arXiv subjects

Satoshi Takabe

Publications and source records attributed to Satoshi Takabe.

At least 19 recordsLinked to original sources

arXiv2026

Slack-Free Deep-Unfolded Combinatorial Optimization Solver for Inequality Constraints

Quantum annealing (QA) is used to solve combinatorial optimization problems (COPs). When COPs are implemented on quantum annealers, they are typically encoded as quadratic unconstrained binary optimization (QUBO) problems, but constraint encodings often increase the number of qubits and the embedding overhead. This issue is particularly important for COPs with inequality constraints, where standard slack-variable formulations introduce additional binary variables. Unbalanced penalization (UP) avoids slack variables, but the original UP formulation requires tuning two penalty coefficients and contains a squared residual term that can increase the number of quadratic couplings. In this paper, we propose the unbalanced penalization Ohzeki method (UPOM), which combines UP with the Ohzeki method for inequality-constrained COPs. UPOM replaces the two static penalty coefficients of original UP with an auxiliary-variable update and removes the squared residual term from the Hamiltonian used for sampling. We further propose the deep-unfolded unbalanced penalization Ohzeki method (DU-UPOM), which learns the step-size schedule of the UPOM update from training instances. Numerical experiments on random knapsack problems show that UPOM improves over original UP and that DU-UPOM reaches optimal solutions in fewer iterations than fixed-step UPOM and other baseline. These results demonstrate that the proposed framework reduces the tuning and embedding burdens of UP while making the Ohzeki method trainable for inequality constraints.

quant-ph↗

arXiv2026

Physics-Aware Linearized ADMM and Its Unrolling

Recently, partial differential equations (PDEs) have been used to directly model the measurement process in signal processing, although their evaluation is costly. In this paper, we propose a novel alternating direction method of multipliers (ADMM)-based algorithm called physics-aware linearized ADMM (PA-LADMM) for inverse problems from PDE-based measurement processes. The key idea is the linearization of the subproblem with PDEs, leading to a cost-efficient update rule that calls only a PDE solver and its gradient evaluation per iteration. The algorithm has a theoretical convergence guarantee under certain conditions. In addition, we combine it with deep unfolding to unroll the PA-LADMM and train its internal parameters using supervised data. Two distinct experiments, compressed sensing with optical fiber communication and image restoration from noisy anisotropic diffusion, demonstrated the effectiveness of the proposed algorithms.

eess.SP↗

arXiv2026

Refined Gradient-Based Temperature Optimization for the Replica-Exchange Monte-Carlo Method

The replica-exchange Monte-Carlo (RXMC) method is a powerful Markov-chain Monte-Carlo algorithm for sampling from multi-modal distributions, which are challenging for conventional methods. The sampling efficiency of the RXMC method depends highly on the selection of the temperatures, and finding optimal temperatures remains a challenge. In this study, we propose a refined online temperature selection method by extending the gradient-based optimization framework proposed previously. Building upon the existing temperature update approach, we introduce a reparameterization technique to strictly enforce physical constraints, such as the monotonic ordering of inverse temperatures, which were not explicitly addressed in the original formulation. The proposed method defines the variance of acceptance rates between adjacent replicas as a loss function, estimates its gradient using differential information from the sampling process, and optimizes the temperatures via gradient descent. We demonstrate the effectiveness of our method through experiments on benchmark spin systems, including the two-dimensional ferromagnetic Ising model, the two-dimensional ferromagnetic XY model, and the three-dimensional Edwards-Anderson model. Our results show that the method successfully achieves uniform acceptance rates and reduces round-trip times across the temperature space. Furthermore, our proposed method offers a significant advantage over recently proposed policy gradient method that require careful hyperparameter tuning, while simultaneously preventing the constraint violations that destabilize optimization.

physics.comp-ph↗

arXiv2025

Transfer Learning for Deep-Unfolded Combinatorial Optimization Solver with Quantum Annealer

Quantum annealing (QA) has attracted research interest as a sampler and combinatorial optimization problem (COP) solver. A recently proposed sampling-based solver for QA significantly reduces the required number of qubits, being capable of large COPs. In relation to this, a trainable sampling-based COP solver has been proposed that optimizes its internal parameters from a dataset by using a deep learning technique called deep unfolding. Although learning the internal parameters accelerates the convergence speed, the sampler in the trainable solver is restricted to using a classical sampler owing to the training cost. In this study, to utilize QA in the trainable solver, we propose classical-quantum transfer learning, where parameters are trained classically, and the trained parameters are used in the solver with QA. The results of numerical experiments demonstrate that the trainable quantum COP solver using classical-quantum transfer learning improves convergence speed and execution time over the original solver.

quant-ph↗

arXiv2024

Deep Unfolded Local Quantum Annealing

Local quantum annealing (LQA), an iterative algorithm, is designed to solve combinatorial optimization problems. It draws inspiration from QA, which utilizes adiabatic time evolution to determine the global minimum of a given objective function. In the original LQA, the classical Hamiltonian is minimized via gradient descent. The performance of LQA depends on the choice of the parameters. Owing to the non-convex nature of the original cost function, LQA often becomes trapped in local minima, limiting its effectiveness. To address this challenge, we combine LQA with a deep unfolding scheme, which enables us to tune the parameters from the training data via back-propagation. {As a demonstration, we apply the deep unfolded LQA to the Sherrington-Kirkpatrick model, which is a fundamental {model} in statistical physics.} Our findings exhibit that deep unfolded LQA outperforms the original LQA, exhibiting remarkable convergence speed and performance improvement. As the trained parameters can be generalized to unknown instances and different system sizes, our results have significant practical implications and provide valuable insights for real-world applications.

quant-ph↗

arXiv2024

Accelerating Convergence of Stein Variational Gradient Descent via Deep Unfolding

Stein variational gradient descent (SVGD) is a prominent particle-based variational inference method used for sampling a target distribution. SVGD has attracted interest for application in machine-learning techniques such as Bayesian inference. In this paper, we propose novel trainable algorithms that incorporate a deep-learning technique called deep unfolding,into SVGD. This approach facilitates the learning of the internal parameters of SVGD, thereby accelerating its convergence speed. To evaluate the proposed trainable SVGD algorithms, we conducted numerical simulations of three tasks: sampling a one-dimensional Gaussian mixture, performing Bayesian logistic regression, and learning Bayesian neural networks. The results show that our proposed algorithms exhibit faster convergence than the conventional variants of SVGD.

cs.LG↗

arXiv2024

Convergence Acceleration of Markov Chain Monte Carlo-based Gradient Descent by Deep Unfolding

This study proposes a trainable sampling-based solver for combinatorial optimization problems (COPs) using a deep-learning technique called deep unfolding. The proposed solver is based on the Ohzeki method that combines Markov-chain Monte-Carlo (MCMC) and gradient descent, and its step sizes are trained by minimizing a loss function. In the training process, we propose a sampling-based gradient estimation that substitutes auto-differentiation with a variance estimation, thereby circumventing the failure of back propagation due to the non-differentiability of MCMC. The numerical results for a few COPs demonstrated that the proposed solver significantly accelerated the convergence speed compared with the original Ohzeki method.

cond-mat.dis-nn↗

arXiv2023

Deep Unfolded Simulated Bifurcation for Massive MIMO Signal Detection

Multiple-input multiple-output (MIMO) is a key ingredient of next-generation wireless communications. Recently, various MIMO signal detectors based on deep learning techniques and quantum(-inspired) algorithms have been proposed to improve the detection performance compared with conventional detectors. This paper focuses on the simulated bifurcation (SB) algorithm, a quantum-inspired algorithm. This paper proposes two techniques to improve its detection performance. The first is modifying the algorithm inspired by the Levenberg-Marquardt algorithm to eliminate local minima of maximum likelihood detection. The second is the use of deep unfolding, a deep learning technique to train the internal parameters of an iterative algorithm. We propose a deep-unfolded SB by making the update rule of SB differentiable. The numerical results show that these proposed detectors significantly improve the signal detection performance in massive MIMO systems.

cs.IT↗

arXiv2023

Hubbard-Stratonovich Detector for Simple Trainable MIMO Signal Detection

Massive multiple-input multiple-output (MIMO) is a key technology used in fifth-generation wireless communication networks and beyond. Recently, various MIMO signal detectors based on deep learning have been proposed. Especially, deep unfolding (DU), which involves unrolling of an existing iterative algorithm and embedding of trainable parameters, has been applied with remarkable detection performance. Although DU has a lesser number of trainable parameters than conventional deep neural networks, the computational complexities related to training and execution have been problematic because DU-based MIMO detectors usually utilize matrix inversion to improve their detection performance. In this study, we attempted to construct a DU-based trainable MIMO detector with the simplest structure. The proposed detector based on the Hubbard--Stratonovich (HS) transformation and DU is called the trainable HS (THS) detector. It requires only $O(1)$ trainable parameters and its training and execution cost is $O(n^2)$ per iteration, where $n$ is the number of transmitting antennas. Numerical results show that the detection performance of the THS detector is better than that of existing algorithms of the same complexity and close to that of a DU-based detector, which has higher training and execution costs than the THS detector.

cs.IT↗

arXiv2021

Proximal Decoding for LDPC-coded Massive MIMO Channels

We propose a novel optimization-based decoding algorithm for LDPC-coded massive MIMO channels. The proposed decoding algorithm is based on a proximal gradient method for solving an approximate maximum a posteriori (MAP) decoding problem. The key idea is the use of a code-constraint polynomial penalizing a vector far from a codeword as a regularizer in the approximate MAP objective function. The code proximal operator is naturally derived from code-constraint polynomials. The proposed algorithm, called proximal decoding, can be described by a simple recursion consisting of the gradient descent step for a negative log-likelihood function and the code proximal operation. Several numerical experiments show that the proposed algorithm outperforms known massive MIMO detection algorithms, such as an MMSE detector with belief propagation decoding.

cs.IT↗

arXiv2020

Acceleration of Cooperative Least Mean Square via Chebyshev Periodical Successive Over-Relaxation

A distributed algorithm for least mean square (LMS) can be used in distributed signal estimation and in distributed training for multivariate regression models. The convergence speed of an algorithm is a critical factor because a faster algorithm requires less communications overhead and it results in a narrower network bandwidth. The goal of this paper is to present that use of Chebyshev periodical successive over-relaxation (PSOR) can accelerate distributed LMS algorithms in a naturally manner. The basic idea of Chbyshev PSOR is to introduce index-dependent PSOR factors that control the spectral radius of a matrix governing the convergence behavior of the modified fixed-point iteration. Accelerations of convergence speed are empirically confirmed in a wide range of networks, such as known small graphs (e.g., Karate graph), and random graphs, such as Erdos-Renyi (ER) random graphs and Barabasi-Albert random graphs.

cs.IT↗

arXiv2020

Convergence Acceleration via Chebyshev Step: Plausible Interpretation of Deep-Unfolded Gradient Descent

Deep unfolding is a promising deep-learning technique, whose network architecture is based on expanding the recursive structure of existing iterative algorithms. Although convergence acceleration is a remarkable advantage of deep unfolding, its theoretical aspects have not been revealed yet. The first half of this study details the theoretical analysis of the convergence acceleration in deep-unfolded gradient descent (DUGD) whose trainable parameters are step sizes. We propose a plausible interpretation of the learned step-size parameters in DUGD by introducing the principle of Chebyshev steps derived from Chebyshev polynomials. The use of Chebyshev steps in gradient descent (GD) enables us to bound the spectral radius of a matrix governing the convergence speed of GD, leading to a tight upper bound on the convergence rate. The convergence rate of GD using Chebyshev steps is shown to be asymptotically optimal, although it has no momentum terms. We also show that Chebyshev steps numerically explain the learned step-size parameters in DUGD well. In the second half of the study, %we apply the theory of Chebyshev steps and Chebyshev-periodical successive over-relaxation (Chebyshev-PSOR) is proposed for accelerating linear/nonlinear fixed-point iterations. Theoretical analysis and numerical experiments indicate that Chebyshev-PSOR exhibits significantly faster convergence for various examples such as Jacobi method and proximal gradient methods.

cs.LG↗

arXiv2020

Deep Unfolded Multicast Beamforming

Multicast beamforming is a promising technique for multicast communication. Providing an efficient and powerful beamforming design algorithm is a crucial issue because multicast beamforming problems such as a max-min-fair problem are NP-hard in general. Recently, deep learning-based approaches have been proposed for beamforming design. Although these approaches using deep neural networks exhibit reasonable performance gain compared with conventional optimization-based algorithms, their scalability is an emerging problem for large systems in which beamforming design becomes a more demanding task. In this paper, we propose a novel deep unfolded trainable beamforming design with high scalability and efficiency. The algorithm is designed by expanding the recursive structure of an existing algorithm based on projections onto convex sets and embedding a constant number of trainable parameters to the expanded network, which leads to a scalable and stable training process. Numerical results show that the proposed algorithm can accelerate its convergence speed by using unsupervised learning, which is a challenging training process for deep unfolding.

cs.IT↗

arXiv2020

Theoretical Interpretation of Learned Step Size in Deep-Unfolded Gradient Descent

Deep unfolding is a promising deep-learning technique in which an iterative algorithm is unrolled to a deep network architecture with trainable parameters. In the case of gradient descent algorithms, as a result of the training process, one often observes the acceleration of the convergence speed with learned non-constant step size parameters whose behavior is not intuitive nor interpretable from conventional theory. In this paper, we provide a theoretical interpretation of the learned step size of deep-unfolded gradient descent (DUGD). We first prove that the training process of DUGD reduces not only the mean squared error loss but also the spectral radius related to the convergence rate. Next, we show that minimizing the upper bound of the spectral radius naturally leads to the Chebyshev step which is a sequence of the step size based on Chebyshev polynomials. The numerical experiments confirm that the Chebyshev steps qualitatively reproduce the learned step size parameters in DUGD, which provides a plausible interpretation of the learned parameters. Additionally, we show that the Chebyshev steps achieve the lower bound of the convergence rate for the first-order method in a specific limit without learning parameters or momentum terms.

cs.LG↗

arXiv2020

Chebyshev Inertial Landweber Algorithm for Linear Inverse Problems

The Landweber algorithm defined on complex/real Hilbert spaces is a gradient descent algorithm for linear inverse problems. Our contribution is to present a novel method for accelerating convergence of the Landweber algorithm. In this paper, we first extend the theory of the Chebyshev inertial iteration to the Landweber algorithm on Hilbert spaces. An upper bound on the convergence rate clarifies the speed of global convergence of the proposed method. The Chebyshev inertial Landweber algorithm can be applied to wide class of signal recovery problems on a Hilbert space including deconvolution for continuous signals. The theoretical discussion developed in this paper naturally leads to a novel practical signal recovery algorithm. As a demonstration, a MIMO detection algorithm based on the projected Landweber algorithm is derived. The proposed MIMO detection algorithm achieves much smaller symbol error rate compared with the MMSE detector.

cs.IT↗

arXiv2020

Chebyshev Inertial Iteration for Accelerating Fixed-Point Iterations

A novel method which is called the Chebyshev inertial iteration for accelerating the convergence speed of fixed-point iterations is presented. The Chebyshev inertial iteration can be regarded as a valiant of the successive over relaxation or Krasnosel'ski\vı-Mann iteration utilizing the inverse of roots of a Chebyshev polynomial as iteration dependent inertial factors. One of the most notable features of the proposed method is that it can be applied to nonlinear fixed-point iterations in addition to linear fixed-point iterations. Linearization around the fixed point is the key for the analysis on the local convergence rate of the proposed method. The proposed method appears effective in particular for accelerating the proximal gradient methods such as ISTA. It is also proved that the proposed method can successfully accelerate almost any fixed-point iterations if all the eigenvalues of the Jacobian at the fixed point are real.

math.OC↗

arXiv2019

Trainable Projected Gradient Detector for Sparsely Spread Code Division Multiple Access

Sparsely spread code division multiple access (SCDMA) is a promising non-orthogonal multiple access technique for future wireless communications. In this paper, we propose a novel trainable multiuser detector called sparse trainable projected gradient (STPG) detector, which is based on the notion of deep unfolding. In the STPG detector, trainable parameters are embedded to a projected gradient descent algorithm, which can be trained by standard deep learning techniques such as back propagation and stochastic gradient descent. Advantages of the detector are its low computational cost and small number of trainable parameters, which enables us to treat massive SCDMA systems. In particular, its computational cost is smaller than a conventional belief propagation (BP) detector while the STPG detector exhibits nearly same detection performance with a BP detector. We also propose a scalable joint learning of signature sequences and the STPG detector for signature design. Numerical results show that the joint learning improves multiuser detection performance particular in the low SNR regime.

cs.IT↗

arXiv2019

Complex Trainable ISTA for Linear and Nonlinear Inverse Problems

Complex-field signal recovery problems from noisy linear/nonlinear measurements appear in many areas of signal processing and wireless communications. In this paper, we propose a trainable iterative signal recovery algorithm named complex-field TISTA (C-TISTA) which treats complex-field nonlinear inverse problems. C-TISTA is based on the concept of deep unfolding and consists of a gradient descent step with the Wirtinger derivatives followed by a shrinkage step with a trainable complex-valued shrinkage function. Importantly, it contains a small number of trainable parameters so that its training process can be executed efficiently. Numerical results indicate that C-TISTA shows remarkable signal recovery performance compared with existing algorithms.

cs.IT↗