3,653 research outputs found
Quaternion Convolutional Neural Networks for End-to-End Automatic Speech Recognition
Recently, the connectionist temporal classification (CTC) model coupled with
recurrent (RNN) or convolutional neural networks (CNN), made it easier to train
speech recognition systems in an end-to-end fashion. However in real-valued
models, time frame components such as mel-filter-bank energies and the cepstral
coefficients obtained from them, together with their first and second order
derivatives, are processed as individual elements, while a natural alternative
is to process such components as composed entities. We propose to group such
elements in the form of quaternions and to process these quaternions using the
established quaternion algebra. Quaternion numbers and quaternion neural
networks have shown their efficiency to process multidimensional inputs as
entities, to encode internal dependencies, and to solve many tasks with less
learning parameters than real-valued models. This paper proposes to integrate
multiple feature views in quaternion-valued convolutional neural network
(QCNN), to be used for sequence-to-sequence mapping with the CTC model.
Promising results are reported using simple QCNNs in phoneme recognition
experiments with the TIMIT corpus. More precisely, QCNNs obtain a lower phoneme
error rate (PER) with less learning parameters than a competing model based on
real-valued CNNs.Comment: Accepted at INTERSPEECH 201
A Broad Class of Discrete-Time Hypercomplex-Valued Hopfield Neural Networks
In this paper, we address the stability of a broad class of discrete-time
hypercomplex-valued Hopfield-type neural networks. To ensure the neural
networks belonging to this class always settle down at a stationary state, we
introduce novel hypercomplex number systems referred to as real-part
associative hypercomplex number systems. Real-part associative hypercomplex
number systems generalize the well-known Cayley-Dickson algebras and real
Clifford algebras and include the systems of real numbers, complex numbers,
dual numbers, hyperbolic numbers, quaternions, tessarines, and octonions as
particular instances. Apart from the novel hypercomplex number systems, we
introduce a family of hypercomplex-valued activation functions called
-projection functions. Broadly speaking, a
-projection function projects the activation potential onto the
set of all possible states of a hypercomplex-valued neuron. Using the theory
presented in this paper, we confirm the stability analysis of several
discrete-time hypercomplex-valued Hopfield-type neural networks from the
literature. Moreover, we introduce and provide the stability analysis of a
general class of Hopfield-type neural networks on Cayley-Dickson algebras
Surface Networks
We study data-driven representations for three-dimensional triangle meshes,
which are one of the prevalent objects used to represent 3D geometry. Recent
works have developed models that exploit the intrinsic geometry of manifolds
and graphs, namely the Graph Neural Networks (GNNs) and its spectral variants,
which learn from the local metric tensor via the Laplacian operator. Despite
offering excellent sample complexity and built-in invariances, intrinsic
geometry alone is invariant to isometric deformations, making it unsuitable for
many applications. To overcome this limitation, we propose several upgrades to
GNNs to leverage extrinsic differential geometry properties of
three-dimensional surfaces, increasing its modeling power.
In particular, we propose to exploit the Dirac operator, whose spectrum
detects principal curvature directions --- this is in stark contrast with the
classical Laplace operator, which directly measures mean curvature. We coin the
resulting models \emph{Surface Networks (SN)}. We prove that these models
define shape representations that are stable to deformation and to
discretization, and we demonstrate the efficiency and versatility of SNs on two
challenging tasks: temporal prediction of mesh deformations under non-linear
dynamics and generative models using a variational autoencoder framework with
encoders/decoders given by SNs
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