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Computationally hard combinatorial optimization problems are pervasive in science and engineering, yet their NP-hard nature renders them increasingly inefficient to solve on conventional von Neumann architectures as problem size grows.…
Two main challenges preventing efficient training of variational quantum algorithms and quantum machine learning models are local minima and barren plateaus. Typically, barren plateaus are associated with deep circuits, while shallow…
The Expectation-Maximization (EM) algorithm is a commonly used method for finding the maximum likelihood estimates of the parameters in a mixture model via coordinate ascent. A serious pitfall with the algorithm is that in the case of…
Dynamical Ising machines are actively investigated from the perspective of finding efficient heuristics for NP-hard optimization problems. However, the existing data demonstrate super-polynomial scaling of the running time with the system…
Analog models of quantum information processing, such as adiabatic quantum computation and analog quantum simulation, require the ability to subject a system to precisely specified Hamiltonians. Unfortunately, the hardware used to implement…
Ising machines, hardware accelerators for combinatorial optimization and probabilistic sampling problems, have gained significant interest recently. A key element is stochasticity, which enables a wide exploration of configurations, thereby…
Stochastic local search algorithms are frequently used to numerically solve hard combinatorial optimization or decision problems. We give numerical and approximate analytical descriptions of the dynamics of such algorithms applied to random…
In recent years, Ising prior with the network information for the "in" or "out" binary random variable in Bayesian variable selections has received more and more attentions. In this paper, we discover that even without the informative prior…
Feedback optimization has emerged as a promising approach for regulating dynamical systems to optimal steady states that are implicitly defined by underlying optimization problems. Despite their effectiveness, existing methods face two key…
Integrating combinatorial optimization layers into neural networks has recently attracted significant research interest. However, many existing approaches lack theoretical guarantees or fail to perform adequately when relying on inexact…
Evolutionary algorithms have been frequently applied to constrained continuous optimisation problems. We carry out feature based comparisons of different types of evolutionary algorithms such as evolution strategies, differential evolution…
There is a growing cross-disciplinary effort in the broad domain of optimization and learning with streams of data, applied to settings where traditional batch optimization techniques cannot produce solutions at time scales that match the…
Gradient descent and coordinate descent are well understood in terms of their asymptotic behavior, but less so in a transient regime often used for approximations in machine learning. We investigate how proper initialization can have a…
Convergent cross mapping (CCM) provides a powerful technique for exploring causal relationships in nonlinear coupled systems. The method relies on Takens' theorem exploiting that time delay embeddings of infinite length general observations…
For solving combinatorial optimisation problems with metaheuristics, different search operators are applied for sampling new solutions in the neighbourhood of a given solution. It is important to understand the relationship between…
Many combinatorial optimization problems (COPs) are naturally expressed using variables that take on more than two discrete values. To solve such problems using Ising machines (IMs) - specialized analog or digital devices designed to solve…
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,…
Physics-based Ising machines (IM) have been developed as dedicated processors for solving hard combinatorial optimization problems with higher speed and better energy efficiency. Generally, such systems employ local search heuristics to…
Analog Ising machines are dedicated hardware solvers designed to solve NP hard optimization problems. However, the global optimum is often not found as the system gets stuck in local minima. While several strategies exist to increase the…
Oscillator Ising Machines (OIMs) and probabilistic bit (p-bit)-based computing platforms have emerged as promising paradigms for tackling complex combinatorial optimization problems. Although traditionally viewed as distinct approaches,…