Accurate Low-Degree Polynomial Approximation of Non-polynomial Operators for Fast Private Inference in Homomorphic Encryption
arxiv(2024)
摘要
As machine learning (ML) permeates fields like healthcare, facial
recognition, and blockchain, the need to protect sensitive data intensifies.
Fully Homomorphic Encryption (FHE) allows inference on encrypted data,
preserving the privacy of both data and the ML model. However, it slows down
non-secure inference by up to five magnitudes, with a root cause of replacing
non-polynomial operators (ReLU and MaxPooling) with high-degree Polynomial
Approximated Function (PAF). We propose SmartPAF, a framework to replace
non-polynomial operators with low-degree PAF and then recover the accuracy of
PAF-approximated model through four techniques: (1) Coefficient Tuning (CT) –
adjust PAF coefficients based on the input distributions before training, (2)
Progressive Approximation (PA) – progressively replace one non-polynomial
operator at a time followed by a fine-tuning, (3) Alternate Training (AT) –
alternate the training between PAFs and other linear operators in the decoupled
manner, and (4) Dynamic Scale (DS) / Static Scale (SS) – dynamically scale PAF
input value within (-1, 1) in training, and fix the scale as the running max
value in FHE deployment. The synergistic effect of CT, PA, AT, and DS/SS
enables SmartPAF to enhance the accuracy of the various models approximated by
PAFs with various low degrees under multiple datasets. For ResNet-18 under
ImageNet-1k, the Pareto-frontier spotted by SmartPAF in latency-accuracy
tradeoff space achieves 1.42x 13.64x accuracy improvement and 6.79x 14.9x
speedup than prior works. Further, SmartPAF enables a 14-degree PAF (f1^2
g_1^2) to achieve 7.81x speedup compared to the 27-degree PAF obtained by
minimax approximation with the same 69.4
is available at https://github.com/TorchFHE/SmartPAF.
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