HEAT: Faster Fully Homomorphic Inference via Approximations-Weights Co-Adaptation

@misc{zirilli2026heatfasterfullyhomomorphic,
      title={HEAT: Faster Fully Homomorphic Inference via Approximations-Weights Co-Adaptation}, 
      author={Alessandro Zirilli and Davide Marincione and Evgenios M. Kornaropoulos and Giuseppe Ateniese and Emanuele Rodolà},
      year={2026},
      eprint={2609.01730},
      archivePrefix={arXiv},
      primaryClass={cs.CR},
      url={https://arxiv.org/abs/2609.01730}, 
}

Under fully homomorphic encryption every nonlinearity must be approximated iteratively, and each iteration spends multiplicative depth. More iterations buy precision but exhaust the budget faster and trigger more bootstraps, which dominate latency. Existing approaches fix these counts uniformly across the model, ignoring that each site has its own error tolerance. HEAT optimizes them directly against the task objective, with no architectural changes and no retraining from scratch.

HEAT is our fine-tuning method that makes the iteration counts of nonlinearity approximations learnable, letting weights and approximation co-adapt instead of being tuned in isolation. On encrypted GPT-2 decoding it cuts iterations by 3.1×, bootstraps by 1.6×, and end-to-end latency by 1.4×, while improving decode agreement over the calibrated baseline.

You can read the full paper on arXiv. At 🤗 this page you can find the fine-tuned checkpoint, while in the card below there is our codebase with detailed instructions to reproduce our experiments.