aligned_mtl.py

# The code of this file was partly adapted from
# https://github.com/SamsungLabs/MTL/tree/master/code/optim/aligned.
# It is therefore also subject to the following license.
#
# MIT License
#
# Copyright (c) 2022 Samsung
#
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# of this software and associated documentation files (the "Software"), to deal
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import torch
from torch import Tensor

from ._pref_vector_utils import pref_vector_to_str_suffix, pref_vector_to_weighting
from .bases import _WeightedAggregator, _Weighting
from .mean import _MeanWeighting


class AlignedMTL(_WeightedAggregator):
    """
    :class:`~torchjd.aggregation.bases.Aggregator` as defined in Algorithm 1 of
    `Independent Component Alignment for Multi-Task Learning
    <https://openaccess.thecvf.com/content/CVPR2023/papers/Senushkin_Independent_Component_Alignment_for_Multi-Task_Learning_CVPR_2023_paper.pdf>`_.

    :param pref_vector: The preference vector to use.

    .. admonition::
        Example

        Use AlignedMTL to aggregate a matrix.

        >>> from torch import tensor
        >>> from torchjd.aggregation import AlignedMTL
        >>>
        >>> A = AlignedMTL()
        >>> J = tensor([[-4., 1., 1.], [6., 1., 1.]])
        >>>
        >>> A(J)
        tensor([0.2133, 0.9673, 0.9673])

    .. note::
        This implementation was adapted from the `official implementation
        <https://github.com/SamsungLabs/MTL/tree/master/code/optim/aligned>`_.
    """

    def __init__(self, pref_vector: Tensor | None = None):
        weighting = pref_vector_to_weighting(pref_vector, default=_MeanWeighting())
        self._pref_vector = pref_vector

        super().__init__(weighting=_AlignedMTLWrapper(weighting))

    def __repr__(self) -> str:
        return f"{self.__class__.__name__}(pref_vector={repr(self._pref_vector)})"

    def __str__(self) -> str:
        return f"AlignedMTL{pref_vector_to_str_suffix(self._pref_vector)}"


class _AlignedMTLWrapper(_Weighting):
    """
    Wrapper of :class:`~torchjd.aggregation.bases._Weighting` that corrects the extracted
    weights with the balance transformation defined in Algorithm 1 of `Independent Component
    Alignment for Multi-Task Learning
    <https://openaccess.thecvf.com/content/CVPR2023/papers/Senushkin_Independent_Component_Alignment_for_Multi-Task_Learning_CVPR_2023_paper.pdf>`_.

    :param weighting: The wrapped :class:`~torchjd.aggregation.bases._Weighting`
        responsible for extracting weight vectors from the input matrices.
    """

    def __init__(self, weighting: _Weighting):
        super().__init__()
        self.weighting = weighting

    def forward(self, matrix: Tensor) -> Tensor:
        w = self.weighting(matrix)

        G = matrix.T
        B = self._compute_balance_transformation(G)
        alpha = B @ w

        return alpha

    @staticmethod
    def _compute_balance_transformation(G: Tensor) -> Tensor:
        M = G.T @ G

        lambda_, V = torch.linalg.eigh(M, UPLO="U")  # More modern equivalent to torch.symeig
        tol = torch.max(lambda_) * len(M) * torch.finfo().eps
        rank = sum(lambda_ > tol)

        if rank == 0:
            identity = torch.eye(len(M), dtype=M.dtype, device=M.device)
            return identity

        order = torch.argsort(lambda_, dim=-1, descending=True)
        lambda_, V = lambda_[order][:rank], V[:, order][:, :rank]

        sigma_inv = torch.diag(1 / lambda_.sqrt())
        lambda_R = lambda_[-1]
        B = lambda_R.sqrt() * V @ sigma_inv @ V.T
        return B