# ApexQuant: Data-Free Elastic Quantization by Residual Re-Isotropization

arXiv: https://arxiv.org/abs/2610.07904 · HTML: https://mlsanity.com/paper/2610.07904/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 48 references that are in the map.
- First posted on arXiv 6 Oct 2026.

## Builds on (most cited first, 12 of 12)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [Mistral 7B](https://mlsanity.com/paper/2310.06825/) (2023)
- [Gemma 3 Technical Report](https://mlsanity.com/paper/2503.19786/) (2025)
- [TinyLlama: An Open-Source Small Language Model](https://mlsanity.com/paper/2401.02385/) (2024)
- [Textbooks Are All You Need II: phi-1.5 technical report](https://mlsanity.com/paper/2309.05463/) (2023)
- [SpinQuant: LLM quantization with learned rotations](https://mlsanity.com/paper/2405.16406/) (2024)
- [TurboQuant: Online Vector Quantization with Near-optimal Distortion Rate](https://mlsanity.com/paper/2504.19874/) (2025)
- [MoBiQuant: Mixture-of-Bits Quantization for Token-Adaptive Any-Precision LLM](https://mlsanity.com/paper/2602.20191/) (2026)
- [Multi-Bitwidth Quantization for LLMs Using Additive Codebooks](https://mlsanity.com/paper/2606.12876/) (2026)

## Abstract (arXiv)

We introduce ApexQuant, a calibration-free quantization method that recursively re-quantizes the residual error, serving as a refinement layer on top of existing quantizers. We establish that a fresh random rotation returns each residual to the uniform distribution on the hypersphere, which characterizes the rate of progressive error decay across successive passes. This result lets us determine, before any weight is read, how many passes a layer needs for a target weight-space error. Every prefix is itself a valid lower-rate model, so one artifact serves several precisions. We instantiate ApexQuant with three interchangeable stages, scalar, E8 and trellis, and validate it on four open-weight LLMs and on Earth-observation and medical domains where in-distribution data is often unattainable as imagery arrives under restrictive licences or due to patient material under privacy constraints. Progressive re-isotropization comes within a few percent of full precision at four bits and gives the best two-bit arm we measure, in a completely data-free setting.