Quantization Benchmarks for GGML

qtest.py

import math
import random
import numpy as np


class Qx_0:
    def __init__(self, name, bits):
        self.name = name
        self.bits = bits

    def qin(self, x):
        r = 2 ** (self.bits - 1) - 1
        sf = np.abs(np.max(x)) / r
        q = np.round(x / sf).astype(np.int8)
        return sf, q

    def qout(self, sf, q):
        return sf * q


class Qx_1:
    def __init__(self, name, bits):
        self.name = name
        self.bits = bits

    def qin(self, x):
        r = 2**self.bits - 1
        o = np.min(x)
        sf = (np.max(x) - o) / r
        q = np.round((x - o) / sf).astype(np.uint8)
        return o, sf, q

    def qout(self, o, sf, q):
        return o + sf * q


Q8_0 = Qx_0("Q8_0", 8)
Q8_1 = Qx_1("Q8_1", 8)
Q4_0 = Qx_0("Q4_0", 4)
Q4_1 = Qx_1("Q4_1", 4)
Q2_0 = Qx_0("Q2_0", 2)
Q2_1 = Qx_1("Q2_1", 2)


def RMSE(a, b):
    assert len(a) == len(b)
    return np.sqrt(np.mean((a - b) ** 2))


def benchmark(method, iter=100_000, QK=32):
    avg = 0
    for _ in range(iter):
        a = np.clip(np.random.normal(0, 1, QK) * 65536, -65536, 65536)
        q = method.qin(a)
        x = method.qout(*q)
        s = RMSE(a, x)
        # print(a)
        # print(q)
        # print(x)
        avg += s
    return avg / iter


for m in [Q8_0, Q4_0, Q2_0, Q8_1, Q4_1, Q2_1]:
    r = benchmark(m)
    print(m.name, r)

Is the data really clipped that much (to one standard deviation)? And why 2**16 specifically?

Anyway here's what I used for my experiments with Q2, which I shall call Q2_2 to avoid confusion:

class Qx_2:
    def __init__(self, name, bits):
        self.name = name
        self.bits = bits

    def qin(self, x):
        # calculate the signed maximum (= value of largest magnitude, without applying abs),
        # then assign the value -(2^(k-1)) to that maximum.
        # The sign of the shared scaling factor is adjusted to give the right sign of the result.
        r = -(2 ** (self.bits - 1))
        sf = x.flat[np.abs(x).argmax()] / r
        # contrary to the other methods, we may get +2^(k-1) here, so we need to clip
        q = np.round(x / sf).clip(r, -r-1).astype(np.int8)
        return sf, q

    def qout(self, sf, q):
        return sf * q