Vincent Lostanlen

Cyrus Vahidi, Han Han, Changhong Wang et al.

Computer musicians refer to mesostructures as the intermediate levels of articulation between the microstructure of waveshapes and the macrostructure of musical forms. Examples of mesostructures include melody, arpeggios, syncopation, polyphonic grouping, and textural contrast. Despite their central role in musical expression, they have received limited attention in deep learning. Currently, autoencoders and neural audio synthesizers are only trained and evaluated at the scale of microstructure: i.e., local amplitude variations up to 100 milliseconds or so. In this paper, we formulate and address the problem of mesostructural audio modeling via a composition of a differentiable arpeggiator and time-frequency scattering. We empirically demonstrate that time--frequency scattering serves as a differentiable model of similarity between synthesis parameters that govern mesostructure. By exposing the sensitivity of short-time spectral distances to time alignment, we motivate the need for a time-invariant and multiscale differentiable time--frequency model of similarity at the level of both local spectra and spectrotemporal modulations.

Ines Nolasco, Burooj Ghani, Shubhr Singh et al.

Few-shot bioacoustic event detection consists in detecting sound events of specified types, in varying soundscapes, while having access to only a few examples of the class of interest. This task ran as part of the DCASE challenge for the third time this year with an evaluation set expanded to include new animal species, and a new rule: ensemble models were no longer allowed. The 2023 few shot task received submissions from 6 different teams with F-scores reaching as high as 63% on the evaluation set. Here we describe the task, focusing on describing the elements that differed from previous years. We also take a look back at past editions to describe how the task has evolved. Not only have the F-score results steadily improved (40% to 60% to 63%), but the type of systems proposed have also become more complex. Sound event detection systems are no longer simple variations of the baselines provided: multiple few-shot learning methodologies are still strong contenders for the task.

Vincent Lostanlen, Daniel Haider, Han Han et al.

Waveform-based deep learning faces a dilemma between nonparametric and parametric approaches. On one hand, convolutional neural networks (convnets) may approximate any linear time-invariant system; yet, in practice, their frequency responses become more irregular as their receptive fields grow. On the other hand, a parametric model such as LEAF is guaranteed to yield Gabor filters, hence an optimal time-frequency localization; yet, this strong inductive bias comes at the detriment of representational capacity. In this paper, we aim to overcome this dilemma by introducing a neural audio model, named multiresolution neural network (MuReNN). The key idea behind MuReNN is to train separate convolutional operators over the octave subbands of a discrete wavelet transform (DWT). Since the scale of DWT atoms grows exponentially between octaves, the receptive fields of the subsequent learnable convolutions in MuReNN are dilated accordingly. For a given real-world dataset, we fit the magnitude response of MuReNN to that of a well-established auditory filterbank: Gammatone for speech, CQT for music, and third-octave for urban sounds, respectively. This is a form of knowledge distillation (KD), in which the filterbank ''teacher'' is engineered by domain knowledge while the neural network ''student'' is optimized from data. We compare MuReNN to the state of the art in terms of goodness of fit after KD on a hold-out set and in terms of Heisenberg time-frequency localization. Compared to convnets and Gabor convolutions, we find that MuReNN reaches state-of-the-art performance on all three optimization problems.

John Muradeli, Cyrus Vahidi, Changhong Wang et al.

Joint time-frequency scattering (JTFS) is a convolutional operator in the time-frequency domain which extracts spectrotemporal modulations at various rates and scales. It offers an idealized model of spectrotemporal receptive fields (STRF) in the primary auditory cortex, and thus may serve as a biological plausible surrogate for human perceptual judgments at the scale of isolated audio events. Yet, prior implementations of JTFS and STRF have remained outside of the standard toolkit of perceptual similarity measures and evaluation methods for audio generation. We trace this issue down to three limitations: differentiability, speed, and flexibility. In this paper, we present an implementation of time-frequency scattering in Python. Unlike prior implementations, ours accommodates NumPy, PyTorch, and TensorFlow as backends and is thus portable on both CPU and GPU. We demonstrate the usefulness of JTFS via three applications: unsupervised manifold learning of spectrotemporal modulations, supervised classification of musical instruments, and texture resynthesis of bioacoustic sounds.

Han Han, Vincent Lostanlen, Mathieu Lagrange

Sound matching algorithms seek to approximate a target waveform by parametric audio synthesis. Deep neural networks have achieved promising results in matching sustained harmonic tones. However, the task is more challenging when targets are nonstationary and inharmonic, e.g., percussion. We attribute this problem to the inadequacy of loss function. On one hand, mean square error in the parametric domain, known as "P-loss", is simple and fast but fails to accommodate the differing perceptual significance of each parameter. On the other hand, mean square error in the spectrotemporal domain, known as "spectral loss", is perceptually motivated and serves in differentiable digital signal processing (DDSP). Yet, spectral loss is a poor predictor of pitch intervals and its gradient may be computationally expensive; hence a slow convergence. Against this conundrum, we present Perceptual-Neural-Physical loss (PNP). PNP is the optimal quadratic approximation of spectral loss while being as fast as P-loss during training. We instantiate PNP with physical modeling synthesis as decoder and joint time-frequency scattering transform (JTFS) as spectral representation. We demonstrate its potential on matching synthetic drum sounds in comparison with other loss functions.

Christopher Mitcheltree, Vincent Lostanlen, Emmanouil Benetos et al.

The Euclidean distance between wavelet scattering transform coefficients (known as paths) provides informative gradients for perceptual quality assessment of deep inverse problems in computer vision, speech, and audio processing. However, these transforms are computationally expensive when employed as differentiable loss functions for stochastic gradient descent due to their numerous paths, which significantly limits their use in neural network training. Against this problem, we propose "Scattering transform with Random Paths for machine Learning" (SCRAPL): a stochastic optimization scheme for efficient evaluation of multivariable scattering transforms. We implement SCRAPL for the joint time-frequency scattering transform (JTFS) which demodulates spectrotemporal patterns at multiple scales and rates, allowing a fine characterization of intermittent auditory textures. We apply SCRAPL to differentiable digital signal processing (DDSP), specifically, unsupervised sound matching of a granular synthesizer and the Roland TR-808 drum machine. We also propose an initialization heuristic based on importance sampling, which adapts SCRAPL to the perceptual content of the dataset, improving neural network convergence and evaluation performance. We make our code and audio samples available and provide SCRAPL as a Python package.

Daniel Haider, Vincent Lostanlen, Martin Ehler et al.

What makes waveform-based deep learning so hard? Despite numerous attempts at training convolutional neural networks (convnets) for filterbank design, they often fail to outperform hand-crafted baselines. These baselines are linear time-invariant systems: as such, they can be approximated by convnets with wide receptive fields. Yet, in practice, gradient-based optimization leads to suboptimal approximations. In our article, we approach this phenomenon from the perspective of initialization. We present a theory of large deviations for the energy response of FIR filterbanks with random Gaussian weights. We find that deviations worsen for large filters and locally periodic input signals, which are both typical for audio signal processing applications. Numerical simulations align with our theory and suggest that the condition number of a convolutional layer follows a logarithmic scaling law between the number and length of the filters, which is reminiscent of discrete wavelet bases.

Daniel Haider, Felix Perfler, Vincent Lostanlen et al.

Convolutional layers with 1-D filters are often used as frontend to encode audio signals. Unlike fixed time-frequency representations, they can adapt to the local characteristics of input data. However, 1-D filters on raw audio are hard to train and often suffer from instabilities. In this paper, we address these problems with hybrid solutions, i.e., combining theory-driven and data-driven approaches. First, we preprocess the audio signals via a auditory filterbank, guaranteeing good frequency localization for the learned encoder. Second, we use results from frame theory to define an unsupervised learning objective that encourages energy conservation and perfect reconstruction. Third, we adapt mixed compressed spectral norms as learning objectives to the encoder coefficients. Using these solutions in a low-complexity encoder-mask-decoder model significantly improves the perceptual evaluation of speech quality (PESQ) in speech enhancement.

Modan Tailleur, Vincent Lostanlen, Jean-Philippe Rivière et al.

Oxygenators, alarm devices, and footsteps are some of the most common sound sources in a hospital. Detecting them has scientific value for environmental psychology but comes with challenges of its own: namely, privacy preservation and limited labeled data. In this paper, we address these two challenges via a combination of edge computing and cloud computing. For privacy preservation, we have designed an acoustic sensor which computes third-octave spectrograms on the fly instead of recording audio waveforms. For sample-efficient machine learning, we have repurposed a pretrained audio neural network (PANN) via spectral transcoding and label space adaptation. A small-scale study in a neonatological intensive care unit (NICU) confirms that the time series of detected events align with another modality of measurement: i.e., electronic badges for parents and healthcare professionals. Hence, this paper demonstrates the feasibility of polyphonic machine listening in a hospital ward while guaranteeing privacy by design.

Vincent Lostanlen, Florian Hecker

This article explains how to apply time--frequency scattering, a convolutional operator extracting modulations in the time--frequency domain at different rates and scales, to the re-synthesis and manipulation of audio textures. After implementing phase retrieval in the scattering network by gradient backpropagation, we introduce scale--rate DAFx, a class of audio transformations expressed in the domain of time--frequency scattering coefficients. One example of scale--rate DAFx is chirp rate inversion, which causes each sonic event to be locally reversed in time while leaving the arrow of time globally unchanged. Over the past two years, our work has led to the creation of four electroacoustic pieces: ``FAVN''; ``Modulator (Scattering Transform)''; ``Experimental Palimpsest''; ``Inspection''; and a remix of Lorenzo Senni's ``XAllegroX'', released by Warp Records on a vinyl entitled ``The Shape of RemiXXXes to Come''. The source code to reproduce experiments and figures is made freely available at: https://github.com/lostanlen/scattering.m. A companion website containing demos is at: https://lostanlen.com/pubs/dafx2019

Yuexuan Kong, Gabriel Meseguer-Brocal, Vincent Lostanlen et al.

In music information retrieval (MIR), contrastive self-supervised learning for general-purpose representation models is effective for global tasks such as automatic tagging. However, for local tasks such as chord estimation, it is widely assumed that contrastively trained general-purpose self-supervised models are inadequate and that more sophisticated SSL is necessary; e.g., masked modeling. Our paper challenges this assumption by revealing the potential of contrastive SSL paired with a transformer in local MIR tasks. We consider a lightweight vision transformer with one-dimensional patches in the time--frequency domain (ViT-1D) and train it with simple contrastive SSL through normalized temperature-scaled cross-entropy loss (NT-Xent). Although NT-Xent operates only over the class token, we observe that, potentially thanks to weight sharing, informative musical properties emerge in ViT-1D's sequence tokens. On global tasks, the temporal average of class and sequence tokens offers a performance increase compared to the class token alone, showing useful properties in the sequence tokens. On local tasks, sequence tokens perform unexpectedly well, despite not being specifically trained for. Furthermore, high-level musical features such as onsets emerge from layer-wise attention maps and self-similarity matrices show different layers capture different musical dimensions. Our paper does not focus on improving performance but advances the musical interpretation of transformers and sheds light on some overlooked abilities of contrastive SSL paired with transformers for sequence modeling in MIR.

Daniel Haider, Vincent Lostanlen, Martin Ehler et al.

Using a stride in a convolutional layer inherently introduces aliasing, which has implications for numerical stability and statistical generalization. While techniques such as the parametrizations via paraunitary systems have been used to promote orthogonal convolution and thus ensure Parseval stability, a general analysis of aliasing and its effects on the stability has not been done in this context. In this article, we adapt a frame-theoretic approach to describe aliasing in convolutional layers with 1D kernels, leading to practical estimates for stability bounds and characterizations of Parseval stability, that are tailored to take short kernel sizes into account. From this, we derive two computationally very efficient optimization objectives that promote Parseval stability via systematically suppressing aliasing. Finally, for layers with random kernels, we derive closed-form expressions for the expected value and variance of the terms that describe the aliasing effects, revealing fundamental insights into the aliasing behavior at initialization.

Ilyass Moummad, Nicolas Farrugia, Romain Serizel et al.

Multi-label imbalanced classification poses a significant challenge in machine learning, particularly evident in bioacoustics where animal sounds often co-occur, and certain sounds are much less frequent than others. This paper focuses on the specific case of classifying anuran species sounds using the dataset AnuraSet, that contains both class imbalance and multi-label examples. To address these challenges, we introduce Mixture of Mixups (Mix2), a framework that leverages mixing regularization methods Mixup, Manifold Mixup, and MultiMix. Experimental results show that these methods, individually, may lead to suboptimal results; however, when applied randomly, with one selected at each training iteration, they prove effective in addressing the mentioned challenges, particularly for rare classes with few occurrences. Further analysis reveals that Mix2 is also proficient in classifying sounds across various levels of class co-occurrences.

Sripathi Sridhar, Vincent Lostanlen

Octave equivalence serves as domain-knowledge in MIR systems, including chromagram, spiral convolutional networks, and harmonic CQT. Prior work has applied the Isomap manifold learning algorithm to unlabeled audio data to embed frequency sub-bands in 3-D space where the Euclidean distances are inversely proportional to the strength of their Pearson correlations. However, discovering octave equivalence via Isomap requires visual inspection and is not scalable. To address this problem, we define "helicality" as the goodness of fit of the 3-D Isomap embedding to a Shepherd-Risset helix. Our method is unsupervised and uses a custom Frank-Wolfe algorithm to minimize a least-squares objective inside a convex hull. Numerical experiments indicate that isolated musical notes have a higher helicality than speech, followed by drum hits.

Christopher Ick, Vincent Lostanlen

Deep convolutional networks (convnets) show a remarkable ability to learn disentangled representations. In recent years, the generalization of deep learning to Lie groups beyond rigid motion in $\mathbb{R}^n$ has allowed to build convnets over datasets with non-trivial symmetries, such as patterns over the surface of a sphere. However, one limitation of this approach is the need to explicitly define the Lie group underlying the desired invariance property before training the convnet. Whereas rotations on the sphere have a well-known symmetry group ($\mathrm{SO}(3)$), the same cannot be said of many real-world factors of variability. For example, the disentanglement of pitch, intensity dynamics, and playing technique remains a challenging task in music information retrieval. This article proposes a machine learning method to discover a nonlinear transformation of the space $\mathbb{R}^n$ which maps a collection of $n$-dimensional vectors $(\boldsymbol{x}_i)_i$ onto a collection of target vectors $(\boldsymbol{y}_i)_i$. The key idea is to approximate every target $\boldsymbol{y}_i$ by a matrix--vector product of the form $\boldsymbol{\widetilde{y}}_i = \boldsymbolφ(t_i) \boldsymbol{x}_i$, where the matrix $\boldsymbolφ(t_i)$ belongs to a one-parameter subgroup of $\mathrm{GL}_n (\mathbb{R})$. Crucially, the value of the parameter $t_i \in \mathbb{R}$ may change between data pairs $(\boldsymbol{x}_i, \boldsymbol{y}_i)$ and does not need to be known in advance.

Mark Cartwright, Jason Cramer, Ana Elisa Mendez Mendez et al.

We present SONYC-UST-V2, a dataset for urban sound tagging with spatiotemporal information. This dataset is aimed for the development and evaluation of machine listening systems for real-world urban noise monitoring. While datasets of urban recordings are available, this dataset provides the opportunity to investigate how spatiotemporal metadata can aid in the prediction of urban sound tags. SONYC-UST-V2 consists of 18510 audio recordings from the "Sounds of New York City" (SONYC) acoustic sensor network, including the timestamp of audio acquisition and location of the sensor. The dataset contains annotations by volunteers from the Zooniverse citizen science platform, as well as a two-stage verification with our team. In this article, we describe our data collection procedure and propose evaluation metrics for multilabel classification of urban sound tags. We report the results of a simple baseline model that exploits spatiotemporal information.

Vincent Lostanlen, Christian El-Hajj, Mathias Rossignol et al.

Instrumental playing techniques such as vibratos, glissandos, and trills often denote musical expressivity, both in classical and folk contexts. However, most existing approaches to music similarity retrieval fail to describe timbre beyond the so-called "ordinary" technique, use instrument identity as a proxy for timbre quality, and do not allow for customization to the perceptual idiosyncrasies of a new subject. In this article, we ask 31 human subjects to organize 78 isolated notes into a set of timbre clusters. Analyzing their responses suggests that timbre perception operates within a more flexible taxonomy than those provided by instruments or playing techniques alone. In addition, we propose a machine listening model to recover the cluster graph of auditory similarities across instruments, mutes, and techniques. Our model relies on joint time--frequency scattering features to extract spectrotemporal modulations as acoustic features. Furthermore, it minimizes triplet loss in the cluster graph by means of the large-margin nearest neighbor (LMNN) metric learning algorithm. Over a dataset of 9346 isolated notes, we report a state-of-the-art average precision at rank five (AP@5) of $99.0\%\pm1$. An ablation study demonstrates that removing either the joint time--frequency scattering transform or the metric learning algorithm noticeably degrades performance.

Han Han, Vincent Lostanlen

Disentangling and recovering physical attributes, such as shape and material, from a few waveform examples is a challenging inverse problem in audio signal processing, with numerous applications in musical acoustics as well as structural engineering. We propose to address this problem via a combination of time--frequency analysis and supervised machine learning. We start by synthesizing a dataset of sounds using the functional transformation method. Then, we represent each percussive sound in terms of its time-invariant scattering transform coefficients and formulate the parametric estimation of the resonator as multidimensional regression with a deep convolutional neural network. We interpolate scattering coefficients over the surface of the drum as a surrogate for potentially missing data, and study the response of the neural network to interpolated samples. Lastly, we resynthesize drum sounds from scattering coefficients, therefore paving the way towards a deep generative model of drum sounds whose latent variables are physically interpretable.

Carmine Emanuele Cella, Daniele Ghisi, Vincent Lostanlen et al.

This paper introduces OrchideaSOL, a free dataset of samples of extended instrumental playing techniques, designed to be used as default dataset for the Orchidea framework for target-based computer-aided orchestration. OrchideaSOL is a reduced and modified subset of Studio On Line, or SOL for short, a dataset developed at Ircam between 1996 and 1998. We motivate the reasons behind OrchideaSOL and describe the differences between the original SOL and our dataset. We will also show the work done in improving the dynamic ranges of orchestral families and other aspects of the data.

Vincent Lostanlen, Alice Cohen-Hadria, Juan Pablo Bello

With the aim of constructing a biologically plausible model of machine listening, we study the representation of a multicomponent stationary signal by a wavelet scattering network. First, we show that renormalizing second-order nodes by their first-order parents gives a simple numerical criterion to assess whether two neighboring components will interfere psychoacoustically. Secondly, we run a manifold learning algorithm (Isomap) on scattering coefficients to visualize the similarity space underlying parametric additive synthesis. Thirdly, we generalize the "one or two components" framework to three sine waves or more, and prove that the effective scattering depth of a Fourier series grows in logarithmic proportion to its bandwidth.

Vincent Lostanlen, Kaitlin Palmer, Elly Knight et al.

This paper proposes to perform unsupervised detection of bioacoustic events by pooling the magnitudes of spectrogram frames after per-channel energy normalization (PCEN). Although PCEN was originally developed for speech recognition, it also has beneficial effects in enhancing animal vocalizations, despite the presence of atmospheric absorption and intermittent noise. We prove that PCEN generalizes logarithm-based spectral flux, yet with a tunable time scale for background noise estimation. In comparison with pointwise logarithm, PCEN reduces false alarm rate by 50x in the near field and 5x in the far field, both on avian and marine bioacoustic datasets. Such improvements come at moderate computational cost and require no human intervention, thus heralding a promising future for PCEN in bioacoustics.

Vincent Lostanlen, Sripathi Sridhar, Brian McFee et al.

To explain the consonance of octaves, music psychologists represent pitch as a helix where azimuth and axial coordinate correspond to pitch class and pitch height respectively. This article addresses the problem of discovering this helical structure from unlabeled audio data. We measure Pearson correlations in the constant-Q transform (CQT) domain to build a K-nearest neighbor graph between frequency subbands. Then, we run the Isomap manifold learning algorithm to represent this graph in a three-dimensional space in which straight lines approximate graph geodesics. Experiments on isolated musical notes demonstrate that the resulting manifold resembles a helix which makes a full turn at every octave. A circular shape is also found in English speech, but not in urban noise. We discuss the impact of various design choices on the visualization: instrumentarium, loudness mapping function, and number of neighbors K.

Vincent Lostanlen

With the aim of constructing a biologically plausible model of machine listening, we study the representation of a multicomponent stationary signal by a wavelet scattering network. First, we show that renormalizing second-order nodes by their first-order parents gives a simple numerical criterion to establish whether two neighboring components will interfere psychoacoustically. Secondly, we generalize the `one or two components' framework to three sine waves or more, and show that a network of depth $M = \log_2 N$ suffices to characterize the relative amplitudes of the first $N$ terms in a Fourier series, while enjoying properties of invariance to frequency transposition and component-wise phase shifts.

Vincent Lostanlen, Justin Salamon, Andrew Farnsworth et al.

Bioacoustic sensors, sometimes known as autonomous recording units (ARUs), can record sounds of wildlife over long periods of time in scalable and minimally invasive ways. Deriving per-species abundance estimates from these sensors requires detection, classification, and quantification of animal vocalizations as individual acoustic events. Yet, variability in ambient noise, both over time and across sensors, hinders the reliability of current automated systems for sound event detection (SED), such as convolutional neural networks (CNN) in the time-frequency domain. In this article, we develop, benchmark, and combine several machine listening techniques to improve the generalizability of SED models across heterogeneous acoustic environments. As a case study, we consider the problem of detecting avian flight calls from a ten-hour recording of nocturnal bird migration, recorded by a network of six ARUs in the presence of heterogeneous background noise. Starting from a CNN yielding state-of-the-art accuracy on this task, we introduce two noise adaptation techniques, respectively integrating short-term (60 milliseconds) and long-term (30 minutes) context. First, we apply per-channel energy normalization (PCEN) in the time-frequency domain, which applies short-term automatic gain control to every subband in the mel-frequency spectrogram. Secondly, we replace the last dense layer in the network by a context-adaptive neural network (CA-NN) layer. Combining them yields state-of-the-art results that are unmatched by artificial data augmentation alone. We release a pre-trained version of our best performing system under the name of BirdVoxDetect, a ready-to-use detector of avian flight calls in field recordings.

Mathieu Andreux, Tomás Angles, Georgios Exarchakis et al.

The wavelet scattering transform is an invariant signal representation suitable for many signal processing and machine learning applications. We present the Kymatio software package, an easy-to-use, high-performance Python implementation of the scattering transform in 1D, 2D, and 3D that is compatible with modern deep learning frameworks. All transforms may be executed on a GPU (in addition to CPU), offering a considerable speed up over CPU implementations. The package also has a small memory footprint, resulting inefficient memory usage. The source code, documentation, and examples are available undera BSD license at https://www.kymat.io/

Vincent Lostanlen

Time-frequency scattering is a mathematical transformation of sound waves. Its core purpose is to mimick the way the human auditory system extracts information from its environment. In the context of improving the artificial intelligence of sounds, it has found succesful applications in automatic speech transcription as well as the recognition of urban sounds and musical sounds. In this article, we show that time-frequency scattering can also be useful for applications in contemporary music creations.

Vincent Lostanlen

We introduce a new multidimensional representation, named eigenprogression transform, that characterizes some essential patterns of Western tonal harmony while being equivariant to time shifts and pitch transpositions. This representation is deep, multiscale, and convolutional in the piano-roll domain, yet incurs no prior training, and is thus suited to both supervised and unsupervised MIR tasks. The eigenprogression transform combines ideas from the spiral scattering transform, spectral graph theory, and wavelet shrinkage denoising. We report state-of-the-art results on a task of supervised composer recognition (Haydn vs. Mozart) from polyphonic music pieces in MIDI format.

Vincent Lostanlen, Joakim Andén, Mathieu Lagrange

The expressive variability in producing a musical note conveys information essential to the modeling of orchestration and style. As such, it plays a crucial role in computer-assisted browsing of massive digital music corpora. Yet, although the automatic recognition of a musical instrument from the recording of a single "ordinary" note is considered a solved problem, automatic identification of instrumental playing technique (IPT) remains largely underdeveloped. We benchmark machine listening systems for query-by-example browsing among 143 extended IPTs for 16 instruments, amounting to 469 triplets of instrument, mute, and technique. We identify and discuss three necessary conditions for significantly outperforming the traditional mel-frequency cepstral coefficient (MFCC) baseline: the addition of second-order scattering coefficients to account for amplitude modulation, the incorporation of long-range temporal dependencies, and metric learning using large-margin nearest neighbors (LMNN) to reduce intra-class variability. Evaluating on the Studio On Line (SOL) dataset, we obtain a precision at rank 5 of 99.7% for instrument recognition (baseline at 89.0%) and of 61.0% for IPT recognition (baseline at 44.5%). We interpret this gain through a qualitative assessment of practical usability and visualization using nonlinear dimensionality reduction.

Joakim Andén, Vincent Lostanlen, Stéphane Mallat

In time series classification and regression, signals are typically mapped into some intermediate representation used for constructing models. Since the underlying task is often insensitive to time shifts, these representations are required to be time-shift invariant. We introduce the joint time-frequency scattering transform, a time-shift invariant representation which characterizes the multiscale energy distribution of a signal in time and frequency. It is computed through wavelet convolutions and modulus non-linearities and may therefore be implemented as a deep convolutional neural network whose filters are not learned but calculated from wavelets. We consider the progression from mel-spectrograms to time scattering and joint time-frequency scattering transforms, illustrating the relationship between increased discriminability and refinements of convolutional network architectures. The suitability of the joint time-frequency scattering transform for time-shift invariant characterization of time series is demonstrated through applications to chirp signals and audio synthesis experiments. The proposed transform also obtains state-of-the-art results on several audio classification tasks, outperforming time scattering transforms and achieving accuracies comparable to those of fully learned networks.

Vincent Lostanlen, Carmine-Emanuele Cella

Musical performance combines a wide range of pitches, nuances, and expressive techniques. Audio-based classification of musical instruments thus requires to build signal representations that are invariant to such transformations. This article investigates the construction of learned convolutional architectures for instrument recognition, given a limited amount of annotated training data. In this context, we benchmark three different weight sharing strategies for deep convolutional networks in the time-frequency domain: temporal kernels; time-frequency kernels; and a linear combination of time-frequency kernels which are one octave apart, akin to a Shepard pitch spiral. We provide an acoustical interpretation of these strategies within the source-filter framework of quasi-harmonic sounds with a fixed spectral envelope, which are archetypal of musical notes. The best classification accuracy is obtained by hybridizing all three convolutional layers into a single deep learning architecture.

Vincent Lostanlen, Stéphane Mallat

We present a new representation of harmonic sounds that linearizes the dynamics of pitch and spectral envelope, while remaining stable to deformations in the time-frequency plane. It is an instance of the scattering transform, a generic operator which cascades wavelet convolutions and modulus nonlinearities. It is derived from the pitch spiral, in that convolutions are successively performed in time, log-frequency, and octave index. We give a closed-form approximation of spiral scattering coefficients for a nonstationary generalization of the harmonic source-filter model.

Joakim Andén, Vincent Lostanlen, Stéphane Mallat

We introduce the joint time-frequency scattering transform, a time shift invariant descriptor of time-frequency structure for audio classification. It is obtained by applying a two-dimensional wavelet transform in time and log-frequency to a time-frequency wavelet scalogram. We show that this descriptor successfully characterizes complex time-frequency phenomena such as time-varying filters and frequency modulated excitations. State-of-the-art results are achieved for signal reconstruction and phone segment classification on the TIMIT dataset.

Vincent Lostanlen, Stéphane Mallat

We introduce a scattering representation for the analysis and classification of sounds. It is locally translation-invariant, stable to deformations in time and frequency, and has the ability to capture harmonic structures. The scattering representation can be interpreted as a convolutional neural network which cascades a wavelet transform in time and along a harmonic spiral. We study its application for the analysis of the deformations of the source-filter model.