arXiv subjects

Ignacio Rozada

Publications and source records attributed to Ignacio Rozada.

9 recordsLinked to original sources

arXiv2026

Performance of QUBO-Formulated MIMO Detection Under Hardware Precision Constraints

The evolution of multiple-input, multiple-output (MIMO) systems requires the efficient detection algorithms to overcome the exponential computational complexity of optimal maximum likelihood detection. Reformulating MIMO detection as a quadratic unconstrained binary optimization (QUBO) problem enables the use of highly parallel, physics-inspired, hardware-accelerated solvers and non-von Neumann architectures. However, embedding continuous-valued QUBO coefficients into hardware introduces quantization noise due to finite precision, which can severely degrade detection accuracy. This paper presents a rigorous analysis of the performance impact of finite-precision, hardware-accelerated QUBO solvers in MIMO detection. We analytically derive the probability distribution functions of the QUBO matrix entries and introduce novel homogeneous and heterogeneous quantization schemes based on either instantaneous channel state information or its statistical features. We further derive a sufficient condition on the precision required to maintain the optimal solution after quantization. Extensive numerical experiments, across various MIMO system sizes and modulation orders (up to 256-QAM), show that heterogeneous quantization matches the full-precision baseline bit error rate using significantly fewer bits than homogeneous approaches. We provide hardware-aware guidelines for selecting the optimal quantization strategy.

cs.IT↗

arXiv2025

Accelerating Hybrid XOR$-$CNF Boolean Satisfiability Problems Natively with In-Memory Computing

The Boolean satisfiability (SAT) problem is a computationally challenging decision problem central to many industrial applications. For SAT problems in cryptanalysis, circuit design, and telecommunication, solutions can often be found more efficiently by representing them with a combination of exclusive OR (XOR) and conjunctive normal form (CNF) clauses. We propose a hardware accelerator architecture that natively embeds and solves such hybrid XOR--CNF problems using in-memory computing hardware. To achieve this, we introduce an algorithm and demonstrate, both experimentally and through simulations, how it can be efficiently implemented with memristor crossbar arrays. Compared to the conventional approaches that translate XOR--CNF problems to pure CNF problems, our simulations show that the accelerator improves computation speed, energy efficiency, and chip area utilization of in-memory accelerators by $\sim$10$\times$ for a set of hard cryptographic benchmarking problems. Moreover, the accelerator achieves a $\sim$10$\times$ speedup and a $\sim$1000$\times$ gain in energy efficiency over state-of-the-art SAT solvers running on CPUs.

cs.ET↗

arXiv2025

A Statistical Analysis for Per-Instance Evaluation of Stochastic Optimizers: Avoiding Unreliable Conclusions

A key trait of stochastic optimizers is that multiple runs of the same optimizer in attempting to solve the same problem can produce different results. As a result, their performance is evaluated over several repeats, or runs, on the problem. However, the accuracy of the estimated performance metrics depends on the number of runs and should be studied using statistical tools. We present a statistical analysis of the common metrics, and develop guidelines for experiment design to measure the optimizer's performance using these metrics to a high level of confidence and accuracy. To this end, we first discuss the confidence interval of the metrics and how they are related to the number of runs of an experiment. We then derive a lower bound on the number of repeats in order to guarantee achieving a given accuracy in the metrics. Using this bound, we propose an algorithm to adaptively adjust the number of repeats needed to ensure the accuracy of the evaluated metric. Our simulation results demonstrate the utility of our analysis and how it allows us to conduct reliable benchmarking as well as hyperparameter tuning and prevent us from drawing premature conclusions regarding the performance of stochastic optimizers.

cs.LG↗

arXiv2025

Hardware-Compatible Single-Shot Feasible-Space Heuristics for Solving the Quadratic Assignment Problem

Research into the development of special-purpose computing architectures designed to solve quadratic unconstrained binary optimization (QUBO) problems has flourished in recent years. It has been demonstrated in the literature that such special-purpose solvers can outperform traditional complementary metal--oxide--semiconductor architectures by orders of magnitude with respect to timing metrics on synthetic problems. However, they face challenges with constrained problems such as the quadratic assignment problem (QAP), where mapping to binary formulations such as QUBO introduces overhead and limits parallelism. In-memory computing (IMC) devices, such as memristor-based analog Ising machines, offer significant speed-ups and efficiency gains over traditional CPU-based solvers, particularly for solving combinatorial optimization problems. In this work, we present a novel hardware-aware QAP optimization framework designed for IMC hardware. By co-designing the local search heuristic with the underlying hardware, we exploit the intrinsic massive parallelism that allows for computing of full neighbourhoods simultaneously to make update decisions. We ensure binary solutions remain feasible by selecting local moves that lead to neighbouring feasible solutions, leveraging feasible-space search heuristics and the underlying structure of a given problem. Our approach is compatible with both digital computers and analog hardware. We demonstrate its effectiveness in CPU implementations by comparing it with state-of-the-art heuristics for solving the QAP.

math.OC↗

arXiv2025

Solving Boolean satisfiability problems with resistive content addressable memories

Solving optimization problems is a highly demanding workload requiring high-performance computing systems. Optimization solvers are usually difficult to parallelize in conventional digital architectures, particularly when stochastic decisions are involved. Recently, analog computing architectures for accelerating stochastic optimization solvers have been presented, but they were limited to academic problems in quadratic polynomial format. Here we present KLIMA, a k-Local In-Memory Accelerator with resistive Content Addressable Memories (CAMs) and Dot-Product Engines (DPEs) to accelerate the solution of high-order industry-relevant optimization problems, in particular Boolean Satisfiability. By co-designing the optimization heuristics and circuit architecture we improve the speed and energy to solution up to 182x compared to the digital state of the art.

cs.ET↗

arXiv2024

Parallel Tempering-Inspired Distributed Binary Optimization with In-Memory Computing

In-memory computing (IMC) has been shown to be a promising approach for solving binary optimization problems while significantly reducing energy and latency. Building on the advantages of parallel computation, we propose an IMC-compatible parallelism framework based on the physics-inspired parallel tempering (PT) algorithm, enabling cross-replica communication to improve the performance of IMC solvers. This framework enables an IMC solver not only to improve performance beyond what can be achieved through parallelization, but also affords greater flexibility for the search process with low hardware overhead. We justify that the framework can be applied to almost any IMC solver. We demonstrate the effectiveness of the framework for the Boolean satisfiability (SAT) problem, using the WalkSAT heuristic as a proxy for existing IMC solvers. The resulting PT-inspired cooperative WalkSAT (PTIC-WalkSAT) algorithm outperforms the standard WalkSAT heuristic in terms of the iterations-to-solution in 84.0% of the tested problem instances and its na\"ive parallel variant (PA-WalkSAT) does so in 64.9% of the instances, and with a higher success rate in the majority of instances. An estimate of the energy overhead of the PTIC framework for two hardware accelerator architectures indicates that in both cases the overhead of running the PTIC framework would be less than 1% of the total energy required to run each accelerator.

cs.ET↗

arXiv2022

Automated Design of Pulse Sequences for Magnetic Resonance Fingerprinting using Physics-Inspired Optimization

Magnetic Resonance Fingerprinting (MRF) is a method to extract quantitative tissue properties such as T1 and T2 relaxation rates from arbitrary pulse sequences using conventional magnetic resonance imaging hardware. MRF pulse sequences have thousands of tunable parameters which can be chosen to maximize precision and minimize scan time. Here we perform de novo automated design of MRF pulse sequences by applying physics-inspired optimization heuristics. Our experimental data suggests systematic errors dominate over random errors in MRF scans under clinically-relevant conditions of high undersampling. Thus, in contrast to prior optimization efforts, which focused on statistical error models, we use a cost function based on explicit first-principles simulation of systematic errors arising from Fourier undersampling and phase variation. The resulting pulse sequences display features qualitatively different from previously used MRF pulse sequences and achieve fourfold shorter scan time than prior human-designed sequences of equivalent precision in T1 and T2. Furthermore, the optimization algorithm has discovered the existence of MRF pulse sequences with intrinsic robustness against shading artifacts due to phase variation.

physics.med-ph↗

arXiv2021

A Fast MR Fingerprinting Simulator for Direct Error Estimation and Sequence Optimization

MR Fingerprinting is a novel quantitative MR technique that could simultaneously provide multiple tissue property maps. When optimizing MRF scans, modeling undersampling errors and field imperfections in cost functions will make the optimization results more practical and robust. However, this process is computationally expensive and impractical for sequence optimization algorithms when MRF signal evolutions need to be generated for each optimization iteration. Here, we introduce a fast MRF simulator to simulate aliased images from actual scan scenarios including undersampling and system imperfections, which substantially reduces computational time and allows for direct error estimation and efficient sequence optimization. By constraining the total number of tissues present in a brain phantom, MRF signals from highly undersampled scans can be simulated as the product of the spatial response functions based on sampling patterns and sequence-dependent temporal functions. During optimization, the spatial response function is independent of sequence design and does not need to be recalculated. We evaluate the performance and computational speed of the proposed approach by simulations and in vivo experiments. We also demonstrate the power of applying the simulator in MRF sequence optimization. The simulation results from the proposed method closely approximate the signals and MRF maps from in vivo scans, with 158 times shorter processing time than the conventional simulation method using Non-uniform Fourier transform. Incorporating the proposed simulator in the MRF optimization framework makes direct estimation of undersampling errors during the optimization process feasible, and provide optimized MRF sequences that are robust against undersampling factors and system inhomogeneity.

eess.IV↗

arXiv2019

Effects of setting the temperatures in the parallel tempering Monte Carlo algorithm

Parallel tempering Monte Carlo has proven to be an efficient method in optimization and sampling applications. Having an optimized temperature set enhances the efficiency of the algorithm through more-frequent replica visits to the temperature limits. The approaches for finding an optimal temperature set can be divided into two main categories. The methods of the first category distribute the replicas such that the swapping ratio between neighbouring replicas is constant and independent of the temperature values. The second-category techniques including the feedback-optimized method, on the other hand, aim for a temperature distribution that has higher density at simulation bottlenecks, resulting in temperature-dependent replica-exchange probabilities. In this paper, we compare the performance of various temperature setting methods on both sparse and fully-connected spin-glass problems as well as fully-connected Wishart problems that have planted solutions. These include two classes of problems that have either continuous or discontinuous phase transitions in the order parameter. Our results demonstrate that there is no performance advantage for the methods that promote nonuniform swapping probabilities on spin-glass problems where the order parameter has a smooth transition between phases at the critical temperature. However, on Wishart problems that have a first-order phase transition at low temperatures, the feedback-optimized method exhibits a time-to-solution speedup of at least a factor of two over the other approaches.

physics.comp-ph↗