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preprint · arXiv (Cornell University) · 2026

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

A. Zirilli, Davide Marincione, Evgenios M. Kornaropoulos, Giuseppe Ateniese, Emanuele Rodolà

Cited by 1Open access

Abstract

Fully homomorphic encryption (FHE) allows a server to run a language model directly on encrypted user prompts, but current approaches remain prohibitively slow. Ciphertexts natively support only addition, multiplication, and rotation, and multiplications may be composed only to a bounded depth before a costly bootstrapping operation is required to continue. Every nonlinearity must therefore be approximated by an iterative method; each iteration increasing the number of multiplications. A higher iteration count buys precision but exhausts the available depth more frequently and thus triggers more bootstraps, which dominate latency. We introduce Homomorphic Encryption-Aware Training (HEAT), a fine-tuning method that makes the per-nonlinearity iteration counts learnable, enabling them and the model weights to co-adapt during training. HEAT optimizes iterations with respect to the task objective, allowing the model to adapt to approximation errors encountered during inference without architectural changes or retraining from scratch. We further relate iteration count to quantization bit width and bound, at fixed weights, the gap between our objective and quantization-aware training. On encrypted GPT-2 decoding, HEAT reduces iterations by $3.1\times$, bootstraps by $1.6\times$, and end-to-end latency by $1.4\times$, while improving decode agreement over the calibrated encrypted baseline.

Cite this paper

APA 7

Zirilli, A., Marincione, D., Kornaropoulos, E. M., Ateniese, G., & Rodolà, E. (2026). HEAT: Faster Fully Homomorphic Inference via Approximations-Weights Co-Adaptation. arXiv (Cornell University). https://doi.org/10.48550/arxiv.2609.01730

MLA 9

Zirilli, A., et al. “HEAT: Faster Fully Homomorphic Inference via Approximations-Weights Co-Adaptation.” arXiv (Cornell University), 2026, https://doi.org/10.48550/arxiv.2609.01730.

Chicago

Zirilli, A., Davide Marincione, Evgenios M. Kornaropoulos, Giuseppe Ateniese, and Emanuele Rodolà. 2026. “HEAT: Faster Fully Homomorphic Inference via Approximations-Weights Co-Adaptation.” arXiv (Cornell University). https://doi.org/10.48550/arxiv.2609.01730.

Harvard

Zirilli, A. et al. (2026) ‘HEAT: Faster Fully Homomorphic Inference via Approximations-Weights Co-Adaptation’, arXiv (Cornell University). Available at: https://doi.org/10.48550/arxiv.2609.01730.

BibTeX
@misc{zirilli2026heat,
  title = {{HEAT: Faster Fully Homomorphic Inference via Approximations-Weights Co-Adaptation}},
  author = {Zirilli, A. and Marincione, Davide and Kornaropoulos, Evgenios M. and Ateniese, Giuseppe and Rodolà, Emanuele},
  journal = {arXiv (Cornell University)},
  year = {2026},
  doi = {10.48550/arxiv.2609.01730}
}

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