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Published as a conference paper at ICLR 2021

LEAF: A LEARNABLE FRONTEND FOR AUDIO

CLASSIFICATION

Neil Zeghidour, Olivier Teboul, F�lix de Chaumont Quitry & Marco Tagliasacchi

Google Research

{neilz, oliviert, fcq, mtagliasacchi}@google.com

ABSTRACT

Mel-filterbanks are fixed, engineered audio features which emulate human percep-

tion and have been used through the history of audio understanding up to today.

However, their undeniable qualities are counterbalanced by the fundamental lim-

itations of handmade representations. In this work we show that we can train a

single learnable frontend that outperforms mel-filterbanks on a wide range of au-

dio signals, including speech, music, audio events and animal sounds, providing a

general-purpose learned frontend for audio classification. To do so, we introduce

a new principled, lightweight, fully learnable architecture that can be used as a

drop-in replacement of mel-filterbanks. Our system learns all operations of au-

dio features extraction, from filtering to pooling, compression and normalization,

and can be integrated into any neural network at a negligible parameter cost. We

perform multi-task training on eight diverse audio classification tasks, and show

consistent improvements of our model over mel-filterbanks and previous learn-

able alternatives. Moreover, our system outperforms the current state-of-the-art

learnable frontend on Audioset, with orders of magnitude fewer parameters.

1 INTRODUCTION

Learning representations by backpropagation in deep neural networks has become the standard in

audio understanding, ranging from automatic speech recognition (ASR) (Hinton et al., 2012; Se-

nior et al., 2015) to music information retrieval (Arcas et al., 2017), as well as animal vocaliza-

tions (Lostanlen et al., 2018) and audio events (Hershey et al., 2017; Kong et al., 2019). Still, a strik-

ing constant along the history of audio classification is the mel-filterbanks, a fixed, hand-engineered

representation of sound. Mel-filterbanks first compute a spectrogram, using the squared modulus of

the short-term Fourier transform (STFT). Then, the spectrogram is passed through a bank of triangu-

lar bandpass filters, spaced on a logarithmic scale (the mel-scale) to replicate the non-linear human

perception of pitch (Stevens & Volkmann, 1940). Eventually, the resulting coefficients are passed

through a logarithm compression, to replicate our non-linear sensitivity to loudness (Fechner et al.,

1966). This approach of drawing inspiration from the human auditory system to design features

for machine learning has been historically successful (Davis & Mermelstein, 1980; Mogran et al.,

2004). Moreover, decades after the design of mel-filterbanks, And�n & Mallat (2014) showed that

they coincidentally exhibit desirable mathematical properties for representation learning, in particu-

lar shift-invariance and stability to small deformations. Hence, both from an auditory and a machine

learning perspective, mel-filterbanks represent strong audio features.

However, the design of mel-filterbanks is also flawed by biases. First, not only has the mel-scale been

revised multiple times (O’Shaughnessy, 1987; Umesh et al., 1999), but also the auditory experiments

that led their original design could not be replicated afterwards (Greenwood, 1997). Similarly, better

alternatives to log-compression have been proposed, like cubic root for speech enhancement (Lyons

& Paliwal, 2008) or 10th root for ASR (Schluter et al., 2007). Moreover, even though matching

human perception provides good inductive biases for some application domains, e.g., ASR or music

understanding, these biases may also be detrimental, e.g. for tasks that require fine-grained resolu-

tion at high frequencies. Finally, the recent history of other fields like computer vision, in which the

rise of deep learning methods has allowed learning representations from raw pixels rather than from

engineered features (Krizhevsky et al., 2012), inspired us to take the same path.

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arXiv:2101.08596v1 [cs.SD] 21 Jan 2021

Published as a conference paper at ICLR 2021

GABOR

| | 2

GAUSSIAN

LOWPASS

sPCEN

LEAF

CONV1D

| | 2

LOWPASS

LOG

TD-FILTERBANKS

SINC

LRELU

MAXPOOL

LAYERNORM

SINCNET

MEL

| | 2

STFT

LOG

MEL-FILTERBANKS

Figure 1: Breakdown of the computation of mel-filterbanks, Time-Domain filterbanks, SincNet,

and the proposed LEAF frontend. Orange boxes are fixed, while computations in blue boxes are

learnable. Grey boxes represent activation functions.

These observations motivated replacing mel-filterbanks with learnable neural layers, ranging from

standard convolutional layers (Palaz et al., 2015) to dilated convolutions (Schneider et al., 2019),

as well as structured filters exploiting the characteristics of known filter families, such as Gamma-

tone (Sainath et al., 2015), Gabor (Zeghidour et al., 2018a; No� et al., 2020), Sinc (Ravanelli &

Bengio, 2018; Pariente et al., 2020) or Spline (Balestriero et al., 2018) filters. While tasks such as

speech separation have already successfully adopted learnable frontends (Luo & Mesgarani, 2019;

Luo et al., 2019), we observe that most state-of-the art approaches for audio classification (Kong

et al., 2019), ASR (Synnaeve et al., 2019) and speaker recognition (Villalba et al., 2020) still em-

ploy mel-filterbanks as input features, regardless of the backbone architecture.

In this work, we argue that a credible alternative to mel-filterbanks for classification should be

evaluated across many tasks, and propose the first extensive study of learnable frontends for audio

over a wide and diverse range of audio signals, including speech, music, audio events, and ani-

mal sounds. By breaking down mel-filterbanks into three components (filtering, pooling, compres-

sion/normalization), we propose LEAF, a novel frontend that is fully learnable in all its operations,

while being controlled by just a few hundred parameters. In a multi-task setting over 8 datasets,

we show that we can learn a single set of parameters that outperforms mel-filterbanks, as well as

previously proposed learnable alternatives. Moreover, these findings are replicated when training a

different model for each individual task. We also confirm these results on a challenging, large-scale

benchmark: classification on Audioset (Gemmeke et al., 2017). In addition, we show that the general

inductive bias of our frontend (i.e., learning bandpass filters, lowpass filtering before downsampling,

learning a per-channel compression) is general enough to benefit other systems, and propose a new,

improved version of SincNet (Ravanelli & Bengio, 2018). To foster application to new tasks, we

will release the source code of all our models and baselines, as well as pre-trained frontends.

2 RELATED WORK

In the last decade, several works addressed the problem of learning the audio frontend, as an alter-

native to mel-filterbanks. The first notable contributions in this field emerged for ASR, with Jaitly

& Hinton (2011) pretraining Restricted Boltzmann Machines from the waveform, and Palaz et al.

(2013) training a hybrid DNN-HMM model, replacing mel-filterbanks by several layers of convo-

lution. However, these alternatives, as well as others proposed more recently (Tjandra et al., 2017;

Schneider et al., 2019), are composed of many layers, which makes a fair comparison with mel-

filterbanks difficult. In the following section, we focus on frontends that provide a lightweight,

drop-in replacement to mel-filterbanks, with comparable capacity.

2.1 LEARNING FILTERS FROM WAVEFORMS

A first attempt at learning the filters of mel-filterbanks was proposed by Sainath et al. (2013), where

a filterbank is initialized using the mel-scale and then learned together with the rest of the net-

work, taking a spectrogram as input. Instead, Sainath et al. (2015) and Hoshen et al. (2015) later

proposed to learn convolutional filters directly from raw waveforms, initialized with Gammatone fil-

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Published as a conference paper at ICLR 2021

ters (Schluter et al., 2007). In the same spirit, Zeghidour et al. (2018a) used the scattering transform

approximation of mel-filterbanks (And�n & Mallat, 2014) to propose the time-domain filterbanks, a

learnable frontend that approximates mel-filterbanks at initialization and can then be learned without

constraints (see Figure 1). More recently, the SincNet (Ravanelli & Bengio, 2018) model was pro-

posed, which computes a convolution with sine cardinal filters, a non-linearity and a max-pooling

operator (see Figure 1), as well as a variant using Gabor filters (No� et al., 2020).

We take inspiration from these works to design a new learnable filtering layer. As detailed in Sec-

tion 3.1.2, we parametrize a complex-valued filtering layer with Gabor filters. Gabor filters are opti-

mally localized in time and frequency (Gabor, 1946), unlike Sinc filters that require using a window

function (Ravanelli & Bengio, 2018). Moreover, unlike No� et al. (2020), who use complex-valued

layers in the rest of the network, we describe in Section 3.1.2 how using a squared modulus not only

brings back the signal to the real-valued domain (leading to compatibility with standard architec-

tures), but also performs shift-invariant Hilbert envelope extraction. Zeghidour et al. (2018a) also

apply a squared modulus non-linearity, however as described in Section 3.1.1, training unconstrained

filters can lead to overfitting and stability issues, which we solve with our approach.

2.2 LEARNING THE COMPRESSION AND THE NORMALIZATION

The problem of learning a compression and/or normalization function has received less attention in

the past literature. A notable contribution is the Per-Channel Energy Normalization (PCEN) (Wang

et al., 2017; Lostanlen et al., 2019), which was originally proposed for keyword spotting, outper-

forming log-compression. Later, Battenberg et al. (2017) and Lostanlen et al. (2018) confirmed the

advantages of PCEN, respectively for large scale ASR and animal bioacoustics. However, these pre-

vious works learn a compression on top of fixed mel-filterbanks. Instead, in this work we propose a

new version of PCEN and show for the first time that combining learnable filters, learnable pooling,

and learnable compression and normalization outperforms all other approaches.

3 MODEL

Let x ∈ RT denote a one-dimensional waveform of T samples, available at the sampling frequency

Fs [Hz]. We decompose the frontend into a sequence of three components: i) filtering, which

passes x through a bank of bandpass filters followed by a non-linearity, operating at the original

sampling rate Fs; ii) pooling, which decimates the signal to reduce its temporal resolution; iii)

compression/normalization, which applies a non-linearity to reduce the dynamic range. Overall, the

frontend can be represented as a function Fψ : RT → RM�N , which maps the input waveform to a

2-dimensional feature space, where M denotes the number of temporal frames (typically M<T),

N the number of feature channels (which might correspond to frequency bins) and ψ the frontend

parameters. The features computed by the frontend are then fed to a model gθ(�) parametrized by θ.

The frontend and the model parameters are estimated by solving a supervised classification problem:

θ∗,ψ∗ = arg min

θ,ψ

E(x,y)∈D L(gθ(Fψ(x)),y),

(1)

where (x, y) are samples in a labelled dataset D and L is a loss function. Our goal is to learn the

frontend parameters ψ end-to-end with the model parameters θ. To achieve this, it is necessary to

make all the frontend components learnable, so that we can solve the optimization problem in equa-

tion 1 with gradient descent. In the following we detail the design choices of each component.

3.1 FILTERING

The first block of the learnable frontend takes x as input, and computes a convolution with a bank

of complex-valued filters (ϕn)n=1..N , followed by a squared modulus operator, which brings back

its output to the real-valued domain. This convolution step has a stride of 1, therefore keeping the

input temporal resolution, and outputs the following time-frequency representation:

fn = |x ∗ ϕn|2 ∈ RT , n = 1,...,N,

(2)

where ϕn ∈ CW is a complex-valued 1-D filter of length W. It is possible to compute equation 2

without explicitly manipulating complex numbers. As proposed by Zeghidour et al. (2018a), to

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Published as a conference paper at ICLR 2021

NormalizedConv1D

0.4

0.2

0.0

0.2

0.4

GaborConv1D

Figure 2: Frequency response of filters at convergence for two parametrizations: normalized 1D

filters and Gabor filters, both initialized on a mel scale. We highlight two filters among the 40 of the

filterbank: one in yellow in the low frequency range and one in pink at high frequencies.

produce the squared-modulus of a complex-valued convolution with N filters, we compute instead

the convolution with 2N real-valued filters ˜ϕn,n = 1,..., 2N, and perform squared l2-pooling

with size 2 and stride 2 along the channel axis to obtain the squared modulus, using adjacent filters

as real and imaginary part of ϕn. Formally:

fn = |x ∗ ˜ϕ2n−1|2 + |x ∗ ˜ϕ2n|2 ∈ RT , n = 1,...,N.

(3)

We explore two different parametrizations for ϕn. One relies on standard fully parametrized convo-

lutional filters while the other makes use of learnable Gabor filters.

3.1.1 NORMALIZED 1D-CONVOLUTION

Inspired by Zeghidour et al. (2018a), the first version of our filtering component is a standard 1D

convolution, initialized with a bank of Gabor filters, which approximates the computation of a mel-

filterbank. Thus, at initialization, the output of the frontend is identical to that of a mel-filterbank, but

during training the filters can be learned by backpropagation. In our early experiments, we observed

several limitations of this approach. First, due to the unconstrained optimization, these filters not

only learn to select frequency bands of interest, but also learn a scaling factor. This might lead to

instability during training, because the same form of scaling can be also computed by the filter-wise

compression component, which is applied at a later stage in the frontend. We address this issue by

applying l2-normalization to the filter coefficients before computing the convolution. Second, the

unconstrained parametrization increases the number of degrees of freedom, making training prone

to overfitting. The first panel in Figure 2 shows the frequency response of a bank of N = 40 filters,

each parametrized with W = 401 coefficients. We observe that, at convergence, they are widely

spread across the frequency axis, and include negative frequencies. Moreover, the filters are very

spiky rather than smooth. To alleviate these issues, in the next section we introduce a parametrization

based on a bank of Gabor filters, which reduces the number of parameters to learn, while at the same

time enforcing during training a stable and interpretable representation.

3.1.2 GABOR 1D-CONVOLUTION

Gabor filters are produced by modulating a Gaussian kernel with a sinusoidal signal. These filters

provide several desirable properties. First, they have an optimal trade-off between localization in

time and frequency (Gabor, 1946), which makes them a suitable choice for a convolutional network

with finite-sized filters. This is in contrast to Sinc filters (Ravanelli & Bengio, 2018), which require

using a window function to smooth abrupt variations on each side of the filter. Second, the time

and frequency response of Gabor filters have the same functional form, thus leading to interpretable

bandpass filters, unlike the unconstrained filters described in the previous section. Finally, Gabor

filters are quasi-analytic (i.e., their frequency response is almost zero for negative frequencies) and

when combined with the squared modulus the resulting filterbank can be interpreted as a set of

subband Hilbert envelopes, which are invariant to small shifts. Due to this desirable property, they

have been previously used as (fixed) features for speech and speaker recognition (Falk & Chan,

2009; Thomas et al., 2008). Formally, Gabor filters are parametrized by their center frequencies

(ηn)n=1..N and inverse bandwidths (σn)n=1..N as follows:

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Published as a conference paper at ICLR 2021

ϕn(t) = ei2πηnt

1

√

2πσn

e

− t2

2σ2n , n = 1,...,N, t = −W/2,...,W/2.

(4)

The frequency response of ϕn is a Gaussian centered at frequency ηn and of bandwidth 1/σn, both

expressed in normalized frequency units in [−1/2, +1/2]. Therefore, learning these parameters al-

lows learning a bank of smooth, quasi-analytic bandpass filters, with controllable center frequency

and bandwidth. In practice, to compute the output of the filtering component, we obtain the im-

pulse response of the Gabor filters ϕn(t) over the range t = −W/2,...,W/2, and convolve these

impulse responses with the input waveform. To ensure stability during training, we clip the center

frequencies (ηn)n=1..N to be in [0, 1/2], so that they lie in the positive part of the frequency range.

We also constrain the bandwidths (σn)n=1..N in the range [4

√

2 log 2, 2W

√

2 log 2], such that the

full-width at half-maximum of the frequency response is within 1/W and 1/2.

Gabor filters have significantly fewer parameters than the normalized 1D-convolutions described in

Section 3.1.1. N filters of length W are described by 2N parameters, N for the center frequencies

and N for the bandwidths, against W � N for a standard 1D-convolution. In particular, when using

a window length of 25 ms, operating at a sampling rate of 16 kHz, then W = 401 samples, and

Gabor-based filtering accounts for 200 times fewer parameters than their unconstrained alternatives.

3.1.3 TIME-FREQUENCY ANALYSIS AND LEARNABLE FILTERS

A spectrogram, in linear or mel scale, provides an ordered time-frequency representation: adjacent

frames represent consecutive time-steps, while frequencies monotonically increase along the feature

axis. A learnable frontend that performs filtering by means of convolution with a set of bandpass

filters also preserves ordering along the temporal axis. However, the ordering along the feature

axis is unconstrained. This can be problematic when applying subsequent operations that rely on

frequency ordering. These include, for example: i) operations that leverage local frequency infor-

mation, e.g., two-dimensional convolutions, which compute a feature representation based on local

time-frequency patches; ii) operations that leverage long-range dependencies along the frequency

axis, e.g., to capture the harmonic structure of the underlying signal; and iii) augmentation methods

that mask adjacent frequency bands, like SpecAugment (Park et al., 2019). To evaluate the impact

of enforcing an explicit ordering of the center frequencies of the learned filters, we compared the

result of training a frontend using Gabor filters with or without explicitly enforcing ordering of the

center frequencies. Interestingly, we observe that even without an explicit constraint, filters that are

ordered at the initialization tend to keep the same ordering throughout training, and that enforcing

sorted filters has no effect on the performance.

3.2 LEARNABLE LOWPASS POOLING

The output of the filtering component has the same temporal resolution as the input waveform. The

second step of a learnable frontend is to downsample the output of the filterbank to a lower sam-

pling rate, similarly to what happens in the STFT when computing mel-filterbanks. Previous work

relied on max-pooling (Sainath et al., 2015; Ravanelli & Bengio, 2018; No� et al., 2020), lowpass-

filtering (Zeghidour et al., 2018a) or average pooling (Balestriero et al., 2018). Zeghidour et al.

(2018b) compare these methods on a speech recognition task and show a systematic improvement

when using lowpass filtering instead of max-pooling. More recently, Zhang (2019) showed that in

standard 2D convolutional architectures, including ResNet (He et al., 2016) and DenseNet (Huang

et al., 2017), a drop-in replacement of max-pooling and average pooling layers with a (fixed) low-

pass filter improves the performance for image classification. In the proposed frontend, we extend

the pooling layer of Zeghidour et al. (2018a) in two ways. First, while Zeghidour et al. (2018a)

adopt a single shared lowpass filter for all input channels, we implement lowpass filtering by means

of depthwise convolution, such that each input channel is associated with one lowpass filter. This

is useful because each channel in the learnable frontend is characterized by a different bandwidth,

and a specific lowpass filter can be learned for each of them. Second, we parametrize these lowpass

filters to have a Gaussian impulse response:

φn(t) =

1

√

2πσn

e

− t2

2σ2n , t = −W/2,...,W/2.

(5)

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Published as a conference paper at ICLR 2021

Note that this is a particular case of Gabor filters with center frequency equal to 0 and learnable

bandwidth. With this choice, we can learn per-channel lowpass pooling functions while adding only

N parameters to the frontend model. We initialize all channels with a bandwidth of 0.4, which gives

a frequency response close to the Hann window used by mel-filterbanks.

3.3 LEARNING PER-CHANNEL COMPRESSION AND NORMALIZATION

When using a traditional frontend based on a mel-filterbank or STFT, the time-frequency features are

typically passed through a logarithmic compression, to replicate the non-linear human perception of

loudness (Fechner et al., 1966). The first limitation of this approach is that the same compression

function is applied to all frequency bins, regardless of their content. The second limitation is the

fixed choice of the non-linearity used by the compression function. While, in most cases, a loga-

rithmic function is used, other compression functions have been proposed and evaluated in the past,

including the cubic root (Lyons & Paliwal, 2008) and the 10th root (Schluter et al., 2007). This mo-

tivates learning the compression function as part of the model, rather than relying on a handcrafted

choice. In particular, Per-Channel Energy Normalization (Wang et al., 2017) was proposed as a

learnable alternative to log-compression and mean-variance normalization:

PCEN(F(t, n)) =

(

F(t, n)

(ε + M(t, n))

αn + δn

)rn

− δrn

n ,

(6)

where t = 1,...,M denotes the time-step and n = 1,...,N the channel index. In this parametriza-

tion, the time-frequency representation F is first normalized by an exponential moving average of its

past values M(t, n) = (1−s)M(t−1,n)+sF(t, n), controlled by a smoothing coefficient s and an

exponent αn, with ε being a small constant used to avoid dividing by zero. An offset δn is then added

before applying compression with the exponent rn (typically in [0, 1]). Wang et al. (2017) train αn,

δn, and rn, while treating s as a hyperparameter, or learning a convex combination of exponential

moving averages for different, fixed values of s. Instead, in this work we learn channel-dependent

smoothing coefficients sn, jointly with the rest of the parameters. We call this version sPCEN. This

approach was previously used by Schl�ter & Lehner (2018) for singing voice detection, except that

they did not learn the exponents αn, while we learn all these parameters jointly. Our final frontend

cascades a Gabor 1D-convolution, a Gaussian lowpass pooling, and sPCEN. In the rest of the paper,

we refer to this model as LEAF, for “LEarnable Audio Frontend”.

4 EXPERIMENTS

We evaluate our frontend on three supervised learning problems: i) single-task classification; ii)

multi-task classification and iii) multi-label classification on Audioset. As baselines, we compare

our system to log-compressed mel-filterbanks, learnable Time-Domain filterbanks (Zeghidour et al.,

2018a)1 and SincNet (Ravanelli & Bengio, 2018)2. We reimplemented these baselines to match

their official implementation. In all our experiments, we keep the same common backbone network

architecture, which consists of a frontend, a convolutional encoder, and one (or more) head(s). We

adopt the lightweight version of EfficientNet (Tan & Le, 2019) (EfficientNetB0, with 4M param-

eters) as convolutional encoder. On AudioSet, we also experiment with a state-of-the-art CNN14

encoder (Kong et al., 2019), with 81 M parameters. A head is a single linear layer with a number of

outputs equal to the number of classes. In the multi-task setting we use a different head for each of

the target tasks, all sharing the same encoder.

The input signal sampled at Fs = 16 kHz is passed through the frontend which feeds into the convo-

lutional encoder. As baseline, we use a log-compressed mel-filterbank with 40 channels, computed

over windows of 25 ms with a stride of 10 ms. For a fair comparison, both LEAF and the learnable

baselines also have N = 40 filters, each with W = 401 coefficients (≈25 ms at 16 kHz). The learn-

able pooling is computed over 401 samples with a stride of 160 samples (10 ms at 16 kHz), giving

the same output dimension as mel-filterbanks. On AudioSet we use 64 channels instead of 40 as

Kong et al. (2019) observed improvements from using 64 mel-filters.

To address the variable length of the input sequences, we train on randomly sampled 1 second win-

dows. We train with ADAM (Kingma & Ba, 2014) and a learning rate of 10−4 for 1M batches, with

1https://github.com/facebookresearch/tdfbanks

2https://github.com/mravanelli/SincNet

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Published as a conference paper at ICLR 2021

Table 1: Test accuracy (%) for single-task classification.

Task

Mel

TD-fbanks

SincNet

LEAF

Acoustic scenes

99.2 � 0.4

99.5 � 0.3

96.7 � 0.9

99.1 � 0.5

Birdsong detection

78.6 � 1.0

80.9 � 0.9

78.0 � 1.0

81.4 � 0.9

Emotion recognition

49.1 � 2.4

57.1 � 2.4

44.2 � 2.4

57.8 � 2.4

Speaker Id. (VC)

31.9 � 0.7

25.3 � 0.7

43.5 � 0.8

33.1 � 0.7

Music (instrument)

72.0 � 0.6

70.0 � 0.6

70.3 � 0.6

72.0 � 0.6

Music (pitch)

91.5 � 0.3

91.3 � 0.3

83.8 � 0.5

92.0 � 0.3

Speech commands

92.4 � 0.4

87.3 � 0.4

89.2 � 0.4

93.4 � 0.3

Language Id.

76.5 � 0.4

71.6 � 0.5

78.9 � 0.4

86.0 � 0.4

Average

73.9 � 0.8

72.9 � 0.8

73.1 � 0.9

76.9 � 0.8

Table 2: Impact of the compression layer on the performance (single task, average accuracy in %).

mel-filterbank

LEAF- filterbank

log

PCEN

sPCEN

log

PCEN

sPCEN

Average

73.9 � 0.8

76.4 � 0.8

76.0 � 0.7

74.6 � 0.7

76.4 � 0.8

76.9 � 0.8

batch size 256. For Audioset experiments, we train with mixup (Zhang et al., 2017) and SpecAug-

ment (Park et al., 2019). During evaluation, we consider the full-length sequences, splitting them

into consecutive non-overlapping 1 second windows and averaging the output logits over windows.

4.1 SINGLE-TASK AUDIO CLASSIFICATION

We train independent single-task supervised models on 8 distinct classification problems: acoustic

scene classification on TUT (Heittola et al., 2018), birdsong detection (Stowell et al., 2018), emotion

recognition on Crema-D (Cao et al., 2014), speaker identification on VoxCeleb (Nagrani et al., 2017),

musical instrument and pitch detection on NSynth (Engel et al., 2017), keyword spotting on Speech

Commands (Warden, 2018), and language identification on VoxForge (Revay & Teschke, 2019). A

summary of the datasets used in our experiments is illustrated in Table A.1.

Table 1 reports the results for each task, with 95% confidence intervals representing the uncertainty

due to the limited test sample size. No class rebalancing is applied, neither during training, nor

during testing. On average, we observe that LEAF outperforms all alternatives. When considering

results for each individual tasks, we observe that LEAF outperforms or matches the accuracy of

other frontends, with the notable exception of SincNet on Voxceleb. This is consistent with the

fact that SincNet was originally proposed for speaker identification (Ravanelli & Bengio, 2018) and

illustrates the importance of evaluating over a wide range of tasks. To evaluate the robustness of our

results with respect to the choice of the datasets, we apply a statistical bootstrap (Efron & Tibshirani,

1993) to compute the non-parametric distribution of the difference between the accuracy obtained

with LEAF and each of the other frontends, when sampling datasets with replacement among the

eight datasets. We test the null hypothesis that the mean of the difference is zero and measure

the following one-sided p-values: pMel < 10−5, pTD-fbanks < 10−5, pSincNet = 0.059. Figure A.1

illustrates the corresponding bootstrap distribution, showing the statistical significance of our results

with respect to the choice of the datasets.

We dive deeper in the comparison between the mel-filterbanks frontend and LEAF by studying the

effect of the compression component (log, PCEN, sPCEN). Table 2 shows that PCEN improves sig-

nificantly over log-compression on both mel- and learned filterbanks. The proposed LEAF frontend

adopts sPCEN, which gives the best performance. We also observe that for any choice of the com-

pression function, the learnable frontend matches or outperforms the corresponding mel-filterbank.

4.2 MULTI-TASK AUDIO CLASSIFICATION

To learn a general-purpose frontend that generalizes across tasks, we train a multi-task model that

uses the same LEAF parameters and encoder for all tasks, with a task-specific linear head. More

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Table 3: Test accuracy (%) for multi-task classification.

Task

Mel

TD-fbanks

SincNet

LEAF

Acoustic scenes

99.1 � 0.5

98.3 � 0.6

91.0 � 1.4

98.9 � 0.5

Birdsong detection

81.3 � 0.9

82.3 � 0.9

78.8 � 0.9

81.9 � 0.9

Emotion recognition

24.1 � 2.1

24.4 � 2.1

26.2 � 2.1

31.9 � 2.3

Speaker Id. (LBS)

100.0 � 0.0

100.0 � 0.0

100.0 � 0.0

100.0 � 0.0

Music (instrument)

70.7 � 0.6

66.3 � 0.6

67.4 � 0.6

70.2 � 0.6

Music (pitch)

88.5 � 0.4

86.4 � 0.4

81.2 � 0.5

88.6 � 0.4

Speech commands

93.6 � 0.3

89.5 � 0.4

91.4 � 0.4

93.6 � 0.3

Language Id.

64.9 � 0.5

58.9 � 0.5

60.8 � 0.5

69.6 � 0.5

Average

77.8 � 0.7

75.8 � 0.7

74.6 � 0.8

79.3 � 0.7

Table 4: Test AUC and d-prime (� standard deviation over three runs) on Audioset, with the number

of learnable parameters per frontend.

EfficientNetB0

CNN14 (ours)

CNN14 (Kong et al., 2019)

Frontend

#Params

AUC

d-prime

AUC

d-prime

AUC

d-prime

Mel

0 0.968 � .001 2.61 � .02 0.972 � .000

2.71 � .01

0.973

2.73

Mel-PCEN

256 0.967 � .000 2.60 � .01 0.973 � .000

2.72 � .00

-

-

Wavegram

300 k 0.958 � .000 2.44 � .00 0.961 � .001

2.50 � .02

0.968

2.61

TD-fbanks

51 k 0.965 � .001 2.57 � .01 0.972 � .000

2.70 � .00

-

-

SincNet

256 0.961 � .000 2.48 � .00 0.970 � .000

2.66 � .01

-

-

SincNet+

448 0.966 � .002 2.58 � .04 0.973 � .001

2.71 � .01

-

-

LEAF

448 0.968 � .001 2.63 � .01 0.974 � .000 2.74 � .01

-

-

specifically, a single network with K heads (hθ1 ,...,hθK ) is trained on mini-batches, uniformly

sampled from the K datasets. A mini-batch of size B can be represented as (xki

i ,yki

i )i=1..B, where

ki is the associated task the example has been sampled from. The multi-task loss function is now

computed on a mini-batch as the sum of the individual loss functions:

L =

B

∑

i=1

K

∑

k=1

Lk

(

hθk

(

gθ(Fψ(xki

i )

)

,yki

i

)

δ(ki,k),

(7)

where θ and ψ represent the shared parameters of the encoder and frontend respectively, θk, k =

1,...,K the task-specific parameters of the heads hθk (�), and δ is the Kronecker delta function.

We use the same set of tasks described in Section 4.1 with one exception, replacing VoxCeleb with

Librispeech as a representative speaker identification task. As illustrated in Table A.1, VoxCeleb

has much more classes (≈1200) than any other task. This creates an imbalance in the number of

parameters in the heads, making training significantly slower and reducing the accuracy on all other

tasks, regardless of the frontend. Table 3 reports the accuracy obtained on each task, for all the

frontends. LEAF shows the best overall performance while matching or outperforming all other

methods on every tasks. We repeated the analysis using the bootstrap to evaluate the statistical

significance of these results with respect to the choice of the datasets and observed the following

p-values: pMel = 0.048, pTD-fbanks < 10−5, pSincNet = 10−5. Figure A.2 illustrates the corresponding

bootstrap distribution. To the best of our knowledge, it is the first time a learnable frontend is shown

to outperform mel-filterbanks over several tasks with a unique parametrization.

4.3 MULTI-LABEL CLASSIFICATION ON AUDIOSET

Table 4 shows the performance (averaged over three runs) of the different frontends on Au-

dioset (Gemmeke et al., 2017), a large-scale multi-label dataset of sounds of all categories, described

by an ontology of 527 classes. Audioset examples are weakly labelled with one or more positive

labels, so we evaluate with the standard metric of this dataset, the balanced d-prime, a non-linear

transformation of the AUC averaged uniformly across all classes. EfficientNetB0 trained with LEAF

achieves a d-prime of 2.63, outperforming the level achieved when using mel-filterbanks (d-prime:

8

Published as a conference paper at ICLR 2021

2.61) or other frontends. We compare this result with the state-of-the-art PANN model (Kong et al.,

2019), which reports a d-prime of 2.73 when trained on mel-filterbanks. Kong et al. (2019) also train

a learnable “Wavegram” frontend made of 9 layers of 1D- and 2D- convolutions, for a total of 300 k

parameters, reporting a d-prime equal to 2.61. EfficientNetB0 on LEAF thus outperforms this sys-

tem, while having a frontend with 670x fewer parameters, and a considerably smaller encoder. To

confirm these results, we also train EfficientNetB0 on the Wavegram and get similar findings. All

these findings are replicated when replacing EfficientNetB0 with our implementation of CNN14:

even though the gap between LEAF and baselines reduces as the scores get higher, CNN14 on

LEAF matches the current state-of-the-art on AudioSet. To conclude these experiments and show

that individual components of LEAF can benefit other frontends, we replace the max-pooling of

SincNet with our Gaussian lowpass filter, and LayerNorm (Ba et al., 2016) with the proposed sP-

CEN. This version, named “SincNet+” in Table 4, significantly outperforms the original version,

regardless of the encoder.

4.4 ANALYSIS OF LEARNED FILTERS, POOLING AND COMPRESSION

Figure A.3 illustrates the center frequencies learned by the Gabor filtering layer of LEAF on Au-

dioSet, and compares them to those of mel-filterbanks. At a high level, these filters do not deviate

much from their mel-scale initialization. On the one hand, this indicates that the mel-scale is a strong

initialization, a result consistent with previous work (Sainath et al., 2015; Zeghidour et al., 2018b).

On the other hand, there are differences at both ends of the range, with LEAF covering a wider

range of frequencies. For example, the lowest frequency filter is centered around 60 Hz, as opposed

to 100 Hz for mel-filterbanks. We believe that is one of the reasons that explain the out-performance

of LEAF on Audioset, as it focuses on a more appropriate frequency range to represent the underly-

ing audio events. Figure A.4 shows the learned Gaussian lowpass filters at convergence. We see that

they all deviate towards a larger frequency bandwidth (characterized by a smaller standard deviation

in the time domain), and that each filter has a different bandwidth, which confirms the utility of using

depthwise pooling. Figure A.5 shows the learned exponents rn (initialized at 2.0) and smoothing

coefficients sn (initialized at 0.04) of sPCEN, ordered by filter index. The exponents are spread in

[1.9, 2.6], which shows the importance of learning per-channel exponents, as well as the appropriate

choice of using a fixed cubic root in previous work (Lyons & Paliwal, 2008), as an alternative to

log-compression. Learning per-channel smoothing coefficients also allows deviating from the ini-

tialization. Interestingly, most filters keep a low coefficient (slowly moving average), except for the

filter with the highest frequency, which has a significantly faster moving average (s≈0.15).

4.5 ROBUSTNESS TO NOISE

We compare the robustness of LEAF and mel-filterbanks to synthetic noise, on the Speech Com-

mands dataset. To do so, we artificially add Gaussian noise to the waveforms both during training

and evaluation, with different gains to obtain a Signal-to-Noise Ratio (SNR) from + inf (no noise)

to −5 dB. Figure A.6 shows that while performance (averaged over three runs) degrades for all

models as SNR decreases, LEAF is more resilient than mel-filterbanks. In particular, when using

a logarithmic compression, the Gabor 1-D convolution and Gaussian pooling of LEAF maintain

a significantly higher accuracy than mel-filterbanks. Using PCEN has an even higher impact on

performance when using mel-filterbanks, the best results being obtained with LEAF + PCEN.

5 CONCLUSION

In this work we introduce LEAF, a fully learnable frontend for audio classification as an alternative

to using handcrafted mel-filterbanks. We demonstrate over a large range of tasks that our model is a

good drop-in replacement to these features with no adjustment to the task at hand, and can even learn

a single set of parameters for general-purpose audio classification while outperforming previously

proposed learnable frontends. In future work, we will move yet a step forward in removing hand-

crafted biases from the model. In particular, our model still relies on an underlying convolutional

architecture, with fixed filter length and stride. Learning these important parameters directly from

data would allow for an easier generalization across tasks with various sampling rates and frequency

content. Moreover, we believe that the general principle of learning to filter, pool and compress can

benefit the analysis of non-audio signals, such as seismic data or physiological recordings.

9

Published as a conference paper at ICLR 2021

6 ACKNOWLEDGMENTS

Authors thank Dick Lyon, Vincent Lostanlen, Matt Harvey, and Alex Park for helpful discussions.

Authors are also thankful to Julie Thomas for helping with the design of Figure 1. Finally, authors

thank the reviewers of ICLR 2021 for their feedback that helped improving the quality of this work.

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A APPENDIX

Table A.1: Datasets used in the experiments. Default train/test splits are always adopted.

Task

Name

Classes Train examples Test examples

Audio events

Audioset

527

1,832,720

17,695

Acoustic scenes

TUT Urban 2018

10

7,829

810

Birdsong detection

DCASE2018

2

32,129

3,561

Emotion recognition

Crema-D

6

5,146

820

Speaker Id.

Voxceleb

1,251

138,361

8,249

Speaker Id.

Librispeech

251

25,740

2,799

Music (instrument)

Nsynth

11

289,205

12,678

Music (pitch)

Nsynth

128

289,205

12,678

Speech commands

Speech commands

35

84,771

10,700

Language Id.

Voxforge

6

126,610

18,378

10.0 7.5 5.0 2.5 0.0 2.5 5.0 7.5 10.0

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

LEAF - mel (p= 0.000)

10.0 7.5 5.0 2.5 0.0 2.5 5.0 7.5 10.0

LEAF - tdfbanks (p= 0.000)

10.0 7.5 5.0 2.5 0.0 2.5 5.0 7.5 10.0

LEAF - SincNet (p= 0.059)

Figure A.1: Distribution of the difference between the accuracy (%) obtained with LEAF and each

of the other frontends when sampling 8 datasets with replacement, in the single task setting.

10.0 7.5 5.0 2.5 0.0 2.5 5.0 7.5 10.0

0.0

0.1

0.2

0.3

0.4

0.5

LEAF - mel (p= 0.048)

10.0 7.5 5.0 2.5 0.0 2.5 5.0 7.5 10.0

LEAF - tdfbanks (p= 0.000)

10.0 7.5 5.0 2.5 0.0 2.5 5.0 7.5 10.0

LEAF - SincNet (p= 0.000)

Figure A.2: Distribution of the difference between the accuracy obtained with LEAF and each of

the other frontends when sampling 8 datasets with replacement, in the multi-task setting.

14

Published as a conference paper at ICLR 2021

0

5

10

15

20

25

30

35

40

Filter index

102

103

104

Frequency [Hz]

mel-spectrogram

LEAF (on AudioSet)

Figure A.3: Comparison between the filters learned by LEAF and the mel scale.

0

50 100 150 200 250 300 350 400

0.0

0.2

0.4

0.6

0.8

1.0

Learned depthwise Gaussian lowpass filters

init

Figure A.4: Learned Gaussian lowpass filters of LEAF on AudioSet. The dotted line represents the

initialization, identical for all filters.

0 10 20 30 40 50 60

0.04

0.06

0.08

0.10

0.12

0.14

0.16

PCEN smooth coefficients

0 10 20 30 40 50 60

2.0

2.1

2.2

2.3

2.4

2.5

2.6

PCEN root coefficients

Figure A.5: Values of learned sPCEN parameters of LEAF trained on AudioSet. The dotted lines

represent the initialization, identical for all filters.

15

Published as a conference paper at ICLR 2021

11

5

5

SNR

40%

50%

60%

70%

80%

90%

Accuracy

LEAF-PCEN

LEAF-log

Mel-PCEN

Mel-log

Figure A.6: Test accuracy (%) on the test set of the Speech Commands dataset with varying SNR.

16