## 4 Experimental Performance Evaluation
### Evaluation Results and Discussions

Table 2: Performance comparison of the baseline model and the proposed models in terms of the WER and their relative improvements (shown in parentheses) from the baseline. For the compact notation, the following abbreviations were used: SS-ASR (single-speaker automatic speech recognition); MS-ASR (multi-speaker automatic speech recognition); SAT (speaker-attributed training); and DPRNN-TasNet (dual-path recurrent neural network-based time-domain audio separation network). The second and third columns show the number of parameters to be trained (where ‘M’ stands for million) and the time required by a single NVIDIA GTX Titan GPU to train those parameters, respectively. The forth column shows the word error rates on the test set. Figure 5: Comparison of the number of profile utterances on the _LibriMix_ dataset by WER. The third row is the Transformer-based multi-speaker automatic speech recognition (MS-ASR) method [6]. This model corresponds to Figure 2-(b), which uses a split encoder for the multi-speaker speech inputs. It requires training a split encoder (Enc\({}_{\text{mix}}\) in Figure 3), speaker differentiation encoder (Enc\({}_{\text{diff}}\)), and recognition encoder (Enc\({}_{\text{rec}}\)). The total number of trainable parameters was about 60 million, and they were trained with the _train-clean_ subset of _Libri2 Mix_, whose size is 64,700 utterances and 270 h of mixed speech, as shown in Table 1. The training time was 320 GPU hours, excluding the time for the pretrained Enc\({}_{\text{speaker}}\), Dec\({}_{\text{speaker}}\), and Dec\({}_{\text{rec}}\) in Figure 3. The evaluated WER on the same test set was 8.43%, which represents a significant improvement over the other conventional methods. The next three rows are the results of the proposed method described in Section 3.1 and correspond to Figure 3. Three different types of speaker embedding vectors were concatenated with the input features of mixed speech to emphasize the information of the speakers. Then, the proposed speaker-attributed training (SAT) technique in Algorithm 3 was applied to the baseline MS-ASR. The number of trainable parameters for the \(i\)-vectors was the same as that of the baseline MS-ASR because there were no additional layers. In the case of the \(d\)- and \(x\)-vectors, 11.2 and 4.2 million trainable parameters were added. The training times with the same _train-clean_ set of _Libri2 Mix_ were 320, 336, and 328 GPU hours, respectively. The increased training time was less than 5% compared to the baseline. However, these methods also require the decoders of the pretrained SS-ASR model so one should also consider the overhead of training SS-ASR if it is not available. The WER of the \(i\)-vectors on the test set was 8.5%, which is worse than the baseline's WER of 8.43%. The \(d\)-vectors' WER was 8.32%, whose relative improvement was 1.3% from the baseline. For the \(x\)-vectors, a WER of 8.1% and 3.9% relative improvement were obtained, and they achieved the best results among the methods with speaker-attributed training using speaker embedding vectors directly. The bottom three rows present the results of the method described in Section 3.2 and are shown in Figure 4. The same speaker embedding vectors were used, but the extracted vectors were replaced by the linear combinations of the profile embedding vectors from the 20 selected utterances. The differences from the method in Section 3.1 were due to the attention weighting provided by Algorithm 4 and the forward inference by Algorithm 5. The storage size and computation time of the profile matrix was almost negligible so the number of trainable parameters and training times were almost the same as SAT without profile weighting. The evaluated WERs on the test set were 8.27%, 8.18%, and 7.48% for the \(i\)-, \(d\)-, and \(x\)-vectors, respectively. All of the WERs were improved with the addition of speaker profiles. In particular, the \(x\)-vectors achieved a 11.2% relative improvement from the baseline, which was the best among all the cases.