Which weight to quantize next

ProofIntermediate⏱ 30 minQuantizationgreedyselectionordering

Problem

Using $\mathcal E_q = (w_q-\operatorname{quant}(w_q))^2/(2[H^{-1}]_{qq})$ :

Explain what large and small $[H^{-1}]_{qq}$ mean geometrically.
Show that a weight already on the quantization grid costs nothing, whatever the Hessian.
Construct a two-coordinate example where the greedy order and the reverse order give different final errors, demonstrating that order matters.

Write a complete argument. Every inequality you use should be one you could state precisely.

Opening this before you have a real attempt on paper is the fastest way to feel like you understand something you cannot reproduce.

Problem	Field	Type	Difficulty	Time
Derive the optimal weight update abyss	Quantization	Proof	Advanced	1 hour
Implement Hessian-aware rounding run	Quantization	Coding	Advanced	1 day
The rank-one inverse update abyss	Quantization	Proof	Graduate	1 hour