| import torch |
|
|
|
|
| def compute_local_perms(diag_H, groupsize): |
| """ |
| For each group, compute a permutation that orders the indices in descending order |
| based on the corresponding diagonal values of H. |
| |
| Args: |
| diag_H (Tensor): 1D tensor representing the diagonal of the Hessian. |
| groupsize (int): Number of columns/weights per group. |
| |
| Returns: |
| local_perms (list of Tensors): Each element is a permutation (indices) for that group. |
| """ |
| n = diag_H.numel() |
| num_groups = n // groupsize |
| local_perms = [] |
| for g in range(num_groups): |
| start = g * groupsize |
| end = start + groupsize |
| sub_diag = diag_H[start:end] |
| |
| local_perm = torch.argsort(sub_diag, descending=True) |
| local_perms.append(local_perm) |
| return local_perms |
|
|
| def compute_global_perm(diag_H, groupsize): |
| """ |
| Compute a permutation for the groups themselves. Here we choose the maximum diagonal value |
| within each group as the group metric and sort the groups in descending order. |
| |
| Args: |
| diag_H (Tensor): 1D tensor representing the diagonal of the Hessian. |
| groupsize (int): Number of columns/weights per group. |
| |
| Returns: |
| global_perm (Tensor): 1D tensor of length num_groups with the new order of groups. |
| """ |
| n = diag_H.numel() |
| num_groups = n // groupsize |
| group_metric = [] |
| for g in range(num_groups): |
| start = g * groupsize |
| end = start + groupsize |
| group_metric.append(diag_H[start:end].max().item()) |
| |
| group_metric = torch.tensor(group_metric, device=diag_H.device) |
| global_perm = torch.argsort(group_metric, descending=True) |
| return global_perm |
|
|
| def compose_final_perm(local_perms, global_perm, groupsize): |
| """ |
| Compose the final overall permutation from the local and global permutations. |
| |
| Args: |
| local_perms (list of Tensors): Local permutation for each group. |
| global_perm (Tensor): Global group permutation. |
| groupsize (int): Number of indices per group. |
| |
| Returns: |
| final_perm (Tensor): 1D tensor that maps original indices to new positions. |
| """ |
| num_groups = len(local_perms) |
| final_perm = [] |
| |
| for new_group in range(num_groups): |
| |
| orig_group = global_perm[new_group].item() |
| offset = orig_group * groupsize |
| local_perm = local_perms[orig_group] |
| |
| for idx in local_perm: |
| final_perm.append(idx.item() + offset) |
| return torch.tensor(final_perm, dtype=torch.long) |
|
|
| def invert_perm(perm): |
| """ |
| Compute the inverse of a permutation vector. |
| |
| Args: |
| perm (Tensor): A 1D tensor containing a permutation of indices. |
| |
| Returns: |
| inv (Tensor): The inverse permutation such that inv[perm] == torch.arange(len(perm)). |
| """ |
| inv = torch.empty_like(perm) |
| inv[perm] = torch.arange(perm.numel(), device=perm.device) |
| return inv |
|
|