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Fix decoupled weight decay ordering in the CUDA Adam/AdEMAMix kernels #2040

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Fix decoupled weight decay ordering in the CUDA Adam/AdEMAMix kernels #2040

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17 changes: 9 additions & 8 deletions csrc/kernels.cu
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Original file line number Diff line number Diff line change
Expand Up @@ -690,23 +690,24 @@ __launch_bounds__(TH, 1) __global__ void kOptimizer32bit2State(
// nu update: nu = beta2 * nu + (1-beta2) * g^2
s2_vals[j] = (s2_vals[j] * beta2) + ((1.0f - beta2) * (float)g_vals[j] * (float)g_vals[j]);

p_vals[j] = (float)p_vals[j] - lr * (((s1_vals[j] / correction1) + (alpha * s3_vals[j])) /
((sqrtf(s2_vals[j]) / correction2) + eps));

if (weight_decay > 0.0f)
p_vals[j] = ((float)p_vals[j]) * (1.0f - (lr * weight_decay));

p_vals[j] = (float)p_vals[j] - lr * (((s1_vals[j] / correction1) + (alpha * s3_vals[j])) /
((sqrtf(s2_vals[j]) / correction2) + eps));

break;
case ADAM:

if (!skip_zeros || (skip_zeros && ((float)g_vals[j] != 0.0f))) {
s1_vals[j] = s1_vals[j] * beta1 + ((1.0f - beta1) * ((float)g_vals[j]));
s2_vals[j] = s2_vals[j] * beta2 + ((1.0f - beta2) * (((float)g_vals[j]) * ((float)g_vals[j])));
p_vals[j] = ((float)p_vals[j]) +
(update_scale * step_size * (s1_vals[j] / (sqrtf(s2_vals[j]) + (eps * correction2))));

if (weight_decay > 0.0f)
p_vals[j] = ((float)p_vals[j]) * (1.0f - (lr * weight_decay));

p_vals[j] = ((float)p_vals[j]) +
(update_scale * step_size * (s1_vals[j] / (sqrtf(s2_vals[j]) + (eps * correction2))));
}
break;
}
Expand Down Expand Up @@ -1090,6 +1091,9 @@ __launch_bounds__(256, 3) __global__ void kOptimizerStatic8bit2StateBlockwise(
for (unsigned int j = 0; j < N_PER_TH; j++) {
// if(!skip_zeros || (skip_zeros && ((float)g_vals[j] != 0.0f)))
if (!isnan((float)g_vals[j]) && !isinf((float)g_vals[j])) {
if (weight_decay > 0.0f)
p_vals[j] = ((float)p_vals[j]) * (1.0f - (lr * weight_decay));

if (OPTIMIZER == ADEMAMIX) {
p_vals[j] =
T((float)p_vals[j] - lr * (((s1_vals[j] / correction1) + (alpha * s3_vals[j])) /
Expand All @@ -1099,9 +1103,6 @@ __launch_bounds__(256, 3) __global__ void kOptimizerStatic8bit2StateBlockwise(
(T)(((float)p_vals[j]) +
((step_size * (__fdividef(s1_vals[j], (sqrtf(s2_vals[j]) + (correction2 * eps)))))));
}

if (weight_decay > 0.0f)
p_vals[j] = ((float)p_vals[j]) * (1.0f - (lr * weight_decay));
}
}

Expand Down
101 changes: 101 additions & 0 deletions tests/test_optim.py
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Original file line number Diff line number Diff line change
Expand Up @@ -292,6 +292,107 @@ def test_lion32bit_weight_decay(dim1, dim2, gtype, device):
p2.copy_(p1.data)


# Decoupled weight decay multiplies the *previous* parameter and leaves the
# gradient-based update unscaled: p_new = p_old*(1 - lr*wd) + step_size*update.
# See Loshchilov & Hutter, arXiv:1711.05101 Algorithm 2 for AdamW and
# Pagliardini et al., arXiv:2409.03137 for AdEMAMix; torch.optim.AdamW does the same.
str2optimizers_weight_decay = {
"adamw": (torch.optim.AdamW, bnb.optim.AdamW),
"ademamix": (bnb.optim.ademamix._ReferenceAdEMAMix, bnb.optim.AdEMAMix),
}

str2optimizers_weight_decay_8bit = {
"adamw8bit_blockwise": bnb.optim.AdamW8bit,
"ademamix8bit_blockwise": bnb.optim.AdEMAMix8bit,
}


@pytest.mark.parametrize("optim_name", list(str2optimizers_weight_decay), ids=id_formatter("opt"))
@pytest.mark.parametrize("dim1", [1024], ids=id_formatter("dim1"))
@pytest.mark.parametrize("dim2", [32, 1024], ids=id_formatter("dim2"))
@pytest.mark.parametrize("device", get_available_devices(), ids=id_formatter("device"))
def test_optimizer32bit_weight_decay(dim1, dim2, optim_name, device):
"""AdamW/AdEMAMix must apply decoupled weight decay to the previous parameter, not to
the parameter after the update has been added.

The two orderings differ by lr*wd*|update| per step, so the separation grows with
lr*lr*wd while the kernel's own arithmetic error only grows with lr. test_optimizer32bit
runs these optimizers at the default weight_decay of 0, and at the lr=1e-3, wd=0.01 an
Adam user would typically pick the orderings stay 1.7e-7 apart, inside its 1e-6
tolerance. At lr=0.1, wd=0.1 they are ~1e-3 apart while agreement with the reference
stays at 3.9e-5 on CUDA, which is the gap this tolerance sits in.

fp32 only: the ordering is a property of the float math inside the kernel and does not
depend on the parameter storage dtype, and the 16-bit variants of test_optimizer32bit
resynchronise the parameters after every step, so at most one step of divergence is
ever visible and it stays inside the looser 16-bit tolerances.
"""
lr, weight_decay = 0.1, 0.1

p1 = torch.randn(dim1, dim2, device=device) * 0.1
p2 = p1.clone()

ref_cls, bnb_cls = str2optimizers_weight_decay[optim_name]
torch_optimizer = ref_cls([p1], lr=lr, weight_decay=weight_decay)
bnb_optimizer = bnb_cls([p2], lr=lr, weight_decay=weight_decay)

for _ in range(k):
g = torch.randn(dim1, dim2, device=device) * 0.01
p1.grad = g.clone()
p2.grad = g.clone()

bnb_optimizer.step()
torch_optimizer.step()

assert_most_approx_close(p1, p2, atol=1e-4, rtol=1e-3, max_error_count=0)


@pytest.mark.parametrize("optim_name", list(str2optimizers_weight_decay_8bit), ids=id_formatter("opt"))
@pytest.mark.parametrize("dim1", [1024], ids=id_formatter("dim1"))
@pytest.mark.parametrize("dim2", [32, 1024], ids=id_formatter("dim2"))
@pytest.mark.parametrize("device", get_available_devices(), ids=id_formatter("device"))
def test_optimizer8bit_weight_decay(dim1, dim2, optim_name, device):
"""Same decoupled weight decay requirement for the 8-bit blockwise kernels.

Comparing a full run against a 32-bit reference cannot see this: the state
quantization error is ~6.6e-4 per step while the two decay orderings differ by
~1.6e-6. The first step is exempt, because the optimizer state is still zero and
therefore quantizes exactly, so one step from a fresh optimizer has a closed form:

m = (1-b1)g, v = (1-b2)g^2 => update = -lr*g/(|g| + eps)

and AdEMAMix also mixes in alpha*(1-b3)*g. Decoupled decay then gives
p1 = p0*(1 - lr*wd) + update, while applying decay afterwards scales the update
term by an extra (1 - lr*wd), which at these hyperparameters is 1.0e-3 away.

The tolerance is set above the 3.0e-6 the CUDA kernels leave against the closed form,
which comes from their fast intrinsics (__powf, __fdividef) rather than from the decay.
"""
if device == "mps":
pytest.skip("8-bit optimizers are not implemented for MPS")

lr, weight_decay, eps = 0.1, 0.1, 1e-8

p0 = torch.randn(dim1, dim2, device=device) * 0.1
p = p0.clone()
g = torch.randn(dim1, dim2, device=device) * 0.01

bnb_optimizer = str2optimizers_weight_decay_8bit[optim_name]([p], lr=lr, weight_decay=weight_decay, eps=eps)
p.grad = g.clone()
bnb_optimizer.step()

update = -lr * g / (g.abs() + eps)
if optim_name.startswith("ademamix"):
group = bnb_optimizer.param_groups[0]
alpha = group["alpha"]
beta3 = group["betas"][2]
update = update * (1.0 + alpha * (1.0 - beta3))

expected = p0 * (1.0 - lr * weight_decay) + update

torch.testing.assert_close(p, expected, atol=1e-5, rtol=1e-4)


@pytest.mark.parametrize("dim1", [1024], ids=id_formatter("dim1"))
@pytest.mark.parametrize("dim2", [32, 1024, 4097], ids=id_formatter("dim2"))
@pytest.mark.parametrize("gtype", [torch.float32, torch.float16], ids=describe_dtype)
Expand Down