Efficient optimization with higher-order Ising machines

Bybee, Connor; Kleyko, Denis; Nikonov, Dmitri E.; Khosrowshahi, Amir; Olshausen, Bruno A.; Sommer, Friedrich T.

doi:10.1038/s41467-023-41214-9

Cited by 14 publications

(4 citation statements)

References 57 publications

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“…where z * i and z * j are the i-th and j-th components of z * = argmin z E(θ , Γ , z), respectively. Since the optimal spin configuration z * also depends on Γ (and θ ), we should consider the derivatives ∂ z * l /∂ Γ i j for l = 1, ..., n in the final step outlined in (15). However, it must be noted that the function z * l = z * l (θ , Γ ) is piecewise constant.…”

Section: Training Processmentioning

confidence: 99%

“…Furthermore, it highlights the fact that the discontinuity observed in the derivative of the optimal spin configuration z * , as discussed in the proof of Theorem 3, does not hinder the model's ability to minimize the loss function. In essence, the assumption made in (15) regarding the computation of the partial derivatives proves to be sufficiently accurate.…”

Section: Random Datamentioning

confidence: 99%

“…The difference between Boltzmann and Ising machines lies in the fact that Boltzmann machines are parametric generative models. In contrast, Ising machines are considered as solvers of combinatorial optimization problems [15][16][17]. However, in this paper, we propose a supervised learning model for Ising machines whose training is inspired by the training of Boltzmann machines.…”

Section: Introductionmentioning

confidence: 99%

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A general learning scheme for classical and quantum Ising machines

Schmid,

Zardini,

Pastorello

2024

SciPost Phys. Core

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An Ising machine is any hardware specifically designed for finding the ground state of the Ising model. Relevant examples are coherent Ising machines and quantum annealers. In this paper, we propose a new machine learning model that is based on the Ising structure and can be efficiently trained using gradient descent. We provide a mathematical characterization of the training process, which is based upon optimizing a loss function whose partial derivatives are not explicitly calculated but estimated by the Ising machine itself. Moreover, we present some experimental results on the training and execution of the proposed learning model. These results point out new possibilities offered by Ising machines for different learning tasks. In particular, in the quantum realm, the quantum resources are used for both the execution and the training of the model, providing a promising perspective in quantum machine learning.

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Section: Training Processmentioning

confidence: 99%

Section: Random Datamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A general learning scheme for classical and quantum Ising machines

Schmid,

Zardini,

Pastorello

2024

SciPost Phys. Core

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show abstract

“…To address these challenges, Ising machines and Boltzmann machines involving higher-order interactions 19 , 24 , 28 – 31 have been explored. In the context of GSPL, linear programming 19 , 29 , 32 has been employed to find the configuration parameters of small-scale GSPL gates involving many-body interactions among p-bits, albeit at the cost of additional algorithmic complexity.…”

Section: Introductionmentioning

confidence: 99%

Direct design of ground-state probabilistic logic using many-body interactions for probabilistic computing

He,

Luo,

Fang

et al. 2024

Sci Rep

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In this work, an innovative design model aimed at enhancing the efficacy of ground-state probabilistic logic with a binary energy landscape (GSPL-BEL) is presented. This model enables the direct conversion of conventional CMOS-based logic circuits into corresponding probabilistic graphical representations based on a given truth table. Compared to the conventional approach of solving the configuration of Ising model-basic probabilistic gates through linear programming, our model directly provides configuration parameters with embedded many-body interactions. For larger-scale probabilistic logic circuits, the GSPL-BEL model can fully utilize the dimensions of many-body interactions, achieving minimal node overhead while ensuring the simplest binary energy landscape and circumventing additional logic synthesis steps. To validate its effectiveness, hardware implementations of probabilistic logic gates were conducted. Probabilistic bits were introduced as Ising cells, and cascaded conventional XNOR gates along with passive resistor networks were precisely designed to realize many-body interactions. HSPICE circuit simulation results demonstrate that the probabilistic logic circuits designed based on this model can successfully operate in free, forward, and reverse modes, exhibiting the simplest binary probability distributions. For a 2-bit × 2-bit integer factorizer involving many-body interactions, compared to the logic synthesis approach, the GSPL-BEL model significantly reduces the number of consumed nodes, the solution space (in the free-run mode), and the number of energy levels from 12, 4096, and 9–8, 256, and 2, respectively. Our findings demonstrate the significant potential of the GSPL-BEL model in optimizing the structure and performance of probabilistic logic circuits, offering a new robust tool for the design and implementation of future probabilistic computing systems.

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Computing high-degree polynomial gradients in memory

Bhattacharya,

Hutchinson,

Pedretti

et al. 2024

Nat Commun

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Specialized function gradient computing hardware could greatly improve the performance of state-of-the-art optimization algorithms. Prior work on such hardware, performed in the context of Ising Machines and related concepts, is limited to quadratic polynomials and not scalable to commonly used higher-order functions. Here, we propose an approach for massively parallel gradient calculations of high-degree polynomials, which is conducive to efficient mixed-signal in-memory computing circuit implementations and whose area scales proportionally with the product of the number of variables and terms in the function and, most importantly, independent of its degree. Two flavors of such an approach are proposed. The first is limited to binary-variable polynomials typical in combinatorial optimization problems, while the second type is broader at the cost of a more complex periphery. To validate the former approach, we experimentally demonstrated solving a small-scale third-order Boolean satisfiability problem based on integrated metal-oxide memristor crossbar circuits, with competitive heuristics algorithm. Simulation results for larger-scale, more practical problems show orders of magnitude improvements in area, speed and energy efficiency compared to the state-of-the-art. We discuss how our work could enable even higher-performance systems after co-designing algorithms to exploit massively parallel gradient computation.

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Efficient optimization with higher-order Ising machines

Cited by 14 publications

References 57 publications

A general learning scheme for classical and quantum Ising machines

A general learning scheme for classical and quantum Ising machines

Direct design of ground-state probabilistic logic using many-body interactions for probabilistic computing

Computing high-degree polynomial gradients in memory

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