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import math
from typing import Optional, Tuple
import torch
import torch.nn as nn
from torch_harmonics.truncation import truncate_sht
from .distributed_quadrature import DistributedQuadratureS2
from .distributed_sht import DistributedInverseRealSHT, DistributedRealSHT
from .primitives import copy_to_azimuth_region, copy_to_polar_region
from .utils import azimuth_group_rank, azimuth_group_size, polar_group_rank, polar_group_size
[docs]
class DistributedSpectralConvS2(nn.Module):
r"""
Distributed spectral convolution layer on :math:`S^2` implemented with
distributed real SHT (Driscoll-Healy formulation, see https://api.semanticscholar.org/CorpusID:122817218).
Computation is split across polar and azimuth communicator groups.
**Distribution scheme.**
The forward and inverse SHTs are performed by
:class:`DistributedRealSHT` and :class:`DistributedInverseRealSHT`
respectively — see their docstrings for the all-to-all transpose
sequence. After the forward SHT, the spectral coefficients are split so
that degrees ``l`` are distributed across polar ranks and orders ``m``
across azimuth ranks. The learnable spectral weight
``K[groups, c_in, c_out, l]`` is stored with its ``l`` dimension sharded
across polar ranks (each rank holds only its local ``lmax_local`` slice).
The spectral contraction is therefore fully local — no communication is
needed for the channel mixing.
.. note::
When saving a checkpoint to a single file, the weight tensor must be
gathered across polar ranks along the ``l`` dimension to recover the
full ``(groups, c_in, c_out, lmax)`` shape. Likewise, when loading a
serial checkpoint into the distributed module, the ``l`` dimension must
be split according to
:func:`~torch_harmonics.distributed.compute_split_shapes`.
.. note::
The spectral weight ``K[g, c_in, c_out, l]`` has no ``m`` dimension —
it is broadcast over the spectral orders during the contraction.
Because orders are split across azimuth ranks, each rank computes only
a partial sum of the weight gradient (over its local ``m`` modes).
For correct gradients the user must **all-reduce (sum) the weight
gradients across azimuth ranks**. This can be implemented via
:class:`torch.nn.parallel.DistributedDataParallel` communication hooks
or :meth:`torch.Tensor.register_post_accumulate_grad_hook`.
.. seealso::
:class:`torch_harmonics.SpectralConvS2`
Serial counterpart with full mathematical description and parameter
documentation.
Parameters
----------
in_shape : Tuple[int]
Spatial input grid shape ``(nlat, nlon)``.
out_shape : Tuple[int]
Spatial output grid shape ``(nlat, nlon)``.
in_channels : int
Number of input channels.
out_channels : int
Number of output channels.
num_groups : int, optional
Number of channel groups for grouped spectral weights, by default 1.
grid_in : str, optional
Grid used for the forward distributed SHT (``"equiangular"``,
``"legendre-gauss"``, ``"lobatto"``, ``"equiangular-trapezoidal"``), by default
``"equiangular"``.
grid_out : str, optional
Grid used for the inverse distributed SHT, same options as ``grid_in``.
bias : bool, optional
If ``True``, adds a learnable spectral bias computed from the spatial
integral (replicated across process groups as needed), by default
``False``.
Raises
------
AssertionError
If ``in_channels`` or ``out_channels`` is not divisible by
``num_groups``.
Returns
-------
torch.Tensor
Tensor of shape ``(..., out_channels, out_shape[0], out_shape[1])``.
Notes
-----
The layer truncates ``lmax``/``mmax`` to the distributed SHT limits, and
uses local ``lmax``/``mmax`` slices when constructing spectral weights. The
grouped contraction is performed with ``_contract_lwise``.
"""
def __init__(
self,
in_shape: Tuple[int],
out_shape: Tuple[int],
in_channels: int,
out_channels: int,
num_groups: Optional[int] = 1,
grid_in: Optional[str] = "equiangular",
grid_out: Optional[str] = "equiangular",
bias: Optional[bool] = False,
):
super().__init__()
if in_channels % num_groups != 0:
raise ValueError(f"in_channels ({in_channels}) must be divisible by num_groups ({num_groups})")
if out_channels % num_groups != 0:
raise ValueError(f"out_channels ({out_channels}) must be divisible by num_groups ({num_groups})")
# copy inputs
self.in_channels = in_channels
self.out_channels = out_channels
self.num_groups = num_groups
# get the comms grid:
self.comm_size_polar = polar_group_size()
self.comm_rank_polar = polar_group_rank()
self.comm_size_azimuth = azimuth_group_size()
self.comm_rank_azimuth = azimuth_group_rank()
# compute truncation
lmax_in, mmax_in = truncate_sht(in_shape[0], in_shape[1], grid=grid_in)
lmax_out, mmax_out = truncate_sht(out_shape[0], out_shape[1], grid=grid_out)
# compute lmax and lmin
lmax = min(lmax_in, lmax_out)
mmax = min(mmax_in, mmax_out)
self.lmax = min(lmax, mmax)
self.mmax = self.lmax
# set up sht layers
self.sht = DistributedRealSHT(*in_shape, grid=grid_in, lmax=self.lmax, mmax=self.mmax)
self.isht = DistributedInverseRealSHT(*out_shape, grid=grid_out, lmax=self.lmax, mmax=self.mmax)
# extract sht parameters
self.l_shapes = self.isht.l_shapes
self.m_shapes = self.isht.m_shapes
self.lmax_local = self.l_shapes[self.comm_rank_polar]
self.mmax_local = self.m_shapes[self.comm_rank_azimuth]
# weight shape
weight_shape = [num_groups, in_channels // num_groups, out_channels // num_groups, self.lmax_local]
# Compute scaling factor for correct initialization
scale = math.sqrt(1.0 / (in_channels // num_groups)) * torch.ones(self.lmax_local, dtype=torch.complex64)
# seemingly the first weight is not really complex, so we need to account for that
scale[0] *= math.sqrt(2.0)
self.weight = nn.Parameter(scale * torch.randn(*weight_shape, dtype=torch.complex64))
if bias:
self.spectral_bias = nn.Parameter(torch.zeros(1, self.in_channels, self.lmax_local, self.mmax_local, dtype=torch.complex64))
self.quadrature = DistributedQuadratureS2(img_shape=in_shape, grid=grid_in, normalize=False)
@torch.compile
def _contract_lwise(self, ac: torch.Tensor, bc: torch.Tensor) -> torch.Tensor:
resc = torch.einsum("bgixy,giox->bgoxy", ac, bc)
return resc
def forward(self, x):
dtype = x.dtype
# compute integral in case if bias is used
if hasattr(self, "spectral_bias"):
integral = self.quadrature(x)
if self.comm_size_polar > 1:
integral = copy_to_polar_region(integral)
if self.comm_size_azimuth > 1:
integral = copy_to_azimuth_region(integral)
with torch.amp.autocast(device_type=x.device.type, enabled=False):
x = x.to(torch.float32)
x = self.sht(x).contiguous()
# store the shapes
B, C, H, W = x.shape
# deal with bias
if hasattr(self, "spectral_bias"):
x = x + integral.reshape(B, C, 1, 1) * self.spectral_bias
# perform contraction
x = x.reshape(B, self.num_groups, C // self.num_groups, H, W)
xp = self._contract_lwise(x, self.weight)
x = xp.reshape(B, self.out_channels, H, W).contiguous()
with torch.amp.autocast(device_type=x.device.type, enabled=False):
x = self.isht(x)
# convert datatype
x = x.to(dtype=dtype)
return x
