code: def _fast_inference_update_state(
      inputs, state, mask_for_predict=None
  ):
      """Updates state of a causal attention layer for fast inference.
  
      The layer state stores arrays with cached values of keys and values,
      as well as an index. To make shapes static, keys and values in the state are
      long, and the index indicates where the new keys and values from inputs need
      to be appended.
  
      During update, we append new_keys and new_values to keys and values at
      position given by index. And we increment index by length of new keys.
      We also create a mask to be 1 at appropriate positions (causal mask).
  
      Args:
        inputs: a triple (new_queries, new_keys, new_values)
        state: layer state with (keys, values, index)
        mask_for_predict: mask used for predict mode. This is used only in
          Terraformer.
  
      Returns:
        Updated state and mask to be used.
      """
      # Fast inference: run step-by-step, storing the sequence
      # of keys and values calculated so far in state.
      (_, new_k, new_v) = inputs
      if mask_for_predict is not None:
          (state_mask_for_predict, ks, vs, idx) = state
      else:
          (ks, vs, idx) = state
      length = new_k.shape[1]
      # TODO(lukaszkaiser): benchmark speed and decide if using a separate code path
      # with index_update when length == 1 is worth it.
      # Keys and values are of shape [batch_size, length, d_kv].
      ks = fastmath.dynamic_update_slice_in_dim(ks, new_k, idx, axis=1)
      vs = fastmath.dynamic_update_slice_in_dim(vs, new_v, idx, axis=1)
      k_length = ks.shape[1]
  
      # Mask is of shape [1, q_length, k_length].
      # Mask should be true for every pair of (query_token, key_token) such that
      # index of query_token is equal or larger to index of key_token.
      mask = jnp.reshape(
          jnp.arange(k_length), (1, 1, k_length)
      ) <= jnp.reshape(jnp.arange(length) + idx, (1, length, 1))
      if mask_for_predict is None:
          return (ks, vs, idx + length), mask
      else:
          state_mask_for_predict = fastmath.dynamic_update_slice_in_dim(
              state_mask_for_predict != 0,
              mask_for_predict.reshape((-1)) != 0,
              0,
              axis=0,
          )
  
          state_mask_for_predict = fastmath.dynamic_update_slice_in_dim(
              state_mask_for_predict != 0,
              jnp.ones((1,)) != 0,
              jnp.sum(mask_for_predict, dtype=jnp.int32),
              axis=0,
          )
  
          state_mask_for_predict = fastmath.dynamic_update_slice_in_dim(
              state_mask_for_predict != 0,
              jnp.ones((1,)) != 0,
              idx,
              axis=0,
          )
          placeholder = jnp.reshape(
              state_mask_for_predict != 0,
              (
                  1,
                  1,
                  mask.shape[2],
              ),
          )
          mask = mask * placeholder
  
          return (state_mask_for_predict, ks, vs, idx + length), mask
  
imports: import numpy
  from trax import fastmath
  from trax.fastmath import numpy
  from trax.layers import base
  from trax.layers import combinators
  from trax.layers import convolution
  from trax.layers import core
  from trax.layers import initializers
  from trax.layers.assert_shape import assert_shape
  from trax.layers.base import Fn
  from trax.layers.research import sparsity
label_desc: Use image node_id 14 for calling a global function with example usage: _fast_inference_update_state(inputs, state, mask_for_predict) and returns: ks,  vs,  unknown,  mask, state_mask_for_predict,  ks,  vs,  unknown,  mask