FPTQuant: Function-Preserving Transforms for LLM Quantization
Authors: Boris van Breugel, Yelysei Bondarenko, Paul Whatmough, Markus Nagel
Organizations: Qualcomm AI Research, Amsterdam, Netherlands
Abstract
Large language models (LLMs) require substantial compute, and thus energy, at inference time. While quantizing weights and activations is effective at improving efficiency, naive quantization of LLMs can significantly degrade performance due to large magnitude outliers. This paper describes FPTQuant, which introduces three novel, lightweight, and expressive function-preserving transforms (FPTs) to facilitate quantization of transformers: (1) a mergeable pre-RoPE transform for queries and keys, (2) a mergeable transform for values, and (3) a cheap, dynamic per-token scaling transform. By leveraging the equivariances and independencies inherent to canonical transformer operation, we designed these FPTs to maintain the model's function while shaping the intermediate activation distributions to be more quantization friendly. FPTQuant requires no custom kernels and adds virtually no overhead during inference. The FPTs are trained both locally to reduce outliers, and end-to-end such that the outputs of the quantized and full-precision models match. FPTQuant enables static INT4 quantization with minimal overhead and shows SOTA speed-up of up to 3.9X over FP. Empirically, FPTQuant has an excellent accuracy-speed trade-off -- it is performing on par or exceeding most prior work and only shows slightly lower accuracy compared to a method that is up to 29% slower.
We revisit Kashin-decomposition-based weight quantization for large language models and propose an improved algorithm with stronger convergence properties and structured, efficient orthogonal transforms. The method retains the core factorization of each weight into two components -- one with bounded infinity norm and the other with bounded infinity norm after an orthogonal transformation -- but replaces the dense random orthogonal matrix with a sign-randomized Discrete Cosine Transform (DCT), reducing the per-iteration cost from O(N2) to O(NlogN). The proposed greedy algorithm with alternating updates guarantees the four-peak distribution required for stable 2-bit clustering of each factor and admits closed-form initialization of cluster centers, removing the multi-restart k-means bottleneck of prior work. Composed with OPTQ-style sequential error compensation and QuIP-style incoherence preprocessing, the resulting JAX pipeline is competitive with OPTQ, QuIP, QuIP-RG and a fine-tuning- and vector-quantization-free variant of QuIP# at 4-bit per channel on OPT, Llama-2 and Pythia, with favorable wall-clock scaling. The bounded-ℓ∞ factorization is also notably robust: on stress configurations where QuIP variants diverge to four-digit perplexity (Pythia-6.9B) or abort with NaNs in LDL back-substitution (Mistral-7B), Kashin-DCT remains numerically stable and stays close to FP16 baseline. At inference time, each weight decomposes into two 2-bit factor codes per channel that are structurally suited to native-2-bit hardware.
Daria Cherniuk, Alexander Rudikov, Boris Kashin +1
Post-training quantization (PTQ) is one of the most practical ways to reduce the serving cost of Large Language Models (LLMs), but activation quantization remains difficult because outlier-dominated channels lead to large quantization errors. This paper investigates whether part of this degradation is caused by over-migration in scaling-based equivalent transformations. We introduce a quantile-robust scaling policy for SmoothRot-style transforms by replacing max-based activation statistics with high quantiles, and we complement it with constrained gradient-based optimization of channel scales. On LLaMA-3.2-1B under W4A4 quantization, quantile-only policy search improves selected-layer error by 11.1% over the SmoothRot baseline, joint (alpha, q) search improves it by 12%, and training reaches 18.5%. Replaying the best selected-layer policy on all decoder-block down-projection layers reduces the corresponding full-layer mean error from 97.51 to 78.08 (19.9%). The results show that robust migration control and lightweight scale learning provide consistent gains over max-based fixed policies while preserving the equivalent-transform framework.
Low-bit activation quantization remains a major bottleneck in efficient large language model (LLM) deployment. The difficulty is not only that activations contain outliers, but that their distributions are often poorly matched to a low-bit uniform quantizer. Existing post-training quantization (PTQ) methods suppress peaks, balance channels, or minimize reconstruction error, yet they rarely specify what activation distribution is actually easy to discretize. As a result, activations may appear numerically smoother while still incurring large quantization error because the quantization range remains wide or most values collapse into a few levels near the mean. We recast activation transformation as quantizer-facing distribution design and analyze quantization error from an information-theoretic perspective. Our analysis shows that quantization-friendly activations should jointly have a smaller numerical range and sufficient dispersion within that range. Guided by this analysis, we propose InfoQuant, a train-free method that employs Peak Suppression Orthogonal Transformation (PSOT) to shape activations into more quantization-friendly distributions. We further introduce adaptive outlier-token selection to improve the robustness of PSOT during optimization. Across multiple LLM families, InfoQuant consistently outperforms prior PTQ and end-to-end training baselines. Under W4A4KV4, it preserves 97% of floating-point accuracy on average and reduces the LLaMA-2 13B performance gap by 42% over the previous state of the art. Code is available at https://github.com/LLIKKE/InfoQuant