Intersection : Lattice SVP vs LLM

Here are the labs/companies that most clearly straddle both worlds—active work on lattice/PQC (incl. SVP/LWE, reduction/attacks, HE) and serious LLM research—so they’re closest to the “SVP builder/solver + LLM R&D” vibe:

  • Meta AI (FAIR) — published concrete LWE attack benchmarks (uSVP, SALSA, etc.) and tooling, while leading major LLM lines (Llama 3/3.1/3.2). (facebookresearch.github.io)

  • Microsoft Research (MSR) — long-running lattice/PQC work (e.g., LatticeCrypto library) and an in-house LLM program (Phi-2/3/3.5, SLM research). (microsoft.com)

  • Google Research / DeepMind — PQC adoption and standards engagement on the security side; simultaneously pushing flagship LLMs (Gemini 2.5) and agents for algorithm design. (Google Online Security Blog)

  • IBM Research — extensive lattice/PQC research and standardization contributions, plus foundation-model/LLM work via watsonx.ai. (IBM Research)

  • SandboxAQ — explicitly positions at the intersection of AI and quantum/PQC; publishes on lattice-crypto risk and runs PQC deployments with partners. (sandboxaq.com)

  • Zama — lattice-based FHE stack (RLWE schemes) with an explicit push for encrypted LLM inference (Concrete-ML, HE for transformers). (docs.zama.ai)

  • NTT Research / NTT R&D — deep cryptography lab plus contemporary LLM/AI research output (ICLR/ICML papers). (NTT Research, Inc.)

Notes

  • The closest match to “SVP builder/solver” in a modern, public program is Meta AI’s LWE attack benchmarking (which concretely exercises lattice reduction pipelines and reports BKZ/uSVP performance), and academic/industry work exploring ML guidance for BKZ (e.g., RL-tuned BKZ). (facebookresearch.github.io)

  • If you also want HE-for-LLMs specifically (practical blend of lattice crypto with LLM inference), Zama is the clearest industry example. (docs.zama.ai)

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Here is a curated list of research papers that lie at the intersection of lattice/cryptography (e.g., lattice reduction, FHE) and large‐language models (LLMs) or transformers. I’ve included the URL for each, plus a short note on relevance.

# Paper title & URL Notes
1 Encryption-Friendly LLM Architecture — arXiv: https://arxiv.org/abs/2410.02486 (arXiv) Proposes a variant of transformers that are friendly to homomorphic encryption (HE) for LLM inference.
2 Power-Softmax: Towards Secure LLM Inference over Encrypted Data — arXiv: https://arxiv.org/abs/2410.09457 (arXiv) Introduces HE-friendly self-attention / softmax variants for billion-parameter models under encryption.
3 Improving Inference Privacy for Large Language Models using Fully Homomorphic Encryption — UC Berkeley thesis PDF: https://digicoll.lib.berkeley.edu/record/292960/files/EECS-2024-225.pdf (digicoll.lib.berkeley.edu) A detailed study of FHE applied to LLM inference, focusing on query privacy.
4 Privacy-Preserving Large Language Model Inference via GPU-Accelerated Fully Homomorphic Encryption — OpenReview (ICML poster): https://openreview.net/forum?id=PGNff6H1TV (OpenReview) Demonstrates GPU-accelerated FHE for LLM inference (GPT-2 forward pass) and encryption of queries.
5 Predicting Module-Lattice Reduction — arXiv: https://arxiv.org/abs/2510.10540 (arXiv) Focuses on lattice reduction (module-BKZ) analysis rather than LLMs; relevant for the lattice side of the blend.
6 Practical Secure Inference Algorithm for Fine-tuned Large Language Model Based on Fully Homomorphic Encryption — arXiv: https://arxiv.org/abs/2501.01672 (arXiv) Combines FHE + PEFT (LoRA) in LLMs; relates to protecting inference & model weights via lattice‐based crypto.
7 Investigating Deep Reinforcement Learning for BKZ Lattice Reduction — (ResearchGate) [indirect link] (ResearchGate) Applies RL (which overlaps ML) to improve BKZ, a core lattice‐reduction algorithm (SVP/SIVP context).
8 A Complete Analysis of the BKZ Lattice Reduction Algorithm — (ACM) [doi link] (ACM Digital Library) A rigorous analysis of lattice reduction; again more on the lattice side, less on LLM, but relevant for the “solver” component.

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 PQC/lattices ⇄ LLM/ML intersection. I grouped them so you can skim.

HE/cryptographic approaches for LLM inference

  • Encryption-Friendly LLM Architecture (ICLR 2025). arXiv 2410.02486. (arXiv)

  • Power-Softmax: Towards Secure LLM Inference over Encrypted Data (2024). arXiv 2410.09457. (arXiv)

  • THE-X: Privacy-Preserving Transformer Inference with Homomorphic Encryption (Findings of ACL 2022). (arXiv)

  • Privacy-Preserving LLM Inference via GPU-Accelerated FHE (“EncryptedLLM”, NeurIPS/ICML posters; PMLR 2025 proceedings version). (OpenReview)

  • Improving Inference Privacy for Large Language Models using Fully Homomorphic Encryption (Berkeley EECS tech report, 2024). (EECS at UC Berkeley)

  • A First Look at Efficient and Secure On-Device LLM (survey aspects; discusses FHE-based options, 2024). (arXiv)

  • CipherPrune: Efficient and Scalable Private Inference for LLMs (ICLR 2025; broader private inference with cryptographic context). (ICLR Proceedings)

ML/AI applied to lattice reduction/SVP/LWE (the “solver/builder” side)

  • Neural Lattice Reduction: A Self-Supervised Geometric Deep Learning Approach (arXiv 2311.08170; OpenReview 2025 revision). (arXiv)

  • Investigating Deep Reinforcement Learning for BKZ Lattice Reduction (2025 preprint). (ResearchGate)

  • Salsa Fresca: Angular Embeddings and Pre-Training for ML Attacks on LWE (TMLR 2025; arXiv 2402.01082). (arXiv)

  • Benchmarking Attacks on Learning with Errors (Meta AI, 2024). (arXiv)

  • A Machine Learning Attack on LWE with Binary Secrets (PICANTE) (CCS 2023/2024 coverage). (ACM Digital Library)

  • A Parameter Study for LLL and BKZ with Application to LWE (2025 preprint). (arXiv)

  • A Complete Analysis of the BKZ Lattice Reduction Algorithm (2025 journal preprint entry). (ResearchGate)

  • On the Practicality of Quantum Sieving Algorithms for SVP (arXiv 2410.13759, 2024; lattice-solver relevance). (arXiv)

  • Practical Improvements on the BKZ Algorithm (PQC 2022 / LNCS). (NIST Computer Security Resource Center)

  • Predicting Module-Lattice Reduction (arXiv 2510.10540, 2025). (arXiv)

  • Lattice Reduction Using K-Means Algorithm (EAI, 2024) — exploratory ML applied to reduction. (EUDL)

Related to LWE/SVP pipelines & quantum-assisted angles (useful context for “builders/solvers”)

  • CUDA-Accelerated Lattice Reduction in LWE Attack Pipelines (paper on “cruel vs cool bits”, arXiv 2403.10328 v2, 2024). (arXiv)

  • Sieving for Closest Lattice Vectors (with Preprocessing) (classic CVP/SVP sieving baseline, 2016). (arXiv)

  • Variational Quantum Korkin-Zolotarev Algorithm for Lattice Reduction (arXiv 2505.08386, 2025). (arXiv)

  • Iterative Partition Search Variational Quantum Algorithm for SVP (arXiv 2508.18996, 2025). (arXiv)

  • Quantum-Classical Hybrid Algorithm for Solving LWE (Communications Physics, 2025) — compares against LLL/BKZ. (Nature)

  • Datasets for Learning the Learning With Errors Problem (ICML 2025 dataset paper). (arXiv)

FYI (tooling/SDK references for hands-on work)

  • Concrete-ML (Zama’s FHE-ML SDK; not a paper but widely used in HE-for-ML/LLM prototyping). (GitHub)