11,940 research outputs found
Signal Recovery from Pooling Representations
In this work we compute lower Lipschitz bounds of pooling operators
for as well as pooling operators preceded by
half-rectification layers. These give sufficient conditions for the design of
invertible neural network layers. Numerical experiments on MNIST and image
patches confirm that pooling layers can be inverted with phase recovery
algorithms. Moreover, the regularity of the inverse pooling, controlled by the
lower Lipschitz constant, is empirically verified with a nearest neighbor
regression.Comment: 17 pages, 3 figure
Group Invariance, Stability to Deformations, and Complexity of Deep Convolutional Representations
The success of deep convolutional architectures is often attributed in part
to their ability to learn multiscale and invariant representations of natural
signals. However, a precise study of these properties and how they affect
learning guarantees is still missing. In this paper, we consider deep
convolutional representations of signals; we study their invariance to
translations and to more general groups of transformations, their stability to
the action of diffeomorphisms, and their ability to preserve signal
information. This analysis is carried by introducing a multilayer kernel based
on convolutional kernel networks and by studying the geometry induced by the
kernel mapping. We then characterize the corresponding reproducing kernel
Hilbert space (RKHS), showing that it contains a large class of convolutional
neural networks with homogeneous activation functions. This analysis allows us
to separate data representation from learning, and to provide a canonical
measure of model complexity, the RKHS norm, which controls both stability and
generalization of any learned model. In addition to models in the constructed
RKHS, our stability analysis also applies to convolutional networks with
generic activations such as rectified linear units, and we discuss its
relationship with recent generalization bounds based on spectral norms
Sparse Modeling for Image and Vision Processing
In recent years, a large amount of multi-disciplinary research has been
conducted on sparse models and their applications. In statistics and machine
learning, the sparsity principle is used to perform model selection---that is,
automatically selecting a simple model among a large collection of them. In
signal processing, sparse coding consists of representing data with linear
combinations of a few dictionary elements. Subsequently, the corresponding
tools have been widely adopted by several scientific communities such as
neuroscience, bioinformatics, or computer vision. The goal of this monograph is
to offer a self-contained view of sparse modeling for visual recognition and
image processing. More specifically, we focus on applications where the
dictionary is learned and adapted to data, yielding a compact representation
that has been successful in various contexts.Comment: 205 pages, to appear in Foundations and Trends in Computer Graphics
and Visio
Basic Filters for Convolutional Neural Networks Applied to Music: Training or Design?
When convolutional neural networks are used to tackle learning problems based
on music or, more generally, time series data, raw one-dimensional data are
commonly pre-processed to obtain spectrogram or mel-spectrogram coefficients,
which are then used as input to the actual neural network. In this
contribution, we investigate, both theoretically and experimentally, the
influence of this pre-processing step on the network's performance and pose the
question, whether replacing it by applying adaptive or learned filters directly
to the raw data, can improve learning success. The theoretical results show
that approximately reproducing mel-spectrogram coefficients by applying
adaptive filters and subsequent time-averaging is in principle possible. We
also conducted extensive experimental work on the task of singing voice
detection in music. The results of these experiments show that for
classification based on Convolutional Neural Networks the features obtained
from adaptive filter banks followed by time-averaging perform better than the
canonical Fourier-transform-based mel-spectrogram coefficients. Alternative
adaptive approaches with center frequencies or time-averaging lengths learned
from training data perform equally well.Comment: Completely revised version; 21 pages, 4 figure
Deep speech inpainting of time-frequency masks
Transient loud intrusions, often occurring in noisy environments, can
completely overpower speech signal and lead to an inevitable loss of
information. While existing algorithms for noise suppression can yield
impressive results, their efficacy remains limited for very low signal-to-noise
ratios or when parts of the signal are missing. To address these limitations,
here we propose an end-to-end framework for speech inpainting, the
context-based retrieval of missing or severely distorted parts of
time-frequency representation of speech. The framework is based on a
convolutional U-Net trained via deep feature losses, obtained using speechVGG,
a deep speech feature extractor pre-trained on an auxiliary word classification
task. Our evaluation results demonstrate that the proposed framework can
recover large portions of missing or distorted time-frequency representation of
speech, up to 400 ms and 3.2 kHz in bandwidth. In particular, our approach
provided a substantial increase in STOI & PESQ objective metrics of the
initially corrupted speech samples. Notably, using deep feature losses to train
the framework led to the best results, as compared to conventional approaches.Comment: Accepted to InterSpeech202
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