🔥 Challenge: QJL Estimator Calibration

[Snakkaz]

The Problem

The QJL 1-bit error correction estimator in src/qjl/qjl.py is not correctly calibrated. The current implementation adds noise instead of reducing it.

What We Need

An unbiased estimator that computes <query, residual> from:

• Full-precision query vector q
• Sign bits of projected residual sign(S @ residual)
• Random projection matrix S

Paper Reference

• QJL: Quantized Johnson-Lindenstrauss (AAAI 2025)
• The key is deriving the correct scaling factor for the sign-sketch estimator

Current Behavior

PolarQuant (3-bit) mean error: 1.72
TurboQuant (3+1) mean error:   1.66  (barely better, should be much better)

Expected Behavior

QJL correction should significantly reduce dot-product error, not just marginally improve it.

How to Test

python examples/basic_usage.py

This is the hardest open problem in the repo. If you can crack this, you'll have implemented a key part of a brand-new ICLR 2026 paper.