# Learning Perturbations to Extrapolate Your LLM

arXiv: https://arxiv.org/abs/2605.13284 · HTML: https://mlsanity.com/paper/2605.13284/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 39 of its 57 references that are in the map.
- First posted on arXiv 13 May 2026.

## Builds on (most cited first, 30 of 39)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
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- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [OPT: Open Pre-trained Transformer Language Models](https://mlsanity.com/paper/2205.01068/) (2022)
- [Pointer Sentinel Mixture Models](https://mlsanity.com/paper/1609.07843/) (2016)
- [Hierarchical Neural Story Generation](https://mlsanity.com/paper/1805.04833/) (2018)
- [OpenAI GPT-5 System Card](https://mlsanity.com/paper/2601.03267/) (2025)
- [EDA: Easy Data Augmentation Techniques for Boosting Performance on Text Classification Tasks](https://mlsanity.com/paper/1901.11196/) (2019)
- [Discrete Diffusion Modeling by Estimating the Ratios of the Data Distribution](https://mlsanity.com/paper/2310.16834/) (2023)
- [A Systematic Evaluation of Large Language Models of Code](https://mlsanity.com/paper/2202.13169/) (2022)
- [Adversarial Example Generation with Syntactically Controlled Paraphrase Networks](https://mlsanity.com/paper/1804.06059/) (2018)
- [FreeLB: Enhanced Adversarial Training for Natural Language Understanding](https://mlsanity.com/paper/1909.11764/) (2019)
- [Combating Adversarial Misspellings with Robust Word Recognition](https://mlsanity.com/paper/1905.11268/) (2019)
- [Is MAP Decoding All You Need? The Inadequacy of the Mode in Neural Machine Translation](https://mlsanity.com/paper/2005.10283/) (2020)
- [NEFTune: Noisy Embeddings Improve Instruction Finetuning](https://mlsanity.com/paper/2310.05914/) (2023)
- [Noise Contrastive Alignment of Language Models with Explicit Rewards](https://mlsanity.com/paper/2402.05369/) (2024)
- [On the Algorithmic Bias of Aligning Large Language Models with RLHF: Preference Collapse and Matching Regularization](https://mlsanity.com/paper/2405.16455/) (2024)
- [GenAug: Data Augmentation for Finetuning Text Generators](https://mlsanity.com/paper/2010.01794/) (2020)
- [GermanQuAD and GermanDPR: Improving Non-English Question Answering and Passage Retrieval](https://mlsanity.com/paper/2104.12741/) (2021)
- [MAUVE Scores for Generative Models: Theory and Practice](https://mlsanity.com/paper/2212.14578/) (2022)
- [Tailoring Language Generation Models under Total Variation Distance](https://mlsanity.com/paper/2302.13344/) (2023)
- [Demystifying Group Relative Policy Optimization: Its Policy Gradient is a U-Statistic](https://mlsanity.com/paper/2603.01162/) (2026)
- [Dual Active Learning for Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2410.02504/) (2024)
- [Keep Calm and Switch On! Preserving Sentiment and Fluency in Semantic Text Exchange](https://mlsanity.com/paper/1909.00088/) (2019)
- [Empowering Large Language Models for Textual Data Augmentation](https://mlsanity.com/paper/2404.17642/) (2024)
- [MixCE: Training Autoregressive Language Models by Mixing Forward and Reverse Cross-Entropies](https://mlsanity.com/paper/2305.16958/) (2023)
- [Doubly Robust Alignment for Large Language Models](https://mlsanity.com/paper/2506.01183/) (2025)

## Abstract (arXiv)

Recent advancements in large language models demonstrate that injecting perturbations can substantially enhance extrapolation performance. However, current approaches often rely on discrete perturbations with fixed designs, which limits their flexibility. In this work, we propose a framework where token prefixes are perturbed by a learnable transformation of a continuous latent vector within an embedding space. To overcome the challenge of an intractable marginal likelihood, we derive unbiased estimating equations for model parameters and optimize them via stochastic gradient descent. We establish the statistical properties of the resulting estimator in over-parameterized regimes. Empirical evaluations on both synthetic and real-world datasets demonstrate that our proposal yields significant gains in out-of-domain settings over a range of state-of-the-art baseline methods.