# Fiona: Accelerating FHE Inference with Packing-Aware Ternary Weights

arXiv: https://arxiv.org/abs/2609.35352 · HTML: https://mlsanity.com/paper/2609.35352/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 40 references that are in the map.
- First posted on arXiv 28 Sep 2026.

## Builds on (most cited first, 17 of 17)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [RoFormer: Enhanced Transformer with Rotary Position Embedding](https://mlsanity.com/paper/2104.09864/) (2021)
- [Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation](https://mlsanity.com/paper/1308.3432/) (2013)
- [Quantization and Training of Neural Networks for Efficient Integer-Arithmetic-Only Inference](https://mlsanity.com/paper/1712.05877/) (2017)
- [The Era of 1-bit LLMs: All Large Language Models are in 1.58 Bits](https://mlsanity.com/paper/2402.17764/) (2024)
- [BitNet: Scaling 1-bit Transformers for Large Language Models](https://mlsanity.com/paper/2310.11453/) (2023)
- [HeLayers: A Tile Tensors Framework for Large Neural Networks on Encrypted Data](https://mlsanity.com/paper/2011.01805/) (2020)
- [EVA: An Encrypted Vector Arithmetic Language and Compiler for Efficient Homomorphic Computation](https://mlsanity.com/paper/1912.11951/) (2019)
- [AutoFHE: Automated Adaption of CNNs for Efficient Evaluation over FHE](https://mlsanity.com/paper/2310.08012/) (2023)
- [Orion: A Fully Homomorphic Encryption Framework for Deep Learning](https://mlsanity.com/paper/2311.03470/) (2023)
- [PrivCirNet: Efficient Private Inference via Block Circulant Transformation](https://mlsanity.com/paper/2405.14569/) (2024)
- [HECO: Fully Homomorphic Encryption Compiler](https://mlsanity.com/paper/2202.01649/) (2022)
- [ENSI: Efficient Non-Interactive Secure Inference for Large Language Models](https://mlsanity.com/paper/2509.09424/) (2025)

## Abstract (arXiv)

Fully homomorphic encryption (FHE) enables neural network inference directly on encrypted inputs, but it remains orders of magnitude slower than plaintext in- ference. Applying the server's plaintext weights to encrypted activations involves plaintext-ciphertext multiplications (PMult) and accounts for more than half of inference time in recent systems. Ternary quantization can replace these multipli- cations with additions and subtractions, but the savings rarely materialize under packed execution. A single PMult applies a weight group fixed by the packing layout and can be avoided only when all its weights share the same ternary value. Ternarizing all groups, however, largely degrades accuracy. We present FIONA, an offline optimizer that selectively ternarizes weights within a given packing layout based on the estimated effect of ternary conversion on the model's performance. FIONA encourages a shared ternary value within each weight group and retains full-precision weights for sensitive groups, so ternar- ized and full-precision paths coexist within a layer. It then compiles these hybrid operators exactly, applying common scaling factors once to accumulated inputs and reusing sums across outputs. Weight ternarization can also narrow the input ranges of downstream polynomials. FIONA fits lower-degree replacements under a cumulative accuracy budget, reducing multiplicative depth and bootstrapping. On VGG11, ViT, and BERT, FIONA reduces PMult operations by 53.4-79.5% and accelerates end-to-end encrypted inference by 2.38x, 1.68x, and 1.84x, re- spectively, with less than 1% accuracy loss across all three models.