Attraction area of minima in quadratic binary optimization

Karandashev, Iakov M.; Kryzhanovsky, Boris

doi:10.3103/s1060992x1402009x

Cited by 8 publications

(5 citation statements)

References 7 publications

(12 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…and the energy-dimensionality dependence is reduced to expression The knowledge of the local minima spectrum is necessary in many fields of science. In informatics it is essential for tackling quadratic minimization problems [1][2][3][4][5][6][7][8][9][10], generating algorithms for searching the global minimum [11][12][13][14][15][16][17][18] and the optimal graph cross section [19][20][21][22][23][24][25][26]. In neuroinformatics the knowledge of spectra is necessary for building associative memory systems [27][28][29][30][31][32][33][60][61], developing neural nets and neural minimization algorithms [34][35][36][37][38][39][40].…”

Section: ∑∑mentioning

confidence: 99%

The spectra of local minima in spin-glass models

Kryzhanovsky

Malsagov

2016

Opt. Mem. Neural Networks

Self Cite

View full text Add to dashboard Cite

Abstract. The spectra of spin models have been investigated in computation experiments. For the Sherrington-Kirkpatrick and Edwards-Anderson models we have determined the basic spectral characteristics: the average depth of a local minimum, the spectrum width, the depth of the global minimum. The experimental data are used to build the relations between these quantities and the model dimensionality N and find their asymptotic values for N→∞.

show abstract

Section: ∑∑mentioning

confidence: 99%

The spectra of local minima in spin-glass models

Kryzhanovsky

Malsagov

2016

Opt. Mem. Neural Networks

Self Cite

View full text Add to dashboard Cite

show abstract

“…Our modification, termed AmplifySAT, is inspired by the quantum AA algorithm, and has the qualitative effect of "amplifying", or "deepening" the global optimum of an objective function encoding a SAT problem. Transformations of the objective function that target the extrema are not common, but have been explored in some works, e.g., [33], [34]. The iterative nature of AA means that the degree of amplification of the extrema can be coarsely controlled.…”

Section: Introductionmentioning

confidence: 99%

A Quantum-Inspired Classical Solver for Boolean k-Satisfiability Problems

Lanham¹,

Cour²

2021

Preprint

View full text Add to dashboard Cite

In this paper we detail a classical algorithmic approach to the k-satisfiability (k-SAT) problem that is inspired by the quantum amplitude amplification algorithm. This work falls under the emerging field of quantum-inspired classical algorithms. To propose our modification, we adopt an existing problem model for k-SAT known as Universal SAT (UniSAT), which casts the Boolean satisfiability problem as a non-convex global optimization over a real-valued space. The quantuminspired modification to UniSAT is to apply a conditioning operation to the objective function that has the effect of "amplifying" the function value at points corresponding to optimal solutions. We describe the algorithm for achieving this amplification, termed "AmplifySAT," which follows a familiar twostep process of applying an oracle-like operation followed by a reflection about the average. We then discuss opportunities for meaningfully leveraging this processing in a classical digital or analog computing setting, attempting to identify the strengths and limitations of AmplifySAT in the context of existing non-convex optimization strategies like simulated annealing and gradient descent.

show abstract

“…In many fields of science, it is necessary to know the global energy minimum for different systems. Namely, in informatics we use it when solving problems of quadratic optimization [1][2][3][4][5][6], developing search algorithms for the global minimum [7][8][9][10][11][12] and solving max-cut problems [13][14][15][16][17]. In neuroinformatics, we have to know the global minimum when developing associative memory systems [18][19][20][21] and constructing neural networks and neural network minimization algorithms [22][23][24].…”

Section: Introductionmentioning

confidence: 99%

Global Minimum Depth in Edwards-Anderson Model

Karandashev¹,

Kryzhanovsky²

2019

Engineering Applications of Neural Networks

View full text Add to dashboard Cite

In the literature the most frequently cited data are quite contradictory, and there is no consensus on the global minimum value of 2D Edwards-Anderson (2D EA) Ising model. By means of computer simulations, with the help of exact polynomial Schraudolph-Kamenetsky algorithm, we examined the global minimum depth in 2D EA-type models. We found a dependence of the global minimum depth on the dimension of the problem N and obtained its asymptotic value in the limit N→∞. We believe these evaluations can be further used for examining the behavior of 2D Bayesian models often used in machine learning and image processing.

show abstract

Attraction area of minima in quadratic binary optimization

Cited by 8 publications

References 7 publications

The spectra of local minima in spin-glass models

The spectra of local minima in spin-glass models

A Quantum-Inspired Classical Solver for Boolean k-Satisfiability Problems

Global Minimum Depth in Edwards-Anderson Model

Contact Info

Product

Resources

About