Transformer quantization has sprinted from barely fitting a 7B model in INT8 without losing accuracy to routinely packing a 70B model into 4‑bits on a single GPU. Existing tutorials split between singular techniques or library usage, leaving practitioners without a cohesive roadmap. The new series aims to stitch those gaps, starting with fundamentals: definition, challenges, and underlying math.

Quantization replaces high‑precision weights with lower‑bit integers, cutting memory roughly in half for 8‑bit and by a factor of four for 4‑bits representations. Mark Horowitz’s 2014 energy study showed int8 add consumes 30× less energy than fp32 add and int8 mul 18× less. These savings translate to faster compute for matrix‑multiply‑heavy workloads and lower bandwidth pressure during LLM decoding.

The core hardware element is the Multiply‑Accumulate (MAC) unit, where each processing element multiplies a weight by an input and accumulates into a bias‑initialized register. Quantization maps a float x to an integer via scale s and zero‑point z, then clamps to the integer range. Fake‑quant simulation inserts quant‑dequant pairs in a floating‑point graph, letting developers measure rounding and clipping errors before deploying to fixed‑point silicon.