Pure Leveled CKKS for CNN Inference: The Finite Limb Depth Bound and ResNet-20 Stress-Test

Mohamed Khattab, Lydia Bouzar-Benlabiod
Proceedings of the The 39th Canadian Conference on Artificial Intelligence, PMLR 318:1200-1203, 2026.

Abstract

This paper presents a systems-level boundary analysis of pure Leveled CKKS homomorphic encryption applied to deep CNN inference, using two algorithmic co-designs as probing mechanisms: (Singular Value Decomposition) SVD-based kernel decomposition and scale-1 integer quantization. We formalize the Finite Limb Depth Bound, showing that scale-1 quantization delays but cannot eliminate rescaling, as the accumulated bit- width is bounded by the RNS prime limb width. A TinyConvNet smoke test confirms pipeline correctness (max noise 2.25$\times$10-4). Stress-testing ResNet-20 under a maxi-mized 60-prime chain at N =65536 reveals that residual shortcut additions induce exact linear RNS level divergence dk = 3 + 7k, exhausting the prime budget at the predicted shortcut index k$*$=8 after 169,741 rotations and 555.7 s. Under the tested 95% SVD energy threshold, average rank 1.9 on 3$\times$3 kernels exceeded the K/2 crossover, producing a 30.7% Ct-Pt overhead. Under the tested parameter regime, algorithmic co-designs alone were insufficient to eliminate bootstrapping; we outline a bootstrap starvation direction that targets reduced bootstrap frequency rather than full elimination.

Cite this Paper

BibTeX
@InProceedings{pmlr-v318-khattab26a, title = {Pure Leveled CKKS for CNN Inference: The Finite Limb Depth Bound and ResNet-20 Stress-Test}, author = {Khattab, Mohamed and Bouzar-Benlabiod, Lydia}, booktitle = {Proceedings of the The 39th Canadian Conference on Artificial Intelligence}, pages = {1200--1203}, year = {2026}, editor = {Bouzar-Benlabiod, Lydia and Leung, Carson}, volume = {318}, series = {Proceedings of Machine Learning Research}, month = {25--29 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v318/main/assets/khattab26a/khattab26a.pdf}, url = {https://proceedings.mlr.press/v318/khattab26a.html}, abstract = {This paper presents a systems-level boundary analysis of pure Leveled CKKS homomorphic encryption applied to deep CNN inference, using two algorithmic co-designs as probing mechanisms: (Singular Value Decomposition) SVD-based kernel decomposition and scale-1 integer quantization. We formalize the Finite Limb Depth Bound, showing that scale-1 quantization delays but cannot eliminate rescaling, as the accumulated bit- width is bounded by the RNS prime limb width. A TinyConvNet smoke test confirms pipeline correctness (max noise 2.25$\times$10-4). Stress-testing ResNet-20 under a maxi-mized 60-prime chain at N =65536 reveals that residual shortcut additions induce exact linear RNS level divergence dk = 3 + 7k, exhausting the prime budget at the predicted shortcut index k$*$=8 after 169,741 rotations and 555.7 s. Under the tested 95% SVD energy threshold, average rank 1.9 on 3$\times$3 kernels exceeded the K/2 crossover, producing a 30.7% Ct-Pt overhead. Under the tested parameter regime, algorithmic co-designs alone were insufficient to eliminate bootstrapping; we outline a bootstrap starvation direction that targets reduced bootstrap frequency rather than full elimination.} }
Endnote
%0 Conference Paper %T Pure Leveled CKKS for CNN Inference: The Finite Limb Depth Bound and ResNet-20 Stress-Test %A Mohamed Khattab %A Lydia Bouzar-Benlabiod %B Proceedings of the The 39th Canadian Conference on Artificial Intelligence %C Proceedings of Machine Learning Research %D 2026 %E Lydia Bouzar-Benlabiod %E Carson Leung %F pmlr-v318-khattab26a %I PMLR %P 1200--1203 %U https://proceedings.mlr.press/v318/khattab26a.html %V 318 %X This paper presents a systems-level boundary analysis of pure Leveled CKKS homomorphic encryption applied to deep CNN inference, using two algorithmic co-designs as probing mechanisms: (Singular Value Decomposition) SVD-based kernel decomposition and scale-1 integer quantization. We formalize the Finite Limb Depth Bound, showing that scale-1 quantization delays but cannot eliminate rescaling, as the accumulated bit- width is bounded by the RNS prime limb width. A TinyConvNet smoke test confirms pipeline correctness (max noise 2.25$\times$10-4). Stress-testing ResNet-20 under a maxi-mized 60-prime chain at N =65536 reveals that residual shortcut additions induce exact linear RNS level divergence dk = 3 + 7k, exhausting the prime budget at the predicted shortcut index k$*$=8 after 169,741 rotations and 555.7 s. Under the tested 95% SVD energy threshold, average rank 1.9 on 3$\times$3 kernels exceeded the K/2 crossover, producing a 30.7% Ct-Pt overhead. Under the tested parameter regime, algorithmic co-designs alone were insufficient to eliminate bootstrapping; we outline a bootstrap starvation direction that targets reduced bootstrap frequency rather than full elimination.
APA
Khattab, M. & Bouzar-Benlabiod, L.. (2026). Pure Leveled CKKS for CNN Inference: The Finite Limb Depth Bound and ResNet-20 Stress-Test. Proceedings of the The 39th Canadian Conference on Artificial Intelligence, in Proceedings of Machine Learning Research 318:1200-1203 Available from https://proceedings.mlr.press/v318/khattab26a.html.

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