LinearWithRepeat layer for NeRF

Summary:
Add custom layer to avoid repeating copied data for every ray position.

This should also save time in the backward pass because there are fewer multiplies with the weights.

Reviewed By: theschnitz

Differential Revision: D28382412

fbshipit-source-id: 1ba7356cd8520ebd598568ae503e47d31d3989eb

projects/nerf/nerf/implicit_function.py

@@ -5,6 +5,7 @@ import torch
 from pytorch3d.renderer import RayBundle, ray_bundle_to_ray_points
 
 from .harmonic_embedding import HarmonicEmbedding
+from .linear_with_repeat import LinearWithRepeat
 
 
 def _xavier_init(linear):
@@ -75,7 +76,7 @@ class NeuralRadianceField(torch.nn.Module):
         self.density_layer.bias.data[:] = 0.0  # fixme: Sometimes this is not enough
 
         self.color_layer = torch.nn.Sequential(
-            torch.nn.Linear(
+            LinearWithRepeat(
                 n_hidden_neurons_xyz + embedding_dim_dir, n_hidden_neurons_dir
             ),
             torch.nn.ReLU(True),
@@ -116,7 +117,6 @@ class NeuralRadianceField(torch.nn.Module):
         and evaluates the color model in order to attach to each
         point a 3D vector of its RGB color.
         """
-        spatial_size = features.shape[:-1]
         # Normalize the ray_directions to unit l2 norm.
         rays_directions_normed = torch.nn.functional.normalize(rays_directions, dim=-1)
 
@@ -129,18 +129,7 @@ class NeuralRadianceField(torch.nn.Module):
             dim=-1,
         )
 
-        # Expand the ray directions tensor so that its spatial size
-        # is equal to the size of features.
-        rays_embedding_expand = rays_embedding[..., None, :].expand(
-            *spatial_size, rays_embedding.shape[-1]
-        )
-
-        # Concatenate ray direction embeddings with
-        # features and evaluate the color model.
-        color_layer_input = torch.cat(
-            (self.intermediate_linear(features), rays_embedding_expand), dim=-1
-        )
-        return self.color_layer(color_layer_input)
+        return self.color_layer((self.intermediate_linear(features), rays_embedding))
 
     def forward(
         self,

projects/nerf/nerf/linear_with_repeat.py

+# Copyright (c) Facebook, Inc. and its affiliates. All rights reserved.
+from typing import Tuple
+
+import torch
+import torch.nn.functional as F
+
+
+class LinearWithRepeat(torch.nn.Linear):
+    """
+    if x has shape (..., k, n1)
+    and y has shape (..., n2)
+    then
+    LinearWithRepeat(n1 + n2, out_features).forward((x,y))
+    is equivalent to
+    Linear(n1 + n2, out_features).forward(
+        torch.cat([x, y.unsqueeze(-2).expand(..., k, n2)], dim=-1)
+    )
+
+    Or visually:
+    Given the following, for each ray,
+
+                feature   ->
+
+    ray         xxxxxxxx
+    position    xxxxxxxx
+      |         xxxxxxxx
+      v         xxxxxxxx
+
+
+    and
+                            yyyyyyyy
+
+    where the y's do not depend on the position
+    but only on the ray,
+    we want to evaluate a Linear layer on both
+    types of data at every position.
+
+    It's as if we constructed
+
+                xxxxxxxxyyyyyyyy
+                xxxxxxxxyyyyyyyy
+                xxxxxxxxyyyyyyyy
+                xxxxxxxxyyyyyyyy
+
+    and sent that through the Linear.
+    """
+
+    def forward(self, input: Tuple[torch.Tensor, torch.Tensor]) -> torch.Tensor:
+        n1 = input[0].shape[-1]
+        output1 = F.linear(input[0], self.weight[:, :n1], self.bias)
+        output2 = F.linear(input[1], self.weight[:, n1:], None)
+        return output1 + output2.unsqueeze(-2)