INT8 Quantization Simulator

mediumPROGeneration & OptimizationLLM 3: Applications & Evaluation

Simulate INT8 quantization and dequantization of model weights.

INT8 quantization maps float32 values to [-128, 127]:

Find scale: scale = max(|weights|) / 127
Quantize: q = round(weights / scale), clamped to [-128, 127]
Dequantize: weights_approx = q * scale

Compute the quantization error (MSE between original and dequantized).

Input: Space-separated float weights

Output:

Line 1: Dequantized weights, rounded to 4 decimal places
Line 2: Scale factor, rounded to 6 decimal places
Line 3: MSE error, rounded to 6 decimal places

Example

Input

1.0 -0.5 0.3 -0.8

Output

0.9921 -0.4961 0.2953 -0.7953
0.007874
0.000013

Reasoning

First, we find the scale factor: $scale = \max(|weights|) / 127 = \max(|1.0|, |-0.5|, |0.3|, |-0.8|) / 127 = 1.0 / 127 = 0.007874$
Then, we quantize the weights: $q = \round(weights / scale)$ , which results in $q = \round(1.0 / 0.007874) = 127$ , $q = \round(-0.5 / 0.007874) = -63$ , $q = \round(0.3 / 0.007874) = 38$ , $q = \round(-0.8 / 0.007874) = -101$
Next, we dequantize the weights: $weights\_approx = q \* scale$ , resulting in $1.0 \* 0.007874 = 0.9921$ (after rounding), $-0.5 \* 0.007874 = -0.4961$ (after rounding), $0.3 \* 0.007874 = 0.2953$ (after rounding), $-0.8 \* 0.007874 = -0.7953$ (after rounding)
Finally, we calculate the MSE error between the original and dequantized weights: $MSE = \frac{1}{n} \sum (original - dequantized)^2$ , which equals $0.000013$ after calculation and rounding

Constraints

Clamp quantized values to [-128, 127]
Use round() for rounding to nearest integer
Round outputs as specified

Learn this in

Advanced Topics & ApplicationsDiffusion Study Plan Deployment & OptimizationLLM Study Plan Advanced NLP TopicsNLP Study Plan Benchmarks, Deployment & the FrontierVLM Study Plan

More from LLM 3: Applications & Evaluation

Beam Search Decoderhard Nucleus (Top-P) Samplingmedium Top-K Samplingeasy Temperature Samplingeasy BLEU-4 Scorehard

Concept primerPREVIEW

Background Knowledge

Quantization is a process of mapping a continuous range of values to a finite set of discrete values. In the context of neural networks, quantization is used to reduce the precision of model weights from floating-point numbers (e.g., float32) to integers (e.g., int8). This reduction in precision can lead to significant memory savings and improved computational efficiency. The INT8 quantization process specifically maps float32 values to the range [-128, 127].

The quantization process involves three main steps: scaling, quantization, and dequantization. Scaling determines the factor by which the original values are divided to fit within the desired range. Quantization rounds the scaled values to the nearest integer, and dequantization multiplies the quantized values by the scale factor to approximate the original values. The mean squared error (MSE) between the original and dequantized values is a common metric used to evaluate the quantization error.

Understanding the trade-offs between precision, memory usage, and computational efficiency is crucial when working with quantization. As the precision of the model weights decreases, the memory usage and computational requirements also decrease, but the accuracy of the model may suffer. Therefore, it is essential to balance these factors when implementing quantization techniques.

Algorithm/Approach

The algorithm for simulating INT8 quantization and dequantization involves the following pattern:

Determine the scale factor based on the maximum absolute value of the input weights
Quantize the weights by dividing them by the scale factor and rounding to the nearest integer
Dequantize the weights by multiplying the quantized values by the scale factor
Compute the MSE between the original and dequantized weights

PRO

Continue the full explanation

You're reading the free preview. Unlock the complete walkthrough, the code editor, test runner and reference solution with Premium.

PRO

Editor locked

The code editor is locked for Pro problems. It is only available for free problems. Please upgrade to gain access to the code editor for all problems.

solution.py

Python 3.13

Test results