# Tuning without Peeking: Provable Generalization Bounds and Robust LLM Post-Training

arXiv: https://arxiv.org/abs/2507.01752 · HTML: https://mlsanity.com/paper/2507.01752/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Backdoor and data poisoning attacks, one of 12 directions in LLM safety and security.
- Builds on 80 of its 144 references that are in the map.
- First posted on arXiv 2 Jul 2025.

## Placed in

- LLM safety and security / [Backdoor and data poisoning attacks](https://mlsanity.com/safety/backdoor-and-data-poisoning-attacks/)

## Builds on (most cited first, 30 of 80)

- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [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)
- [Deep reinforcement learning from human preferences](https://mlsanity.com/paper/1706.03741/) (2017)
- [Deep Learning with Differential Privacy](https://mlsanity.com/paper/1607.00133/) (2016)
- [Emergent Abilities of Large Language Models](https://mlsanity.com/paper/2206.07682/) (2022)
- [Extracting Training Data from Large Language Models](https://mlsanity.com/paper/2012.07805/) (2020)
- [Targeted Backdoor Attacks on Deep Learning Systems Using Data Poisoning](https://mlsanity.com/paper/1712.05526/) (2017)
- [Deep Leakage from Gradients](https://mlsanity.com/paper/1906.08935/) (2019)
- [Are NLP Models really able to Solve Simple Math Word Problems?](https://mlsanity.com/paper/2103.07191/) (2021)
- [Membership Inference Attacks From First Principles](https://mlsanity.com/paper/2112.03570/) (2021)
- [Evolution Strategies as a Scalable Alternative to Reinforcement Learning](https://mlsanity.com/paper/1703.03864/) (2017)
- [How Johnny Can Persuade LLMs to Jailbreak Them: Rethinking Persuasion to Challenge AI Safety by Humanizing LLMs](https://mlsanity.com/paper/2401.06373/) (2024)
- [Textbooks Are All You Need II: phi-1.5 technical report](https://mlsanity.com/paper/2309.05463/) (2023)
- [GSM-Symbolic: Understanding the Limitations of Mathematical Reasoning in Large Language Models](https://mlsanity.com/paper/2410.05229/) (2024)
- [Safety Alignment Should Be Made More Than Just a Few Tokens Deep](https://mlsanity.com/paper/2406.05946/) (2024)
- [Catastrophic Jailbreak of Open-source LLMs via Exploiting Generation](https://mlsanity.com/paper/2310.06987/) (2023)
- [Differentially Private Fine-tuning of Language Models](https://mlsanity.com/paper/2110.06500/) (2021)
- [Complexity-Based Prompting for Multi-Step Reasoning](https://mlsanity.com/paper/2210.00720/) (2022)
- [The CMA Evolution Strategy: A Tutorial](https://mlsanity.com/paper/1604.00772/) (2016)
- [Semi-supervised Knowledge Transfer for Deep Learning from Private Training Data](https://mlsanity.com/paper/1610.05755/) (2016)
- [Deep Models Under the GAN: Information Leakage from Collaborative Deep Learning](https://mlsanity.com/paper/1702.07464/) (2017)
- [Certified Defenses for Data Poisoning Attacks](https://mlsanity.com/paper/1706.03691/) (2017)

## Built on by (most cited first, 1 of 1)

- [Certification Frontiers for Gaussian LoRA: Independent Priors, Posterior Risk, and Prediction-Preserving Balancing](https://mlsanity.com/paper/2609.32271/) (2026)

## Abstract (arXiv)

Gradient-based optimization is the workhorse of deep learning, offering efficient and scalable training via backpropagation. However, exposing gradients during training can leak sensitive information about the underlying data, raising privacy and security concerns such as susceptibility to data poisoning attacks. In contrast, black-box optimization methods, which treat the model as an opaque function, relying solely on function evaluations to guide optimization, offer a promising alternative in scenarios where data access is restricted, adversarial risks are high, or overfitting is a concern. This paper introduces BBoxER, an evolutionary black-box method for LLM post-training that induces an information bottleneck via implicit compression of the training data. Leveraging the tractability of information flow, we provide non-vacuous generalization bounds and strong theoretical guarantees for robustness to data poisoning attacks and extraction attacks, while ensuring privacy by design. In experiments with LLMs, we demonstrate empirically that black-box optimization methods-despite the scalability and computational challenges inherent to black-box approaches-are able to learn, showing how a few iterations of BBoxER improve performance, generalize well on a benchmark of reasoning datasets, and are robust to membership inference attacks. This positions BBoxER as an attractive add-on on top of gradient-based optimization, offering suitability for deployment in restricted environments while also providing non-vacuous generalization guarantees.