arXiv subjects

Arash Behboodi

Publications and source records attributed to Arash Behboodi.

At least 55 records · Page 3Linked to original sources

arXiv2022

MIMO-GAN: Generative MIMO Channel Modeling

We propose generative channel modeling to learn statistical channel models from channel input-output measurements. Generative channel models can learn more complicated distributions and represent the field data more faithfully. They are tractable and easy to sample from, which can potentially speed up the simulation rounds. To achieve this, we leverage advances in GAN, which helps us learn an implicit distribution over stochastic MIMO channels from observed measurements. In particular, our approach MIMO-GAN implicitly models the wireless channel as a distribution of time-domain band-limited impulse responses. We evaluate MIMO-GAN on 3GPP TDL MIMO channels and observe high-consistency in capturing power, delay and spatial correlation statistics of the underlying channel. In particular, we observe MIMO-GAN achieve errors of under 3.57 ns average delay and -18.7 dB power.

cs.IT↗

arXiv2022

Neural RF SLAM for unsupervised positioning and mapping with channel state information

We present a neural network architecture for jointly learning user locations and environment mapping up to isometry, in an unsupervised way, from channel state information (CSI) values with no location information. The model is based on an encoder-decoder architecture. The encoder network maps CSI values to the user location. The decoder network models the physics of propagation by parametrizing the environment using virtual anchors. It aims at reconstructing, from the encoder output and virtual anchor location, the set of time of flights (ToFs) that are extracted from CSI using super-resolution methods. The neural network task is set prediction and is accordingly trained end-to-end. The proposed model learns an interpretable latent, i.e., user location, by just enforcing a physics-based decoder. It is shown that the proposed model achieves sub-meter accuracy on synthetic ray tracing based datasets with single anchor SISO setup while recovering the environment map up to 4cm median error in a 2D environment and 15cm in a 3D environment

cs.IT↗

arXiv2022

Generalization Error Bounds for Iterative Recovery Algorithms Unfolded as Neural Networks

Motivated by the learned iterative soft thresholding algorithm (LISTA), we introduce a general class of neural networks suitable for sparse reconstruction from few linear measurements. By allowing a wide range of degrees of weight-sharing between the layers, we enable a unified analysis for very different neural network types, ranging from recurrent ones to networks more similar to standard feedforward neural networks. Based on training samples, via empirical risk minimization we aim at learning the optimal network parameters and thereby the optimal network that reconstructs signals from their low-dimensional linear measurements. We derive generalization bounds by analyzing the Rademacher complexity of hypothesis classes consisting of such deep networks, that also take into account the thresholding parameters. We obtain estimates of the sample complexity that essentially depend only linearly on the number of parameters and on the depth. We apply our main result to obtain specific generalization bounds for several practical examples, including different algorithms for (implicit) dictionary learning, and convolutional neural networks.

cs.LG↗

arXiv2021

On the Effect of Low-Rank Weights on Adversarial Robustness of Neural Networks

Recently, there has been an abundance of works on designing Deep Neural Networks (DNNs) that are robust to adversarial examples. In particular, a central question is which features of DNNs influence adversarial robustness and, therefore, can be to used to design robust DNNs. In this work, this problem is studied through the lens of compression which is captured by the low-rank structure of weight matrices. It is first shown that adversarial training tends to promote simultaneously low-rank and sparse structure in the weight matrices of neural networks. This is measured through the notions of effective rank and effective sparsity. In the reverse direction, when the low rank structure is promoted by nuclear norm regularization and combined with sparsity inducing regularizations, neural networks show significantly improved adversarial robustness. The effect of nuclear norm regularization on adversarial robustness is paramount when it is applied to convolutional neural networks. Although still not competing with adversarial training, this result contributes to understanding the key properties of robust classifiers.

cs.LG↗

arXiv2021

Neural Augmentation of Kalman Filter with Hypernetwork for Channel Tracking

We propose Hypernetwork Kalman Filter (HKF) for tracking applications with multiple different dynamics. The HKF combines generalization power of Kalman filters with expressive power of neural networks. Instead of keeping a bank of Kalman filters and choosing one based on approximating the actual dynamics, HKF adapts itself to each dynamics based on the observed sequence. Through extensive experiments on CDL-B channel model, we show that the HKF can be used for tracking the channel over a wide range of Doppler values, matching Kalman filter performance with genie Doppler information. At high Doppler values, it achieves around 2dB gain over genie Kalman filter. The HKF generalizes well to unseen Doppler, SNR values and pilot patterns unlike LSTM, which suffers from severe performance degradation.

eess.SP↗

arXiv2021

Compressive Sensing and Neural Networks from a Statistical Learning Perspective

Various iterative reconstruction algorithms for inverse problems can be unfolded as neural networks. Empirically, this approach has often led to improved results, but theoretical guarantees are still scarce. While some progress on generalization properties of neural networks have been made, great challenges remain. In this chapter, we discuss and combine these topics to present a generalization error analysis for a class of neural networks suitable for sparse reconstruction from few linear measurements. The hypothesis class considered is inspired by the classical iterative soft-thresholding algorithm (ISTA). The neural networks in this class are obtained by unfolding iterations of ISTA and learning some of the weights. Based on training samples, we aim at learning the optimal network parameters via empirical risk minimization and thereby the optimal network that reconstructs signals from their compressive linear measurements. In particular, we may learn a sparsity basis that is shared by all of the iterations/layers and thereby obtain a new approach for dictionary learning. For this class of networks, we present a generalization bound, which is based on bounding the Rademacher complexity of hypothesis classes consisting of such deep networks via Dudley's integral. Remarkably, under realistic conditions, the generalization error scales only logarithmically in the number of layers, and at most linear in number of measurements.

math.ST↗

arXiv2020

Tight bounds on the mutual coherence of sensing matrices for Wigner D-functions on regular grids

Many practical sampling patterns for function approximation on the rotation group utilizes regular samples on the parameter axes. In this paper, we relate the mutual coherence analysis for sensing matrices that correspond to a class of regular patterns to angular momentum analysis in quantum mechanics and provide simple lower bounds for it. The products of Wigner d-functions, which appear in coherence analysis, arise in angular momentum analysis in quantum mechanics. We first represent the product as a linear combination of a single Wigner d-function and angular momentum coefficients, otherwise known as the Wigner 3j symbols. Using combinatorial identities, we show that under certain conditions on the bandwidth and number of samples, the inner product of the columns of the sensing matrix at zero orders, which is equal to the inner product of two Legendre polynomials, dominates the mutual coherence term and fixes a lower bound for it. In other words, for a class of regular sampling patterns, we provide a lower bound for the inner product of the columns of the sensing matrix that can be analytically computed. We verify numerically our theoretical results and show that the lower bound for the mutual coherence is larger than Welch bound. Besides, we provide algorithms that can achieve the lower bound for spherical harmonics.

quant-ph↗

arXiv2020

Sensing Matrix Design and Sparse Recovery on the Sphere and the Rotation Group

In this paper, {the goal is to design deterministic sampling patterns on the sphere and the rotation group} and, thereby, construct sensing matrices for sparse recovery of band-limited functions. It is first shown that random sensing matrices, which consists of random samples of Wigner D-functions, satisfy the Restricted Isometry Property (RIP) with proper preconditioning and can be used for sparse recovery on the rotation group. The mutual coherence, however, is used to assess the performance of deterministic and regular sensing matrices. We show that many of widely used regular sampling patterns yield sensing matrices with the worst possible mutual coherence, and therefore are undesirable for sparse recovery. Using tools from angular momentum analysis in quantum mechanics, we provide a new expression for the mutual coherence, which encourages the use of regular elevation samples. We construct low coherence deterministic matrices by fixing the regular samples on the elevation and minimizing the mutual coherence over the azimuth-polarization choice. It is shown that once the elevation sampling is fixed, the mutual coherence has a lower bound that depends only on the elevation samples. This lower bound, however, can be achieved for spherical harmonics, which leads to new sensing matrices with better coherence than other representative regular sampling patterns. This is reflected as well in our numerical experiments where our proposed sampling patterns perfectly match the phase transition of random sampling patterns.

cs.IT↗

arXiv2020

Gradient $\ell_1$ Regularization for Quantization Robustness

We analyze the effect of quantizing weights and activations of neural networks on their loss and derive a simple regularization scheme that improves robustness against post-training quantization. By training quantization-ready networks, our approach enables storing a single set of weights that can be quantized on-demand to different bit-widths as energy and memory requirements of the application change. Unlike quantization-aware training using the straight-through estimator that only targets a specific bit-width and requires access to training data and pipeline, our regularization-based method paves the way for "on the fly'' post-training quantization to various bit-widths. We show that by modeling quantization as a $\ell_\infty$-bounded perturbation, the first-order term in the loss expansion can be regularized using the $\ell_1$-norm of gradients. We experimentally validate the effectiveness of our regularization scheme on different architectures on CIFAR-10 and ImageNet datasets.

cs.LG↗

arXiv2019

Adversarial Risk Bounds for Neural Networks through Sparsity based Compression

Neural networks have been shown to be vulnerable against minor adversarial perturbations of their inputs, especially for high dimensional data under $\ell_\infty$ attacks. To combat this problem, techniques like adversarial training have been employed to obtain models which are robust on the training set. However, the robustness of such models against adversarial perturbations may not generalize to unseen data. To study how robustness generalizes, recent works assume that the inputs have bounded $\ell_2$-norm in order to bound the adversarial risk for $\ell_\infty$ attacks with no explicit dimension dependence. In this work we focus on $\ell_\infty$ attacks on $\ell_\infty$ bounded inputs and prove margin-based bounds. Specifically, we use a compression based approach that relies on efficiently compressing the set of tunable parameters without distorting the adversarial risk. To achieve this, we apply the concept of effective sparsity and effective joint sparsity on the weight matrices of neural networks. This leads to bounds with no explicit dependence on the input dimension, neither on the number of classes. Our results show that neural networks with approximately sparse weight matrices not only enjoy enhanced robustness, but also better generalization.

cs.LG↗

arXiv2019

A Deep Learning Wireless Transceiver with Fully Learned Modulation and Synchronization

In this paper, we present a deep learning based wireless transceiver. We describe in detail the corresponding artificial neural network architecture, the training process, and report on excessive over-the-air measurement results. We employ the end-to-end training approach with an autoencoder model that includes a channel model in the middle layers as previously proposed in the literature. In contrast to other state-of-the-art results, our architecture supports learning time synchronization without any manually designed signal processing operations. Moreover, the neural transceiver has been tested over the air with an implementation in software defined radio. Our experimental results for the implemented single antenna system demonstrate a raw bit-rate of 0.5 million bits per second. This exceeds results from comparable systems presented in the literature and suggests the feasibility of high throughput deep learning transceivers.

eess.SP↗

arXiv2018

Perturbation Analysis of Learning Algorithms: A Unifying Perspective on Generation of Adversarial Examples

Despite the tremendous success of deep neural networks in various learning problems, it has been observed that adding an intentionally designed adversarial perturbation to inputs of these architectures leads to erroneous classification with high confidence in the prediction. In this work, we propose a general framework based on the perturbation analysis of learning algorithms which consists of convex programming and is able to recover many current adversarial attacks as special cases. The framework can be used to propose novel attacks against learning algorithms for classification and regression tasks under various new constraints with closed form solutions in many instances. In particular we derive new attacks against classification algorithms which are shown to achieve comparable performances to notable existing attacks. The framework is then used to generate adversarial perturbations for regression tasks which include single pixel and single subset attacks. By applying this method to autoencoding and image colorization tasks, it is shown that adversarial perturbations can effectively perturb the output of regression tasks as well.

cs.LG↗

arXiv2018

On Generation of Adversarial Examples using Convex Programming

It has been observed that deep learning architectures tend to make erroneous decisions with high reliability for particularly designed adversarial instances. In this work, we show that the perturbation analysis of these architectures provides a framework for generating adversarial instances by convex programming which, for classification tasks, is able to recover variants of existing non-adaptive adversarial methods. The proposed framework can be used for the design of adversarial noise under various desirable constraints and different types of networks. Moreover, this framework is capable of explaining various existing adversarial methods and can be used to derive new algorithms as well. We make use of these results to obtain novel algorithms. The experiments show the competitive performance of the obtained solutions, in terms of fooling ratio, when benchmarked with well-known adversarial methods.

cs.LG↗

arXiv2018

Learning the Localization Function: Machine Learning Approach to Fingerprinting Localization

Considered as a data-driven approach, Fingerprinting Localization Solutions (FPSs) enjoy huge popularity due to their good performance and minimal environment information requirement. This papers addresses applications of artificial intelligence to solve two problems in Received Signal Strength Indicator (RSSI) based FPS, first the cumbersome training database construction and second the extrapolation of fingerprinting algorithm for similar buildings with slight environmental changes. After a concise overview of deep learning design techniques, two main techniques widely used in deep learning are exploited for the above mentioned issues namely data augmentation and transfer learning. We train a multi-layer neural network that learns the mapping from the observations to the locations. A data augmentation method is proposed to increase the training database size based on the structure of RSSI measurements and hence reducing effectively the amount of training data. Then it is shown experimentally how a model trained for a particular building can be transferred to a similar one by fine tuning with significantly smaller training numbers. The paper implicitly discusses the new guidelines to consider about deep learning designs when they are employed in a new application context.

cs.NI↗

arXiv2017

A Mathematical Model for Fingerprinting-based Localization Algorithms

A general theoretical framework for Fingerprinting Localization Algorithms (FPS), given their popularity, can be utilized for their performance studies. In this work, after setting up an abstract model for FPS, it is shown that fingerprinting-based localization problem can be cast as a hypothesis testing (HT) problem and therefore various results in HT literature can be used to provide insights, guidelines and performance bounds for general FPS. This framework results in characterization of scaling limits of localization reliability in terms of number of measurements and other environmental parameters. It is suggested that Kullback-Leibler (KL) divergence between probability distributions of selected feature for fingerprinting at different locations encapsulates information about both accuracy and latency and can be used as a central performance metric for studying FPS. Although developed for an arbitrary fingerprint, the framework is particularly used for studying simple Received Signal Strength (RSS)- based algorithm. The effect of various parameters on the performance of fingerprinting algorithms is discussed, which includes path loss and fading characteristics, number of measurements at each point, number of anchors and their position, and placement of training points. Representative simulations and experimentation are used to verify validity of the theoretical frameworks in realistic setups.

cs.IT↗

arXiv2016

Sparse recovery in Wigner-D basis expansion

We are concerned with the recovery of $s-$sparse Wigner-D expansions in terms of $N$ Wigner-D functions. Considered as a generalization of spherical harmonics, Wigner-D functions are eigenfunctions of Laplace-Beltrami operator and form an orthonormal system. However, since they are not uniformly bounded, the existing results on BOS do not apply. Using previously introduced preconditioning technique, a new orthonormal and bounded system is obtained for which RIP property can be established. We show that the number of sufficient samples for sparse recovery scales with ${N}^{1/6} \,s\, \log^3(s) \,\log(N)$. The phase transition diagram for this problem is also presented. We will also discuss the application of our results in the spherical near-field antenna measurement.

cs.IT↗

arXiv2014

Mixed Noisy Network Coding and Cooperative Unicasting in Wireless Networks

The problem of communicating a single message to a destination in presence of multiple relay nodes, referred to as cooperative unicast network, is considered. First, we introduce "Mixed Noisy Network Coding" (MNNC) scheme which generalizes "Noisy Network Coding" (NNC) where relays are allowed to decode-and-forward (DF) messages while all of them (without exception) transmit noisy descriptions of their observations. These descriptions are exploited at the destination and the DF relays aim to decode the transmitted messages while creating full cooperation among the nodes. Moreover, the destination and the DF relays can independently select the set of descriptions to be decoded or treated as interference. This concept is further extended to multi-hopping scenarios, referred to as "Layered MNNC" (LMNNC), where DF relays are organized into disjoint groups representing one hop in the network. For cooperative unicast additive white Gaussian noise (AWGN) networks we show that -provided DF relays are properly chosen- MNNC improves over all previously established constant gaps to the cut-set bound. Secondly, we consider the composite cooperative unicast network where the channel parameters are randomly drawn before communication starts and remain fixed during the transmission. Each draw is assumed to be unknown at the source and fully known at the destination but only partly known at the relays. We introduce through MNNC scheme the concept of "Selective Coding Strategy" (SCS) that enables relays to decide dynamically whether, in addition to communicate noisy descriptions, is possible to decode and forward messages. It is demonstrated through slow-fading AWGN relay networks that SCS clearly outperforms conventional coding schemes.

cs.IT↗

arXiv2012

Cooperative Strategies for Simultaneous and Broadcast Relay Channels

Consider the \emph{simultaneous relay channel} (SRC) which consists of a set of relay channels where the source wishes to transmit common and private information to each of the destinations. This problem is recognized as being equivalent to that of sending common and private information to several destinations in presence of helper relays where each channel outcome becomes a branch of the \emph{broadcast relay channel} (BRC). Cooperative schemes and capacity region for a set with two memoryless relay channels are investigated. The proposed coding schemes, based on \emph{Decode-and-Forward} (DF) and \emph{Compress-and-Forward} (CF) must be capable of transmitting information simultaneously to all destinations in such set. Depending on the quality of source-to-relay and relay-to-destination channels, inner bounds on the capacity of the general BRC are derived. Three cases of particular interest are considered: cooperation is based on DF strategy for both users --referred to as DF-DF region--, cooperation is based on CF strategy for both users --referred to as CF-CF region--, and cooperation is based on DF strategy for one destination and CF for the other --referred to as DF-CF region--. These results can be seen as a generalization and hence unification of previous works. An outer-bound on the capacity of the general BRC is also derived. Capacity results are obtained for the specific cases of semi-degraded and degraded Gaussian simultaneous relay channels. Rates are evaluated for Gaussian models where the source must guarantee a minimum amount of information to both users while additional information is sent to each of them.

cs.IT↗