sacflow/methods/task_space.py

from __future__ import annotations
import torch
import torch.nn.functional as F


def centered_classifier_basis(W: torch.Tensor, tol: float = 1e-5, foreground_only: bool = False):
    # W: [C,d]
    if foreground_only and W.shape[0] > 1:
        W = W[1:]
    Wc = W - W.mean(dim=0, keepdim=True)
    # U basis in feature dimension for row space of Wc
    U, S, Vh = torch.linalg.svd(Wc.T, full_matrices=False)
    if S.numel() == 0:
        return torch.empty(W.shape[1], 0, device=W.device, dtype=W.dtype)
    r = int((S > tol * S.max()).sum().item())
    return U[:, :max(1, r)]


def random_basis(feature_dim: int, rank: int, device, dtype):
    A = torch.randn(feature_dim, rank, device=device, dtype=dtype)
    Q, _ = torch.linalg.qr(A, mode="reduced")
    return Q


def project_task_and_residual(Fmap: torch.Tensor, Q: torch.Tensor):
    # Fmap [B,d,H,W,D], Q [d,r]
    if Q.numel() == 0:
        return torch.zeros_like(Fmap), Fmap
    B, d, H, W, D = Fmap.shape
    flat = Fmap.permute(0,2,3,4,1).reshape(-1, d)
    task = (flat @ Q) @ Q.T
    task = task.reshape(B,H,W,D,d).permute(0,4,1,2,3).contiguous()
    residual = Fmap - task
    return task, residual


def project_to_residual(x: torch.Tensor, Q: torch.Tensor):
    task, res = project_task_and_residual(x, Q)
    return res