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

Key points

• 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.1
• This result lets us determine, before any weight is read, how many passes a layer needs for a target weight-space error.1
• 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.1
• 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.1

Sources (1)

• [1]ApexQuant: Data-Free Elastic Quantization by Residual Re-Isotropization
  arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 6, 07:49 AM

  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.

Extractive summary: sentences quoted from the sources.