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Fix incorrect (1 - b2) coefficient in scale_by_adan #1715

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Fix incorrect (1 - b2) coefficient in scale_by_adan #1715

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24fab28
Fix incorrect (1 - b2) coefficient in scale_by_adan
codewithfourtix Jun 26, 2026
1fd6340
Wrap scale_by_adan call in test to satisfy 80-col lint
codewithfourtix Jun 26, 2026
eed58f1
Update adan docstring example for corrected update
codewithfourtix Jun 27, 2026
e0bea07
Adopt paper beta convention for adan per review
codewithfourtix Jun 27, 2026
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10 changes: 5 additions & 5 deletions optax/_src/alias.py
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Original file line number Diff line number Diff line change
Expand Up @@ -826,9 +826,9 @@ def adamw(

def adan(
learning_rate: base.ScalarOrSchedule,
b1: jax.typing.ArrayLike = 0.98,
b2: jax.typing.ArrayLike = 0.92,
b3: jax.typing.ArrayLike = 0.99,
b1: jax.typing.ArrayLike = 0.02,
b2: jax.typing.ArrayLike = 0.08,
b3: jax.typing.ArrayLike = 0.01,
eps: jax.typing.ArrayLike = 1e-8,
eps_root: jax.typing.ArrayLike = 1e-8,
weight_decay: base.ScalarOrSchedule = 0.0,
Expand Down Expand Up @@ -921,8 +921,8 @@ def adan(
Objective function: 1.28E+01
Objective function: 1.17E+01
Objective function: 1.07E+01
Objective function: 9.68E+00
Objective function: 8.76E+00
Objective function: 9.69E+00
Objective function: 8.77E+00

References:
Xie et al, `Adan: Adaptive Nesterov Momentum Algorithm for Faster Optimizing
Expand Down
18 changes: 9 additions & 9 deletions optax/_src/transform.py
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Original file line number Diff line number Diff line change
Expand Up @@ -621,9 +621,9 @@ class ScaleByAdanState(NamedTuple):


def scale_by_adan(
b1: jax.typing.ArrayLike = 0.98,
b2: jax.typing.ArrayLike = 0.92,
b3: jax.typing.ArrayLike = 0.99,
b1: jax.typing.ArrayLike = 0.02,
b2: jax.typing.ArrayLike = 0.08,
b3: jax.typing.ArrayLike = 0.01,
eps: jax.typing.ArrayLike = 1e-8,
eps_root: jax.typing.ArrayLike = 0.0,
) -> base.GradientTransformation:
Expand Down Expand Up @@ -662,16 +662,16 @@ def update_fn(updates, state, params=None):
optax.tree.zeros_like(g),
optax.tree.sub(g, state.g),
)
m = optax.tree.update_moment(g, state.m, b1, 1)
v = optax.tree.update_moment(diff, state.v, b2, 1)
m = optax.tree.update_moment(g, state.m, 1 - b1, 1)
v = optax.tree.update_moment(diff, state.v, 1 - b2, 1)

sq = optax.tree.add_scale(g, 1 - b2, diff)

@rdyro rdyro Jun 26, 2026

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I'd prefer optax stick closer to the math and we keep 1 - b2, but update the constructor defaults.

n = optax.tree.update_moment_per_elem_norm(sq, state.n, b3, 2)
n = optax.tree.update_moment_per_elem_norm(sq, state.n, 1 - b3, 2)

t = numerics.safe_increment(state.t)
m_hat = optax.tree.bias_correction(m, b1, t)
v_hat = optax.tree.bias_correction(v, b2, t)
n_hat = optax.tree.bias_correction(n, b3, t)
m_hat = optax.tree.bias_correction(m, 1 - b1, t)
v_hat = optax.tree.bias_correction(v, 1 - b2, t)
n_hat = optax.tree.bias_correction(n, 1 - b3, t)

u = optax.tree.add_scale(m_hat, 1 - b2, v_hat)
denom = jax.tree.map(lambda n_hat: jnp.sqrt(n_hat + eps_root) + eps, n_hat)
Expand Down
33 changes: 33 additions & 0 deletions optax/_src/transform_test.py
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Expand Up @@ -73,6 +73,39 @@ def test_scalers(self, scaler_constr):
test_utils.assert_tree_all_finite((params, updates, state))
test_utils.assert_trees_all_equal_shapes(params, updates)

def test_adan_matches_documented_update(self):
# Reference implementation of the equations documented in `optax.adan`.
b1, b2, b3 = 0.02, 0.08, 0.01
eps, eps_root = 1e-8, 0.0
grads = [
jnp.array([0.5, -1.5, 2.0]),
jnp.array([0.3, -1.0, 2.5]),
jnp.array([-0.2, 0.7, 1.0]),
]

tx = transform.scale_by_adan(
b1=b1, b2=b2, b3=b3, eps=eps, eps_root=eps_root
)
state = tx.init(grads[0])

m = jnp.zeros(3)
v = jnp.zeros(3)
n = jnp.zeros(3)
g_prev = jnp.zeros(3)
for step, g in enumerate(grads, start=1):
diff = jnp.zeros(3) if step == 1 else g - g_prev
m = (1 - b1) * m + b1 * g
v = (1 - b2) * v + b2 * diff
n = (1 - b3) * n + b3 * (g + (1 - b2) * diff) ** 2
m_hat = m / (1 - (1 - b1) ** step)
v_hat = v / (1 - (1 - b2) ** step)
n_hat = n / (1 - (1 - b3) ** step)
expected = (m_hat + (1 - b2) * v_hat) / (jnp.sqrt(n_hat + eps_root) + eps)
g_prev = g

updates, state = tx.update(g, state, None)
test_utils.assert_trees_all_close(updates, expected, atol=1e-4, rtol=1e-4)

def test_apply_every(self):
# The frequency of the application of sgd
k = 4
Expand Down
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