code: # Copyright (c) 2021, NVIDIA CORPORATION & AFFILIATES. All rights reserved.
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  # Software is furnished to do so, subject to the following conditions:
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  # THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
  # IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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  # SPDX-FileCopyrightText: Copyright (c) 2021 NVIDIA CORPORATION & AFFILIATES
  # SPDX-License-Identifier: MIT
  
  
  from typing import Dict
  
  import numpy as np
  import torch
  import torch.nn as nn
  from torch import Tensor
  
  from se3_transformer.model.fiber import Fiber
  
  
  class LinearSE3(nn.Module):
      """
      Graph Linear SE(3)-equivariant layer, equivalent to a 1x1 convolution.
      Maps a fiber to a fiber with the same degrees (channels may be different).
      No interaction between degrees, but interaction between channels.
  
      type-0 features (C_0 channels) ────> Linear(bias=False) ────> type-0 features (C'_0 channels)
      type-1 features (C_1 channels) ────> Linear(bias=False) ────> type-1 features (C'_1 channels)
                                                   :
      type-k features (C_k channels) ────> Linear(bias=False) ────> type-k features (C'_k channels)
      """
  
      def __init__(self, fiber_in: Fiber, fiber_out: Fiber):
          super().__init__()
          self.weights = nn.ParameterDict({
              str(degree_out): nn.Parameter(
                  torch.randn(channels_out, fiber_in[degree_out]) / np.sqrt(fiber_in[degree_out]))
              for degree_out, channels_out in fiber_out
          })
  
      def forward(self, features: Dict[str, Tensor], *args, **kwargs) -> Dict[str, Tensor]:
          return {
              degree: self.weights[degree] @ features[degree]
              for degree, weight in self.weights.items()
          }
  
apis: torch.randn numpy.sqrt