arXiv subjects

Mete Ozay

Publications and source records attributed to Mete Ozay.

At least 73 records · Page 4Linked to original sources

arXiv2020

A New Neural Network Architecture Invariant to the Action of Symmetry Subgroups

We propose a computationally efficient $G$-invariant neural network that approximates functions invariant to the action of a given permutation subgroup $G \leq S_n$ of the symmetric group on input data. The key element of the proposed network architecture is a new $G$-invariant transformation module, which produces a $G$-invariant latent representation of the input data. Theoretical considerations are supported by numerical experiments, which demonstrate the effectiveness and strong generalization properties of the proposed method in comparison to other $G$-invariant neural networks.

cs.LG↗

arXiv2020

Learning from Experience for Rapid Generation of Local Car Maneuvers

Being able to rapidly respond to the changing scenes and traffic situations by generating feasible local paths is of pivotal importance for car autonomy. We propose to train a deep neural network (DNN) to plan feasible and nearly-optimal paths for kinematically constrained vehicles in small constant time. Our DNN model is trained using a novel weakly supervised approach and a gradient-based policy search. On real and simulated scenes and a large set of local planning problems, we demonstrate that our approach outperforms the existing planners with respect to the number of successfully completed tasks. While the path generation time is about 40 ms, the generated paths are smooth and comparable to those obtained from conventional path planners.

cs.RO↗

arXiv2020

A Computationally Efficient Neural Network Invariant to the Action of Symmetry Subgroups

We introduce a method to design a computationally efficient $G$-invariant neural network that approximates functions invariant to the action of a given permutation subgroup $G \leq S_n$ of the symmetric group on input data. The key element of the proposed network architecture is a new $G$-invariant transformation module, which produces a $G$-invariant latent representation of the input data. This latent representation is then processed with a multi-layer perceptron in the network. We prove the universality of the proposed architecture, discuss its properties and highlight its computational and memory efficiency. Theoretical considerations are supported by numerical experiments involving different network configurations, which demonstrate the effectiveness and strong generalization properties of the proposed method in comparison to other $G$-invariant neural networks.

cs.LG↗

arXiv2019

Fine-grained Optimization of Deep Neural Networks

In recent studies, several asymptotic upper bounds on generalization errors on deep neural networks (DNNs) are theoretically derived. These bounds are functions of several norms of weights of the DNNs, such as the Frobenius and spectral norms, and they are computed for weights grouped according to either input and output channels of the DNNs. In this work, we conjecture that if we can impose multiple constraints on weights of DNNs to upper bound the norms of the weights, and train the DNNs with these weights, then we can attain empirical generalization errors closer to the derived theoretical bounds, and improve accuracy of the DNNs. To this end, we pose two problems. First, we aim to obtain weights whose different norms are all upper bounded by a constant number, e.g. 1.0. To achieve these bounds, we propose a two-stage renormalization procedure; (i) normalization of weights according to different norms used in the bounds, and (ii) reparameterization of the normalized weights to set a constant and finite upper bound of their norms. In the second problem, we consider training DNNs with these renormalized weights. To this end, we first propose a strategy to construct joint spaces (manifolds) of weights according to different constraints in DNNs. Next, we propose a fine-grained SGD algorithm (FG-SGD) for optimization on the weight manifolds to train DNNs with assurance of convergence to minima. Experimental results show that image classification accuracy of baseline DNNs can be boosted using FG-SGD on collections of manifolds identified by multiple constraints.

cs.LG↗

arXiv2019

Improving Head Pose Estimation with a Combined Loss and Bounding Box Margin Adjustment

We address a problem of estimating pose of a person's head from its RGB image. The employment of CNNs for the problem has contributed to significant improvement in accuracy in recent works. However, we show that the following two methods, despite their simplicity, can attain further improvement: (i) proper adjustment of the margin of bounding box of a detected face, and (ii) choice of loss functions. We show that the integration of these two methods achieve the new state-of-the-art on standard benchmark datasets for in-the-wild head pose estimation.

cs.CV↗

arXiv2018

Revisiting Single Image Depth Estimation: Toward Higher Resolution Maps with Accurate Object Boundaries

This paper considers the problem of single image depth estimation. The employment of convolutional neural networks (CNNs) has recently brought about significant advancements in the research of this problem. However, most existing methods suffer from loss of spatial resolution in the estimated depth maps; a typical symptom is distorted and blurry reconstruction of object boundaries. In this paper, toward more accurate estimation with a focus on depth maps with higher spatial resolution, we propose two improvements to existing approaches. One is about the strategy of fusing features extracted at different scales, for which we propose an improved network architecture consisting of four modules: an encoder, decoder, multi-scale feature fusion module, and refinement module. The other is about loss functions for measuring inference errors used in training. We show that three loss terms, which measure errors in depth, gradients and surface normals, respectively, contribute to improvement of accuracy in an complementary fashion. Experimental results show that these two improvements enable to attain higher accuracy than the current state-of-the-arts, which is given by finer resolution reconstruction, for example, with small objects and object boundaries.

cs.CV↗

arXiv2018

Deep Structured Energy-Based Image Inpainting

In this paper, we propose a structured image inpainting method employing an energy based model. In order to learn structural relationship between patterns observed in images and missing regions of the images, we employ an energy-based structured prediction method. The structural relationship is learned by minimizing an energy function which is defined by a simple convolutional neural network. The experimental results on various benchmark datasets show that our proposed method significantly outperforms the state-of-the-art methods which use Generative Adversarial Networks (GANs). We obtained 497.35 mean squared error (MSE) on the Olivetti face dataset compared to 833.0 MSE provided by the state-of-the-art method. Moreover, we obtained 28.4 dB peak signal to noise ratio (PSNR) on the SVHN dataset and 23.53 dB on the CelebA dataset, compared to 22.3 dB and 21.3 dB, provided by the state-of-the-art methods, respectively. The code is publicly available.

cs.CV↗

arXiv2018

Exploiting the Potential of Standard Convolutional Autoencoders for Image Restoration by Evolutionary Search

Researchers have applied deep neural networks to image restoration tasks, in which they proposed various network architectures, loss functions, and training methods. In particular, adversarial training, which is employed in recent studies, seems to be a key ingredient to success. In this paper, we show that simple convolutional autoencoders (CAEs) built upon only standard network components, i.e., convolutional layers and skip connections, can outperform the state-of-the-art methods which employ adversarial training and sophisticated loss functions. The secret is to employ an evolutionary algorithm to automatically search for good architectures. Training optimized CAEs by minimizing the $\ell_2$ loss between reconstructed images and their ground truths using the ADAM optimizer is all we need. Our experimental results show that this approach achieves 27.8 dB peak signal to noise ratio (PSNR) on the CelebA dataset and 40.4 dB on the SVHN dataset, compared to 22.8 dB and 33.0 dB provided by the former state-of-the-art methods, respectively.

cs.NE↗

arXiv2017

A vision based system for underwater docking

Autonomous underwater vehicles (AUVs) have been deployed for underwater exploration. However, its potential is confined by its limited on-board battery energy and data storage capacity. This problem has been addressed using docking systems by underwater recharging and data transfer for AUVs. In this work, we propose a vision based framework for underwater docking following these systems. The proposed framework comprises two modules; (i) a detection module which provides location information on underwater docking stations in 2D images captured by an on-board camera, and (ii) a pose estimation module which recovers the relative 3D position and orientation between docking stations and AUVs from the 2D images. For robust and credible detection of docking stations, we propose a convolutional neural network called Docking Neural Network (DoNN). For accurate pose estimation, a perspective-n-point algorithm is integrated into our framework. In order to examine our framework in underwater docking tasks, we collected a dataset of 2D images, named Underwater Docking Images Dataset (UDID), in an experimental water pool. To the best of our knowledge, UDID is the first publicly available underwater docking dataset. In the experiments, we first evaluate performance of the proposed detection module on UDID and its deformed variations. Next, we assess the accuracy of the pose estimation module by ground experiments, since it is not feasible to obtain true relative position and orientation between docking stations and AUVs under water. Then, we examine the pose estimation module by underwater experiments in our experimental water pool. Experimental results show that the proposed framework can be used to detect docking stations and estimate their relative pose efficiently and successfully, compared to the state-of-the-art baseline systems.

cs.CV↗

arXiv2017

Optimization on Product Submanifolds of Convolution Kernels

Recent advances in optimization methods used for training convolutional neural networks (CNNs) with kernels, which are normalized according to particular constraints, have shown remarkable success. This work introduces an approach for training CNNs using ensembles of joint spaces of kernels constructed using different constraints. For this purpose, we address a problem of optimization on ensembles of products of submanifolds (PEMs) of convolution kernels. To this end, we first propose three strategies to construct ensembles of PEMs in CNNs. Next, we expound their geometric properties (metric and curvature properties) in CNNs. We make use of our theoretical results by developing a geometry-aware SGD algorithm (G-SGD) for optimization on ensembles of PEMs to train CNNs. Moreover, we analyze convergence properties of G-SGD considering geometric properties of PEMs. In the experimental analyses, we employ G-SGD to train CNNs on Cifar-10, Cifar-100 and Imagenet datasets. The results show that geometric adaptive step size computation methods of G-SGD can improve training loss and convergence properties of CNNs. Moreover, we observe that classification performance of baseline CNNs can be boosted using G-SGD on ensembles of PEMs identified by multiple constraints.

cs.CV↗

arXiv2017

HyperNetworks with statistical filtering for defending adversarial examples

Deep learning algorithms have been known to be vulnerable to adversarial perturbations in various tasks such as image classification. This problem was addressed by employing several defense methods for detection and rejection of particular types of attacks. However, training and manipulating networks according to particular defense schemes increases computational complexity of the learning algorithms. In this work, we propose a simple yet effective method to improve robustness of convolutional neural networks (CNNs) to adversarial attacks by using data dependent adaptive convolution kernels. To this end, we propose a new type of HyperNetwork in order to employ statistical properties of input data and features for computation of statistical adaptive maps. Then, we filter convolution weights of CNNs with the learned statistical maps to compute dynamic kernels. Thereby, weights and kernels are collectively optimized for learning of image classification models robust to adversarial attacks without employment of additional target detection and rejection algorithms. We empirically demonstrate that the proposed method enables CNNs to spontaneously defend against different types of attacks, e.g. attacks generated by Gaussian noise, fast gradient sign methods (Goodfellow et al., 2014) and a black-box attack(Narodytska & Kasiviswanathan, 2016).

cs.CV↗

arXiv2017

Information Potential Auto-Encoders

In this paper, we suggest a framework to make use of mutual information as a regularization criterion to train Auto-Encoders (AEs). In the proposed framework, AEs are regularized by minimization of the mutual information between input and encoding variables of AEs during the training phase. In order to estimate the entropy of the encoding variables and the mutual information, we propose a non-parametric method. We also give an information theoretic view of Variational AEs (VAEs), which suggests that VAEs can be considered as parametric methods that estimate entropy. Experimental results show that the proposed non-parametric models have more degree of freedom in terms of representation learning of features drawn from complex distributions such as Mixture of Gaussians, compared to methods which estimate entropy using parametric approaches, such as Variational AEs.

cs.LG↗

arXiv2017

Improving Robustness of Feature Representations to Image Deformations using Powered Convolution in CNNs

In this work, we address the problem of improvement of robustness of feature representations learned using convolutional neural networks (CNNs) to image deformation. We argue that higher moment statistics of feature distributions could be shifted due to image deformations, and the shift leads to degrade of performance and cannot be reduced by ordinary normalization methods as observed in experimental analyses. In order to attenuate this effect, we apply additional non-linearity in CNNs by combining power functions with learnable parameters into convolution operation. In the experiments, we observe that CNNs which employ the proposed method obtain remarkable boost in both the generalization performance and the robustness under various types of deformations using large scale benchmark datasets. For instance, a model equipped with the proposed method obtains 3.3\% performance boost in mAP on Pascal Voc object detection task using deformed images, compared to the reference model, while both models provide the same performance using original images. To the best of our knowledge, this is the first work that studies robustness of deep features learned using CNNs to a wide range of deformations for object recognition and detection.

cs.CV↗

arXiv2017

Linear Discriminant Generative Adversarial Networks

We develop a novel method for training of GANs for unsupervised and class conditional generation of images, called Linear Discriminant GAN (LD-GAN). The discriminator of an LD-GAN is trained to maximize the linear separability between distributions of hidden representations of generated and targeted samples, while the generator is updated based on the decision hyper-planes computed by performing LDA over the hidden representations. LD-GAN provides a concrete metric of separation capacity for the discriminator, and we experimentally show that it is possible to stabilize the training of LD-GAN simply by calibrating the update frequencies between generators and discriminators in the unsupervised case, without employment of normalization methods and constraints on weights. In the class conditional generation tasks, the proposed method shows improved training stability together with better generalization performance compared to WGAN that employs an auxiliary classifier.

stat.ML↗

arXiv2017

Truncating Wide Networks using Binary Tree Architectures

Recent study shows that a wide deep network can obtain accuracy comparable to a deeper but narrower network. Compared to narrower and deeper networks, wide networks employ relatively less number of layers and have various important benefits, such that they have less running time on parallel computing devices, and they are less affected by gradient vanishing problems. However, the parameter size of a wide network can be very large due to use of large width of each layer in the network. In order to keep the benefits of wide networks meanwhile improve the parameter size and accuracy trade-off of wide networks, we propose a binary tree architecture to truncate architecture of wide networks by reducing the width of the networks. More precisely, in the proposed architecture, the width is continuously reduced from lower layers to higher layers in order to increase the expressive capacity of network with a less increase on parameter size. Also, to ease the gradient vanishing problem, features obtained at different layers are concatenated to form the output of our architecture. By employing the proposed architecture on a baseline wide network, we can construct and train a new network with same depth but considerably less number of parameters. In our experimental analyses, we observe that the proposed architecture enables us to obtain better parameter size and accuracy trade-off compared to baseline networks using various benchmark image classification datasets. The results show that our model can decrease the classification error of baseline from 20.43% to 19.22% on Cifar-100 using only 28% of parameters that baseline has. Code is available at https://github.com/ZhangVision/bitnet.

cs.CV↗

arXiv2017

Hierarchical Multi-resolution Mesh Networks for Brain Decoding

We propose a new framework, called Hierarchical Multi-resolution Mesh Networks (HMMNs), which establishes a set of brain networks at multiple time resolutions of fMRI signal to represent the underlying cognitive process. The suggested framework, first, decomposes the fMRI signal into various frequency subbands using wavelet transforms. Then, a brain network, called mesh network, is formed at each subband by ensembling a set of local meshes. The locality around each anatomic region is defined with respect to a neighborhood system based on functional connectivity. The arc weights of a mesh are estimated by ridge regression formed among the average region time series. In the final step, the adjacency matrices of mesh networks obtained at different subbands are ensembled for brain decoding under a hierarchical learning architecture, called, fuzzy stacked generalization (FSG). Our results on Human Connectome Project task-fMRI dataset reflect that the suggested HMMN model can successfully discriminate tasks by extracting complementary information obtained from mesh arc weights of multiple subbands. We study the topological properties of the mesh networks at different resolutions using the network measures, namely, node degree, node strength, betweenness centrality and global efficiency; and investigate the connectivity of anatomic regions, during a cognitive task. We observe significant variations among the network topologies obtained for different subbands. We, also, analyze the diversity properties of classifier ensemble, trained by the mesh networks in multiple subbands and observe that the classifiers in the ensemble collaborate with each other to fuse the complementary information freed at each subband. We conclude that the fMRI data, recorded during a cognitive task, embed diverse information across the anatomic regions at each resolution.

cs.NE↗

arXiv2016

Design of Kernels in Convolutional Neural Networks for Image Classification

Despite the effectiveness of Convolutional Neural Networks (CNNs) for image classification, our understanding of the relationship between shape of convolution kernels and learned representations is limited. In this work, we explore and employ the relationship between shape of kernels which define Receptive Fields (RFs) in CNNs for learning of feature representations and image classification. For this purpose, we first propose a feature visualization method for visualization of pixel-wise classification score maps of learned features. Motivated by our experimental results, and observations reported in the literature for modeling of visual systems, we propose a novel design of shape of kernels for learning of representations in CNNs. In the experimental results, we achieved a state-of-the-art classification performance compared to a base CNN model [28] by reducing the number of parameters and computational time of the model using the ILSVRC-2012 dataset [24]. The proposed models also outperform the state-of-the-art models employed on the CIFAR-10/100 datasets [12] for image classification. Additionally, we analyzed the robustness of the proposed method to occlusion for classification of partially occluded images compared with the state-of-the-art methods. Our results indicate the effectiveness of the proposed approach. The code is available in github.com/minogame/caffe-qhconv.

cs.CV↗

arXiv2016

Optimization on Submanifolds of Convolution Kernels in CNNs

Kernel normalization methods have been employed to improve robustness of optimization methods to reparametrization of convolution kernels, covariate shift, and to accelerate training of Convolutional Neural Networks (CNNs). However, our understanding of theoretical properties of these methods has lagged behind their success in applications. We develop a geometric framework to elucidate underlying mechanisms of a diverse range of kernel normalization methods. Our framework enables us to expound and identify geometry of space of normalized kernels. We analyze and delineate how state-of-the-art kernel normalization methods affect the geometry of search spaces of the stochastic gradient descent (SGD) algorithms in CNNs. Following our theoretical results, we propose a SGD algorithm with assurance of almost sure convergence of the methods to a solution at single minimum of classification loss of CNNs. Experimental results show that the proposed method achieves state-of-the-art performance for major image classification benchmarks with CNNs.

cs.CV↗