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Title: Music Source Separation in the Waveform Domain

Paper content:
Source separation for music is the task of isolating contributions, or stems, from different instruments recorded individually and arranged together to form a song.
Such components include voice, bass, drums and any other accompaniments.
While end-to-end models that directly generate the waveform are state-of-the-art in many audio synthesis problems, the best multi-instrument source separation models generate masks on the magnitude spectrum and achieve performances far above current end-to-end, waveform-to-waveform models.
We present an in-depth analysis of a new architecture, which we will refer to as Demucs, based on a (transposed) convolutional autoencoder, with a bidirectional LSTM at the bottleneck layer and skip-connections as in U-Networks (Ronneberger et al., 2015).
Compared to the state-of-the-art waveform-to-waveform model, Wave-U-Net (Stoller et al., 2018), the main features of our approach in addition of the bi-LSTM are the use of trans-posed convolution layers instead of upsampling-convolution blocks, the use of gated linear units, exponentially growing the number of channels with depth and a new careful initialization of the weights.
Results on the MusDB dataset show that our architecture achieves a signal-to-distortion ratio (SDR) nearly 2.2 points higher than the best waveform-to-waveform competitor (from 3.2 to 5.4 SDR).
This makes our model match the state-of-the-art performances on this dataset, bridging the performance gap between models that operate on the spectrogram and end-to-end approaches.
Cherry first noticed the "cocktail party effect" (Cherry, 1953) : how the human brain is able to separate a single conversation out of a surrounding noise from a room full of people chatting.
Bregman later tried to understand how the brain was able to analyse a complex auditory signal and segment it into higher level streams.
His framework for auditory scene analysis (Bregman, 1990 ) spawned its computational counterpart, trying to reproduce or model accomplishments of the brains with algorithmic means (Wang & Brown, 2006) , in particular regarding source separation capabilities.
When producing music, recordings of individual instruments called stems are arranged together and mastered into the final song.
The goal of source separation is to recover those individual stems from the mixed signal.
Unlike the cocktail party problem, there is not a single source of interest to differentiate from an unrelated background noise, but instead a wide variety of tones and timbres playing in a coordinated way.
In the SiSec Mus evaluation campaign for music separation (Stöter et al., 2018) , those individual stems were grouped into 4 broad categories: (1) drums, (2) bass, (3) other, (4) vocals.
Given a music track which is a mixture of these four sources, also called the mix, the goal is to generate four waveforms that correspond to each of the original sources.
We consider here the case of supervised source separation, where the training data contain music tracks (i.e., mixtures), together with the ground truth waveform for each of the sources.
State-of-the-art approaches in music source separation still operate on the spectrograms generated by the short-time Fourier transform (STFT).
They produce a mask on the magnitude spectrums for each frame and each source, and the output audio is generated by running an inverse STFT on the masked spectrograms reusing the input mixture phase Takahashi et al., 2018) .
Several architectures trained end-to-end to directly synthesize the waveforms have been proposed (Lluís et al., 2018; Jansson et al., 2017) , but their performances are far below the state-of-the-art: in Figure 1 : Mel-spectrogram for a 0.8 seconds extract of the bass source from the track "Stich Up" of the MusDB test.
From left to right: ground truth, Conv-Tasnet estimate and Demucs estimate.
We observe that Conv-Tasnet missed one note entirely.
the last SiSec Mus evaluation campaign (Stöter et al., 2018) , the best model that directly predicts waveforms achieves an average signal-to-noise ratio (SDR) over all four sources of 3.2, against 5.3 for the best approach that predicts spectrograms masks (also see Table 1 in Section 6).
An upper bound on the performance of all methods relying on masking spectrograms is given by the SDR obtained when using a mask computed using the ground truth sources spectrograms, for instance the Ideal Ratio Mask (IRM) or the Ideal Binary Mask (IBM) oracles.
For speech source separation, Luo & Mesgarani (2019) proposed Conv-Tasnet, a model that reuses the masking approach of spectrogram methods but learns the masks jointly with a convolutional front-end, operating directly in the waveform domain for both the inputs and outputs.
Conv-Tasnet surpasses both the IRM and IBM oracles.
Our first contribution is to adapt the Conv-Tasnet architecture, originally designed for monophonic speech separation and audio sampled at 8 kHz, to the task of sterephonic music source separation for audio sampled at 44.1 kHz.
Our experiments show that Conv-Tasnet outperforms all previous methods by a large margin, with an SDR of 5.7, but still under the SDR of the IRM oracle at 8.2 (Stöter et al., 2018) .
However, while Conv-Tasnet separates with a high accuracy the different sources, we observed artifacts when listening to the generated audio: a constant broadband noise, hollow instruments attacks or even missing parts.
They are especially noticeable on the drums and bass sources and we give one such example on Figure 1 .
Conv-Tasnet uses an over-complete linear representation on which it applies a mask obtained from a deep convolutional network.
Because both the encoder and decoder are linear, the masking operation cannot synthesize new sounds.
We conjecture that the overlap of multiples instruments sometimes lead to a loss of information that is not reversible by a masking operation.
To overcome the limitations of Conv-Tasnet, our second contribution is to propose Demucs, a new architecture for music source separation.
Similarly to Conv-Tasnet, Demucs is a deep learning model that directly operates on the raw input waveform and generates a waveform for each source.
Demucs is inspired by models for music synthesis rather than masking approaches.
It is a U-net architecture with a convolutional encoder and a decoder based on wide transposed convolutions with large strides inspired by recent work on music synthesis (Défossez et al., 2018) .
The other critical features of the approach are a bidirectional LSTM between the encoder and the decoder, increasing the number of channels exponentially with depth, gated linear units as activation function (Dauphin et al., 2017) which also allow for masking, and a new initialization scheme.
We present experiments on the MusDB benchmark, which first show that both Conv-Tasnet and Demucs achieve performances significantly better than the best methods that operate on the spectrogram, with Conv-Tasnet being better than Demucs in terms of SDR.
We also perform human evaluations that compare Conv-Tasnet and our Demucs, which show that Demucs has significantly better perceived quality.
The smaller SDR of Demucs is explained by more contamination from other sources.
We also conduct an in-depth ablation study of the Demucs architecture to demonstrate the impact of the various design decisions.
Finally, we carry out additional experiments by adding 150 songs to the training set.
In this experiment, Demucs and TasNet both achieve an SDR of 6.3, suggesting that the gap in terms of SDR between the two models diminishes with more data, making the Demucs approach promising.
The 6.3 points of SDR also set a new state-of-the-art, since it improves on the best previous result of 6.0 on the MusDB test set obtained by training with 800 additional songs.
We discuss in more detail the related work in the next Section.
We then describe the original ConvTasnet model of Luo & Mesgarani (2018) and its adaptation to music source separation.
Our Demucs architecture is detailed in Section 4.
We present the experimental protocol in Section 5, and the experimental results compared to the state-of-the-art in Section 6.
Finally, we describe the results of the human evaluation and the ablation study.
We showed that Conv-Tasnet, a state-of-the-art architecture for speech source separation that predicts masks on a learnt front-end over the waveform domain, achieves state-of-the-art performance for music source separation, improving over all previous spectrogram or waveform domain methods by 0.4 SDR.
While Conv-Tasnet has excellent performance to separate sources, it suffers from noticeable artifacts as confirmed by human evaluations.
We developed an alternative approach, Demucs, that combines the ability to mask over a learnt representation with stronger decoder capacity that allows for audio synthesis.
We conjecture that this can be useful when information is lost in the mix of instruments and cannot simply be recovered by masking.
We show that our approach produces audio of significantly higher quality as measures by mean opinion scores and matches the SDR of Conv-Tasnet when trained with 150 extra tracks.
We believe those results make it a promising alternative to methods based on masking only.

assistant: text: We match the performance of spectrogram based model with a model trained end-to-end in the waveform domain