Gaël Richard

Laure Prétet, Gaël Richard, Clément Souchier et al.

We study cross-modal recommendation of music tracks to be used as soundtracks for videos. This problem is known as the music supervision task. We build on a self-supervised system that learns a content association between music and video. In addition to the adequacy of content, adequacy of structure is crucial in music supervision to obtain relevant recommendations. We propose a novel approach to significantly improve the system's performance using structure-aware recommendation. The core idea is to consider not only the full audio-video clips, but rather shorter segments for training and inference. We find that using semantic segments and ranking the tracks according to sequence alignment costs significantly improves the results. We investigate the impact of different ranking metrics and segmentation methods.

Milad Sefidgaran, Amin Gohari, Gaël Richard et al.

Understanding generalization in modern machine learning settings has been one of the major challenges in statistical learning theory. In this context, recent years have witnessed the development of various generalization bounds suggesting different complexity notions such as the mutual information between the data sample and the algorithm output, compressibility of the hypothesis space, and the fractal dimension of the hypothesis space. While these bounds have illuminated the problem at hand from different angles, their suggested complexity notions might appear seemingly unrelated, thereby restricting their high-level impact. In this study, we prove novel generalization bounds through the lens of rate-distortion theory, and explicitly relate the concepts of mutual information, compressibility, and fractal dimensions in a single mathematical framework. Our approach consists of (i) defining a generalized notion of compressibility by using source coding concepts, and (ii) showing that the `compression error rate' can be linked to the generalization error both in expectation and with high probability. We show that in the `lossless compression' setting, we recover and improve existing mutual information-based bounds, whereas a `lossy compression' scheme allows us to link generalization to the rate-distortion dimension -- a particular notion of fractal dimension. Our results bring a more unified perspective on generalization and open up several future research directions.

Victor Letzelter, Mathieu Fontaine, Mickaël Chen et al.

We introduce Resilient Multiple Choice Learning (rMCL), an extension of the MCL approach for conditional distribution estimation in regression settings where multiple targets may be sampled for each training input. Multiple Choice Learning is a simple framework to tackle multimodal density estimation, using the Winner-Takes-All (WTA) loss for a set of hypotheses. In regression settings, the existing MCL variants focus on merging the hypotheses, thereby eventually sacrificing the diversity of the predictions. In contrast, our method relies on a novel learned scoring scheme underpinned by a mathematical framework based on Voronoi tessellations of the output space, from which we can derive a probabilistic interpretation. After empirically validating rMCL with experiments on synthetic data, we further assess its merits on the sound source localization problem, demonstrating its practical usefulness and the relevance of its interpretation.

David Perera, Victor Letzelter, Théo Mariotte et al.

We introduce Annealed Multiple Choice Learning (aMCL) which combines simulated annealing with MCL. MCL is a learning framework handling ambiguous tasks by predicting a small set of plausible hypotheses. These hypotheses are trained using the Winner-takes-all (WTA) scheme, which promotes the diversity of the predictions. However, this scheme may converge toward an arbitrarily suboptimal local minimum, due to the greedy nature of WTA. We overcome this limitation using annealing, which enhances the exploration of the hypothesis space during training. We leverage insights from statistical physics and information theory to provide a detailed description of the model training trajectory. Additionally, we validate our algorithm by extensive experiments on synthetic datasets, on the standard UCI benchmark, and on speech separation.

Karim M. Ibrahim, Elena V. Epure, Geoffroy Peeters et al.

As music has become more available especially on music streaming platforms, people have started to have distinct preferences to fit to their varying listening situations, also known as context. Hence, there has been a growing interest in considering the user's situation when recommending music to users. Previous works have proposed user-aware autotaggers to infer situation-related tags from music content and user's global listening preferences. However, in a practical music retrieval system, the autotagger could be only used by assuming that the context class is explicitly provided by the user. In this work, for designing a fully automatised music retrieval system, we propose to disambiguate the user's listening information from their stream data. Namely, we propose a system which can generate a situational playlist for a user at a certain time 1) by leveraging user-aware music autotaggers, and 2) by automatically inferring the user's situation from stream data (e.g. device, network) and user's general profile information (e.g. age). Experiments show that such a context-aware personalized music retrieval system is feasible, but the performance decreases in the case of new users, new tracks or when the number of context classes increases.

Bernardo Torres, Stefan Lattner, Gaël Richard

Significant strides have been made in creating voice identity representations using speech data. However, the same level of progress has not been achieved for singing voices. To bridge this gap, we suggest a framework for training singer identity encoders to extract representations suitable for various singing-related tasks, such as singing voice similarity and synthesis. We explore different self-supervised learning techniques on a large collection of isolated vocal tracks and apply data augmentations during training to ensure that the representations are invariant to pitch and content variations. We evaluate the quality of the resulting representations on singer similarity and identification tasks across multiple datasets, with a particular emphasis on out-of-domain generalization. Our proposed framework produces high-quality embeddings that outperform both speaker verification and wav2vec 2.0 pre-trained baselines on singing voice while operating at 44.1 kHz. We release our code and trained models to facilitate further research on singing voice and related areas.

Bernardo Torres, Geoffroy Peeters, Gaël Richard

In neural audio signal processing, pitch conditioning has been used to enhance the performance of synthesizers. However, jointly training pitch estimators and synthesizers is a challenge when using standard audio-to-audio reconstruction loss, leading to reliance on external pitch trackers. To address this issue, we propose using a spectral loss function inspired by optimal transportation theory that minimizes the displacement of spectral energy. We validate this approach through an unsupervised autoencoding task that fits a harmonic template to harmonic signals. We jointly estimate the fundamental frequency and amplitudes of harmonics using a lightweight encoder and reconstruct the signals using a differentiable harmonic synthesizer. The proposed approach offers a promising direction for improving unsupervised parameter estimation in neural audio applications.

Teysir Baoueb, Haocheng Liu, Mathieu Fontaine et al.

Generative adversarial network (GAN) models can synthesize highquality audio signals while ensuring fast sample generation. However, they are difficult to train and are prone to several issues including mode collapse and divergence. In this paper, we introduce SpecDiff-GAN, a neural vocoder based on HiFi-GAN, which was initially devised for speech synthesis from mel spectrogram. In our model, the training stability is enhanced by means of a forward diffusion process which consists in injecting noise from a Gaussian distribution to both real and fake samples before inputting them to the discriminator. We further improve the model by exploiting a spectrally-shaped noise distribution with the aim to make the discriminator's task more challenging. We then show the merits of our proposed model for speech and music synthesis on several datasets. Our experiments confirm that our model compares favorably in audio quality and efficiency compared to several baselines.

Haocheng Liu, Teysir Baoueb, Mathieu Fontaine et al.

Diffusion models are receiving a growing interest for a variety of signal generation tasks such as speech or music synthesis. WaveGrad, for example, is a successful diffusion model that conditionally uses the mel spectrogram to guide a diffusion process for the generation of high-fidelity audio. However, such models face important challenges concerning the noise diffusion process for training and inference, and they have difficulty generating high-quality speech for speakers that were not seen during training. With the aim of minimizing the conditioning error and increasing the efficiency of the noise diffusion process, we propose in this paper a new scheme called GLA-Grad, which consists in introducing a phase recovery algorithm such as the Griffin-Lim algorithm (GLA) at each step of the regular diffusion process. Furthermore, it can be directly applied to an already-trained waveform generation model, without additional training or fine-tuning. We show that our algorithm outperforms state-of-the-art diffusion models for speech generation, especially when generating speech for a previously unseen target speaker.

Samir Sadok, Simon Leglaive, Laurent Girin et al.

This article introduces AnCoGen, a novel method that leverages a masked autoencoder to unify the analysis, control, and generation of speech signals within a single model. AnCoGen can analyze speech by estimating key attributes, such as speaker identity, pitch, content, loudness, signal-to-noise ratio, and clarity index. In addition, it can generate speech from these attributes and allow precise control of the synthesized speech by modifying them. Extensive experiments demonstrated the effectiveness of AnCoGen across speech analysis-resynthesis, pitch estimation, pitch modification, and speech enhancement.

Manvi Agarwal, Changhong Wang, Gaël Richard

Music generated by deep learning methods often suffers from a lack of coherence and long-term organization. Yet, multi-scale hierarchical structure is a distinctive feature of music signals. To leverage this information, we propose a structure-informed positional encoding framework for music generation with Transformers. We design three variants in terms of absolute, relative and non-stationary positional information. We comprehensively test them on two symbolic music generation tasks: next-timestep prediction and accompaniment generation. As a comparison, we choose multiple baselines from the literature and demonstrate the merits of our methods using several musically-motivated evaluation metrics. In particular, our methods improve the melodic and structural consistency of the generated pieces.

Alain Riou, Bernardo Torres, Ben Hayes et al.

In this paper, we introduce PESTO, a self-supervised learning approach for single-pitch estimation using a Siamese architecture. Our model processes individual frames of a Variable-$Q$ Transform (VQT) and predicts pitch distributions. The neural network is designed to be equivariant to translations, notably thanks to a Toeplitz fully-connected layer. In addition, we construct pitch-shifted pairs by translating and cropping the VQT frames and train our model with a novel class-based transposition-equivariant objective, eliminating the need for annotated data. Thanks to this architecture and training objective, our model achieves remarkable performances while being very lightweight ($130$k parameters). Evaluations on music and speech datasets (MIR-1K, MDB-stem-synth, and PTDB) demonstrate that PESTO not only outperforms self-supervised baselines but also competes with supervised methods, exhibiting superior cross-dataset generalization. Finally, we enhance PESTO's practical utility by developing a streamable VQT implementation using cached convolutions. Combined with our model's low latency (less than 10 ms) and minimal parameter count, this makes PESTO particularly suitable for real-time applications.

David Perera, François Derrida, Théo Mariotte et al.

Training speech separation models in the supervised setting raises a permutation problem: finding the best assignation between the model predictions and the ground truth separated signals. This inherently ambiguous task is customarily solved using Permutation Invariant Training (PIT). In this article, we instead consider using the Multiple Choice Learning (MCL) framework, which was originally introduced to tackle ambiguous tasks. We demonstrate experimentally on the popular WSJ0-mix and LibriMix benchmarks that MCL matches the performances of PIT, while being computationally advantageous. This opens the door to a promising research direction, as MCL can be naturally extended to handle a variable number of speakers, or to tackle speech separation in the unsupervised setting.

Victor Deng, Changhong Wang, Gael Richard et al.

In recent years, foundation models have significantly advanced data-driven systems across various domains. Yet, their underlying properties, especially when functioning as feature extractors, remain under-explored. In this paper, we investigate the sensitivity to audio effects of audio embeddings extracted from widely-used foundation models, including OpenL3, PANNs, and CLAP. We focus on audio effects as the source of sensitivity due to their prevalent presence in large audio datasets. By applying parameterized audio effects (gain, low-pass filtering, reverberation, and bitcrushing), we analyze the correlation between the deformation trajectories and the effect strength in the embedding space. We propose to quantify the dimensionality and linearizability of the deformation trajectories induced by audio effects using canonical correlation analysis. We find that there exists a direction along which the embeddings move monotonically as the audio effect strength increases, but that the subspace containing the displacements is generally high-dimensional. This shows that pre-trained audio embeddings do not globally linearize the effects. Our empirical results on instrument classification downstream tasks confirm that projecting out the estimated deformation directions cannot generally improve the robustness of pre-trained embeddings to audio effects.

Teysir Baoueb, Xiaoyu Bie, Mathieu Fontaine et al.

Recent advances in diffusion models have positioned them as powerful generative frameworks for speech synthesis, demonstrating substantial improvements in audio quality and stability. Nevertheless, their effectiveness in vocoders conditioned on mel spectrograms remains constrained, particularly when the conditioning diverges from the training distribution. The recently proposed GLA-Grad model introduced a phase-aware extension to the WaveGrad vocoder that integrated the Griffin-Lim algorithm (GLA) into the reverse process to reduce inconsistencies between generated signals and conditioning mel spectrogram. In this paper, we further improve GLA-Grad through an innovative choice in how to apply the correction. Particularly, we compute the correction term only once, with a single application of GLA, to accelerate the generation process. Experimental results demonstrate that our method consistently outperforms the baseline models, particularly in out-of-domain scenarios.

Bernardo Torres, Alain Riou, Gaël Richard et al.

In this paper, we propose an Optimal Transport objective for learning one-dimensional translation-equivariant systems and demonstrate its applicability to single pitch estimation. Our method provides a theoretically grounded, more numerically stable, and simpler alternative for training state-of-the-art self-supervised pitch estimators.

Louis Bahrman, Mathieu Fontaine, Gaël Richard

This paper explores the outcome of training state-ofthe-art dereverberation models with supervision settings ranging from weakly-supervised to fully unsupervised, relying solely on reverberant signals and an acoustic model for training. Most of the existing deep learning approaches typically require paired dry and reverberant data, which are difficult to obtain in practice. We develop instead a sequential learning strategy motivated by a bayesian formulation of the dereverberation problem, wherein acoustic parameters and dry signals are estimated from reverberant inputs using deep neural networks, guided by a reverberation matching loss. Our most data-efficient variant requires only 100 reverberation-parameter-labelled samples to outperform an unsupervised baseline, demonstrating the effectiveness and practicality of the proposed method in low-resource scenarios.

Teysir Baoueb, Xiaoyu Bie, Xi Wang et al.

Breakthroughs in text-to-music generation models are transforming the creative landscape, equipping musicians with innovative tools for composition and experimentation like never before. However, controlling the generation process to achieve a specific desired outcome remains a significant challenge. Even a minor change in the text prompt, combined with the same random seed, can drastically alter the generated piece. In this paper, we explore the application of existing text-to-music diffusion models for instrument editing. Specifically, for an existing audio track, we aim to leverage a pretrained text-to-music diffusion model to edit the instrument while preserving the underlying content. Based on the insight that the model first focuses on the overall structure or content of the audio, then adds instrument information, and finally refines the quality, we show that selecting a well-chosen intermediate timestep, identified through an instrument classifier, yields a balance between preserving the original piece's content and achieving the desired timbre. Our method does not require additional training of the text-to-music diffusion model, nor does it compromise the generation process's speed.

Victor Letzelter, David Perera, Cédric Rommel et al.

Winner-takes-all training is a simple learning paradigm, which handles ambiguous tasks by predicting a set of plausible hypotheses. Recently, a connection was established between Winner-takes-all training and centroidal Voronoi tessellations, showing that, once trained, hypotheses should quantize optimally the shape of the conditional distribution to predict. However, the best use of these hypotheses for uncertainty quantification is still an open question. In this work, we show how to leverage the appealing geometric properties of the Winner-takes-all learners for conditional density estimation, without modifying its original training scheme. We theoretically establish the advantages of our novel estimator both in terms of quantization and density estimation, and we demonstrate its competitiveness on synthetic and real-world datasets, including audio data.

Jayneel Parekh, Sanjeel Parekh, Pavlo Mozharovskyi et al.

This paper tackles two major problem settings for interpretability of audio processing networks, post-hoc and by-design interpretation. For post-hoc interpretation, we aim to interpret decisions of a network in terms of high-level audio objects that are also listenable for the end-user. This is extended to present an inherently interpretable model with high performance. To this end, we propose a novel interpreter design that incorporates non-negative matrix factorization (NMF). In particular, an interpreter is trained to generate a regularized intermediate embedding from hidden layers of a target network, learnt as time-activations of a pre-learnt NMF dictionary. Our methodology allows us to generate intuitive audio-based interpretations that explicitly enhance parts of the input signal most relevant for a network's decision. We demonstrate our method's applicability on a variety of classification tasks, including multi-label data for real-world audio and music.

Jayneel Parekh, Sanjeel Parekh, Pavlo Mozharovskyi et al.

This paper tackles post-hoc interpretability for audio processing networks. Our goal is to interpret decisions of a network in terms of high-level audio objects that are also listenable for the end-user. To this end, we propose a novel interpreter design that incorporates non-negative matrix factorization (NMF). In particular, a carefully regularized interpreter module is trained to take hidden layer representations of the targeted network as input and produce time activations of pre-learnt NMF components as intermediate outputs. Our methodology allows us to generate intuitive audio-based interpretations that explicitly enhance parts of the input signal most relevant for a network's decision. We demonstrate our method's applicability on popular benchmarks, including a real-world multi-label classification task.

Kilian Schulze-Forster, Gaël Richard, Liam Kelley et al.

Supervised deep learning approaches to underdetermined audio source separation achieve state-of-the-art performance but require a dataset of mixtures along with their corresponding isolated source signals. Such datasets can be extremely costly to obtain for musical mixtures. This raises a need for unsupervised methods. We propose a novel unsupervised model-based deep learning approach to musical source separation. Each source is modelled with a differentiable parametric source-filter model. A neural network is trained to reconstruct the observed mixture as a sum of the sources by estimating the source models' parameters given their fundamental frequencies. At test time, soft masks are obtained from the synthesized source signals. The experimental evaluation on a vocal ensemble separation task shows that the proposed method outperforms learning-free methods based on nonnegative matrix factorization and a supervised deep learning baseline. Integrating domain knowledge in the form of source models into a data-driven method leads to high data efficiency: the proposed approach achieves good separation quality even when trained on less than three minutes of audio. This work makes powerful deep learning based separation usable in scenarios where training data with ground truth is expensive or nonexistent.

Javier Nistal, Stefan Lattner, Gaël Richard

Generative Adversarial Networks (GANs) have achieved excellent audio synthesis quality in the last years. However, making them operable with semantically meaningful controls remains an open challenge. An obvious approach is to control the GAN by conditioning it on metadata contained in audio datasets. Unfortunately, audio datasets often lack the desired annotations, especially in the musical domain. A way to circumvent this lack of annotations is to generate them, for example, with an automatic audio-tagging system. The output probabilities of such systems (so-called "soft labels") carry rich information about the characteristics of the respective audios and can be used to distill the knowledge from a teacher model into a student model. In this work, we perform knowledge distillation from a large audio tagging system into an adversarial audio synthesizer that we call DarkGAN. Results show that DarkGAN can synthesize musical audio with acceptable quality and exhibits moderate attribute control even with out-of-distribution input conditioning. We release the code and provide audio examples on the accompanying website.

Laure Prétet, Gaël Richard, Geoffroy Peeters

Recommending automatically a video given a music or a music given a video has become an important asset for the audiovisual industry - with user-generated or professional content. While both music and video have specific temporal organizations, most current works do not consider those and only focus on globally recommending a media. As a first step toward the improvement of these recommendation systems, we study in this paper the relationship between music and video temporal organization. We do this for the case of official music videos, with a quantitative and a qualitative approach. Our assumption is that the movement in the music are correlated to the ones in the video. To validate this, we first interview a set of internationally recognized music video experts. We then perform a large-scale analysis of official music-video clips (which we manually annotated into video genres) using MIR description tools (downbeats and functional segments estimation) and Computer Vision tools (shot detection). Our study confirms that a "language of music-video clips" exists; i.e. editors favor the co-occurrence of music and video events using strategies such as anticipation. It also highlights that the amount of co-occurrence depends on the music and video genres.

Melih Barsbey, Milad Sefidgaran, Murat A. Erdogdu et al.

Neural network compression techniques have become increasingly popular as they can drastically reduce the storage and computation requirements for very large networks. Recent empirical studies have illustrated that even simple pruning strategies can be surprisingly effective, and several theoretical studies have shown that compressible networks (in specific senses) should achieve a low generalization error. Yet, a theoretical characterization of the underlying cause that makes the networks amenable to such simple compression schemes is still missing. In this study, we address this fundamental question and reveal that the dynamics of the training algorithm has a key role in obtaining such compressible networks. Focusing our attention on stochastic gradient descent (SGD), our main contribution is to link compressibility to two recently established properties of SGD: (i) as the network size goes to infinity, the system can converge to a mean-field limit, where the network weights behave independently, (ii) for a large step-size/batch-size ratio, the SGD iterates can converge to a heavy-tailed stationary distribution. In the case where these two phenomena occur simultaneously, we prove that the networks are guaranteed to be '$\ell_p$-compressible', and the compression errors of different pruning techniques (magnitude, singular value, or node pruning) become arbitrarily small as the network size increases. We further prove generalization bounds adapted to our theoretical framework, which indeed confirm that the generalization error will be lower for more compressible networks. Our theory and numerical study on various neural networks show that large step-size/batch-size ratios introduce heavy-tails, which, in combination with overparametrization, result in compressibility.

Javier Nistal, Cyran Aouameur, Stefan Lattner et al.

Influenced by the field of Computer Vision, Generative Adversarial Networks (GANs) are often adopted for the audio domain using fixed-size two-dimensional spectrogram representations as the "image data". However, in the (musical) audio domain, it is often desired to generate output of variable duration. This paper presents VQCPC-GAN, an adversarial framework for synthesizing variable-length audio by exploiting Vector-Quantized Contrastive Predictive Coding (VQCPC). A sequence of VQCPC tokens extracted from real audio data serves as conditional input to a GAN architecture, providing step-wise time-dependent features of the generated content. The input noise z (characteristic in adversarial architectures) remains fixed over time, ensuring temporal consistency of global features. We evaluate the proposed model by comparing a diverse set of metrics against various strong baselines. Results show that, even though the baselines score best, VQCPC-GAN achieves comparable performance even when generating variable-length audio. Numerous sound examples are provided in the accompanying website, and we release the code for reproducibility.

Laure Pretet, Gael Richard, Geoffroy Peeters

In this work, we study music/video cross-modal recommendation, i.e. recommending a music track for a video or vice versa. We rely on a self-supervised learning paradigm to learn from a large amount of unlabelled data. We rely on a self-supervised learning paradigm to learn from a large amount of unlabelled data. More precisely, we jointly learn audio and video embeddings by using their co-occurrence in music-video clips. In this work, we build upon a recent video-music retrieval system (the VM-NET), which originally relies on an audio representation obtained by a set of statistics computed over handcrafted features. We demonstrate here that using audio representation learning such as the audio embeddings provided by the pre-trained MuSimNet, OpenL3, MusicCNN or by AudioSet, largely improves recommendations. We also validate the use of the cross-modal triplet loss originally proposed in the VM-NET compared to the binary cross-entropy loss commonly used in self-supervised learning. We perform all our experiments using the Music Video Dataset (MVD).

Ondřej Cífka, Alexey Ozerov, Umut Şimşekli et al.

Neural style transfer, allowing to apply the artistic style of one image to another, has become one of the most widely showcased computer vision applications shortly after its introduction. In contrast, related tasks in the music audio domain remained, until recently, largely untackled. While several style conversion methods tailored to musical signals have been proposed, most lack the 'one-shot' capability of classical image style transfer algorithms. On the other hand, the results of existing one-shot audio style transfer methods on musical inputs are not as compelling. In this work, we are specifically interested in the problem of one-shot timbre transfer. We present a novel method for this task, based on an extension of the vector-quantized variational autoencoder (VQ-VAE), along with a simple self-supervised learning strategy designed to obtain disentangled representations of timbre and pitch. We evaluate the method using a set of objective metrics and show that it is able to outperform selected baselines.

Javier Nistal, Stefan Lattner, Gaël Richard

In this paper, we compare different audio signal representations, including the raw audio waveform and a variety of time-frequency representations, for the task of audio synthesis with Generative Adversarial Networks (GANs). We conduct the experiments on a subset of the NSynth dataset. The architecture follows the benchmark Progressive Growing Wasserstein GAN. We perform experiments both in a fully non-conditional manner as well as conditioning the network on the pitch information. We quantitatively evaluate the generated material utilizing standard metrics for assessing generative models, and compare training and sampling times. We show that complex-valued as well as the magnitude and Instantaneous Frequency of the Short-Time Fourier Transform achieve the best results, and yield fast generation and inversion times. The code for feature extraction, training and evaluating the model is available online.

Laure Prétet, Gaël Richard, Geoffroy Peeters

Most music streaming services rely on automatic recommendation algorithms to exploit their large music catalogs. These algorithms aim at retrieving a ranked list of music tracks based on their similarity with a target music track. In this work, we propose a method for direct recommendation based on the audio content without explicitly tagging the music tracks. To that aim, we propose several strategies to perform triplet mining from ranked lists. We train a Convolutional Neural Network to learn the similarity via triplet loss. These different strategies are compared and validated on a large-scale experiment against an auto-tagging based approach. The results obtained highlight the efficiency of our system, especially when associated with an Auto-pooling layer.

Umut Şimşekli, Mert Gürbüzbalaban, Thanh Huy Nguyen et al.

The gradient noise (GN) in the stochastic gradient descent (SGD) algorithm is often considered to be Gaussian in the large data regime by assuming that the \emph{classical} central limit theorem (CLT) kicks in. This assumption is often made for mathematical convenience, since it enables SGD to be analyzed as a stochastic differential equation (SDE) driven by a Brownian motion. We argue that the Gaussianity assumption might fail to hold in deep learning settings and hence render the Brownian motion-based analyses inappropriate. Inspired by non-Gaussian natural phenomena, we consider the GN in a more general context and invoke the \emph{generalized} CLT, which suggests that the GN converges to a \emph{heavy-tailed} $α$-stable random vector, where \emph{tail-index} $α$ determines the heavy-tailedness of the distribution. Accordingly, we propose to analyze SGD as a discretization of an SDE driven by a Lévy motion. Such SDEs can incur `jumps', which force the SDE and its discretization \emph{transition} from narrow minima to wider minima, as proven by existing metastability theory and the extensions that we proved recently. In this study, under the $α$-stable GN assumption, we further establish an explicit connection between the convergence rate of SGD to a local minimum and the tail-index $α$. To validate the $α$-stable assumption, we conduct experiments on common deep learning scenarios and show that in all settings, the GN is highly non-Gaussian and admits heavy-tails. We investigate the tail behavior in varying network architectures and sizes, loss functions, and datasets. Our results open up a different perspective and shed more light on the belief that SGD prefers wide minima.

Ondřej Cífka, Umut Şimşekli, Gaël Richard

Research on style transfer and domain translation has clearly demonstrated the ability of deep learning-based algorithms to manipulate images in terms of artistic style. More recently, several attempts have been made to extend such approaches to music (both symbolic and audio) in order to enable transforming musical style in a similar manner. In this study, we focus on symbolic music with the goal of altering the 'style' of a piece while keeping its original 'content'. As opposed to the current methods, which are inherently restricted to be unsupervised due to the lack of 'aligned' data (i.e. the same musical piece played in multiple styles), we develop the first fully supervised algorithm for this task. At the core of our approach lies a synthetic data generation scheme which allows us to produce virtually unlimited amounts of aligned data, and hence avoid the above issue. In view of this data generation scheme, we propose an encoder-decoder model for translating symbolic music accompaniments between a number of different styles. Our experiments show that our models, although trained entirely on synthetic data, are capable of producing musically meaningful accompaniments even for real (non-synthetic) MIDI recordings.

Thanh Huy Nguyen, Umut Şimşekli, Mert Gürbüzbalaban et al.

Stochastic gradient descent (SGD) has been widely used in machine learning due to its computational efficiency and favorable generalization properties. Recently, it has been empirically demonstrated that the gradient noise in several deep learning settings admits a non-Gaussian, heavy-tailed behavior. This suggests that the gradient noise can be modeled by using $α$-stable distributions, a family of heavy-tailed distributions that appear in the generalized central limit theorem. In this context, SGD can be viewed as a discretization of a stochastic differential equation (SDE) driven by a Lévy motion, and the metastability results for this SDE can then be used for illuminating the behavior of SGD, especially in terms of `preferring wide minima'. While this approach brings a new perspective for analyzing SGD, it is limited in the sense that, due to the time discretization, SGD might admit a significantly different behavior than its continuous-time limit. Intuitively, the behaviors of these two systems are expected to be similar to each other only when the discretization step is sufficiently small; however, to the best of our knowledge, there is no theoretical understanding on how small the step-size should be chosen in order to guarantee that the discretized system inherits the properties of the continuous-time system. In this study, we provide formal theoretical analysis where we derive explicit conditions for the step-size such that the metastability behavior of the discrete-time system is similar to its continuous-time limit. We show that the behaviors of the two systems are indeed similar for small step-sizes and we identify how the error depends on the algorithm and problem parameters. We illustrate our results with simulations on a synthetic model and neural networks.

Sanjeel Parekh, Alexey Ozerov, Slim Essid et al.

We tackle the problem of audiovisual scene analysis for weakly-labeled data. To this end, we build upon our previous audiovisual representation learning framework to perform object classification in noisy acoustic environments and integrate audio source enhancement capability. This is made possible by a novel use of non-negative matrix factorization for the audio modality. Our approach is founded on the multiple instance learning paradigm. Its effectiveness is established through experiments over a challenging dataset of music instrument performance videos. We also show encouraging visual object localization results.

Umut Şimşekli, Çağatay Yıldız, Thanh Huy Nguyen et al.

Recent studies have illustrated that stochastic gradient Markov Chain Monte Carlo techniques have a strong potential in non-convex optimization, where local and global convergence guarantees can be shown under certain conditions. By building up on this recent theory, in this study, we develop an asynchronous-parallel stochastic L-BFGS algorithm for non-convex optimization. The proposed algorithm is suitable for both distributed and shared-memory settings. We provide formal theoretical analysis and show that the proposed method achieves an ergodic convergence rate of ${\cal O}(1/\sqrt{N})$ ($N$ being the total number of iterations) and it can achieve a linear speedup under certain conditions. We perform several experiments on both synthetic and real datasets. The results support our theory and show that the proposed algorithm provides a significant speedup over the recently proposed synchronous distributed L-BFGS algorithm.

S. Durand, J. P. Bello, B. David et al.

In this paper, we present a novel state of the art system for automatic downbeat tracking from music signals. The audio signal is first segmented in frames which are synchronized at the tatum level of the music. We then extract different kind of features based on harmony, melody, rhythm and bass content to feed convolutional neural networks that are adapted to take advantage of each feature characteristics. This ensemble of neural networks is combined to obtain one downbeat likelihood per tatum. The downbeat sequence is finally decoded with a flexible and efficient temporal model which takes advantage of the metrical continuity of a song. We then perform an evaluation of our system on a large base of 9 datasets, compare its performance to 4 other published algorithms and obtain a significant increase of 16.8 percent points compared to the second best system, for altogether a moderate cost in test and training. The influence of each step of the method is studied to show its strengths and shortcomings.

Umut Şimşekli, Roland Badeau, A. Taylan Cemgil et al.

Recently, Stochastic Gradient Markov Chain Monte Carlo (SG-MCMC) methods have been proposed for scaling up Monte Carlo computations to large data problems. Whilst these approaches have proven useful in many applications, vanilla SG-MCMC might suffer from poor mixing rates when random variables exhibit strong couplings under the target densities or big scale differences. In this study, we propose a novel SG-MCMC method that takes the local geometry into account by using ideas from Quasi-Newton optimization methods. These second order methods directly approximate the inverse Hessian by using a limited history of samples and their gradients. Our method uses dense approximations of the inverse Hessian while keeping the time and memory complexities linear with the dimension of the problem. We provide a formal theoretical analysis where we show that the proposed method is asymptotically unbiased and consistent with the posterior expectations. We illustrate the effectiveness of the approach on both synthetic and real datasets. Our experiments on two challenging applications show that our method achieves fast convergence rates similar to Riemannian approaches while at the same time having low computational requirements similar to diagonal preconditioning approaches.