fix the implementation of CoPE

egs/librispeech/ASR/zipformer/test_cope.py

@@ -1,14 +1,17 @@
 #!/usr/bin/env python3
 
+import torch
 from zipformer import ContextualPositionalEncoding
 
 
 def test():
     embed_dim = 5
     npos_max = 10
+
     cope = ContextualPositionalEncoding(embed_dim=embed_dim, npos_max=npos_max)
-    q = torch.rand(2, 3, 4, embed_dim)
+    q = torch.rand(2, 3, npos_max, embed_dim)
-    qk = torch.rand(2, 3, 4, 6)
+
+    qk = torch.rand(2, 3, npos_max, npos_max)
 
     p = cope(q=q, qk=qk)
     print(p.shape)
@@ -19,4 +22,5 @@ def main():
 
 
 if __name__ == "__main__":
+    torch.manual_seed(20240703)
     main()

egs/librispeech/ASR/zipformer/zipformer.py

@@ -1402,26 +1402,59 @@ class ContextualPositionalEncoding(torch.nn.Module):
             qk (torch.Tensor): A tensor of shape (head, batch, time1, time2)
         Returns:
           Return a tensor of shape (head, batch, time1, npos_max)
+
+        Note the implementation assumes time1 == time2 and npos_max <= time2.
+        The implementation is reasonable for the streaming ASR encoder where
+        only self attention is used.
         """
+        # The implementation on page 13 Listing 1 from the paper does not use
+        # a mask to ensure that only gates[:, :, i, j] where j < i is computed.
+        #
+        # Here we fix that by introducing a mask
+        mask = torch.triu(
+            torch.full((qk.size(3), qk.size(3)), True, dtype=torch.bool),
+            diagonal=0,
+        )
+        #
+        # if qk.size(3) is 4, mask is
+        #
+        #  tensor([[ True,  True,  True,  True],
+        #          [False,  True,  True,  True],
+        #          [False, False,  True,  True],
+        #          [False, False, False,  True]])
+        #
+        # mask[i, j] is True if i >= j
         gates = torch.sigmoid(qk)
-        pos = gates.sum(dim=-1, keepdim=True)  # (head, batch, dim1, 1)
+
-        # Note: We don't use cumulative sum here for non-streaming
+        # We don't use an in-place operation here for the sake of autograd
-        # speech recognition
+        gates = gates.masked_fill(mask, 0)
+
+        # cumsum() is an inclusive sum in PyTorch
+        pos = gates.flip(-1).cumsum(dim=-1).flip(-1)  # (head, batch, time1, time2)
+        # pos[:, :, i, j] should be 0 for j >= i
+        # pos[:, :, i, j] contains the position between i and j. If gates
+        # is a 0-1 matrix, then pos[:, :, i, j] equals to i - j (for j < i)
+        # Note: The paper says on page 4 it equals to i - j + 1 instead of i - j.
 
         pos = pos.clamp(max=self.npos_max - 1)
         pos_ceil = pos.ceil().long()
         pos_floor = pos.floor().long()
+
+        # We assume query_head_dim equals to embed_dim
+
         logits_int = torch.matmul(
             q, self.embedding.weight.t()
         )  # (head, batch, time1, npos_max)
-        logits_cell = logits_int.gather(-1, pos_ceil.expand(*logits_int.shape))
+
-        logits_floor = logits_int.gather(-1, pos_floor.expand(*logits_int.shape))
+        # We assume that npos_max <= time2
+        logits_cell = logits_int.gather(-1, pos_ceil)
+        logits_floor = logits_int.gather(-1, pos_floor)
 
         w = pos - pos_floor
-        return logits_cell * w + logits_floor * (1 - w)
 
-    def streaming_forward(self):
+        # Note: The code in the paper on page 13 is correct
-        raise RuntimeError("To be implemented")
+        # while the description on page 4 equation (5) is wrong
+        return logits_cell * w + logits_floor * (1 - w)
 
 
 class CompactRelPositionalEncoding(torch.nn.Module):