File size: 2,170 Bytes
995e752 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 | """Reference implementation — the CORRECTNESS SPEC for `quantized_adamw_step`.
This is correct but slow. It defines exactly what your kernel must reproduce; its speed has no
bearing on your score, which is an absolute GB/s number. GENERATED by _factory/build.py.
"""
import torch
BLOCK = 2048 # quantisation block: one fp32 absmax per 2048 consecutive parameters
def _requantise(x, qmap):
"""x -> (dequantised round trip, per-block absmax). Nearest entry of the ascending 256-point map."""
nb = x.numel() // BLOCK
xb = x.view(nb, BLOCK)
absmax = xb.abs().amax(-1) # the NEW scale of this block
c = xb / absmax.clamp(min=1e-30).unsqueeze(-1) # normalised into the map's range
mid = (qmap[:-1] + qmap[1:]) * 0.5 # 255 midpoints, ascending
code = torch.bucketize(c, mid) # index of the nearest map entry
return (qmap[code] * absmax.unsqueeze(-1)).reshape(-1), absmax
def quantized_adamw_step(params, grads, m_code, m_absmax, v_code, v_absmax, qmap1, qmap2, step,
lr=1e-3, beta1=0.9, beta2=0.999, eps=1e-8, wd=0.01):
"""8-bit blockwise AdamW, in fp32.
Correct and simple — it is the numerical SPECIFICATION, not a performance target. Every line
materialises another full-size fp32 temporary in HBM.
"""
m = qmap1[m_code.long()] * m_absmax.repeat_interleave(BLOCK) # dequantise the first moment
v = qmap2[v_code.long()] * v_absmax.repeat_interleave(BLOCK) # dequantise the second moment
g = grads.float()
m_new = beta1 * m + (1.0 - beta1) * g
v_new = beta2 * v + (1.0 - beta2) * g * g
bc1 = 1.0 - beta1 ** step
bc2 = 1.0 - beta2 ** step
denom = (v_new / bc2).sqrt() + eps
upd = (lr / bc1) * m_new / denom
p_out = params.float() * (1.0 - lr * wd) - upd # DECOUPLED weight decay
m_out, m_absmax_out = _requantise(m_new, qmap1) # the state that gets stored back
v_out, v_absmax_out = _requantise(v_new, qmap2)
return p_out.to(torch.bfloat16), m_out, v_out, m_absmax_out, v_absmax_out
|