4,933 research outputs found
Training Faster by Separating Modes of Variation in Batch-normalized Models
Batch Normalization (BN) is essential to effectively train state-of-the-art
deep Convolutional Neural Networks (CNN). It normalizes inputs to the layers
during training using the statistics of each mini-batch. In this work, we study
BN from the viewpoint of Fisher kernels. We show that assuming samples within a
mini-batch are from the same probability density function, then BN is identical
to the Fisher vector of a Gaussian distribution. That means BN can be explained
in terms of kernels that naturally emerge from the probability density function
of the underlying data distribution. However, given the rectifying
non-linearities employed in CNN architectures, distribution of inputs to the
layers show heavy tail and asymmetric characteristics. Therefore, we propose
approximating underlying data distribution not with one, but a mixture of
Gaussian densities. Deriving Fisher vector for a Gaussian Mixture Model (GMM),
reveals that BN can be improved by independently normalizing with respect to
the statistics of disentangled sub-populations. We refer to our proposed soft
piecewise version of BN as Mixture Normalization (MN). Through extensive set of
experiments on CIFAR-10 and CIFAR-100, we show that MN not only effectively
accelerates training image classification and Generative Adversarial networks,
but also reaches higher quality models
Quantum Pseudodots Under the External Vector and Scalar Fields
We study the spherical quantum pseudodots in the Schrodinger equation using
the pseudo-harmonic plus harmonic oscillator potentials considering the effect
of the external electric and magnetic fields. The finite energy levels and the
wave functions are calculated. Furthermore, the behavior of the essential
thermodynamic quantities such as, the free energy, the mean energy, the
entropy, the specific heat, the magnetization, the magnetic susceptibility and
the persistent currents are also studied using the characteristic function. Our
analytical results are found to be in good agreement with the other works. The
numerical results on the energy levels as well as the thermodynamic quantities
have also been given.Comment: 18 Fig
Deep Sparse Representation-based Classification
We present a transductive deep learning-based formulation for the sparse
representation-based classification (SRC) method. The proposed network consists
of a convolutional autoencoder along with a fully-connected layer. The role of
the autoencoder network is to learn robust deep features for classification. On
the other hand, the fully-connected layer, which is placed in between the
encoder and the decoder networks, is responsible for finding the sparse
representation. The estimated sparse codes are then used for classification.
Various experiments on three different datasets show that the proposed network
leads to sparse representations that give better classification results than
state-of-the-art SRC methods. The source code is available at:
github.com/mahdiabavisani/DSRC
Deep Multimodal Subspace Clustering Networks
We present convolutional neural network (CNN) based approaches for
unsupervised multimodal subspace clustering. The proposed framework consists of
three main stages - multimodal encoder, self-expressive layer, and multimodal
decoder. The encoder takes multimodal data as input and fuses them to a latent
space representation. The self-expressive layer is responsible for enforcing
the self-expressiveness property and acquiring an affinity matrix corresponding
to the data points. The decoder reconstructs the original input data. The
network uses the distance between the decoder's reconstruction and the original
input in its training. We investigate early, late and intermediate fusion
techniques and propose three different encoders corresponding to them for
spatial fusion. The self-expressive layers and multimodal decoders are
essentially the same for different spatial fusion-based approaches. In addition
to various spatial fusion-based methods, an affinity fusion-based network is
also proposed in which the self-expressive layer corresponding to different
modalities is enforced to be the same. Extensive experiments on three datasets
show that the proposed methods significantly outperform the state-of-the-art
multimodal subspace clustering methods
Exact solutions of a spatially-dependent mass Dirac equation for Coulomb field plus tensor interaction via Laplace transformation method
The spatially-dependent mass Dirac equation is solved exactly for attractive
scalar and repulsive vector Coulomb potentials including a tensor interaction
potential under the spin and pseudospin (p-spin) symmetric limits by using the
Laplace transformation method (LTM). Closed forms of the energy eigenvalue
equation and wave functions are obtained for arbitrary spin-orbit quantum
number Some numerical results are given too. The effect of the tensor
interaction on the bound states is presented. It is shown that the tensor
interaction removes the degeneracy between two states in the spin doublets. We
also investigate the effects of the spatially-dependent mass on the bound
states under the conditions of the spin symmetric limit and in the absence of
tensor interactionComment: 17 pages, 4 figure
Ring correlations in random networks
We examine the correlations between rings in random network glasses in two
dimensions as a function of their separation. Initially, we use the topological
separation (measured by the number of intervening rings), but this leads to
pseudo-long-range correlations due to a lack of topological charge neutrality
in the shells surrounding a central ring. This effect is associated with the
non-circular nature of the shells. It is, therefore, necessary to use the
geometrical distance between ring centers. Hence we find a generalization of
the Aboav-Weaire law out to larger distances, with the correlations between
rings decaying away when two rings are more than about 3 rings apart.Comment: 7 pages, 8 Figures, v2 updated bibliograph
On stability analysis by using Nyquist and Nichols Charts
This paper reviews stability analysis techniques by using the Nyquist and
Nichols charts. The relationship between the Nyquist and Nichols stability
criteria is fully described by using the crossing concept. The results are
demonstrated through several numerical examples. This tutorial provides useful
insights into the loop-shaping based control systems design such as
Quantitative Feedback Theory
Bayesian inference in non-Markovian state-space models with applications to fractional order systems
Battery impedance spectroscopy models are given by fractional order (FO)
differential equations. In the discrete-time domain, they give rise to
state-space models where the latent process is not Markovian. Parameter
estimation for these models is therefore challenging, especially for
non-commensurate FO models. In this paper, we propose a Bayesian approach to
identify the parameters of generic FO systems. The computational challenge is
tackled with particle Markov chain Monte Carlo methods, with an implementation
specifically designed for the non-Markovian setting. The approach is then
applied to estimate the parameters of a battery non-commensurate FO equivalent
circuit model. Extensive simulations are provided to study the practical
identifiability of model parameters and their sensitivity to the choice of
prior distributions, the number of observations, the magnitude of the input
signal and the measurement noise
ALCN: Meta-Learning for Contrast Normalization Applied to Robust 3D Pose Estimation
To be robust to illumination changes when detecting objects in images, the
current trend is to train a Deep Network with training images captured under
many different lighting conditions. Unfortunately, creating such a training set
is very cumbersome, or sometimes even impossible, for some applications such as
3D pose estimation of specific objects, which is the application we focus on in
this paper. We therefore propose a novel illumination normalization method that
lets us learn to detect objects and estimate their 3D pose under challenging
illumination conditions from very few training samples. Our key insight is that
normalization parameters should adapt to the input image. In particular, we
realized this via a Convolutional Neural Network trained to predict the
parameters of a generalization of the Difference-of-Gaussians method. We show
that our method significantly outperforms standard normalization methods and
demonstrate it on two challenging 3D detection and pose estimation problems.Comment: BMVC' 1
Structural Identifiability Analysis of Fractional Order Models with Applications in Battery Systems
This paper presents a method for structural identifiability analysis of
fractional order systems by using the coefficient mapping concept to determine
whether the model parameters can uniquely be identified from input-output data.
The proposed method is applicable to general non-commensurate fractional order
models. Examples are chosen from battery fractional order equivalent circuit
models (FO-ECMs). The battery FO-ECM consists of a series of parallel resistors
and constant phase elements (CPEs) with fractional derivatives appearing in the
CPEs. The FO-ECM is non-commensurate if more than one CPE is considered in the
model. Currently, estimation of battery FO-ECMs is performed mainly by fitting
in the frequency domain, requiring costly electrochemical impedance
spectroscopy equipment. This paper aims to analyse the structural
identifiability of battery FO-ECMs directly in the time domain. It is shown
that FO-ECMs with finite numbers of CPEs are structurally identifiable. In
particular, the FO-ECM with a single CPE is structurally globally identifiable
- …