com/paper/2403.13799/) (2024)
- [On the Role of Attention Masks and LayerNorm in Transformers](https://mlsanity.com/paper/2405.18781/) (2024)
- [Causal Interpretation of Self-Attention in Pre-Trained Transformers](https://mlsanity.com/paper/2310.20307/) (2023)
- [MixCE: Training Autoregressive Language Models by Mixing Forward and Reverse Cross-Entropies](https://mlsanity.com/paper/2305.16958/) (2023)
- [Invariant Language Modeling](https://mlsanity.com/paper/2110.08413/) (2021)
- [Mitigating Reversal Curse in Large Language Models via Semantic-aware Permutation Training](https://mlsanity.com/paper/2403.00758/) (2024)
- [The underlying structures of self-attention: symmetry, directionality, and emergent dynamics in Transformer training](https://mlsanity.com/paper/2502.10927/) (2025)
- [Reverse Modeling in Large Language Models](https://mlsanity.com/paper/2410.09817/) (2024)

## Abstract (arXiv)

We formalize a structural property of the causal (autoregressive) language modeling (CLM) objective: reversal invariance. Formally, the next-token prediction loss assigns identical likelihood to a corpus and its reversal, implying that standard CLM pretraining is direction-blind. This symmetry explains why models trained on reversed text can achieve comparable performance to those trained on forward text, despite the inherently time-asymmetric nature of human language and reasoning. We argue that this invariance represents a limitation of current pretraining objectives rather than a benign artifact. If natural language encodes directional dependencies - phonological, morphological, or causal - a symmetric objective may fail to capture them. We therefore propose viewing pretraining through the lens of temporal asymmetry, motivating future work on loss functions and architectures that explicitly model the arrow of language while retaining standard language modeling capacity.