code: def test_model_training_with_k2(k2_params):
      pytest.importorskip("k2")
  
      batch_size = 2
      input_size = 10
  
      token_list = ["<blank>", "a", "b", "c", "<space>"]
      vocab_size = len(token_list)
  
      encoder = Encoder(
          input_size,
          [
              {
                  "block_type": "conformer",
                  "hidden_size": 4,
                  "linear_size": 4,
                  "conv_mod_kernel_size": 3,
              }
          ],
      )
      decoder = RNNDecoder(vocab_size, embed_size=8, hidden_size=8)
  
      joint_network = JointNetwork(
          vocab_size,
          encoder.output_size,
          decoder.output_size,
      )
  
      model = ESPnetASRTransducerModel(
          vocab_size,
          token_list,
          frontend=None,
          normalize=None,
          specaug=None,
          encoder=encoder,
          decoder=decoder,
          joint_network=joint_network,
          use_k2_pruned_loss=True,
          k2_pruned_loss_args=k2_params,
          report_cer=True,
          report_wer=True,
      )
  
      feats, labels, feat_len, label_len = prepare(
          model,
          input_size,
          vocab_size,
          batch_size,
          use_k2_modified_loss=True,
      )
  
      _ = model(feats, feat_len, labels, label_len)
  
      model.training = False
      _ = model(feats, feat_len, labels, label_len)
  
imports: from pathlib import Path
  import numpy
  import pytest
  import torch
  from espnet2.asr.specaug.specaug import SpecAug
  from espnet2.asr_transducer.decoder.mega_decoder import MEGADecoder
  from espnet2.asr_transducer.decoder.rnn_decoder import RNNDecoder
  from espnet2.asr_transducer.decoder.rwkv_decoder import RWKVDecoder
  from espnet2.asr_transducer.decoder.stateless_decoder import StatelessDecoder
  from espnet2.asr_transducer.encoder.encoder import Encoder
  from espnet2.asr_transducer.espnet_transducer_model import ESPnetASRTransducerModel
  from espnet2.asr_transducer.joint_network import JointNetwork
  from espnet2.layers.global_mvn import GlobalMVN
  from espnet2.layers.utterance_mvn import UtteranceMVN
label_desc: Use image node_id 6 for calling a global function with example usage: test_model_training_with_k2(k2_params) without return types