In this paper we introduce the Frechet Music Distance (FMD), a novel evaluation metric for generative symbolic music models, inspired by the Frechet Inception Distance (FID) in computer vision and Frechet Audio Distance (FAD) in generative audio. FMD calculates the distance between distributions of reference and generated symbolic music embeddings, capturing abstract musical features. We validate FMD across several datasets and models. Results indicate that FMD effectively differentiates model quality, providing a domain-specific metric for evaluating symbolic music generation, and establishing a reproducible standard for future research in symbolic music modeling.
Symbolic music is widely used in various deep learning tasks, including generation, transcription, synthesis, and Music Information Retrieval (MIR). It is mostly employed with discrete models like Transformers, which require music to be tokenized, i.e., formatted into sequences of distinct elements called tokens. Tokenization can be performed in different ways. As Transformer can struggle at reasoning, but capture more easily explicit information, it is important to study how the way the information is represented for such model impact their performances. In this work, we analyze the common tokenization methods and experiment with time and note duration representations. We compare the performances of these two impactful criteria on several tasks, including composer and emotion classification, music generation, and sequence representation learning. We demonstrate that explicit information leads to better results depending on the task.
Following the success of the transformer architecture in the natural language domain, transformer-like architectures have been widely applied to the domain of symbolic music recently. Symbolic music and text, however, are two different modalities. Symbolic music contains multiple attributes, both absolute attributes (e.g., pitch) and relative attributes (e.g., pitch interval). These relative attributes shape human perception of musical motifs. These important relative attributes, however, are mostly ignored in existing symbolic music modeling methods with the main reason being the lack of a musically-meaningful embedding space where both the absolute and relative embeddings of the symbolic music tokens can be efficiently represented. In this paper, we propose the Fundamental Music Embedding (FME) for symbolic music based on a bias-adjusted sinusoidal encoding within which both the absolute and the relative attributes can be embedded and the fundamental musical properties (e.g., translational invariance) are explicitly preserved. Taking advantage of the proposed FME, we further propose a novel attention mechanism based on the relative index, pitch and onset embeddings (RIPO attention) such that the musical domain knowledge can be fully utilized for symbolic music modeling. Experiment results show that our proposed model: RIPO transformer which utilizes FME and RIPO attention outperforms the state-of-the-art transformers (i.e., music transformer, linear transformer) in a melody completion task. Moreover, using the RIPO transformer in a downstream music generation task, we notice that the notorious degeneration phenomenon no longer exists and the music generated by the RIPO transformer outperforms the music generated by state-of-the-art transformer models in both subjective and objective evaluations.
Structured distributions, i.e. distributions over combinatorial spaces, are commonly used to learn latent probabilistic representations from observed data. However, scaling these models is bottlenecked by the high computational and memory complexity with respect to the size of the latent representations. Common models such as Hidden Markov Models (HMMs) and Probabilistic Context-Free Grammars (PCFGs) require time and space quadratic and cubic in the number of hidden states respectively. This work demonstrates a simple approach to reduce the computational and memory complexity of a large class of structured models. We show that by viewing the central inference step as a matrix-vector product and using a low-rank constraint, we can trade off model expressivity and speed via the rank. Experiments with neural parameterized structured models for language modeling, polyphonic music modeling, unsupervised grammar induction, and video modeling show that our approach matches the accuracy of standard models at large state spaces while providing practical speedups.
Recurrent neural networks have flourished in many areas. Consequently, we can see new RNN cells being developed continuously, usually by creating or using gates in a new, original way. But what if we told you that gates in RNNs are redundant? In this paper, we propose a new recurrent cell called Residual Recurrent Unit (RRU) which beats traditional cells and does not employ a single gate. It is based on the residual shortcut connection, linear transformations, ReLU, and normalization. To evaluate our cell's effectiveness, we compare its performance against the widely-used GRU and LSTM cells and the recently proposed Mogrifier LSTM on several tasks including, polyphonic music modeling, language modeling, and sentiment analysis. Our experiments show that RRU outperforms the traditional gated units on most of these tasks. Also, it has better robustness to parameter selection, allowing immediate application in new tasks without much tuning. We have implemented the RRU in TensorFlow, and the code is made available at https://github.com/LUMII-Syslab/RRU .
An important goal of AutoML is to automate-away the design of neural networks on new tasks in under-explored domains. Motivated by this goal, we study the problem of enabling users to discover the right neural operations given data from their specific domain. We introduce a search space of operations called XD-Operations that mimic the inductive bias of standard multi-channel convolutions while being much more expressive: we prove that it includes many named operations across multiple application areas. Starting with any standard backbone such as ResNet, we show how to transform it into a search space over XD-operations and how to traverse the space using a simple weight-sharing scheme. On a diverse set of tasks -- solving PDEs, distance prediction for protein folding, and music modeling -- our approach consistently yields models with lower error than baseline networks and often even lower error than expert-designed domain-specific approaches.
A great number of deep learning based models have been recently proposed for automatic music composition. Among these models, the Transformer stands out as a prominent approach for generating expressive classical piano performance with a coherent structure of up to one minute. The model is powerful in that it learns abstractions of data on its own, without much human-imposed domain knowledge or constraints. In contrast with this general approach, this paper shows that Transformers can do even better for music modeling, when we improve the way a musical score is converted into the data fed to a Transformer model. In particular, we seek to impose a metrical structure in the input data, so that Transformers can be more easily aware of the beat-bar-phrase hierarchical structure in music. The new data representation maintains the flexibility of local tempo changes, and provides hurdles to control the rhythmic and harmonic structure of music. With this approach, we build a Pop Music Transformer that composes Pop piano music with better rhythmic structure than existing Transformer models.
We address the challenging open problem of learning an effective latent space for symbolic music data in generative music modeling. We focus on leveraging adversarial regularization as a flexible and natural mean to imbue variational autoencoders with context information concerning music genre and style. Through the paper, we show how Gaussian mixtures taking into account music metadata information can be used as an effective prior for the autoencoder latent space, introducing the first Music Adversarial Autoencoder (MusAE). The empirical analysis on a large scale benchmark shows that our model has a higher reconstruction accuracy than state-of-the-art models based on standard variational autoencoders. It is also able to create realistic interpolations between two musical sequences, smoothly changing the dynamics of the different tracks. Experiments show that the model can organise its latent space accordingly to low-level properties of the musical pieces, as well as to embed into the latent variables the high-level genre information injected from the prior distribution to increase its overall performance. This allows us to perform changes to the generated pieces in a principled way.
This paper explores sequential modelling of polyphonic music with deep neural networks. While recent breakthroughs have focussed on network architecture, we demonstrate that the representation of the sequence can make an equally significant contribution to the performance of the model as measured by validation set loss. By extracting salient features inherent to the training dataset, the model can either be conditioned on these features or trained to predict said features as extra components of the sequences being modelled. We show that training a neural network to predict a seemingly more complex sequence, with extra features included in the series being modelled, can improve overall model performance significantly. We first introduce TonicNet, a GRU-based model trained to initially predict the chord at a given time-step before then predicting the notes of each voice at that time-step, in contrast with the typical approach of predicting only the notes. We then evaluate TonicNet on the canonical JSB Chorales dataset and obtain state-of-the-art results.
We propose a new STAckable Recurrent cell (STAR) for recurrent neural networks (RNNs), which has fewer parameters than widely used LSTM and GRU while being more robust against vanishing or exploding gradients. Stacking recurrent units into deep architectures suffers from two major limitations: (i) many recurrent cells (e.g., LSTMs) are costly in terms of parameters and computation resources; and (ii) deep RNNs are prone to vanishing or exploding gradients during training. We investigate the training of multi-layer RNNs and examine the magnitude of the gradients as they propagate through the network in the "vertical" direction. We show that, depending on the structure of the basic recurrent unit, the gradients are systematically attenuated or amplified. Based on our analysis we design a new type of gated cell that better preserves gradient magnitude. We validate our design on a large number of sequence modelling tasks and demonstrate that the proposed STAR cell allows to build and train deeper recurrent architectures, ultimately leading to improved performance while being computationally more efficient.
Convolutional neural networks (CNNs) with dilated filters such as the Wavenet or the Temporal Convolutional Network (TCN) have shown good results in a variety of sequence modelling tasks. However, efficiently modelling long-term dependencies in these sequences is still challenging. Although the receptive field of these models grows exponentially with the number of layers, computing the convolutions over very long sequences of features in each layer is time and memory-intensive, prohibiting the use of longer receptive fields in practice. To increase efficiency, we make use of the "slow feature" hypothesis stating that many features of interest are slowly varying over time. For this, we use a U-Net architecture that computes features at multiple time-scales and adapt it to our auto-regressive scenario by making convolutions causal. We apply our model ("Seq-U-Net") to a variety of tasks including language and audio generation. In comparison to TCN and Wavenet, our network consistently saves memory and computation time, with speed-ups for training and inference of over 4x in the audio generation experiment in particular, while achieving a comparable performance in all tasks.
Recurrent Neural Networks have long been the dominating choice for sequence modeling. However, it severely suffers from two issues: impotent in capturing very long-term dependencies and unable to parallelize the sequential computation procedure. Therefore, many non-recurrent sequence models that are built on convolution and attention operations have been proposed recently. Notably, models with multi-head attention such as Transformer have demonstrated extreme effectiveness in capturing long-term dependencies in a variety of sequence modeling tasks. Despite their success, however, these models lack necessary components to model local structures in sequences and heavily rely on position embeddings that have limited effects and require a considerable amount of design efforts. In this paper, we propose the R-Transformer which enjoys the advantages of both RNNs and the multi-head attention mechanism while avoids their respective drawbacks. The proposed model can effectively capture both local structures and global long-term dependencies in sequences without any use of position embeddings. We evaluate R-Transformer through extensive experiments with data from a wide range of domains and the empirical results show that R-Transformer outperforms the state-of-the-art methods by a large margin in most of the tasks. We have made the code publicly available at \url{https://github.com/DSE-MSU/R-transformer}.
Long Short-Term Memory (LSTM) infers the long term dependency through a cell state maintained by the input and the forget gate structures, which models a gate output as a value in [0,1] through a sigmoid function. However, due to the graduality of the sigmoid function, the sigmoid gate is not flexible in representing multi-modality or skewness. Besides, the previous models lack modeling on the correlation between the gates, which would be a new method to adopt inductive bias for a relationship between previous and current input. This paper proposes a new gate structure with the bivariate Beta distribution. The proposed gate structure enables probabilistic modeling on the gates within the LSTM cell so that the modelers can customize the cell state flow with priors and distributions. Moreover, we theoretically show the higher upper bound of the gradient compared to the sigmoid function, and we empirically observed that the bivariate Beta distribution gate structure provides higher gradient values in training. We demonstrate the effectiveness of bivariate Beta gate structure on the sentence classification, image classification, polyphonic music modeling, and image caption generation.
Machine learning models of music typically break up the task of composition into a chronological process, composing a piece of music in a single pass from beginning to end. On the contrary, human composers write music in a nonlinear fashion, scribbling motifs here and there, often revisiting choices previously made. In order to better approximate this process, we train a convolutional neural network to complete partial musical scores, and explore the use of blocked Gibbs sampling as an analogue to rewriting. Neither the model nor the generative procedure are tied to a particular causal direction of composition. Our model is an instance of orderless NADE (Uria et al., 2014), which allows more direct ancestral sampling. However, we find that Gibbs sampling greatly improves sample quality, which we demonstrate to be due to some conditional distributions being poorly modeled. Moreover, we show that even the cheap approximate blocked Gibbs procedure from Yao et al. (2014) yields better samples than ancestral sampling, based on both log-likelihood and human evaluation.
In this paper we compare different types of recurrent units in recurrent neural networks (RNNs). Especially, we focus on more sophisticated units that implement a gating mechanism, such as a long short-term memory (LSTM) unit and a recently proposed gated recurrent unit (GRU). We evaluate these recurrent units on the tasks of polyphonic music modeling and speech signal modeling. Our experiments revealed that these advanced recurrent units are indeed better than more traditional recurrent units such as tanh units. Also, we found GRU to be comparable to LSTM.
How can we efficiently propagate uncertainty in a latent state representation with recurrent neural networks? This paper introduces stochastic recurrent neural networks which glue a deterministic recurrent neural network and a state space model together to form a stochastic and sequential neural generative model. The clear separation of deterministic and stochastic layers allows a structured variational inference network to track the factorization of the model's posterior distribution. By retaining both the nonlinear recursive structure of a recurrent neural network and averaging over the uncertainty in a latent path, like a state space model, we improve the state of the art results on the Blizzard and TIMIT speech modeling data sets by a large margin, while achieving comparable performances to competing methods on polyphonic music modeling.
In this paper, we propose a new Recurrent Neural Network (RNN) architecture. The novelty is simple: We use diagonal recurrent matrices instead of full. This results in better test likelihood and faster convergence compared to regular full RNNs in most of our experiments. We show the benefits of using diagonal recurrent matrices with popularly used LSTM and GRU architectures as well as with the vanilla RNN architecture, on four standard symbolic music datasets.
For most deep learning practitioners, sequence modeling is synonymous with recurrent networks. Yet recent results indicate that convolutional architectures can outperform recurrent networks on tasks such as audio synthesis and machine translation. Given a new sequence modeling task or dataset, which architecture should one use? We conduct a systematic evaluation of generic convolutional and recurrent architectures for sequence modeling. The models are evaluated across a broad range of standard tasks that are commonly used to benchmark recurrent networks. Our results indicate that a simple convolutional architecture outperforms canonical recurrent networks such as LSTMs across a diverse range of tasks and datasets, while demonstrating longer effective memory. We conclude that the common association between sequence modeling and recurrent networks should be reconsidered, and convolutional networks should be regarded as a natural starting point for sequence modeling tasks. To assist related work, we have made code available at http://github.com/locuslab/TCN .