Ask what should change when the equation is manipulated, then let the visualization test that expectation.
Foundation Lab
Quantization: Compressing Models to Integers
How you run 70B models on consumer GPUs: 4-bit quantization fits in 24GB VRAM
#63QuantizationEfficiency
key equation
w_q = \text{round}\left(\frac{w - w_{min}}{\Delta}\right)Selected Foundation Object
Keep the equation fixed; move through the evidence.
Concept 63 of 100QuantizationEfficiency / Phase 6: Modern efficiency & inference
Current question
Neural nets are surprisingly robust to quantization—most precision is wasted
w_q = \text{round}\left(\frac{w - w_{min}}{\Delta}\right)Use the runnable panel, the key equation, and canonical papers as separate forms of evidence for the same object.
The useful learning product is the reusable mechanism you can carry into another model, paper, or engineering tradeoff.
This atlas page keeps the working demo; the domain notebook carries the fuller Intuition -> Math -> Code -> Demo sequence.
Why It Matters for Modern Models
- How you run 70B models on consumer GPUs: 4-bit quantization fits in 24GB VRAM
- GPTQ/AWQ/GGML are standard for deploying open-weight LLMs
- INT8 inference is ~2× faster than FP16 on modern GPUs (tensor cores)
What Tutorials Skip
What is still poorly explained in textbooks and papers:
- Neural nets are surprisingly robust to quantization—most precision is wasted
- Outliers are the enemy: a few large activations force bad scaling for everything else
- Quantization-aware training (QAT) is better than post-training quantization (PTQ), but expensive
Interactive Visualization
Core Math (Optional Deep Dive)
If you want intuition first, start with the key equation and the visualization. Come back here for the full walkthrough.
Key Equation
Map FP32 weights to INT8 (or INT4):
Uniform quantization:
Dequantization:
Per-channel scaling (better quality):
Memory: FP32 → INT8 = 4× reduction. INT4 = 8× reduction.