A continuous-time MaxSAT solver with high analog performance

Molnár, Botond; Molnár, Ferenc; Varga, Melinda; Toroczkai, Zoltán; Ercsey-Ravasz, Mária

doi:10.1038/s41467-018-07327-2

Cited by 38 publications

(24 citation statements)

References 59 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…At this point, we note that there are several other streams of work on physical optimization in the literature that we shall not be dealing with in this paper. These works include a variety of Lagrange-like continuous-time solvers (16,17), Memcomputing methods (18), Reservoir Computing (19,20), adiabatic solvers using Kerr nonlinear oscillators (21), and probabilistic bit logic (22). A brief discussion of adiabatic Kerr oscillator systems (21) is presented in SI Appendix, section 4.…”

Section: Significancementioning

confidence: 99%

Physics successfully implements Lagrange multiplier optimization

Vadlamani

Xiao

Yablonovitch

2020

Proc. Natl. Acad. Sci. U.S.A.

View full text Add to dashboard Cite

Optimization is a major part of human effort. While being mathematical, optimization is also built into physics. For example, physics has the Principle of Least Action; the Principle of Minimum Power Dissipation, also called Minimum Entropy Generation; and the Variational Principle. Physics also has Physical Annealing, which, of course, preceded computational Simulated Annealing. Physics has the Adiabatic Principle, which, in its quantum form, is called Quantum Annealing. Thus, physical machines can solve the mathematical problem of optimization, including constraints. Binary constraints can be built into the physical optimization. In that case, the machines are digital in the same sense that a flip–flop is digital. A wide variety of machines have had recent success at optimizing the Ising magnetic energy. We demonstrate in this paper that almost all those machines perform optimization according to the Principle of Minimum Power Dissipation as put forth by Onsager. Further, we show that this optimization is in fact equivalent to Lagrange multiplier optimization for constrained problems. We find that the physical gain coefficients that drive those systems actually play the role of the corresponding Lagrange multipliers.

show abstract

Section: Significancementioning

confidence: 99%

Physics successfully implements Lagrange multiplier optimization

Vadlamani

Xiao

Yablonovitch

2020

Proc. Natl. Acad. Sci. U.S.A.

View full text Add to dashboard Cite

show abstract

“…Pure and mixed-mode analog accelerators have been developed for accelerating a broad range of applications, including neural networks, SAT solvers, and neuromorphic computations [4,11,19,26,28,32,37]. One prominent line of work focuses on analog accelerators that target dynamical systems [7,8,15,18,34,41,43,45,46].…”

Section: Related Workmentioning

confidence: 99%

Noise-Aware Dynamical System Compilation for Analog Devices with Legno

Achour

Rinard

2020

Proceedings of the Twenty-Fifth International Conference on Architectural Support for Programming Languages and Operating Syste

View full text Add to dashboard Cite

Reconfigurable analog devices are a powerful new computing substrate especially appropriate for executing computationally intensive dynamical system computations in an energy efficient manner. We present Legno, a compilation toolchain for programmable analog devices. Legno targets the HCDCv2, a programmable analog device designed to execute general nonlinear dynamical systems. To the best of our knowledge, Legno is the first compiler to successfully target a physical (as opposed to simulated) programmable analog device for dynamical systems and this paper is the first to present experimental results for any compiled computation executing on any physical programmable analog device of this class. The Legno compiler synthesizes analog circuits from parametric and specialized blocks and accounts for analog noise, quantization error, and manufacturing variations within the device. We evaluate the compiled configurations on the Sendyne S100Asy RevU development board on twelve benchmarks from physics, controls, and biology. Our results show that Legno produces accurate computations on the analog device. The computations execute in 0.50-5.92 ms and consume 0.28-5.67 µJ of energy. CCS Concepts. • Computer systems organization → Analog computers; • Software and its engineering → Compilers.

show abstract

“…In a series of seminal papers [32,33,58], the authors construct a dynamical systems approach to study satisfiability problems. They construct a dynamical system that computes the solutions of SAT instances.…”

Section: Overviewmentioning

confidence: 99%

Dynamical Systems Theory and Algorithms for NP-hard Problems

Sahai¹

2020

Preprint

View full text Add to dashboard Cite

This article surveys the burgeoning area at the intersection of dynamical systems theory and algorithms for NP-hard problems. Traditionally, computational complexity and the analysis of non-deterministic polynomial-time (NP)-hard problems have fallen under the purview of computer science and discrete optimization. However, over the past few years, dynamical systems theory has increasingly been used to construct new algorithms and shed light on the hardness of problem instances. We survey a range of examples that illustrate the use of dynamical systems theory in the context of computational complexity analysis and novel algorithm construction. In particular, we summarize a) a novel approach for clustering graphs using the wave equation partial differential equation, b) invariant manifold computations for the traveling salesman problem, c) novel approaches for building quantum networks of Duffing oscillators to solve the MAX-CUT problem, d) applications of the Koopman operator for analyzing optimization algorithms, and e) the use of dynamical systems theory to analyze computational complexity.

show abstract

A continuous-time MaxSAT solver with high analog performance

Cited by 38 publications

References 59 publications

Physics successfully implements Lagrange multiplier optimization

Physics successfully implements Lagrange multiplier optimization

Noise-Aware Dynamical System Compilation for Analog Devices with Legno

Dynamical Systems Theory and Algorithms for NP-hard Problems

Contact Info

Product

Resources

About