Mean attention distance

attention_distance.py

# Copyright 2022 Google LLC.
# SPDX-License-Identifier: Apache-2.0
# Author: Maithra Raghu <[email protected]>


def compute_distance_matrix(patch_size, num_patches, length):
  """Helper function to compute distance matrix."""

  distance_matrix = np.zeros((num_patches, num_patches))

  for i in range(num_patches):
    for j in range(num_patches):
      if i == j: # zero distance
        continue

      xi, yi = (int(i/length)), (i % length)
      xj, yj = (int(j/length)), (j % length)

      distance_matrix[i, j] = patch_size*np.linalg.norm([xi - xj, yi - yj])
  
  return distance_matrix



def compute_mean_attention_dist(patch_size, attention_weights):
  num_patches = attention_weights.shape[-1]
  length = int(np.sqrt(num_patches))
  assert (length**2 == num_patches), ("Num patches is not perfect square")

  distance_matrix = compute_distance_matrix(patch_size, num_patches, length)
  h, w = distance_matrix.shape

  distance_matrix = distance_matrix.reshape((1, 1, h, w))
  mean_distances = attention_weights*distance_matrix
  mean_distances = np.sum(mean_distances, axis=-1) # sum along last axis to get average distance per token
  mean_distances = np.mean(mean_distances, axis=-1) # now average across all the tokes

  return mean_distances

Hey! I had a quick question regarding the attention distance calculation. Since the attention scores are softmaxed over all tokens (including the CLS token), removing the CLS token would mean we're slicing out a portion of the normalized distribution. That would make the attention weights over the 196 patch tokens no longer sum to 1.
Shouldn't we re-normalize the remaining 196 attention weights after excluding the CLS token? Otherwise, the computed mean attention distance wouldn’t truly reflect a proper expectation under a valid probability distribution. Curious if this step was intentionally skipped or if there's a rationale for not re-normalizing.

Thanks in advance!