# Public-Decay Homomorphic State Space Models for Private Sequence Inference

arXiv: https://arxiv.org/abs/2605.16647 · HTML: https://mlsanity.com/paper/2605.16647/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 13 references that are in the map.
- First posted on arXiv 15 May 2026.

## Builds on (most cited first, 9 of 9)

- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [Transformers are SSMs: Generalized Models and Efficient Algorithms Through Structured State Space Duality](https://mlsanity.com/paper/2405.21060/) (2024)
- [Simplified State Space Layers for Sequence Modeling](https://mlsanity.com/paper/2208.04933/) (2022)
- [Diagonal State Spaces are as Effective as Structured State Spaces](https://mlsanity.com/paper/2203.14343/) (2022)
- [THE-X: Privacy-Preserving Transformer Inference with Homomorphic Encryption](https://mlsanity.com/paper/2206.00216/) (2022)
- [Cachemir: Fully Homomorphic Encrypted Inference of Generative Large Language Model with KV Cache](https://mlsanity.com/paper/2602.11470/) (2026)
- [Inhibitor Transformers and Gated RNNs for Torus Efficient Fully Homomorphic Encryption](https://mlsanity.com/paper/2308.05629/) (2023)
- [AEGIS: Scaling Long-Sequence Homomorphic Encrypted Transformer Inference via Hybrid Parallelism on Multi-GPU Systems](https://mlsanity.com/paper/2604.03425/) (2026)

## Abstract (arXiv)

Fully homomorphic encryption (FHE) changes sequence-model design because rotations, encrypted products, ciphertext materialization, multiplicative depth, and bootstrapping pressure can dominate ordinary neural-network costs. This paper presents public-decay homomorphic state space models (HSSMs), recurrent/state-space blocks whose carried state is updated through ciphertext-plaintext public decay while ciphertext-ciphertext multiplication remains on a local write path. The design keeps a fixed encrypted state across the sequence. The evaluated workflow separates client-side tokenization, frozen fastText lookup, projection, clipping, encryption, decryption, and thresholding from server-side encrypted evaluation over bounded projected features. On full Rotten Tomatoes and SST-2 validation splits, the encrypted HSSM path exactly matches plaintext classifications and reaches 0.7505 and 0.7420 accuracy. Against HE-friendly polynomial attention on the same fastText workloads, HSSM matches or exceeds full-sequence task quality while running about 5x faster. Paired L40S operation-level rows show 1.34-1.62x lower latency than cached final-token polynomial attention, 30-258x lower latency than full-sequence polynomial attention, and lower logical encrypted-state footprint. A T = 16/32 comparator with encrypted public-linear input and Q/K/V projections shows projected HSSM succeeding under depth 8/ring 32768, while projected attention succeeds under depth 10/ring 65536. A matched T = 8 OpenFHE/FIDESlib trace finishes at final level 3 and noise-scale degree 2 on both backends. These results make public-decay carry a practical FHE co-design lever for encrypted sequence inference from bounded projected features.