Six decibels per bit, and what outliers cost

NumericalBeginner⏱ 30 minQuantizationsqnrloading factoroutliers

Problem

Compute SQNR for a symmetric 8-bit quantizer with loading factor $A/\sigma = 4$ .
Repeat at 4 bits with the same loading factor.
A tensor has one value at $50\sigma$ . Compute the SQNR at 8 bits when $A$ is set to the maximum, and state how many bits are effectively wasted.

Compute the requested quantities and say what they mean. A number without an interpretation is not an answer.

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
The round-trip error bound	Quantization	Proof	Foundation	15 min
The true bit width of a group-quantized format	Quantization	Numerical	Foundation	15 min
Effective bits lost to dynamic range	Quantization	Numerical	Beginner	15 min
The Δ²/12 noise variance	Quantization	Proof	Beginner	15 min
Optimal clipping for a Laplace-distributed tensor	Quantization	Proof	Advanced	1 hour