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Magnitude-direction decoupling #1

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3331f7f
Magnitude-direction decoupling
decahedron1 Jul 31, 2026
4629efa
Do some stuff inplace
decahedron1 Aug 1, 2026
23ba219
MD for Adam params
decahedron1 Aug 3, 2026
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115 changes: 87 additions & 28 deletions thorn/thorn.py
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Original file line number Diff line number Diff line change
Expand Up @@ -25,6 +25,7 @@
import torch.distributed as dist
from torch.distributed.tensor import DTensor, Replicate, Shard
import torch.nn as nn
import torch.nn.functional as F
from torch.nn import Parameter
from torch.optim import Optimizer
from torch.optim.optimizer import _get_value
Expand Down Expand Up @@ -320,7 +321,7 @@ class _THORNParameterGroup:
betas: tuple[float, float] = field(default_factory=lambda: (0.95, 0.95))
iters: int = field(default=5)
rectify: bool = field(default=True)
target_rms: float = field(default=0.2)
gain_lr: float = field(default=1e-3)
lower_bound: float = field(default=1e-3)
safety_factor: float = field(default=0.05)
cushion: float = field(default=0.02)
Expand Down Expand Up @@ -404,14 +405,8 @@ def _weight_decay(
update.addcmul_(p, mask.mul_(weight_decay))
return update

def _lr_scale_ortho(p: torch.Tensor, target_rms: float = 0.2):
if target_rms != 0.0:
# Scale LR to match RMS update of AdamW so AdamW's LR can be reused
# per formula 4 of https://arxiv.org/pdf/2502.16982
return target_rms * (max(1, *p.shape[-2:]) ** 0.5)
else:
# Match original behavior of Jordan et al
return max(1, p.size(-2) / p.size(-1)) ** 0.5
def _lr_scale_ortho(p: torch.Tensor):
return (max(*p.shape[-2:]) / min(*p.shape[-2:])) ** 0.5

@torch.no_grad()
def _compute_rect(group: _THORNParameterGroup, step: float | int):
Expand Down Expand Up @@ -446,6 +441,26 @@ def _momentum_aligned_mask(g: torch.Tensor, state: dict, group: _THORNParameterG
state['random_state'], mask = _w1rand(state['random_state'])
return state['s'] * (1.0 if mask % 2 == 0 else 0.0)

def _adam_step(
g: torch.Tensor,
momentum: torch.Tensor,
variance: torch.Tensor,
step: int | torch.Tensor,
beta1: float = 0.9,
beta2: float = 0.95,
degenerate = False
):
momentum.lerp_(g, weight=1 - beta1)
variance.mul_(beta2).addcmul_(g, g, value=1 - beta2)
if not degenerate:
denom = variance.div(1 - beta2 ** step).sqrt_()
# atan2 instead of div per https://arxiv.org/pdf/2407.05872
u = momentum.div(1 - beta1 ** step).atan2_(denom)
else:
# clone because we might later call _weight_decay which modifies in place
u = momentum.clone()
return u

@dataclass
class _DistributedTHORNState:
worker_rank: int
Expand Down Expand Up @@ -605,7 +620,7 @@ def update_param(
self.computed_u = None

u = _weight_decay(p, self.scattered_u, group.weight_decay)
p.data.sub_(u, alpha=group.lr * _lr_scale_ortho(u, target_rms=group.target_rms) * scale)
p.data.sub_(u, alpha=group.lr * _lr_scale_ortho(u) * scale)

self.scattered_u = None
u_dtensor = None
Expand All @@ -622,7 +637,7 @@ class THORNOrthogonalizedParameterGroup(TypedDict, total=True):
lower_bound: NotRequired[float]
safety_factor: NotRequired[float]
cushion: NotRequired[float]
target_rms: NotRequired[float]
gain_lr: NotRequired[float]
rectify: NotRequired[bool]
momentum_align: NotRequired[bool]
coeffs: NotRequired[list[tuple[float, float, float]]]
Expand Down Expand Up @@ -782,12 +797,30 @@ def _base_ortho_step(self, p: Parameter, group: _THORNParameterGroup):
g = p.grad

magma_scale = _momentum_aligned_mask(g, state, group)

# recover direction
row_gain = F.softplus(state['row_gain'])
col_gain = F.softplus(state['col_gain'])
gain = row_gain * col_gain
p.div_(gain)
p_g = p * g
g.mul_(gain)

u = self._update_momentum(p, g, group)
if magma_scale != 0.0 and (state['step'] + 1) % self._update_rate == 0:
u = _polar_decomp(u, group).to(dtype=p.dtype)
u = _per_neuron_norm(u, state['moment2'], group)
u = _weight_decay(p, u, group.weight_decay)
p.data.sub_(u, alpha=group.lr * _lr_scale_ortho(u, target_rms=group.target_rms) * magma_scale)

p.sub_(u, alpha=group.lr * _lr_scale_ortho(u) * magma_scale)
p.mul_(state['target_norm'] / (p.norm(dim=(-2, -1), keepdim=True) + 1e-8))

grad_row = (p_g * col_gain).sum(dim=-1).mul_(F.sigmoid(state['row_gain']).squeeze(-1))
grad_col = (p_g * row_gain).sum(dim=-2).mul_(F.sigmoid(state['col_gain']).squeeze(-2))
state['row_gain'].sub_(_adam_step(grad_row.unsqueeze(-1), state['row_gain_moment'], state['row_gain_variance'], state['step']), alpha=group.gain_lr)
state['col_gain'].sub_(_adam_step(grad_col.unsqueeze(-2), state['col_gain_moment'], state['col_gain_variance'], state['step']), alpha=group.gain_lr)

# reassemble
p.mul_(F.softplus(state['row_gain']))
p.mul_(F.softplus(state['col_gain']))

if group.none_grad:
del g
Expand Down Expand Up @@ -883,10 +916,21 @@ def _step_params(self, params: list[torch.nn.Parameter], group: _THORNParameterG
state['s'] = 1.0
if group.orthogonalize:
state['moment'] = torch.zeros_like(g)
state['moment2'] = torch.zeros((*g.shape[:-1], 1), dtype=g.dtype, device=g.device)
else:
state['moment'] = torch.zeros_like(g)
state['variance'] = torch.zeros_like(g)
# softplus(ln(e - 1)) = 1
if p.ndim > 1:
state['row_gain'] = torch.full((*g.shape[:-1], 1), 0.5413248546, dtype=g.dtype, device=g.device)
state['col_gain'] = torch.full((*g.shape[:-2], 1, *g.shape[-1:]), 0.5413248546, dtype=g.dtype, device=g.device)
for k in ['row_gain', 'col_gain']:
state[f'{k}_moment'] = torch.zeros_like(state[k])
state[f'{k}_variance'] = torch.zeros_like(state[k])
else:
state['gain'] = torch.full((), 0.5413248546, dtype=g.dtype, device=g.device)
state['gain_moment'] = torch.zeros((), dtype=g.dtype, device=g.device)
state['gain_variance'] = torch.zeros((), dtype=g.dtype, device=g.device)
state['target_norm'] = p.norm(dim=(-2, -1) if g.ndim > 1 else -1, keepdim=True)

if isinstance(p.data, DTensor):
if all(isinstance(placement, Replicate) for placement in cast(DTensor, p).placements) or not group.orthogonalize:
Expand All @@ -912,24 +956,39 @@ def _step_params(self, params: list[torch.nn.Parameter], group: _THORNParameterG
magma_scale = _momentum_aligned_mask(g, state, group)
rect = _compute_rect(group, step)

momentum = state['moment']
variance = state['variance']

momentum.lerp_(g, weight=1 - beta1)
variance.mul_(beta2).addcmul_(g, g, value=1 - beta2)
if rect > 0.0:
denom = variance.div(1 - beta2 ** step).sqrt_()
# atan2 instead of div per https://arxiv.org/pdf/2407.05872
u = momentum.div(1 - beta1 ** step).atan2_(denom)
# recover direction
if p.ndim > 1:
row_gain = F.softplus(state['row_gain'])
col_gain = F.softplus(state['col_gain'])
gain = row_gain * col_gain
else:
# clone because _weight_decay modifies in place
u = momentum.clone()
gain = F.softplus(state['gain'])
p.div_(gain)
p_g = p * g
g.mul_(gain)

u = _adam_step(g, state['moment'], state['variance'], step, beta1, beta2, degenerate=rect == 0.0)

should_update = magma_scale != 0.0 and (state['step'] + 1) % self._update_rate == 0
if should_update:
u = _weight_decay(p, u, group.weight_decay)

p.sub_(u, alpha=group.lr * rect * magma_scale)
p.sub_(u, alpha=group.lr * rect * magma_scale)
p.mul_(state['target_norm'] / (p.norm(dim=(-2, -1) if p.ndim > 1 else -1, keepdim=True) + 1e-8))

if p.ndim > 1:
grad_row = (p_g * col_gain).sum(dim=-1).mul_(F.sigmoid(state['row_gain']).squeeze(-1))
grad_col = (p_g * row_gain).sum(dim=-2).mul_(F.sigmoid(state['col_gain']).squeeze(-2))
state['row_gain'].sub_(_adam_step(grad_row.unsqueeze(-1), state['row_gain_moment'], state['row_gain_variance'], state['step']), alpha=group.gain_lr)
state['col_gain'].sub_(_adam_step(grad_col.unsqueeze(-2), state['col_gain_moment'], state['col_gain_variance'], state['step']), alpha=group.gain_lr)
else:
grad_gain = (p_g * gain).sum().mul_(F.sigmoid(state['gain']))
state['gain'].sub_(_adam_step(grad_gain, state['gain_moment'], state['gain_variance'], state['step']), alpha=group.gain_lr)

if p.ndim > 1:
p.mul_(F.softplus(state['row_gain']))
p.mul_(F.softplus(state['col_gain']))
else:
p.mul_(F.softplus(state['gain']))

if group.none_grad:
del g
Expand Down