arXiv subjects

Ozgur Yilmaz

Publications and source records attributed to Ozgur Yilmaz.

At least 19 recordsLinked to original sources

arXiv2026

CableTract: A Co-Designed Cable-Driven Field Robot for Low-Compaction, Off-Grid Capable Agriculture

Conventional field operations spend most of their energy moving the tractor body, not the implement. Yet feasibility studies for novel agricultural vehicles rarely tie mechanics, energy harvest, draft, field geometry, economics, life-cycle CO2, and uncertainty quantification together on a single reproducible code path. This paper builds such a framework and applies it to CableTract, a two-module cable-driven field robot. A stationary Main Unit (winch + motor + battery + harvester module) (MU) and a lighter Anchor module (held by helical screw piles) tension a cable across a strip while a lightweight implement carriage rolls along it. The heavy bodies stay on the headland; only the carriage enters the field. The carriage runs a 10-implement library co-designed for the cable architecture. This co-design is the paper's central analytical lever. The framework is prototype-free. It chains a catenary cable model, a drivetrain efficiency chain, a stochastic draft model fitted to the co-designed library, an hourly solar + wind + battery simulator on six sites, a polygon coverage planner on a 50-field corpus, a contact-pressure compaction model, a discounted cash-flow economics engine with battery replacement and life-cycle CO2, and a global sensitivity analysis on 20 inputs. An operating-envelope sweep and an architectural-variant comparison close the loop. The full implementation is open source. Applied to the codesigned reference, the framework yields energy, compaction advantages and potential off-grid operation.

cs.RO↗

arXiv2026

ArrowFlow: Hierarchical Machine Learning in the Space of Permutations

We introduce ArrowFlow, a machine learning architecture that operates entirely in the space of permutations. Its computational units are ranking filters, learned orderings that compare inputs via Spearman's footrule distance and update through permutation-matrix accumulation, a non-gradient rule rooted in displacement evidence. Layers compose hierarchically: each layer's output ranking becomes the next layer's input, enabling deep ordinal representation learning without any floating-point parameters in the core computation. We connect the architecture to Arrow's impossibility theorem, showing that violations of social-choice fairness axioms (context dependence, specialization, symmetry breaking) serve as inductive biases for nonlinearity, sparsity, and stability. Experiments span UCI tabular benchmarks, MNIST, gene expression cancer classification (TCGA), and preference data, all against GridSearchCV-tuned baselines. ArrowFlow beats all baselines on Iris (2.7% vs. 3.3%) and is competitive on most UCI datasets. A single parameter, polynomial degree, acts as a master switch: degree 1 yields noise robustness (8-28% less degradation), privacy preservation (+0.5pp cost), and missing-feature resilience; higher degrees trade these for improved clean accuracy. ArrowFlow is not designed to surpass gradient-based methods. It is an existence proof that competitive classification is possible in a fundamentally different computational paradigm, one that elevates ordinal structure to a first-class citizen, with natural alignment to integer-only and neuromorphic hardware.

cs.LG↗

arXiv2026

Partially deterministic sampling for compressed sensing with denoising guarantees

We study compressed sensing when the sampling vectors are chosen from the rows of a unitary matrix. In the literature, these sampling vectors are typically chosen randomly; the use of randomness has enabled major empirical and theoretical advances in the field. However, in practice there are often certain crucial sampling vectors, in which case practitioners will depart from the theory and sample such rows deterministically. In this work, we derive an optimized sampling scheme for Bernoulli selectors which naturally combines random and deterministic selection of rows, thus rigorously deciding which rows should be sampled deterministically. This sampling scheme provides measurable improvements in image compressed sensing for both generative and sparse priors when compared to with-replacement and without-replacement sampling schemes, as we show with theoretical results and numerical experiments. Additionally, our theoretical guarantees feature improved sample complexity bounds compared to previous works, and novel denoising guarantees in this setting.

cs.IT↗

arXiv2025

Denoising guarantees for optimized sampling schemes in compressed sensing

Compressed sensing with subsampled unitary matrices benefits from \emph{optimized} sampling schemes, which feature improved theoretical guarantees and empirical performance relative to uniform subsampling. We provide, in a first of its kind in compressed sensing, theoretical guarantees showing that the error caused by the measurement noise vanishes with an increasing number of measurements for optimized sampling schemes, assuming that the noise is Gaussian. We moreover provide similar guarantees for measurements sampled with-replacement with arbitrary probability weights. All our results hold on prior sets contained in a union of low-dimensional subspaces. Finally, we demonstrate that this denoising behavior appears in empirical experiments with a rate that closely matches our theoretical guarantees when the prior set is the range of a generative ReLU neural network and when it is the set of sparse vectors.

stat.ML↗

arXiv2023

Model-adapted Fourier sampling for generative compressed sensing

We study generative compressed sensing when the measurement matrix is randomly subsampled from a unitary matrix (with the DFT as an important special case). It was recently shown that $\textit{O}(kdn\| \boldsymbolα\|_{\infty}^{2})$ uniformly random Fourier measurements are sufficient to recover signals in the range of a neural network $G:\mathbb{R}^k \to \mathbb{R}^n$ of depth $d$, where each component of the so-called local coherence vector $\boldsymbolα$ quantifies the alignment of a corresponding Fourier vector with the range of $G$. We construct a model-adapted sampling strategy with an improved sample complexity of $\textit{O}(kd\| \boldsymbolα\|_{2}^{2})$ measurements. This is enabled by: (1) new theoretical recovery guarantees that we develop for nonuniformly random sampling distributions and then (2) optimizing the sampling distribution to minimize the number of measurements needed for these guarantees. This development offers a sample complexity applicable to natural signal classes, which are often almost maximally coherent with low Fourier frequencies. Finally, we consider a surrogate sampling scheme, and validate its performance in recovery experiments using the CelebA dataset.

cs.IT↗

arXiv2023

Artificial intelligence as a gateway to scientific discovery: Uncovering features in retinal fundus images

Purpose: Convolutional neural networks can be trained to detect various conditions or patient traits based on retinal fundus photographs, some of which, such as the patient sex, are invisible to the expert human eye. Here we propose a methodology for explainable classification of fundus images to uncover the mechanism(s) by which CNNs successfully predict the labels. We used patient sex as a case study to validate our proposed methodology. Approach: First, we used a set of 4746 fundus images, including training, validation and test partitions, to fine-tune a pre-trained CNN on the sex classification task. Next, we utilized deep learning explainability tools to hypothesize possible ways sex differences in the retina manifest. We measured numerous retinal properties relevant to our hypotheses through image segmentation to identify those significantly different between males and females. To tackle the multiple comparisons problem, we shortlisted the parameters by testing them on a set of 100 fundus images distinct from the images used for fine-tuning. Finally, we used an additional 400 images, not included in any previous set, to reveal significant sex differences in the retina. Results: We observed that the peripapillary area is darker in males compared to females ($p=.023, d=.243$). We also observed that males have richer retinal vasculature networks by showing a higher number of branches ($p=.016, d=.272$) and nodes ($p=.014, d=.299$) and a larger total length of branches ($p=.045, d=.206$) in the vessel graph. Also, vessels cover a greater area in the superior temporal quadrant of the retina in males compared to females ($p=0.048, d=.194$). Conclusions: Our methodology reveals retinal features in fundus photographs that allow CNNs to predict traits currently unknown, but meaningful to experts.

cs.CV↗

arXiv2020

NBIHT: An Efficient Algorithm for 1-bit Compressed Sensing with Optimal Error Decay Rate

The Binary Iterative Hard Thresholding (BIHT) algorithm is a popular reconstruction method for one-bit compressed sensing due to its simplicity and fast empirical convergence. There have been several works about BIHT but a theoretical understanding of the corresponding approximation error and convergence rate still remains open. This paper shows that the normalized version of BIHT (NBHIT) achieves an approximation error rate optimal up to logarithmic factors. More precisely, using $m$ one-bit measurements of an $s$-sparse vector $x$, we prove that the approximation error of NBIHT is of order $O \left(1 \over m \right)$ up to logarithmic factors, which matches the information-theoretic lower bound $Ω\left(1 \over m \right)$ proved by Jacques, Laska, Boufounos, and Baraniuk in 2013. To our knowledge, this is the first theoretical analysis of a BIHT-type algorithm that explains the optimal rate of error decay empirically observed in the literature. This also makes NBIHT the first provable computationally-efficient one-bit compressed sensing algorithm that breaks the inverse square root error decay rate $O \left(1 \over m^{1/2} \right)$.

cs.IT↗

arXiv2020

Memoryless scalar quantization for random frames

Memoryless scalar quantization (MSQ) is a common technique to quantize frame coefficients of signals (which are used as a model for generalized linear samples), making them compatible with our digital technology. The process of quantization is generally not invertible, and thus one can only recover an approximation to the original signal from its quantized coefficients. The non-linear nature of quantization makes the analysis of the corresponding approximation error challenging, often resulting in the use of a simplifying assumption, called the "white noise hypothesis" (WNH) that simplifies this analysis. However, the WNH is known to be not rigorous and, at least in certain cases, not valid. Given a fixed, deterministic signal, we assume that we use a random frame, whose analysis matrix has independent isotropic sub-Gaussian rows, to collect the measurements, which are consecutively quantized via MSQ. For this setting, the numerically observed decay rate seems to agree with the prediction by the WNH. We rigorously establish sharp non-asymptotic error bounds without using the WNH that explains the observed decay rate. Furthermore, we show that the reconstruction error does not necessarily diminish as redundancy increases. We also extend this approach to the compressed sensing setting, obtaining rigorous error bounds that agree with empirical observations, again, without resorting to the WNH.

math.NA↗

arXiv2019

RIP constants for deterministic compressed sensing matrices-beyond Gershgorin

Compressed sensing (CS) is a signal acquisition paradigm to simultaneously acquire and reduce dimension of signals that admit sparse representations. This is achieved by collecting linear, non-adaptive measurements of a signal, which can be formalized as multiplying the signal with a "measurement matrix". If the measurement satisfies the so-called restricted isometry property (RIP), then it will be appropriate to be used in compressed sensing. While a wide class of random matrices provably satisfy the RIP with high probability, explicit and deterministic constructions have been shown (so far) to satisfy the RIP only in a significantly suboptimal regime. In this paper, we propose two novel approaches for improving the RIP constant estimates based on Gershgorin circle theorem for a specific deterministic construction based on Paley tight frames, obtaining an improvement over the Gershgorin bound by a multiplicative constant. In one approach we use a recent result on the spectra of the skew-adjacency matrices of oriented graphs. In the other approach, we use the so-called Dembo bounds on the extreme eigenvalues of a positive semidefinite Hermitian matrix. We also generalize these bounds and we combine the new bounds with a conjecture we make regarding the distribution of quadratic residues in a finite field to provide a potential path to break the so-called "square-root barrier"-we provide a proof based on the assumption that the conjecture holds.

cs.IT↗

arXiv2019

Deterministic partial binary circulant compressed sensing matrices

Compressed sensing (CS) is a signal acquisition paradigm to simultaneously acquire and reduce dimension of signals that admit sparse representation. This is achieved by collecting linear, non-adaptive measurements of a signal, which can be formalized as multiplying the signal with a "measurement matrix". Most of matrices used in CS are random matrices as they satisfy the restricted isometry property (RIP) in an optimal regime of number of measurements with high probability. However, these matrices have their own caveats and for this reason, deterministic measurement matrices have been proposed. While there is a wide classes of deterministic matrices in the literature, we propose a novel class of deterministic matrices using the Legendre symbol. This construction has a simple structure, it enjoys being a binary matrix, and having a partial circulant structure which provides a fast matrix-vector multiplication and a fast reconstruction algorithm. We will derive a bound on the sparsity level of signals that can be measured (and be reconstructed) with this class of matrices. We perform quantization using these matrices, and we verify the performance of these matrices (and compare with other existing constructions) numerically.

cs.IT↗

arXiv2019

On one-stage recovery for $ΣΔ$-quantized compressed sensing

Compressed sensing (CS) is a signal acquisition paradigm to simultaneously acquire and reduce dimension of signals that admit sparse representations. When such a signal is acquired according to the principles of CS, the measurements still take on values in the continuum. In today's "digital" world, a subsequent quantization step, where these measurements are replaced with elements from a finite set is crucial. We focus on one of the approaches that yield efficient quantizers for CS: $ΣΔ$ quantization, followed by a one-stage tractable reconstruction method, which was developed by Saab et al. with theoretical error guarantees in the case of sub-Gaussian matrices. We propose two alternative approaches that extend this result to a wider class of measurement matrices including (certain unitary transforms of) partial bounded orthonormal systems and deterministic constructions based on chirp sensing matrices.

cs.IT↗

arXiv2019

U-CATCH: Using Color ATtribute of image patCHes in binary descriptors

In this study, we propose a simple yet very effective method for extracting color information through binary feature description framework. Our method expands the dimension of binary comparisons into RGB and YCbCr spaces, showing more than 100% matching improve ment compared to non-color binary descriptors for a wide range of hard-to-match cases. The proposed method is general and can be applied to any binary descriptor to make it color sensitive. It is faster than classical binary descriptors for RGB sampling due to the abandonment of grayscale conversion and has almost identical complexity (insignificant compared to smoothing operation) for YCbCr sampling.

cs.CV↗

arXiv2018

Learning tensors from partial binary measurements

In this paper we generalize the 1-bit matrix completion problem to higher order tensors. We prove that when $r=O(1)$ a bounded rank-$r$, order-$d$ tensor $T$ in $\mathbb{R}^{N} \times \mathbb{R}^{N} \times \cdots \times \mathbb{R}^{N}$ can be estimated efficiently by only $m=O(Nd)$ binary measurements by regularizing its max-qnorm and M-norm as surrogates for its rank. We prove that similar to the matrix case, i.e., when $d=2$, the sample complexity of recovering a low-rank tensor from 1-bit measurements of a subset of its entries is the same as recovering it from unquantized measurements. Moreover, we show the advantage of using 1-bit tensor completion over matricization both theoretically and numerically. Specifically, we show how the 1-bit measurement model can be used for context-aware recommender systems.

math.ST↗

arXiv2017

Multi-View Product Image Search Using Deep ConvNets Representations

Multi-view product image queries can improve retrieval performance over single view queries significantly. In this paper, we investigated the performance of deep convolutional neural networks (ConvNets) on multi-view product image search. First, we trained a VGG-like network to learn deep ConvNets representations of product images. Then, we computed the deep ConvNets representations of database and query images and performed single view queries, and multi-view queries using several early and late fusion approaches. We performed extensive experiments on the publicly available Multi-View Object Image Dataset (MVOD 5K) with both clean background queries from the Internet and cluttered background queries from a mobile phone. We compared the performance of ConvNets to the classical bag-of-visual-words (BoWs). We concluded that (1) multi-view queries with deep ConvNets representations perform significantly better than single view queries, (2) ConvNets perform much better than BoWs and have room for further improvement, (3) pre-training of ConvNets on a different image dataset with background clutter is needed to obtain good performance on cluttered product image queries obtained with a mobile phone.

cs.CV↗

arXiv2015

Classification of Occluded Objects using Fast Recurrent Processing

Recurrent neural networks are powerful tools for handling incomplete data problems in computer vision, thanks to their significant generative capabilities. However, the computational demand for these algorithms is too high to work in real time, without specialized hardware or software solutions. In this paper, we propose a framework for augmenting recurrent processing capabilities into a feedforward network without sacrificing much from computational efficiency. We assume a mixture model and generate samples of the last hidden layer according to the class decisions of the output layer, modify the hidden layer activity using the samples, and propagate to lower layers. For visual occlusion problem, the iterative procedure emulates feedforward-feedback loop, filling-in the missing hidden layer activity with meaningful representations. The proposed algorithm is tested on a widely used dataset, and shown to achieve 2$\times$ improvement in classification accuracy for occluded objects. When compared to Restricted Boltzmann Machines, our algorithm shows superior performance for occluded object classification.

cs.CV↗

arXiv2015

Connectionist-Symbolic Machine Intelligence using Cellular Automata based Reservoir-Hyperdimensional Computing

We introduce a novel framework of reservoir computing, that is capable of both connectionist machine intelligence and symbolic computation. Cellular automaton is used as the reservoir of dynamical systems. Input is randomly projected onto the initial conditions of automaton cells and nonlinear computation is performed on the input via application of a rule in the automaton for a period of time. The evolution of the automaton creates a space-time volume of the automaton state space, and it is used as the reservoir. The proposed framework is capable of long short-term memory and it requires orders of magnitude less computation compared to Echo State Networks. We prove that cellular automaton reservoir holds a distributed representation of attribute statistics, which provides a more effective computation than local representation. It is possible to estimate the kernel for linear cellular automata via metric learning, that enables a much more efficient distance computation in support vector machine framework. Also, binary reservoir feature vectors can be combined using Boolean operations as in hyperdimensional computing, paving a direct way for concept building and symbolic processing.

cs.ET↗

arXiv2015

Sparse regression with highly correlated predictors

We consider a linear regression $y=Xβ+u$ where $X\in\mathbb{\mathbb{R}}^{n\times p}$, $p\gg n,$ and $β$ is $s$-sparse. Motivated by examples in financial and economic data, we consider the situation where $X$ has highly correlated and clustered columns. To perform sparse recovery in this setting, we introduce the \emph{clustering removal algorithm} (CRA), that seeks to decrease the correlation in $X$ by removing the cluster structure without changing the parameter vector $β$. We show that as long as certain assumptions hold about $X$, the decorrelated matrix will satisfy the restricted isometry property (RIP) with high probability. We also provide examples of the empirical performance of CRA and compare it with other sparse recovery techniques.

cs.IT↗

arXiv2015

Quantization of compressive samples with stable and robust recovery

In this paper we study the quantization stage that is implicit in any compressed sensing signal acquisition paradigm. We propose using Sigma-Delta quantization and a subsequent reconstruction scheme based on convex optimization. We prove that the reconstruction error due to quantization decays polynomially in the number of measurements. Our results apply to arbitrary signals, including compressible ones, and account for measurement noise. Additionally, they hold for sub-Gaussian (including Gaussian and Bernoulli) random compressed sensing measurements, as well as for both high bit-depth and coarse quantizers, and they extend to 1-bit quantization. In the noise-free case, when the signal is strictly sparse we prove that by optimizing the order of the quantization scheme one can obtain root-exponential decay in the reconstruction error due to quantization.

cs.IT↗