Adrien Bitton

Philippe Esling

Antoine Caillon

Martin Fouilleul

ASSISTED SOUND SAMPLE GENERATION WITH MUSICAL CONDITIONING IN ADVERSARIAL AUTO-ENCODERS

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ASSISTED SOUND SAMPLE GENERATION WITH MUSICAL CONDITIONING IN ADVERSARIAL AUTO-ENCODERS

Adrien Bitton, Philippe Esling, Antoine Caillon, Martin Fouilleul Institut de Recherche et Coordination Acoustique-Musique (IRCAM) CNRS -UMR 9912, UPMC -Sorbonne Universite 1 Place Igor Stravinsky, F-75004 Paris, France adrien.bitton@ircam.fr

ABSTRACT

Deep generative neural networks have thrived in the field of computer vision, enabling unprecedented intelligent image processes. Yet the results in audio remain less advanced and many applications are still to be investigated. Our project targets real-time sound synthesis from a reduced set of high-level parameters, including semantic controls that can be adapted to different sound libraries and specific tags. These generative variables should allow expressive modulations of target musical qualities and continuously mix into new styles.

To this extent we train auto-encoders on an orchestral database of individual note samples, along with their intrinsic attributes: note class, timbre domain (an instrument subset) and extended playing techniques. We condition the decoder for explicit control over the rendered note attributes and use latent adversarial training for learning expressive style parameters that can ultimately be mixed. We evaluate both generative performances and correlations of the attributes with the latent representation. Our ablation study demonstrates the effectiveness of the musical conditioning.

The proposed model generates individual notes as magnitude spectrograms from any probabilistic latent code samples (each latent point maps to a single note), with expressive control of orchestral timbres and playing styles. Its training data subsets can directly be visualized in the 3-dimensional latent representation. Waveform rendering can be done offline with the Griffin-Lim algorithm.

In order to allow real-time interactions, we fine-tune the decoder with a pretrained magnitude spectrogram inversion network and embed the full waveform generation pipeline in a plugin. Moreover the encoder could be used to process new input samples, after manipulating their latent attribute representation, the decoder can generate sample variations as an audio effect would. Our solution remains rather light-weight and fast to train, it can directly be applied to other sound domains, including an user's libraries with custom sound tags that could be mapped to specific generative controls. As a result, it fosters creativity and intuitive audio style experimentations. Sound examples and additional visualizations are available on Github1 , as well as codes after the review process.

INTRODUCTION

Modern music production techniques rely on large and heterogeneous sound sample libraries along with diverse digital instruments and effects. It opens to a great variety of sound design possibilities and limitless contents to compose with, however principled interactions and scaled visualisations are still lacking in order to efficiently explore such potential and use it to generate target sound qualities. Unsupervised generative models learn an underlying data distribution solely based on the observation of examples, in order to consistently generate novel content. They have been successfully applied to complex computer vision tasks such as processing facial expressions, landscapes, visual styles and paintings. Some solutions to audio emerged more recently, including pioneer musical systems such as NSynth (Neural Synthesizer [START_REF] Engel | Neural audio synthesis of musical notes with wavenet autoencoders[END_REF]) for real-time high-quality sound synthesis. However, the heavy model architecture and prohibitive training time restrict its dissemination. The learned internal representation remains mostly uninformative and its many generative parameters are still too little correlated to explicit semantic qualities.

In this paper, we develop a high-level sound synthesis system with meaningful data visualisations and explicit musical controls. It is a lighter non-autoregressive model that can be trained fast on small datasets, including an user's personal libraries. Our goal is to learn expressive style variables from any sound tags, so that the model fosters creativity and assists digital interactions in music production. Considering note samples of orchestral instruments, we could for instance synthesise novel timbres or playing style hybrids.

3x Linear AdaIN 5x Up. Conv. We train Wasserstein Auto-Encoders (WAEs [START_REF] Tolstikhin | Wasserstein auto-encoders[END_REF][3]) on Mel-spectrogram magnitudes to organise a generative latent representation of individual note samples spanning the tessitura of 12 orchestral instruments. The considered database has intrinsic attributes: note classes, playing styles and timbres (each instrument subset), that we wish to control when generating new notes from the latent space. Thus we extend the WAE model with musical conditioning in the decoder and Adaptive Instance Normalization (AdaIN [START_REF] Huang | Arbitrary style transfer in real-time with adaptive instance normalization[END_REF]).

AdaIN O z i z ⇠ N(0, 1) 3x Linear (y i ) (y i ) 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 concat.
Using Feature Wise Linear Modulation (FiLM [START_REF] Perez | Film: Visual reasoning with a general conditioning layer[END_REF]) and adversarial training with a Fader latent discriminator [START_REF] Lample | Fader networks: Manipulating images by sliding attributes[END_REF], our WAE-Fader model effectively learns these generative controls along with expressive style variables that can be mixed continuously.

We evaluate these features in terms of generative performances and representation. We perform an ablation study and show that the model can sustain a good test reconstruction quality while achieving an accurate attribute-conditional generation. The success of the method relies on an attribute-free latent representation so that the decoder is pushed to learn the conditioning. These distributions can be visualized directly in the 3-dimensional latent space where clusters denote an undesired attribute encoding. We measure it with inter-class statistics and latent post-classification. The experiment validates correlations between low attribute encoding and effective conditioning.

We obtain an expressive note sample generator with 3-dimensional representations of the training sound domains, decoding probabilistic latent samples with explicit control over the rendered note qualities. The learned style variables of the orchestra can ultimately be mixed continuously, as faders do, in order to intuitively explore new musical effects. Generated spectrogram magnitudes can approximately be inverted to waveform with the Griffin-Lim iterative algorithm (GLA [START_REF] Griffin | Signal estimation from modified short-time fourier transform[END_REF]). Ultimately we fine-tune the decoder with a pretrained inversion network [START_REF] Lample | Fast spectrogram inversion using multihead convolutional neural networks[END_REF] for real-time waveform synthesis. We embed the resulting generative system in a plugin allowing for MIDI mapping, live exploration and Digital Audio Workstation (DAW) integration.

STATE-OF-ART

Generative models and regularized auto-encoders

Generative models aim to find the underlying probability distribution of the data p(x) based on a set of examples in x ∈ R dx . To do so, we consider latent variables defined in a lower-dimensional space z ∈ R dz (dz dx), a higher-level representation that could have led to generate any given example. The latent variable generative model is defined by the joint probability distribution p(x, z) = p(x|z)p(z), where the prior p(z) is usually modelled with simpler distributions such as Gaussian or uniform while a complex conditional distribution p(x|z) maps latent codes to the data space. The model could be evaluated with the maximum marginal likelihood over the considered dataset. However for complex distributions that could model real-world data, integration cannot be computed in closed form. Regularized auto-encoders have been used to reformulate the problem as an optimization by jointly learning the generative mapping p θ (x|z) ∈ G and an encoding distribution q φ (z|x) ∈ Q from families G, Q of approximate densities both parameterized with neural networks. This was initially proposed through Variational Inference in the Variational Auto-Encoder (VAE [START_REF] Kingma | Auto-encoding variational bayes[END_REF]) that maximizes a lower bound of the data log-likelihood:

E q φ (z|x) log pθ(x|z) -DKL qφ(z|x) pθ(z) ≤ log pθ(x) (1)
This amounts to optimizing the Evidence Lower Bound Objective (ELBO) that can be interpreted as follow, the first term is the Negative Log-Likelihood (NLL) data reconstruction cost and the second is the Kullback-Leibler Divergence (KLD) that quantifies the error made by using the approximate q φ (z|x) rather than the true p θ (z). This latent regularization pushes the encoder to remain close to the prior latent density and can be weighted with a β parameter that balances these two objectives.

L ELBO θ,φ = -E q φ (z|x) log pθ(x|z) + β • DKL qφ(z|x) pθ(z) (2)
The VAE is implemented with a stochastic encoder that parameterises an isotropic Gaussian latent distribution q φ (z|x) ∼ N (µ φ (x), σ φ (x)) regularized against an unit variance prior. These assumptions allow analytical KLD computation and differentiable latent sampling for direct optimization of the ELBO. The KLD forces each individual latent code to resemble the prior, which implicitly matches the whole encoded distribution. However a fitted ELBO value does not always result in an effective inference. Since the latent codes of different inputs are individually regularized, the KLD may prevent the encoder from learning any useful features (posterior collapse [START_REF] Zhao | Towards deeper understanding of variational autoencoding model[END_REF]) while the decoder only produces p θ (x) regardless of the encoded information. Other conflicting solutions of the ELBO lead to undesired solutions and known limitations of VAEs such as blurriness of generated samples or uninformative latent dimensions ( [START_REF] Yeung | Tackling over-pruning in variational autoencoders[END_REF]). With justifications stemming both from Likelihood-free Optimization (InfoVAE [START_REF] Zhao | Infovae: Information maximizing variational autoencoders[END_REF]) and the theory of Optimal Transport (WAE [START_REF] Tolstikhin | Wasserstein auto-encoders[END_REF]), a more general framework for training regularized auto-encoders was recently proposed and that we call Wasserstein Auto-Encoders (WAEs). Considering a deterministic decoder G θ : z → x and any family of conditional encoder distribution Q φ (z|x) ∈ Q, it is sufficient that the marginal QZ (z) := EX Q(z|x) matches any prior PZ . In comparisons with VAEs, WAEs can optimize any non-negative cost function C and any divergence measure DZ between latent distributions, without requiring a stochastic encoder nor restricting the latent model to Gaussian prior:

LWAE := inf Q(z|x)∈Q EX E Q(z|x) C(x, G(z)) + β • DZ (QZ (z), PZ ) (3)
Thus we set our experiment in the more flexible WAE framework. These regularized auto-encoders are powerful unsupervised representation learning models, rather light-weight and fast to train, performing both inference (encoder) and generation (decoder). They are effective on small datasets (hundreds of training examples), learning a structured latent representation with disentangling capacities encouraged when β > 1. Once trained, probabilistic samples of the latent prior are consistently decoded into new samples and latent interpolations map to smooth data variations.

Maximum Mean Discrepancy Regularization

As shown for VAEs, the choice of latent divergence heavily impacts the resulting model performances. Since the point-wise KLD has strong intrinsic limitations, a more flexible regularization is required for WAEs. Such differentiable divergence on latent distributions was developed in the Reproducing Kernel Hilbert Space (RKHS) as a distance between probabilistic moments µp,q computed with a non-parametric kernel k:

||µp -µq|| 2 H = µp -µq, µp -µq (4)
= Ep,pk(x, x ) + Eq,qk(y, y ) -2Ep,qk(x, y)

It defines the Maximum Mean Discrepancy (MMD [START_REF] Gretton | A kernel two-sample test[END_REF]) between two distributions x ∼ p(x) and y ∼ q(y), where Ep,q is the expectation that can be evaluated with the Radial Basic Function (RBF) kernel of free parameter Σ:

k(RBF)(x, y) = exp ||x -y|| 2 -2Σ 2 (5)
To the extent of latent regularization, MMD can be computed between every deterministic mini-batch encoding zencoder = Q(x) and random samples from any latent prior zprior ∼ PZ . Throughout the model optimization, MMD is thus matching the aggregated encoder posterior to the prior rather than regularizing each latent point individually. In comparisons with KLD, WAE-MMD allows for less constrained inference and richer latent representations. For instance, increasing β to two orders of magnitude above the reconstruction cost does not impede the decoder training. Since the WAE objective does not optimize the bounded NLL, the overall generative performances can be improved.

Other kernel functions can be used, which may be more discriminating at the expense of heavier computations. Alternatively to MMD, the WAE-GAN uses an adversarial latent discriminator to assess the divergence, thus optimizing a parametric function that could match even closer the encoder to the prior. However, since we consider a low-dimensional latent space of only 3 dimensions and remain with a simple isotropic Gaussian prior, MMD-RBF is sufficient yet light and stable to train on.

Conditioning and feature normalizations

Regularization in auto-encoders encourages disentanglement of independent generative factors onto separate latent dimensions that would in turn control the corresponding decoded data variations. However this is only partly achieved on toy datasets (β-VAE [START_REF] Higgins | beta-vae: Learning basic visual concepts with a constrained variational framework[END_REF]) and in most cases the unsupervised latent dimensions are hardly related to explicit generative parameters. An additional supervision signal may be applied to the generative neural network in order to control and render specific attributes of the data. Thus we consider observations x paired with attribute annotations y, and condition the decoder as G : {z, y} → x.

The simplest conditioning for categorical attributes is to encode them into one-hot vectors that are concatenated to the latent codes before being processed by the decoder. However more advanced conditioning techniques have been developed as for visual style transfer, using full images as conditions (conditional style transfer [START_REF] Ghiasi | Exploring the structure of a real-time, arbitrary neural artistic stylization network[END_REF]). In the Feature-wise Linear Modulation (FiLM [START_REF] Perez | Film: Visual reasoning with a general conditioning layer[END_REF]) approach, a separate generator learns a mapping from any style inputs to adaptive biases βFiLM(y) and scales γFiLM(y) applied to the conditional network computations. This modulation may be placed anywhere within the architecture and proved to be particularly suited to Adaptive Instance Normalization (AdaIN [START_REF] Huang | Arbitrary style transfer in real-time with adaptive instance normalization[END_REF]). Considering the l-th hidden layer output activations h l = g l (h l-1 ) of a generative neural network, the conditional modulation is thus be computed as:

AdaIN(h l , y) = γ l FiLM (y) h l -µ(h l ) σ(h l ) + β l FiLM (y) (6)
in which mean and standard deviation {µ,σ} are computed across features, independently for each channel and each sample. In the context of style transfer, it can be interpreted as aligning the mean and variance of the content features with those of the style condition. It is a versatile conditioning technique, requiring little additional computations (particularly when applied channel-wise in convolution layers). It also suits well to handling multiple conditions that may more efficiently be mapped throughout the network rather than arbitrarily concatenated to the input. Thus we will use FiLM and AdaIN for conditioning the decoder on both note and style classes. However, such normalization is not suited to classification tasks since content features are individually normalized.

In order to preserve its inference power, we will use Batch Normalization (BN) on the encoder's hidden activations.

Adversarial latent training

Adversarial regularization was proposed as an alternative to MMD in the WAE-GAN. For simple low-dimensional latent distributions, the expense of an additional parametric adversarial regularizer is not required. Nonetheless, adversarial latent training remains relevant for expressive conditioning. As detailed in the previous section, adaptive conditioning techniques paired with specific feature normalizations substantially improved feed-forward style transfer. However, in an auto-encoder setting, if the latent space implicitly encodes the attributes of interest, the decoder bypasses the conditioning and does not learn any effective generative controls. This problem was tackled in image generation with the introduction of an adversarial Fader latent discriminator F (Fader Networks [START_REF] Lample | Fader networks: Manipulating images by sliding attributes[END_REF]) that competes with the non-conditional encoder in order to prevent correlations between attributes and latent distributions. As for the conditional models, we consider annotated data samples {x, y} and for simplicity, a categorical one-hot representation y ∈ {0, 1} n with a single yi = 1 and its opposite ȳ := 1 ny. Such attribute-free latent representation is implemented in two separate optimization steps, first latent classification of the true attribute F : z → ŷ ∼ p ψ (y|Q(x)), then adversarial confusion of the latent classifier at predicting the opposite:

L class. (ψ|φ) = - x,y log(p ψ (y|Q(x))) L adv. (φ|ψ) = - x,y log(p ψ (ȳ|Q(x))) (7)
As the encoder is pushed to remain invariant to attributes, the decoder is forced to learn the conditioning in order to reconstruct every input samples along with their source attributes. Thus it replaces adversarial training in the high-dimensional pixel space with latent attribute confusion in the low-dimensional latent space in order to efficiently learn style transfer variables. Applied to facial expressions, these Fader variables can continuously modulate complex visual features such as gender (female ↔ male) or age (younger ↔ older). Moreover, in mixing several attributes, one could generate new style qualities.

Audio synthesis

Neural networks can be trained on spectrogram magnitudes (and other spectral features) for audio analysis purpose. It eases the subsequent modelling task, often involving pattern detection, from a pre-processed structured sound representation. However, for generative purpose, an inversion from magnitude to waveform is required since the complex phase information was discarded. It is commonly done offline with GLA [START_REF] Griffin | Signal estimation from modified short-time fourier transform[END_REF].

x |STFT| ---→ |S| MCNN ---→ x STFT ---→ Ŝ =⇒ L MCNN (S, Ŝ) L MCNN = λ0 • L SC + λ1 • L logSC + λ2 • L IF + λ3 • L WP (8)
where |S| can be any spectrogram magnitude (including Mel-scaled frequencies). The model is well tailored to audio with multiple heads of 1-dimensional temporal up-sample convolutions. These heads focus on different spectral components and sum into waveform. It remains light-weight and could be adapted in an end-toend waveform auto-encoder. Four objectives were originally proposed, using the complex STFT for the Instantaneous Frequency (IF) and Weighted Phase (WP) losses, that we could not optimize successfully. Hence we will only use the Spectral Convergence (SC) and log-scale magnitude (logSC) losses:

L SC (S, Ŝ) = |S|-| Ŝ| F / |S| F with . F the Frobenius norm L logSC (S, Ŝ) = log(|S| + ) -log(| Ŝ| + ) 1 (9)

METHOD

Our experiment begins with the WAE-MMD, isotropic unit variance Gaussian prior zprior ∼ N (0, 1), RBF kernel and BN in both encoder and decoder in order to structure a 3-dimensional generative latent sound representation. Given a magnitude spectrogram |S| and a corresponding set of annotated attributes y, we are learning

Q : |S| → z and G : z → | Ŝ| such as |S| ≈ | Ŝ| = G(Q(|S|))
with Binary Cross-Entropy (BCE) reconstruction cost:

LWAE = BCE(|S|, | Ŝ|) + β • MMDRBF(z, zprior) BCE(x, x) = -x log x + (1 -x) log(1 -x) ; |x| < 1 (10)
We can sample random codes from the latent prior and consistently decode new magnitude samples, however there is no control on the output features. For the orchestra, we consider y = {ynote, ystyle} with ynote = {semitone, octave}. We define the timbre attribute as the class of an instrument subset, which comprises the Ordinario mode as well as diverse extended playing techniques such as Staccato, Flatterzunge or Pizzicato. When considering a single subset, we thus aim at controlling the playing techniques of the considered instrument as ystyle. When considering multiple instruments,

with ȳstyle := 1-ystyle and α that weights the adversarial loss in the encoder. Classification is optimized on the NLL with Softmax probilities. The resulting attribute confusion prevents the latent space from implicitly encoding the style distributions, thus the decoder is forced to use the conditioning to reconstruct the source features from the attribute-free code. Ultimately these learned style variables can continuously be mixed, as actual faders do. We refer to this final model as WAE-Fader, that still uses MMD regularization. It allows for controlling the strength of each rendered attribute and intuitively exploring hybrid sound effects from any custom tags, here either chosen from extended playing techniques or from diverse orchestral timbre domains. The resulting generative system maps any latent coordinate z ∼ N (0, 1) ∈ R 3 to target note spectrograms with expressive musical style controls. Inversion from spectrogram magnitudes to audio waveforms can be done offline with GLA. Alternatively, we pretrain a MCNN on a larger corpus of musical note samples to allow real-time rendering. In order to improve the final audio quality, we fine-tune the full generative model by freezing the encoder parameters and jointly optimizing the learned decoder with the pretrained MCNN as:

x STFT ---→ S |Mels| ---→ |S| Q -→ z G•MCNN -----→ x STFT ---→ Ŝ =⇒ L MCNN (S, Ŝ) (12)
This waveform pipeline {G • MCNN} is embed in a plugin for live interactions and DAW integration. Using a MIDI interface, we can for instance trigger target note classes ynote with keys and map the continuous generative parameters to faders. These are the latent dimensions z, that can also be randomly sampled, and most interestingly the adversarially learned style variables ystyle that can be mixed to explore new sound effects. Signal reconstruction: The above described model trains on inputs with 128 frames of Mel-spectrogram, which amount to 34560 waveform samples according to our STFT settings. The generated Mel-magnitudes can be approximated back to the linear frequency scale and iteratively inverted with GLA for 100 to 300 iterations. To allow real-time rendering and a possibly improved audio quality, we reproduce the original MCNN architecture for Mel-spectrogram magnitudes inversion. We use 8 heads, λ0 = 1 and λ1 = 6. We could not successfully optimize the complex losses, however, we compute these magnitude losses on both the linear and Mel frequency scales. We pretrain this model on a larger dataset of around 50 hours audio comprising SOL and subsets of the Vienna Symphonic Library (VSL). Ultimately, we fine-tune the trained decoder with this pretrained MCNN. To do so, we freeze the encoder weights and optimize G • MCNN on the model train set. In equation ( 12), the auto-encoder pair G, Q maps to Melspectrogram magnitudes |S| which are inverted to signals by the MCNN. However, the loss computation L MCNN (S, Ŝ) is not necessarily restricted to this frequency scale. Thus we evaluate and sum L SC L logSC from equation ( 9) on both linear and Mel frequency scaled magnitudes. classified attribute (nstyle) train set validation test Semitone [START_REF] Gretton | A kernel two-sample test[END_REF] 1.00 0.99 0.99 Octave [START_REF] Kingma | Auto-encoding variational bayes[END_REF] 1.00 0.99 1.00 Ordinario timbres [START_REF] Gretton | A kernel two-sample test[END_REF] 1.00 1.00 1.00 Extended timbres [START_REF] Gretton | A kernel two-sample test[END_REF] 1.00 1.00 1.00 Violin playing styles [START_REF] Zhao | Towards deeper understanding of variational autoencoding model[END_REF] 1.00 0.97 0.95 Clarinet playing styles [START_REF] Zhao | Towards deeper understanding of variational autoencoding model[END_REF] 1.00 0.96 0.94 Piano playing styles [START_REF] Zhao | Towards deeper understanding of variational autoencoding model[END_REF] 1.00 0.92 0.95 Trumpet playing styles [START_REF] Zhao | Towards deeper understanding of variational autoencoding model[END_REF] 1.00 0.92 0.94 Alto-Saxophone pl. styles [START_REF] Zhao | Towards deeper understanding of variational autoencoding model[END_REF] 1.00 0.98 1.00 Tenor-Trombone pl. styles [START_REF] Yeung | Tackling over-pruning in variational autoencoders[END_REF] 1.00 0.90 0.90 Table 1: Reference F1-scores of the pretrained data classifiers used for the evaluation of conditional note generations

Evaluations

Generative performances: First, we evaluate the ability of our models to produce accurate spectrograms by computing the reconstruction scores on the test set with Root-Mean Squared Error (RMSE) and Log-Spectral Distance LSD = 10 log 10 (|S|/| Ŝ|)

2 . Regarding the conditioning aspects, we first pretrain data classifiers to reliably discriminate the different attribute classes and report their performances in Table 1. These classifiers share the same architecture as the encoder but map to the nstyle classes of interest. We use them as references to evaluate the effectiveness of the conditioning. Then, we sample an evaluation batch of 1000 random latent points from the prior, along with random semitone and octave targets. This evaluation batch is decoded to each attribute of the model (either playing styles or timbres) and classified with the corresponding reference classifier. A high accuracy means an effective conditioning for the task of musical note generation. We report the average accuracy for all the target conditions, with random octaves both in [0-8] (full orchestral range) or in [START_REF] Zhao | Infovae: Information maximizing variational autoencoders[END_REF][START_REF] Huang | Arbitrary style transfer in real-time with adaptive instance normalization[END_REF] where models train on the overlap of every instrument tessitura.

Latent space structure: The effectiveness of the conditioning relies on learning an attribute-free latent representation of the data. If the attribute distributions are clustered, the decoder may learn their correlations with latent dimensions and bypass the conditioning signal. This phenomenon is alleviated with adversarial training of the non-conditional encoder against a Fader latent discriminator. As we map to 3-dimensional spaces, we can directly visualize this latent organization. We also propose two evaluations of the attribute representations. First, we compute the average inter-class latent statistics with MMD. In this case, low values mean that the attribute distributions blend in the final representation. Second, we also perform a post-classification task by training classifiers at predicting the attributes from the learned latent representation. These models use the same architecture as the Fader discriminator, and [START_REF] Zhao | Infovae: Information maximizing variational autoencoders[END_REF][START_REF] Huang | Arbitrary style transfer in real-time with adaptive instance normalization[END_REF] (the overlap of every tessitura) and [0-8] (the full orchestra range), we report the accuracy of the conditioning with respect to the targets note34,08 (st. is semitone classe and oct. is octave classe) and style 34,08 .

we report their final accuracy. In this case, low scores mean that the latent representation did not encode the attributes.

RESULTS

Ablation study

We defined both generative and representation evaluations to assess the effectiveness of our proposed musical conditioning. To study the benefits and compromises of each model feature, we train the base WAE-MMD and compare it with ablations of the WAE-Fader. The incremental model comparisons are WAE-MMD (no conditioning), WAE-note (semitone and octave conditioning), WAE-style (note and style conditioning) and WAE-Fader. In order to simplify the notation, we do not specify the MMD but this regularization is used for all models. We performed this ablation study on the violin subset that has the following annotated playing styles: Ordinario, Sustained, Short, Non-vibrato, Staccato, Pizzicato-secco, Medium-vibrato-short, Tremolo, Mediumvibrato-sustained and Pizzicato-l-vib. We also compare the WAE-Fader on instrument timbres, either in ordinario or for all extended techniques mixed per instrument subset. Table 2 reports the successive generative performances of the models. Table 3 reports the latent evaluations, showing how the conditioning tasks are reflected in the learned representations. It confirms the effectiveness of the expressive conditioning when the attribute-invariance assumption is achieved.

As we can see, conditioning WAE-note on the semitone and octave classes shows that the WAE-MMD model can partly learn the note controls with FiLM conditioning. Accordingly, the latent space structure does not exhibit strong correlations with the note classes anymore but with the style attributes that become the main unsupervised data feature. We also notice that this additional supervision improves the reconstruction quality. However, when adding the style conditioning in WAE-style, it seems that most performances drop. Indeed, the overall conditioning becomes little effective, both for the target note and style conditions. results show that the adversarial latent training enables the WAE-Fader model to effectively learn the complete conditioning, at the expense of a possible drop in its reconstruction accuracy. It also seems that the task of modelling the playing styles when learning on a single instrument is more challenging than changing the timbres across multiple instruments. This can be seen in the lower performance of the WAE-style model applied to the violin. This may also be explained by the reduced size of the training data when the learning is restricted to single instrument subsets. These observations are supported by the resulting audio outputs of the conditional note generations. Indeed, it appears that meaningful and expressive variations when switching to any attribute conditions are only achieved with our proposed WAE-Fader model. This is successful for conditioning applied on both timbre attributes or playing styles.

Expressive note sample generations

In this section, we report additional experiments on the WAE-Fader models when conditioned on the playing styles of different instruments and families. As shown in Table 4, our model seems to train successfully on playing styles in every instrument families, as well as across the 12 instrument timbres of the orchestra as shown in the previous ablation study. This amounts to a great variety of sound qualities spanning extended modes of the orchestra, and let us hypothesize that the model could be applied to other sound domains as long as the tags are consistent with the data. Furthermore, the style variables learned with the Fader latent discriminator are continuous independent controls that can be mixed. Hence, this can allow our system to modulate the strength of rendered styles and create new effects by combining multiple attributes. Our model can also be used for sample modifications, akin to traditional audio effects, by encoding a given sample and manipulating the attribute conditions in order to decode different sample transformations.

Audio outputs and plugin development

As discussed previously, our proposed models can generate magnitude spectrograms, while controling their expressive qualities. These spectrograms can be either inverted to waveform offline with GLA or real-time if paired with MCNN. When fine-tuning the learned decoders with the pretrained MCNN on magnitude losses, we obtain a quality almost equivalent to the GLA approximation. We provide audio examples of test set reconstructions and conditional note generations inverted with both GLA and MCNN for individual listening evaluation on the companion webpage. While the audio quality of these results can still be improved, we can already confirm the ability of the model to provide semantic controls. As the learned style variables of WAE-Fader can be mixed continuously, we also provide some sound examples that were generated when modifying multiple orchestral attributes.

Our proposal provides intuitive sound synthesis of target sound qualities with learned style variables that can be modulated and combined. The unsupervised latent dimensions organize remaining data features, which can be directly visualized in a 3-d. space, in order to perform sampling or explicit control. These features allow to generate timbres, playing styles and hybrid effects across multiple attribute combinations through intuitive interactions. We provide a real-time implementation of our models by relying on the fine-tuned {G • MCNN} generation. This implementation relies on the LibTorch C++ API, which converts trained PyTorch models, that we further embed in a PureData external. This plugin can be mapped to a MIDI controller or integrated in a DAW for composition and musical performance. This allows to play notes with a keyboard, while using continuous faders to control latent coordinates and mix style conditions.

CONCLUSION

We We fine-tuned the decoders with a Mel magnitude spectrogram inversion network that allows real-time waveform rendering and are currently working on refining the audio quality. This results in a note sample generator with meaningful data visualizations and intuitive controls of audio styles. These parameters can be mixed, as faders, in order to explore hybrid sound effects. Our final generative model is embed in a plugin for MIDI mapping and live interactions. This system provides assisted music production and fosters creative sound experimentations. We provide sound examples from our orchestral models, either inverted offline with GLA or with the fine-tuned waveform generation pipeline. These sounds allow for subjective evaluation of both semantic and audio qualities of our solution.

Although we used clearly defined metadata attributes pertaining to instrumental playing styles, the model can potentially be applied to any sound domain. For instance, a user library with custom tags could be mapped to sound synthesis parameters. Furthermore, as the architecture is rather light and scales to small datasets, it could be trained on user libraries. Future experiments will target the quality of the waveform modelling systems for variable note lengths and real-time synthesis. Ultimately, our models could be implemented as a standalone instrument with physical controls that can be mapped to pretrained style variables. This would allow an intuitive and creative exploration across a vast amount of sound variations with a reduced set of adaptive parameters.

Figure 1 :

 1 Figure 1: High-level note sample generation from the latent representation and musical conditioning in the decoder with FiLM. Intermediate features are modulated by the note targets and expressive style controls in order to synthesize new timbres and effects.

p

  class. (y style |Q(|S|))

Figure 2 :

 2 Figure 2: How information flows in the adversarial optimization of the WAE-Fader

  We use the Studio-On-Line (SOL[START_REF] Ballet | Studio online 3.0: An internet "killer application" for remote access to ircam sounds and processing tools[END_REF]) library of around 15000 individual note samples, across the tessitura of 12 orchestral instruments grouped in 4 families and with many extended playing techniques, that may be specific or shared across instrument families. These are Wind (Alto-Saxophone, Bassoon, Clarinet, Flute, Oboe), Brass (English-Horn, French-Horn, Tenor-Trombone, Trumpet), String (Cello, Violin) and Keyboard (Piano). Notes are consistently tagged with the intrinsic attributes of the dataset: note classes (12 semitones across 9 octaves), several dynamics and playing styles of every instrument. We define two style experiments for the orchestra. If training on a single instrument, we aim for expressive synthesis of its playing styles. If training on multiple instruments, we aim for timbre control. Each instrument subset defines a timbre domain, either in Ordinario (its common mode) or with all styles mixed. Audio files are down-sampled to 22050Hz and pre-processed into Mel-spectrograms with a FFT size of 2048, hop size of 256 and 500 bins ranging the full spectrum. As we consider a generator of individual notes, we set a common audio length of 34560 samples (∼1.6s) from the attack which amounts to 128 STFT frames. We choose this duration as a trade-off between input and latent dimensionality, limiting the amount of silence after shorter playing modes (eg. Pizzicato) while keeping some sustain for longer notes (from which some sustain and decay may have been cropped). Magnitudes are floored to 1e-3 and log-scaled in [0,1] according to the BCE range. Each playing style subset of each instrument is split into 80% training, 10% validation and 10% test notes. In average each instrument has 10 playing styles and 100 to 200 notes for each.4.2. Implementation detailsArchitecture of the WAE-Fader: Our experiments have been implemented in the PyTorch environment and our codes will be shared with this dependency. All convolution layers use 2-d. square kernels, an input zero-padding of half the kernel size and are followed by 2-dimensional feature normalization. All fully-connected linear layers are followed by 1-dimensional feature normalization. The non-linear activation used after every normalization is CELU. The deterministic encoder has 5 convolution layers with[START_REF] Gretton | A kernel two-sample test[END_REF] 24, 48, 96, 128] output channels, kernel size 5 and stride 2, that downsample the input spectrograms into 128 output maps that are flattened into an intermediate feature vector of size 8192. It is followed with a bottleneck of 3 linear layers of output sizes [1024, 512, 3] mapping to the latent space. For input Mel-spectrograms of size (500,128), it amounts to a dimensionality reduction of more that 5 orders of magnitude. All normalizations are BN. The decoder mirrors this structure with 3 linear layers of output sizes [512, 1024, 8192]. This vector is then reshaped into 128 maps. To avoid the known checkerboard artifacts[START_REF] Odena | Deconvolution and checkerboard artifacts[END_REF] of the transposed convolution, we use nearest neighbor up-sampling followed with convolution of stride 1. These maps are processed with 4 up-sampling of ratios 3, the last one directly mapping to the input dimensionality of (500,128), and 5 convolutions with [96, 48, 24, 12, 1] output channels and kernel sizes[START_REF] Perez | Film: Visual reasoning with a general conditioning layer[END_REF][START_REF] Perez | Film: Visual reasoning with a general conditioning layer[END_REF][START_REF] Griffin | Signal estimation from modified short-time fourier transform[END_REF][START_REF] Kingma | Auto-encoding variational bayes[END_REF][START_REF] Griffin | Signal estimation from modified short-time fourier transform[END_REF]. All normalizations are AdaIN and the decoder output activation is sigmoid, bounded in [0,1] according to the BCE range. The FiLM conditioning is applied feature-wise at the output of the first two linear layers and channel-wise after. It amounts to 3688 modulation weights computed by an additional FiLM generator of 3 linear layers of output sizes[512, 1024, 3688]. Its output is split into biases and scales of sizes[512, 1024, 128, 96, 48, 24,[START_REF] Gretton | A kernel two-sample test[END_REF]. The Fader latent discriminator has 3 linear layers of output sizes [1024, 1024, nstyle] with LeakyReLU activations and a dropout ratio of 0.3, mapping latent codes to probabilities of the nstyle classes.

Figure 3 :

 3 Figure 3: The Fader latent discriminator tries to infer the true style attribute while the encoder adversarially aims at fooling it. It encourages attribute invariance in the latent representation and learning of continuous generative controls in the decoder.

  Further advances in generative neural networks for audio have targeted raw waveform modelling through specific architecture design. Wavenet[START_REF] Van Den | Wavenet: A generative model for raw audio[END_REF][1] is amongst them the most popular solution. It uses several stacks of dilated causal convolutions in order to aggregate multiple temporal granularities and structure long-term dependencies, which is challenging at the high audio sample rate. The output is a single auto-regressive sample prediction given all the previous sample context p(xt|x1..xt-1). It results in high-quality real-time audio synthesis. However this sample level modelling requires long training times, heavy architectures that offer little knowledge over their learned features. The Multi-head Convolutional Neural Network (MCNN[START_REF] Lample | Fast spectrogram inversion using multihead convolutional neural networks[END_REF]), a recent alternative for audio waveform modelling, was designed as a feed-forward real-time magnitude spectrogram inversion system that is not restricted to linear frequency scale. It proved to outperform GLA quality for speech. The use of differentiable GPUbased STFT computations enables a faster optimization onto spectral losses, rather than auto-regressive sample predictions:

Table 2 :

 2 The ablation study confirms the effectiveness of the WAE-Fader conditioning, both on target notes and playing styles or timbres. The conditional latent sampling is either performed with random octaves in

Table 3 :

 3 The ablation study allows to monitor the latent organization in the different models and throughout their training, as shown in Figure4. We use both inter-class statistics and latent post-classification to estimate the final attribute invariance in the learned representation.

  Latent organization as the WAE-Fader model trains on the ordinario timbres, each instrument domain being represented by a separate color. In A, at epoch 24, the encoder does not optimize the adversarial loss yet. Its unsupervised representation exhibits the attribute classes. In B, at epoch 674, the α-warmup is finished and the adversarial latent training had blended the attribute distributions. The 2-dimensional projections are performed with t-Distributed Stochastic Neighbor Embedding (TSNE).

	TSNE → 2D
	A	B
	epoch 24	epoch 674
	Figure 4:

Table 4 :

 4 developed an expressive musical conditioning of the Wasserstein Auto-Encoders able to model a collection of orchestral note samples. The model learns effective target semitone and octave Additional WAE-Fader results on the playing techniques of instruments in other orchestral families controls as well as continuous style variables. We considered extended playing techniques and timbre subsets as attributes, and used adversarial latent training to encourage an attribute-invariant representation in the WAE-Fader. Our ablation study validates the effectiveness of style conditioning when this invariance condition is obtained.

	model	test rec.		note cond. acc.		style cond. acc.	inter-class MMD	post-class. acc.
		MSE LSD st.34 oct.34 st.08 oct.08 style34 style08	st.	oct. style	st.	oct. style
	Clarinet	0.87	116	0.96	0.99	0.98	0.45	0.97	0.92	0.05 0.58 0.12 0.15 0.76 0.41
	Piano	0.99	113	0.53	0.91	0.47	0.72	0.72	0.64	0.03 0.03 0.08 0.16 0.20 0.43
	Trumpet	0.90	107	0.91	0.93	0.96	0.37	0.90	0.87	0.60 0.11 0.02 0.42 0.50 0.29
	Alto-Sax.	1.22	131	0.96	0.99	0.98	0.40	0.76	0.71	0.14 0.09 0.50 0.08 0.48 0.48
	T. Trombone 0.96	100	1.00	1.00	0.92	0.41	0.83	0.77	0.04 0.14 0.34 0.06 0.55 0.47

Proceedings of the 22 nd International Conference on Digital Audio Effects (DAFx-19), Birmingham, UK, September 2-6, 2019

https://github.com/acids-ircam/Expressive_WAE_FADER

ACKNOWLEDGEMENTS

This work was supported by the MAKIMOno project 17-CE38-0015-01 funded by the French ANR and the Canadian NSERC (STPG 507004-17), the ACTOR Partnership funded by the Canadian SSHRC (895-2018-1023) and an NVIDIA GPU Grant. We acknowledge and thank the initial contributions of Jean-Baptiste Dakeyo and Geoffroy Thibault, as well as the further collaboration of Antoine Caillon and Martin Fouilleul.


Sébastien Gadal
email: sebastien.gadal@c3ed.uvsq.fr

Hervé Gazel
email: gazel.rv@wanadoo.fr

MASS GIS E-LEARNING LECTURE: BACK EXPERIMENT

Keywords: GIS e-learning, Mass lectures, Assessment and follow-up automation

The integration of distance e-learning system in some French Master, and more especially in Geographic information system courses, has tree interests: open and extend the Master education to French speaking students around the Wold by the way of the World French University Agency (Agence Universitaire de la Francophonie); increase the number of students admit in Master for the same number of lecturers; and update the quality and the flexibility of education. Its result from this educational policy in GIS lectures for the AIGEME Master around 160 students for only one lecturer. This situation has imposed to develop specific material and content, automatic methods of assessments and monitoring.

Introduction

In France the move transition to the university level system LMD or Licence, Master, Doctorate has given of some Master with the support of university e-campus the implementation of elearning training and distance digital Master education including geographic information systems theoretical and practical trainings. The coming of GIS e-learning, still marginal in the French university system of education, has changed some aspects of GIS education: it is allowing the generalisation of GIS courses in different disciplinary. E-learning is developed as a way of increase the number of students, a tool to improving GIS mass lectures. Also, within the network of the World French University Speaking Agency (AUF), give access into some developing countries to GIS courses and develop local GI applies. But the high number of master students to manage and monitoring has quickly imposed to create specific material and content, automatic methods of assessments.

1 GIS e-learning: flexibility and economies of scales

The e-learning philosophy

For the Ministry of national education and scientist research, and quite more as some of French universities the moving to digital pedagogy and material lectures in GIS has allowed to upgrade and transform the content of lectures and exercises. In parallel to this increase of the formal level of education, the true interest to promote and develop e-learning and distance learning GIS courses is three. First, it to have material supports in GIS for students are learning GIS lectures at directly at AIGEME Master (University of Marne-la-Vallée). Second, it to increase the number of students can be accepted in Master and in GIS courses that are 160 people around at 2005/2006. The courses organisation is structured in two periods: one day each month of face to face lectures and practises in classroom with the lecturer in four class group; tree weeks of elearning lectures at university or at home. During the three weeks of GIS e-learning courses, students must send each end of week practical exercise in geographic information system. The e-learning platform used is WebCT, the GIS software Intergraph Geomedia. All students have the last version Intergraph of Geomedia at home for free during time of GIS courses. Thirdly, the development of e-learning courses in GIS increases and opens to the French speaking students in the World and come from more especially from ex French colonies in Africa, in Caribbean and South East Asia. These students, structured in tree virtual classrooms (Asia, Africa and America) allow lectures in full distance learning without any physical contact with lecturers. Courses are structured in tree parts: audio chat and audio conferences lectures each two weeks for each virtual classroom during one day, two weeks of individual training and learning on digital materials and courses with practical exercise to sent, and research thesis in GIS, cartography or remote sensing to do. The choice don't to implement video streaming or video conferences is link to the low speed Internet access in some countries like the Niger, Thad, etc. inside the World French speaking digital campus receiving local students. In some countries like the Comoros, the problem is more the numerous short Internet cuttings limitation the use of video conferences. The friendly Intergraph agreement giving possibilities to all students around the World to practise during some months geographic information systems and to develop locally applications on specific needs and topics: forestry, environmental monitoring and impacts, epidemiology, land planning and land change, etc. Most of them don't have financial possibilities to GIS software, as temporary for one year.

Mass lectures and economy of scales

The development of e-learning courses and more mass student training of more one hundred people is appreciated as a way of scale economy. The financial investment for the creation and the starting of digital material lectures, exercises and GIS software's is round about 10000 Euros, tutoring and lectures for 2500 Euros each year. Only one temporary lecturer giving extra courses teaching and managing digital lectures for decrease credits affected to GIS e-learning. He monitors the different classrooms that are 160 students for this university year during a semester. The development of the e-learning educations also allows universities and the State of the substantial economies of scale. GIS e-learning lectures are perceived as a means to make decrease the cost of the educations by the decrease of the number of lectures, quite as the number of temporary lecturers, senior lecturers or professors. They were also conceived or more exactly presented as such. The substantial replacement of the number of classroom lectures and teachers in geomatic by the digital e-learning educations placed every professor to follow and to manage directly, alone, around 160 Master students. If teaching to 160 students shared out between face-to-face or virtual classrooms conferences doesn't give specifically problems, the daily student is monitoring and the week correction of practical exercises making full of job for only one teacher. The important increase of the professor's workload led very quickly to transform the GIS e-lecture contents and especially the modes and the modalities of the student follow-up and controls. The teacher has also to learn e-learning tools to manage his course, tools such as tools for organize pages (synopsis, links), tools for contents of course (program course, banks of image, glossary, index), tools of communication (forum, mail, chat, divide table, calendars, tricks and easy ways for students, audio-forum,…), tools for evaluation and activities (quiz, auto-assessment, student works or presentation). That accentuates the workload, but gives a full control and management of GIS e-learning courses. Among this tools, the tools of communication such as mail, because they are not specific to e-learning and well known are the most use by students. They are an important source of work which is not or insufficiently integrated in the professor's workload by institutions. Moreover, e-mails are not always correctly used: they are not an urgency tool but they are frequently used in that way…

2.

Pedagogy aspects of mass GIS e-learning courses

Mass GIS training and increases of GI applications

The mass GIS e-learning lectures are giving a more large audience to geographic information sciences in general and more particularly to geographic information systems towards students coming from different disciplinary, to geomatic applies interests and functional possibilities in environment, land planning, economy, engineering, etc. Futures AIGEME student engineers and executives can be discover GIS applies as a part of the information system world and connect GI with other lectures and training they have in programming, databases and information systems. After the semester of GIS courses, some students don't come from "classical" GI users like environmentalists, geographers, computer scientists are able to develop geomatic applied in economy and multimedia in the way of the master thesis. It is one of the positive aspects of mass GIS lectures. World French Speaking University Agency's students are in distance training courses are the most new important GIS users in the large topics of themes, more especially in Africa: epidemiology, economy, urbanism, forestry, tourisms, etc. The absence or the obsolescence of geographic information, of socio-economical or urban database systems, updated database census, the territories complexity and the rapid growth and land structure changes of the lands in developing countries improve the use of geographic information systems and remote sensing data. Development of distance e-learning courses towards students of developing countries by the way of the AUF e-campus participate at a more flexible and direct transfers of knowledge, practises and use of geographic information systems.

2.2.

Mass lectures and follow-up GIS work

But if the digital and distance lectures in GIS allow to extend the teaching of GI and to participate at it expansion, the high number of students to monitoring, teaching and evaluate are bit hard for only one lecturer. The problem is not the GIS course content, but the weekly followup work of students, the estimate of GIS practises and exercises, the proofreading of examination. The e-learning course summary is organised in tree points: the conceptual and theoretical chapter, the training lecture on Intergraph GeoMedia Pro, and the memo chapter including history of GIS, geographic information definitions and characteristics, reference systems, databases systems, etc. The content of lectures is separated in two parts: the conceptual and theoretical aspects of geographic information systems including in addition numerous articles, chapter extracts of books, reports, PhD memories, and a practical GIS training part. This second part, the GIS training part include all Geomedia functions with practical exercises to do at computer room or at home and to send every week.

The first chapter structured in four parts [(1) GIS definition, multiplicity of concepts, from GIS to geographic information sciences, etc. (2) GIS used, GIS functions, GIS structures, databases, conceptual GIS models, etc. (3) geo-encoding, geo -referencing, referenced systems, etc., and (4) GIS analysis, GIS cartography, Web GIS, etc.] is one of the most common e-learning lectures students can be find. In each 4 parts of this chapter are included a specific lecture segment on questions of Cultures géomatiques (Geomatic Cultures in English). This specific segment of lectures incorporated in each part chapter has several pedagogical objectives: first, to set in motion the students to read a minimum of literature in Geographic information systems. Second, read, learn, the panel of uses and applied of GIS. Thirdly, push the students that GIS are not only technical tools, but concepts, approaches and methodologies of spatial and territorial analysis and modelling giving an understanding and knowledge of geographical space. The last interest of this "geomatic cultural" part of lectures is to give to GIS students some elements of methodological appropriation in GIS by the articles, books, reports analysis and commentaries process calculus. The evaluation consist to deposit on the WebCT platform every weeks a summary of one to two pages with the problematic of the paper, the topic objectives, data, flow chart process, results and limits of methodological approach. The goal is "to immerse" GIS students inside the geomatic culture approaches for appropriate gradually during the lecture semester different ways of work in geographic information systems.

2.3.

GIS training and automation

The second chapter, the training course of this teaching is divided in three parts: (1) Introduction to Geomedia, (2) work sequence "display and analyze", (3) Geomedia: the first handling. A fourth part proposes these different parts in light files. It was added after chat sessions. Students with low speed Internet access from developing countries asked for it. They could more easily practice without having to be connected. The first part presents the software Geomedia, its concepts, its terminology and the essential notions of geoworkspace and entity. Then, a practical exercise from the creation of a geoworkspace to the impression of a map is offer to the student. This sequence introduce to systems of coordinated, warehouses and connections, map windows, data windows, queries, thematic mapping and labelling. The third part of this training course explains with interactive chart process how to practically use the GIS software. The students have to follow step to step the chart to learn the handling. These charts concern geoworkspaces, warehouses, entities, coordinate systems, scalable maps, and display. Finally, to the students interested by GIS creation, the teacher suggests to explore a more advanced practical exercise from the creation of a geoworkspace to the data export. This sequence explains how to create new entities, to change entities, to georeference and to validate geographical data. GIS training course is regularly "updated": new exercises proposing new sequences associating different GIS functions learned during the conceptual and theoretical aspects of geographic information systems (chapter 1) are added.

First pedagogic results and back experiments

3.1.

Evaluation and monitoring

The concept of knowledge acquisition is doing automatically by QCM system every week. This type of evaluation and student follow up concern the first and second chapters: conceptual and theoretical aspects of geographic information systems and GIS practical training. The teacher implements questions and responses possibilities, and the system giving automatically for each student, score, mark and corrections. A question database is progressively completed. Questions are picked from the database. After two years, the number of registered questions is important. Numerous combinations are possible and a lot of different QCM realized. The student monitoring takes several forms: (1) time and period of student connection on digital lectures chapters, (2) GIS lecture forum ; each student exchanging questions, answering, help and information, (3) directs discussions with the GIS teacher by internal email and by chat sessions, (4) practical training supports with in addition materials given by Intergraph. For example, for a training started on November 2005, some student's first connection was from November 7, 2005 and some from February 3, 2006: three months difference! About the number of connection between November and May, differences are also important: from 0 to 879! During the same period, 139 messages were sent on the GIS student forum. 64 were exchanging about exercises. 733 mails were exchanged (615 sent, 118 received) between teacher and students.

The teacher sent much more mails because of he often inform all the students on the WebCT platform. Two years of experiment in AIGEME Master (University of Marne-la-Vallée) authorize an assessment (tab.1) Students with one day each month of face to face lectures and practises in classroom with the lecturer seems to have better results than students, structured in virtual classrooms with lectures in full distance learning without any physical contact with lecturers. At least, last category of students appear in 2006, with one day each month of face to face lectures and practises in classroom with the lecturer and tree weeks of work in enterprise with eventually e-learning lectures at home, has even better results.

3.2.

The question of monitoring time

The central problem is the growth of the time spent to follow the students and to correct the practices and GIS work. This time spent is accentuated by the technical management of the GIS e-learning lecture on the WebCT platform. All this time is not taken in the load of teaching and monitoring. The GIS audience has increased because of the digital lecture development. With the growth of the number of students, the question of monitoring becomes a hard problem. One of the ways had been the automation of some examinations, and the increase of the GIS student autonomy work.

Concerning the planning, instead of having one or two days each month of face to face lectures and practises in classroom with the lecturer in four class group and tree weeks of e-learning lectures at university or at home (table 2), the new timetable would propose one entire week of face to face for each group (table3). Students would have an intensive training course. Their works would be the experiment of the management of a GIS project related to the local territory. This organisation should increase both autonomy of the students and their ability to work in group. Nevertheless, the possibility would be effective only for the students registered at the University of Marne-la-Vallée because it seems it will be very difficult for students living in developing country registered at the World French University Agency (AUF) to work in group with low Internet access. The work in group appears as one the possible response to the problem of monitoring numerous students by only one teacher. For the teacher, the number of works to evaluate could be divided by 3 or 4, and for the students it would be an initiation to professional framework of GIS project. The main difficulty still remaining is to identify correctly the part of each member of the group, (but this is not particularly linked to e-learning and could be managed by a teacher used to).

Conclusion

E-learning seems to be more effective associated with face to face lectures. Does it mean that knowledge acquisition needs physical presence? Does it rather mean that the e-learning course has to be improved? Or, does it mean the students of the network of the World French University Speaking Agency (AUF) have much different than those of the French university? Anyway, with about 150 students and intensive use of web technologies, the teacher has additional time to follow (forum, mail, chat) and evaluate the knowledge acquisition (QCM, look at student's GIS production). He is also very much in demand to update more frequently course and practical exercises. Weekly monitoring and updating are probably the most serious limit to the development of GIS e-learning courses.

Table 1

 1

	: GIS e-learning: results of the AIGEME Master (UMLV) in 2005 and 2006
	UMLV	UMLV	%	AUF	AUF	%	CFA	CFA	%
	students	students	positive	students	students	positive	students	students	positive
		passed	result		passed	result		passed	result
	2005 58	45	78	20	9	45	0	0	-
	2006 74	62	84	24	13	54	46	45

Table 3 :

 3 An example of planning on 16 weeks for students and lecturer

	Group	Week	Day	GIS Lecture	GIS Self-learning	GIS Exams
	1	1	1	9h00-12h00	14h00-18h00
	2	2	1	9h00-12h00	14h00-18h00
	3	3	1	9h00-12h00	14h00-18h00
	4	4	1	9h00-12h00	14h00-18h00
	1	5	1	9h00-12h00	14h00-18h00
	1	5	2	9h00-12h00	14h00-18h00
	2	6	1	9h00-12h00	14h00-18h00
	2	6	2	9h00-12h00	14h00-18h00
	3	7	1	9h00-12h00	14h00-18h00
	3	7	2	9h00-12h00	14h00-18h00
	4	8	1	9h00-12h00	14h00-18h00
	4	8	2	9h00-12h00	14h00-18h00
	1	9	1			9h00-12h00

Table 3 :

 3 An example of planning on 1 week for students and lecturer

	Group	Week	Day	GIS lecture	Gis project
	1	1	1	9h-12h	14h-18h
	1	1	2	9h-12h	14h-18h
	1	1	3	9h-12h	14h-18h
	1	1	4	9h-12h	14h-18h
	2	2	1	9h-12h	14h-18h
	2	2	2	9h-12h	14h-18h
	2	2	3	9h-12h	14h-18h
	2	2	4	9h-12h	14h-18h
	3	3	1	9h-12h	14h-18h
	3	3	2	9h-12h	14h-18h
	3	3	3	9h-12h	14h-18h
	3	3	4	9h-12h	14h-18h
	4	4	1	9h-12h	14h-18h
	4	4	2	9h-12h	14h-18h
	4	4	3	9h-12h	14h-18h
	4	4	4	9h-12h	14h-18h