## 1 Introduction  
Automatic speech recognition (ASR) aims at understanding naturally spoken human speech to be used as text inputs to machines so that they can understand the human speaker's intent and further communicate with the talker. The natural speaking environments include speaking in the presence of ambient sounds, or other non-target human speakers. In multi-speaker environments, where multiple speakers are talking simultaneously with a large amount of overlap, a significant performance degradation may occur with conventional ASR systems if trained by recordings of single talkers. This is called the cocktail party problem [1], and it occurs when the speeches of multiple speakers mix together, making it intractable for traditional single-speaker speech recognition models to understand what each person is independently saying. As an example, a dual speakers condition is shown in Figure 1. Two speakers are talking together, which is given by a single recording, and is denoted by **x**. The multi-speaker ASR system is expected to generate the original text sets of what the two independent speakers are saying, denoted by \(\mathbf{y}^{(1)}\) and \(\mathbf{y}^{(2)}\). We use parenthesized and superscripted numbers for the speaker index on the variables, which is not to be confused with exponential notations. In Figure 1, the overlapped speech **x** in the middle is quite different from the first speaker's voice (top left), as well as the second speaker's (top right). Recovering the original texts, such as \"Hello, this is me.\" and \"She goes to school.\", by listening to the mixed sound **x** only is very hard even for human listeners, and this is because adding two sounds may create unexpected artifacts and break the original sounding characteristics. However, these multi-speaker conditions are quite common, such as in ordinary conversations or in speaking with background human speakers. Therefore, multi-speaker speech recognition is required to build ASR systems that are utilizable in any circumstance. Conventional noise suppression techniques may not be applicable because they cannot separate sources with the same characteristics. Many approaches have been proposed to address the challenge of multi-speaker ASR. Techniques such as deep clustering (DPCL) [2] and permutation invariant training (PIT) [3] have been proposed. These techniques are combined with a single-speaker ASR model by bypassing explicit separation outputs as inputs to the ASR model. These methods use either the hybrid ASR framework [4] or the end-to-end ASR framework [5; 6]. The other types of approaches in multi-speaker ASR involve the utilization of speaker embeddings. Various models use speaker embedding as an additional input [7] or joint modeling with the speaker recognition model to create a multi-speaker ASR solution. Well-known methods include speaker-attributed training [8; 9]. Speaker embedding techniques like \(x\)-vectors have been explored to improve the separation and the recognition of overlapped speech. However, these methods encounter challenges, including performance degradation due to speech signal distortion, high computational complexity, and the need for extensive training data. The persistent challenge of recognizing individual speaker speeches in overlapping speech highlights the need for more robust and improved multi-speaker ASR solutions. To solve the aforementioned challenges, we propose a novel speaker-attributed training (SAT) method. The proposed method incorporates speaker embedding information as an additional input. The embedding information for each of the speakers in the training set is extracted as a numeric vector, and all of the embedding vectors are stacked to construct a speaker profile matrix. The profile matrix from the training dataset enables finding the similarities of the embedding vectors to those of the speakers of the input recordings in test conditions, and it helps to separately recognize the multiple speakers' voices mixed in the input.