arXiv subjects

Arian Eamaz

Publications and source records attributed to Arian Eamaz.

At least 19 recordsLinked to original sources

arXiv2026

Training Under Challenge: Executable Certificates and Challenge-Closed Optimality for Neural Networks

A flat training curve does not reveal whether a neural network has reached a global optimum, is locally trapped, is representation-limited, or is mismatched to its trainer. We introduce Training Under Challenge, an executable-certificate framework in which predeclared, architecture-valid procedures construct complete alternatives in the same certified class and reevaluate the same objective. Any lower-valued candidate is a replayable witness that lower-bounds the checkpoint's empirical global-optimality gap. Passing a finite suite is only suite-relative; global-gap conclusions require a separately justified coverage mechanism. We define a resource-indexed challenge-power modulus that characterizes the largest gap compatible with passage. For squared loss, current block-decrease operators make coverage checkable and yield uniform and realized-residual bounds. We prove the converse frontier: without coverage, a first-order ReLU trainer can reach infinitely many exact conditional head optima while converging to a non-global point. On a channel-gated ResNet-18 distillation problem with known optimum, eight internal challenges cover all 240 audited output directions, and realized-residual bounds lie within factors of 1.74--3.02 of the true gap. Paired predictive certificates separate decoder under-use from representation insufficiency, while quantized-denoising studies demonstrate diagnosis, repair, and current-state recertification.

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arXiv2026

Trust, but Verify: Peeling Low-Bit Transformer Networks for Training Monitoring

Understanding whether deep neural networks are effectively optimized remains challenging, as training occurs in highly nonconvex landscapes and standard metrics provide limited visibility into layer-wise learning quality. This challenge is particularly acute for transformer-based language models, where training is expensive, models are often reused in frozen form, and poorly optimized layers can silently degrade performance. We propose a layer-wise peeling framework for monitoring training dynamics, in which each transformer layer is locally optimized against intermediate representations of the trained model. By constructing lightweight, layer-specific reference solutions and projecting layers onto multiple intermediate outputs via different permutations, we obtain achievable baselines that enable fine-grained diagnosis of under-optimized layers. Experiments on decoder-only transformer models show that these layer-wise reference bounds can match or even surpass the trained model at various stages of training, exposing inefficiencies that remain hidden in aggregate loss curves. We further demonstrate that this analysis remains effective under binarization and quantized settings, where training dynamics are particularly fragile. Across all numerical results, the proposed bounds consistently separate apparent convergence from effective optimality, highlighting optimization opportunities that are invisible when relying on training loss alone.

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arXiv2025

Sample Abundance for Signal Processing: A Brief Introduction

This paper reports, by way of introduction, on the advances made by our group and the broader signal processing community on the concept of sample abundance; a phenomenon that naturally arises in one-bit and few-bit signal processing frameworks. By leveraging large volumes of low-precision measurements, we show how traditionally costly constraints, such as matrix semi-definiteness and rank conditions, become redundant, yielding simple overdetermined linear feasibility problems. We illustrate key algorithms, theoretical guarantees via the Finite Volume Property, and the sample abundance singularity phenomenon, where computational complexity sharply drops.

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arXiv2025

Physics-Inspired Binary Neural Networks: Interpretable Compression with Theoretical Guarantees

Why rely on dense neural networks and then blindly sparsify them when prior knowledge about the problem structure is already available? Many inverse problems admit algorithm-unrolled networks that naturally encode physics and sparsity. In this work, we propose a Physics-Inspired Binary Neural Network (PIBiNN) that combines two key components: (i) data-driven one-bit quantization with a single global scale, and (ii) problem-driven sparsity predefined by physics and requiring no updates during training. This design yields compression rates below one bit per weight by exploiting structural zeros, while preserving essential operator geometry. Unlike ternary or pruning-based schemes, our approach avoids ad-hoc sparsification, reduces metadata overhead, and aligns directly with the underlying task. Experiments suggest that PIBiNN achieves advantages in both memory efficiency and generalization compared to competitive baselines such as ternary and channel-wise quantization.

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arXiv2024

Data-Aware Training Quality Monitoring and Certification for Reliable Deep Learning

Deep learning models excel at capturing complex representations through sequential layers of linear and non-linear transformations, yet their inherent black-box nature and multi-modal training landscape raise critical concerns about reliability, robustness, and safety, particularly in high-stakes applications. To address these challenges, we introduce YES training bounds, a novel framework for real-time, data-aware certification and monitoring of neural network training. The YES bounds evaluate the efficiency of data utilization and optimization dynamics, providing an effective tool for assessing progress and detecting suboptimal behavior during training. Our experiments show that the YES bounds offer insights beyond conventional local optimization perspectives, such as identifying when training losses plateau in suboptimal regions. Validated on both synthetic and real data, including image denoising tasks, the bounds prove effective in certifying training quality and guiding adjustments to enhance model performance. By integrating these bounds into a color-coded cloud-based monitoring system, we offer a powerful tool for real-time evaluation, setting a new standard for training quality assurance in deep learning.

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arXiv2024

Deep Learning-Enabled One-Bit DoA Estimation

Unrolled deep neural networks have attracted significant attention for their success in various practical applications. In this paper, we explore an application of deep unrolling in the direction of arrival (DoA) estimation problem when coarse quantization is applied to the measurements. We present a compressed sensing formulation for DoA estimation from one-bit data in which estimating target DoAs requires recovering a sparse signal from a limited number of severely quantized linear measurements. In particular, we exploit covariance recovery from one-bit dither samples. To recover the covariance of transmitted signal, the learned iterative shrinkage and thresholding algorithm (LISTA) is employed fed by one-bit data. We demonstrate that the upper bound of estimation performance is governed by the recovery error of the transmitted signal covariance matrix. Through numerical experiments, we demonstrate the proposed LISTA-based algorithm's capability in estimating target locations. The code employed in this study is available online.

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arXiv2024

Collaborative Automotive Radar Sensing via Mixed-Precision Distributed Array Completion

This paper investigates the effects of coarse quantization with mixed precision on measurements obtained from sparse linear arrays, synthesized by a collaborative automotive radar sensing strategy. The mixed quantization precision significantly reduces the data amount that needs to be shared from radar nodes to the fusion center for coherent processing. We utilize the low-rank properties inherent in the constructed Hankel matrix of the mixed-precision array, to recover azimuth angles from quantized measurements. Our proposed approach addresses the challenge of mixed-quantized Hankel matrix completion, allowing for accurate estimation of the azimuth angles of interest. To evaluate the recovery performance of the proposed scheme, we establish a quasi-isometric embedding with a high probability for mixed-precision quantization. The effectiveness of our proposed scheme is demonstrated through numerical results, highlighting successful reconstruction.

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arXiv2023

Automotive Radar Sensing with Sparse Linear Arrays Using One-Bit Hankel Matrix Completion

The design of sparse linear arrays has proven instrumental in the implementation of cost-effective and efficient automotive radar systems for high-resolution imaging. This paper investigates the impact of coarse quantization on measurements obtained from such arrays. To recover azimuth angles from quantized measurements, we leverage the low-rank properties of the constructed Hankel matrix. In particular, by addressing the one-bit Hankel matrix completion problem through a developed singular value thresholding algorithm, our proposed approach accurately estimates the azimuth angles of interest. We provide comprehensive insights into recovery performance and the required number of one-bit samples. The effectiveness of our proposed scheme is underscored by numerical results, demonstrating successful reconstruction using only one-bit data.

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arXiv2023

From Quasi-Isometric Embeddings to Finite-Volume Property: A Theoretical Framework for Quantized Matrix Completion

We delve into the impact of memoryless scalar quantization on matrix completion. Our primary motivation for this research is to evaluate the recovery performance of nuclear norm minimization in handling quantized matrix problems without the use of any regularization terms such as those stemming from maximum likelihood estimation. We broaden our theoretical discussion to encompass the coarse quantization scenario with a dithering scheme, where the only available information for low-rank matrix recovery is a few-bit low-resolution data. We furnish theoretical guarantees for both scenarios: when access to dithers is available during the reconstruction process, and when we have access solely to the statistical properties of the dithers. Additionally, we conduct a comprehensive analysis of the effects of sign flips and prequantization noise on the recovery performance, particularly when the impact of sign flips is quantified using the well-known Hamming distance in the upper bound of recovery error.

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arXiv2023

Submodular Optimization for Placement of Intelligent Reflecting Surfaces in Sensing Systems

Intelligent reflecting surfaces (IRS) and their optimal deployment are the new technological frontier in sensing applications. Recently, IRS have demonstrated potential in advancing target estimation and detection. While the optimal phase-shift of IRS for different tasks has been studied extensively in the literature, the optimal placement of multiple IRS platforms for sensing applications is less explored. In this paper, we design the placement of IRS platforms for sensing by maximizing the mutual information. In particular, we use this criterion to determine an approximately optimal placement of IRS platforms to illuminate an area where the target has a hypothetical presence. After demonstrating the submodularity of the mutual information criteria, we tackle the design problem by means of a constant-factor approximation algorithm for submodular optimization. Numerical results are presented to validate the proposed submodular optimization framework for optimal IRS placement with worst case performance bounded to $1-1/e\approx 63 \%$.

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arXiv2023

Matrix Completion from One-Bit Dither Samples

We explore the impact of coarse quantization on matrix completion in the extreme scenario of dithered one-bit sensing, where the matrix entries are compared with time-varying threshold levels. In particular, instead of observing a subset of high-resolution entries of a low-rank matrix, we have access to a small number of one-bit samples, generated as a result of these comparisons. In order to recover the low-rank matrix using its coarsely quantized known entries, we begin by transforming the problem of one-bit matrix completion (one-bit MC) with time-varying thresholds into a nuclear norm minimization problem. The one-bit sampled information is represented as linear inequality feasibility constraints. We then develop the popular singular value thresholding (SVT) algorithm to accommodate these inequality constraints, resulting in the creation of the One-Bit SVT (OB-SVT). Our findings demonstrate that incorporating multiple time-varying sampling threshold sequences in one-bit MC can significantly improve the performance of the matrix completion algorithm. In pursuit of achieving this objective, we utilize diverse thresholding schemes, namely uniform, Gaussian, and discrete thresholds. To accelerate the convergence of our proposed algorithm, we introduce three variants of the OB-SVT algorithm. Among these variants is the randomized sketched OB-SVT, which departs from using the entire information at each iteration, opting instead to utilize sketched data. This approach effectively reduces the dimension of the operational space and accelerates the convergence. We perform numerical evaluations comparing our proposed algorithm with the maximum likelihood estimation method previously employed for one-bit MC, and demonstrate that our approach can achieve a better recovery performance.

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arXiv2023

HDR Imaging With One-Bit Quantization

Modulo sampling and dithered one-bit quantization frameworks have emerged as promising solutions to overcome the limitations of traditional analog-to-digital converters (ADCs) and sensors. Modulo sampling, with its high-resolution approach utilizing modulo ADCs, offers an unlimited dynamic range, while dithered one-bit quantization offers cost-efficiency and reduced power consumption while operating at elevated sampling rates. Our goal is to explore the synergies between these two techniques, leveraging their unique advantages, and to apply them to non-bandlimited signals within spline spaces. One noteworthy application of these signals lies in High Dynamic Range (HDR) imaging. In this paper, we expand upon the Unlimited One-Bit (UNO) sampling framework, initially conceived for bandlimited signals, to encompass non-bandlimited signals found in the context of HDR imaging. We present a novel algorithm rigorously examined for its ability to recover images from one-bit modulo samples. Additionally, we introduce a sufficient condition specifically designed for UNO sampling to perfectly recover non-bandlimited signals within spline spaces. Our numerical results vividly demonstrate the effectiveness of UNO sampling in the realm of HDR imaging.

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arXiv2023

Low-rank Matrix Sensing With Dithered One-Bit Quantization

We explore the impact of coarse quantization on low-rank matrix sensing in the extreme scenario of dithered one-bit sampling, where the high-resolution measurements are compared with random time-varying threshold levels. To recover the low-rank matrix of interest from the highly-quantized collected data, we offer an enhanced randomized Kaczmarz algorithm that efficiently solves the emerging highly-overdetermined feasibility problem. Additionally, we provide theoretical guarantees in terms of the convergence and sample size requirements. Our numerical results demonstrate the effectiveness of the proposed methodology.

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arXiv2023

Harnessing the Power of Sample Abundance: Theoretical Guarantees and Algorithms for Accelerated One-Bit Sensing

One-bit quantization with time-varying sampling thresholds (also known as random dithering) has recently found significant utilization potential in statistical signal processing applications due to its relatively low power consumption and low implementation cost. In addition to such advantages, an attractive feature of one-bit analog-to-digital converters (ADCs) is their superior sampling rates as compared to their conventional multi-bit counterparts. This characteristic endows one-bit signal processing frameworks with what one may refer to as sample abundance. We show that sample abundance plays a pivotal role in many signal recovery and optimization problems that are formulated as (possibly non-convex) quadratic programs with linear feasibility constraints. Of particular interest to our work are low-rank matrix recovery and compressed sensing applications that take advantage of one-bit quantization. We demonstrate that the sample abundance paradigm allows for the transformation of such problems to merely linear feasibility problems by forming large-scale overdetermined linear systems -- thus removing the need for handling costly optimization constraints and objectives. To make the proposed computational cost savings achievable, we offer enhanced randomized Kaczmarz algorithms to solve these highly overdetermined feasibility problems and provide theoretical guarantees in terms of their convergence, sample size requirements, and overall performance. Several numerical results are presented to illustrate the effectiveness of the proposed methodologies.

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arXiv2023

Moving Target Detection via Multi-IRS-Aided OFDM Radar

An intelligent reflecting surface (IRS) consists of passive reflective elements capable of altering impinging waveforms. The IRS-aided radar systems have recently been shown to improve detection and estimation performance by exploiting the target information collected via non-line-of-sight paths. However, the waveform design problem for an IRS-aided radar has remained relatively unexplored. In this paper, we consider a multi-IRS-aided orthogonal frequency-division multiplexing (OFDM) radar and study the theoretically achievable accuracy of target detection. In addition, we jointly design the OFDM signal and IRS phase-shifts to optimize the target detection performance via an alternating optimization approach. To this end, we formulate the IRS phase-shift design problem as a unimodular bi-quadratic program which is tackled by a computationally cost-effective approach based on power-method-like iterations. Numerical experiments illustrate that our proposed joint design of IRS phase-shifts and the OFDM code improves the detection performance in comparison with conventional OFDM radar.

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arXiv2023

One-Bit Quadratic Compressed Sensing: From Sample Abundance to Linear Feasibility

One-bit quantization with time-varying sampling thresholds has recently found significant utilization potential in statistical signal processing applications due to its relatively low power consumption and low implementation cost. In addition to such advantages, an attractive feature of one-bit analog-to-digital converters (ADCs) is their superior sampling rates as compared to their conventional multi-bit counterparts. This characteristic endows one-bit signal processing frameworks with what we refer to as sample abundance. On the other hand, many signal recovery and optimization problems are formulated as (possibly non-convex) quadratic programs with linear feasibility constraints in the one-bit sampling regime. We demonstrate, with a particular focus on quadratic compressed sensing, that the sample abundance paradigm allows for the transformation of such quadratic problems to merely a linear feasibility problem by forming a large-scale overdetermined linear system; thus removing the need for costly optimization constraints and objectives. To efficiently tackle the emerging overdetermined linear feasibility problem, we further propose an enhanced randomized Kaczmarz algorithm, called Block SKM. Several numerical results are presented to illustrate the effectiveness of the proposed methodologies.

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arXiv2023

Joint Waveform and Passive Beamformer Design in Multi-IRS-Aided Radar

Intelligent reflecting surface (IRS) technology has recently attracted a significant interest in non-light-of-sight radar remote sensing. Prior works have largely focused on designing single IRS beamformers for this problem. For the first time in the literature, this paper considers multi-IRS-aided multiple-input multiple-output (MIMO) radar and jointly designs the transmit unimodular waveforms and optimal IRS beamformers. To this end, we derive the Cramer-Rao lower bound (CRLB) of target direction-of-arrival (DoA) as a performance metric. Unimodular transmit sequences are the preferred waveforms from a hardware perspective. We show that, through suitable transformations, the joint design problem can be reformulated as two unimodular quadratic programs (UQP). To deal with the NP-hard nature of both UQPs, we propose unimodular waveform and beamforming design for multi-IRS radar (UBeR) algorithm that takes advantage of the low-cost power method-like iterations. Numerical experiments illustrate that the MIMO waveforms and phase shifts obtained from our UBeR algorithm are effective in improving the CRLB of DoA estimation.

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arXiv2023

Quantized Phase-Shift Design of Active IRS for Integrated Sensing and Communications

Integrated sensing and communications (ISAC) is a spectrum-sharing paradigm that allows different users to jointly utilize and access the crowded electromagnetic spectrum. In this context, intelligent reflecting surfaces (IRSs) have lately emerged as an enabler for non-line-of-sight (NLoS) ISAC. Prior IRS-aided ISAC studies assume passive surfaces and rely on the continuous-valued phase-shift model. In practice, the phase-shifts are quantized. Moreover, recent research has shown substantial performance benefits with active IRS. In this paper, we include these characteristics in our IRS-aided ISAC model to maximize the receive radar and communications signal-to-noise ratios (SNR) subjected to a unimodular IRS phase-shift vector and power budget. The resulting optimization is a highly non-convex unimodular quartic optimization problem. We tackle this problem via a bi-quadratic transformation to split the design into two quadratic sub-problems that are solved using the power iteration method. The proposed approach employs the M-ary unimodular sequence design via relaxed power method-like iteration (MaRLI) to design the quantized phase-shifts. Numerical experiments employ continuous-valued phase shifts as a benchmark and demonstrate that our active-IRS-aided ISAC design with MaRLI converges to a higher value of SNR with an increase in the number of IRS quantization bits.

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