Basics

A ragged tensor or ragged array in k2 can be used to store the following kinds of data:

  1. A list of lists. Each sub list may contain different number of entries. That is, they can have different lengths.

a = [ [1, 2], [2, 3, 4], [], [1] ]

  1. A list-of-list of lists.

b = [ [[1., 2.5], [2, 3, 4]], [[]], [[10, 20], []] ]

  1. A list-of-list-of-list-of… lists. List can be nested in any number of levels.

Note

Ragged arrays are the core data structures in k2, designed by us independently. We were later told that TensorFlow was using the same ideas (See tf.ragged).

In k2, a ragged tensor contains two parts:

  • a shape, which is of type k2.RaggedShape

  • a value, which can be accessed as a contiguous PyTorch tensor.

Hint

The value is stored contiguously in memory.

Attention

What is the dimension of the value as a torch tensor? (Click ▶ to see it)

It depends on the data type of of the ragged tensor. For instance,

  • if the data type is int32_t, the value is accessed as a 1-D torch tensor with dtype torch.int32.

  • if the data type is float, the value is accessed as a 1-D torch tensor with dtype torch.float32.

  • if the data type is double, the value is accessed as a 1-D torch tensor with dtype torch.float64.

If the data type is k2::Arc, which has the following definition in C++:

struct Arc {
  int32_t src_state;
  int32_t dest_state;
  int32_t label;
  float score;
};

the value is acessed as a 2-D torch tensor with dtype torch.int32. The 2-D tensor has 4 columns: the first column contains src_state, the second column contains dest_state, the third column contains label, and the fourth column contains score (The float type is reinterpreted as int type without any conversions).

There are only 1-D and 2-D value tensors in k2 at present.