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Domain-specific hardware to solve computationally hard optimization problems has generated tremendous excitement. Here, we evaluate probabilistic bit (p-bit) based Ising Machines (IM) on the 3-regular 3-Exclusive OR Satisfiability (3R3X),…
Biclustering is an unsupervised machine learning technique that simultaneously clusters rows and columns in a data matrix. Biclustering has emerged as an important approach and plays an essential role in various applications such as…
The problem of best subset selection in linear regression is considered with the aim to find a fixed size subset of features that best fits the response. This is particularly challenging when the total available number of features is very…
We propose a novel type of minor-embedding (ME) in simulated-annealing-based Ising machines. The Ising machines can solve combinatorial optimization problems. Many combinatorial optimization problems are mapped to find the ground…
Sampling Boltzmann probability distributions plays a key role in machine learning and optimization, motivating the design of hardware accelerators such as Ising machines. While the Ising model can in principle encode arbitrary optimization…
People solve different problems and know that some of them are simple, some are complex and some insoluble. The main goal of this work is to develop a mathematical theory of algorithmic complexity for problems. This theory is aimed at…
We propose a clustering-based iterative algorithm to solve certain optimization problems in machine learning, where we start the algorithm by aggregating the original data, solving the problem on aggregated data, and then in subsequent…
The emergence of specialized optimization hardware such as CMOS annealers and adiabatic quantum computers carries the promise of solving hard combinatorial optimization problems more efficiently in hardware. Recent work has focused on…
A method is suggested for treating those complicated physical problems for which exact solutions are not known but a few approximation terms of a calculational algorithm can be derived. The method permits one to answer the following rather…
Stochastic Ising machines, sIMs, are highly promising accelerators for optimization and sampling of computational problems that can be formulated as an Ising model. Here we investigate the computational advantage of sIM for simulations of…
We consider the problem of approximating partition functions for Ising models. We make use of recent tools in combinatorial optimization: the Sherali-Adams and Lasserre convex programming hierarchies, in combination with variational methods…
We present a procedure to solve the inverse Ising problem, that is to find the interactions between a set of binary variables from the measure of their equilibrium correlations. The method consists in constructing and selecting specific…
The design of nonlinear dynamical systems whose gradient flows minimize the Ising Hamiltonian has emerged as a compelling paradigm for realizing Ising machines, forming the foundation of architectures including coherent Ising machines,…
The complete framework for the $\epsilon$-machine construction of the one dimensional Ising model is presented correcting previous mistakes on the subject. The approach follows the known treatment of the Ising model as a Markov random…
This paper studies a combinatorial optimization problem which is obtained by combining the flow shop scheduling problem and the shortest path problem. The objective of the obtained problem is to select a subset of jobs that constitutes a…
Ising machines based on nonlinear analog systems are a promising method to accelerate computation of NP-hard optimization problems. Yet, their analog nature is also causing amplitude inhomogeneity which can deteriorate the ability to find…
The coherent Ising machine is expected to find a near-optimal solution in various combinatorial optimization problems, which has been experimentally confirmed with optical parametric oscillators (OPOs) and a field programmable gate array…
We present a method for determining optimal modes of operation for autonomously oscillating systems with uncertain parameters. In a typical application of the method, a nonlinear dynamical system is optimized with respect to an economic…
This paper surveys the trend of leveraging machine learning to solve mixed integer programming (MIP) problems. Theoretically, MIP is an NP-hard problem, and most of the combinatorial optimization (CO) problems can be formulated as the MIP.…
Ising machines (IM) have recently been proposed as unconventional hardware-based computation accelerators for solving NP-hard problems. In this work, we present a model for a time-multiplexed IM based on the nonlinear oscillations in a…