## 1 Introduction  
Automatic music transcription (AMT) is a process of transcribing a musical audio signal into a symbolic representation, such as a piano roll or music score. It has many applications in music information retrieval, composition, music education, and music visualization. AMT has been researched for four decades (since 1977) [1; 2], and it is still a challenging problem. While the transcription of monophonic music is considered solved, polyphonic AMT remains open because the signal is more complex. In polyphonic music, many notes overlap in the time domain and interact in the frequency domain. Additionally, the complexity of polyphony increases with the number of sound sources. For example, the concurrent notes in orchestral music come from instruments of different timbral properties, and the corresponding AMT performance is poor. Note is the basic unit of music, and the main problem of transcription is to extract the information of every note in the music [3]. For each note, a set of information includes: pitch, onset, offset, loudness, and timbre. Pitch is a major attribute of auditory sensation, which can be reliably related to the fundamental frequency (F0). Onset refers to the beginning time of a note, and offset refers to the ending time. Loudness is the characteristic related to the amplitude of a sound. Timbre is that perceptual attribute in which a listener can judge that two sounds having the same loudness and pitch are dissimilar. In general, we only focus on which notes are played and when they appear in the music. Therefore, the pitch and onset time are necessary in the results of AMT. The approaches to polyphonic transcription can be divided into frame-based methods and note-based methods [4]. The frame-based approaches estimate pitches in each time frame and form frame-level results in a post-processing stage. The most straightforward solution is to analyze the time-frequency representation of audio and compute the fundamental frequencies [5]. Short-time Fourier transform (STFT) [6; 7] and constant Q transform (CQT) [8] are two widely used time-frequency analysis methods. [PERSON] proposed resonator time-frequency image (RTFI), in which a first-order complex resonator filter bank is adopted to the analysis of music [9]. [PERSON] used multi-resolution STFT, and the pitch was estimated by detecting peaks in the weighted spectrum [10]. Spectrogram factorization techniques are also very popular in AMT, such as non-negative matrix factorization (NMF) [11]. Probabilistic latent component analysis (PLCA) is another factorization technique, which aims to fit a latent variable probabilistic model to normalised spectrograms [12; 13]. Apart from the discriminative approaches, deep neural networks have been used to identify pitches recently. [PERSON] superimposed a support vector machine (SVM) on top of a deep belief network (DBN) to learn feature representations [14]. [PERSON] compared the performance of neural networks and proposed a recurrent neural network (RNN) language model for music transcription [15]. [PERSON] utilized both a ConvNet and an AUNet in transcription, and investigated the glass ceiling effect of deep neural networks [16]. The note-based transcription approaches directly estimate notes, including pitches and onsets. One solution is combining the estimation of pitches and onsets into a single framework [17; 18]. [PERSON] [19] used harmonic temporal structured clustering to estimate the attributes of notes simultaneously. In [20], [PERSON] used an RNN with bidirectional long short-term memory (LSTM) units. Similarly, [PERSON] utilized three kinds of neural networks to transfer the input audio to a list of notes, along with the corresponding pitches and onset times [21]. Another solution is employing a separate onset detection stage and an additional pitch estimation stage. The approaches in this category often estimate the pitches using the segments between two successive onsets, and an accurate onset detection benefits the transcription.