Efficient Decoding Methods for Language Models on Encrypted Data

Large language models (LLMs) power modern AI applications, but processing sensitive data on untrusted servers raises privacy concerns. Homomorphic encryption (HE) enables computation on encrypted data for secure inference. However, neural text generation requires decoding methods like argmax and sampling, which are non-polynomial and thus computationally expensive under encryption, creating a significant performance bottleneck. We introduce cutmax, an HE-friendly argmax algorithm that reduces ciphertext operations compared to prior methods, enabling practical greedy decoding under encryption. We also propose the first HE-compatible nucleus (top-p) sampling method, leveraging cutmax for efficient stochastic decoding with provable privacy guarantees. Both techniques are polynomial, supporting efficient inference in privacy-preserving settings. Moreover, their differentiability facilitates gradient-based sequence-level optimization as a polynomial alternative to straight-through estimators. We further provide strong theoretical guarantees for cutmax, proving it converges globally to a unique two-level fixed point, independent of the input values beyond the identity of the maximizer, which explains its rapid convergence in just a few iterations. Evaluations on realistic LLM outputs show latency reductions of 24x-35x over baselines, advancing secure text generation.

Power-Softmax: Towards Secure LLM Inference over Encrypted Data

Modern cryptographic methods for implementing privacy-preserving LLMs such as Homomorphic Encryption (HE) require the LLMs to have a polynomial form. Forming such a representation is challenging because Transformers include non-polynomial components, such as Softmax and layer normalization. Previous approaches have either directly approximated pre-trained models with large-degree polynomials, which are less efficient over HE, or replaced non-polynomial components with easier-to-approximate primitives before training, e.g., Softmax with pointwise attention. The latter approach might introduce scalability challenges. We present a new HE-friendly variant of self-attention that offers a stable form for training and is easy to approximate with polynomials for secure inference. Our work introduces the first polynomial LLMs with 32 layers and over a billion parameters, exceeding the size of previous models by more than tenfold. The resulting models demonstrate reasoning and in-context learning (ICL) capabilities comparable to standard transformers of the same size, representing a breakthrough in the field. Finally, we provide a detailed latency breakdown for each computation over encrypted data, paving the way for further optimization, and explore the differences in inductive bias between transformers relying on our HE-friendly variant and standard transformers. Our code is attached as a supplement.

What Changed? Converting Representational Interventions to Natural Language

Interventions targeting the representation space of language models (LMs) have emerged as effective means to influence model behavior. These methods are employed, for example, to eliminate or alter the encoding of demographic information such as gender within the model's representations, creating a counterfactual representation. However, since the intervention operates within the representation space, understanding precisely which features it modifies poses a challenge. We show that representation-space counterfactuals can be converted into natural language counterfactuals. We demonstrate that this approach enables us to analyze the linguistic alterations corresponding to a given representation-space intervention and to interpret the features utilized for encoding a specific concept. Moreover, the resulting counterfactuals can be used to mitigate bias in classification.