# Optimistic Verifiable Training by Controlling Hardware Nondeterminism

arXiv: https://arxiv.org/abs/2403.09603 · HTML: https://mlsanity.com/paper/2403.09603/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Placed in Prompt injection and agent security, one of 12 directions in LLM safety and security.
- Builds on 15 of its 43 references that are in the map.
- First posted on arXiv 14 Mar 2024.

## Placed in

- LLM safety and security / [Prompt injection and agent security](https://mlsanity.com/safety/prompt-injection-and-agent-security/)

## Builds on (most cited first, 15 of 15)

- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Sleeper Agents: Training Deceptive LLMs that Persist Through Safety Training](https://mlsanity.com/paper/2401.05566/) (2024)
- [Poisoning Language Models During Instruction Tuning](https://mlsanity.com/paper/2305.00944/) (2023)
- [On the Necessity of Auditable Algorithmic Definitions for Machine Unlearning](https://mlsanity.com/paper/2110.11891/) (2021)
- [Compute Trends Across Three Eras of Machine Learning](https://mlsanity.com/paper/2202.05924/) (2022)
- [Stronger Data Poisoning Attacks Break Data Sanitization Defenses](https://mlsanity.com/paper/1811.00741/) (2018)
- [Proof-of-Learning: Definitions and Practice](https://mlsanity.com/paper/2103.05633/) (2021)
- [Randomness In Neural Network Training: Characterizing The Impact of Tooling](https://mlsanity.com/paper/2106.11872/) (2021)
- [An Empirical Analysis of Backward Compatibility in Machine Learning Systems](https://mlsanity.com/paper/2008.04572/) (2020)
- [Scaling up Trustless DNN Inference with Zero-Knowledge Proofs](https://mlsanity.com/paper/2210.08674/) (2022)
- [Tools for Verifying Neural Models' Training Data](https://mlsanity.com/paper/2307.00682/) (2023)
- [A scalable verification solution for blockchains](https://mlsanity.com/paper/1908.04756/) (2019)
- [A Survey of Published Attacks on Intel SGX](https://mlsanity.com/paper/2006.13598/) (2020)
- [Dissecting Tensor Cores via Microbenchmarks: Latency, Throughput and Numeric Behaviors](https://mlsanity.com/paper/2206.02874/) (2022)
- [Can Membership Inferencing be Refuted?](https://mlsanity.com/paper/2303.03648/) (2023)

## Built on by (most cited first, 7 of 7)

- [SoK: Blockchain-Based Decentralized AI (DeAI)](https://mlsanity.com/paper/2411.17461/) (2024)
- [Hawkeye: Reproducing GPU-Level Non-Determinism](https://mlsanity.com/paper/2603.20421/) (2026)
- [TAO: Tolerance-Aware Optimistic Verification for Floating-Point Neural Networks](https://mlsanity.com/paper/2510.16028/) (2025)
- [Trust, but Verify: Peeling Low-Bit Transformer Networks for Training Monitoring](https://mlsanity.com/paper/2605.02853/) (2026)
- [OPEN-1B: A Fully Auditable Training Run](https://mlsanity.com/paper/2609.17380/) (2026)
- [OVIG: Optimistic Verification of AI Training Integrity via Gradient Signals](https://mlsanity.com/paper/2606.21045/) (2026)
- [OPFL: Optimistic Verification of Federated Learning via Empirical Boundary](https://mlsanity.com/paper/2609.37011/) (2026)

## Abstract (arXiv)

The increasing compute demands of AI systems have led to the emergence of services that train models on behalf of clients lacking necessary resources. However, ensuring correctness of training and guarding against potential training-time attacks, such as data poisoning and backdoors, poses challenges. Existing works on verifiable training largely fall into two classes: proof-based systems, which are difficult to scale, and ``optimistic'' methods that consider a third-party auditor who can replicate the training process and contest the trainer. A key challenge with the latter is that nondeterminism between GPU types during training prevents exact replication of the training process, resulting in schemes that are non-robust. We propose a method that combines training in a higher precision than the target, rounding after intermediate computations, and sharing rounding decisions based on an adaptive thresholding procedure, to successfully control for nondeterminism. Across three different NVIDIA GPUs (A40, Titan XP, RTX 2080 Ti), we achieve exact training replication at FP32 precision for both full-training and fine-tuning of ResNet-50 (23M) and GPT-2 (117M) models. Our verifiable training scheme significantly decreases the storage and time costs compared to proof-based systems, and is publicly released at https://github.com/meghabyte/verifiable-training.