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1. Combinatorial optimization by weight annealing in memristive hopfield networks

   https://doi.org/10.1038/s41598-020-78944-5  

   Fahimi, Z.; Mahmoodi, M. R.; Nili, H.; Polishchuk, Valentin; Strukov, D. B. (December 2021, Scientific Reports)

   Abstract The increasing utility of specialized circuits and growing applications of optimization call for the development of efficient hardware accelerator for solving optimization problems. Hopfield neural network is a promising approach for solving combinatorial optimization problems due to the recent demonstrations of efficient mixed-signal implementation based on emerging non-volatile memory devices. Such mixed-signal accelerators also enable very efficient implementation of various annealing techniques, which are essential for finding optimal solutions. Here we propose a “weight annealing” approach, whose main idea is to ease convergence to the global minima by keeping the network close to its ground state. This is achieved by initially setting all synaptic weights to zero, thus ensuring a quick transition of the Hopfield network to its trivial global minima state and then gradually introducing weights during the annealing process. The extensive numerical simulations show that our approach leads to a better, on average, solutions for several representative combinatorial problems compared to prior Hopfield neural network solvers with chaotic or stochastic annealing. As a proof of concept, a 13-node graph partitioning problem and a 7-node maximum-weight independent set problem are solved experimentally using mixed-signal circuits based on, correspondingly, a 20 × 20 analog-grade TiO 2 memristive crossbar and a 12 × 10 eFlash memory array. 

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2. Learning Hard Optimization Problems: A Data Generation Perspective

   Kotary, James; Fioretto, Ferdinando; Van Hentenryck, Pascal (January 2021, Advances in Neural Information Processing Systems 34 (NeurIPS 2021))

   Optimization problems are ubiquitous in our societies and are present in almost every segment of the economy. Most of these optimization problems are NP-hard and computationally demanding, often requiring approximate solutions for large-scale instances. Machine learning frameworks that learn to approximate solutions to such hard optimization problems are a potentially promising avenue to address these difficulties, particularly when many closely related problem instances must be solved repeatedly. Supervised learning frameworks can train a model using the outputs of pre-solved instances. However, when the outputs are themselves approximations, when the optimization problem has symmetric solutions, and/or when the solver uses randomization, solutions to closely related instances may exhibit large differences and the learning task can become inherently more difficult. This paper demonstrates this critical challenge, connects the volatility of the training data to the ability of a model to approximate it, and proposes a method for producing (exact or approximate) solutions to optimization problems that are more amenable to supervised learning tasks. The effectiveness of the method is tested on hard non-linear nonconvex and discrete combinatorial problems. 

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3. Neuromorphic Swarm on RRAM Compute-in-Memory Processor for Solving QUBO Problem

   https://doi.org/10.1109/DAC56929.2023.10247852  

   Lele, Ashwin Sanjay; Chang, Muya; Spetalnick, Samuel D.; Crafton, Brian; Raychowdhury, Arijit; Fang, Yan (July 2023, IEEE)

   Combinatorial optimization problems prevail in engineering and industry. Some are NP-hard and thus become difficult to solve on edge devices due to limited power and computing resources. Quadratic Unconstrained Binary Optimization (QUBO) problem is a valuable emerging model that can formulate numerous combinatorial problems, such as Max-Cut, traveling salesman problems, and graphic coloring. QUBO model also reconciles with two emerging computation models, quantum computing and neuromorphic computing, which can potentially boost the speed and energy efficiency in solving combinatorial problems. In this work, we design a neuromorphic QUBO solver composed of a swarm of spiking neural networks (SNN) that conduct a population-based meta-heuristic search for solutions. The proposed model can achieve about x20 40 speedup on large QUBO problems in terms of time steps compared to a traditional neural network solver. As a codesign, we evaluate the neuromorphic swarm solver on a 40nm 25mW Resistive RAM (RRAM) Compute-in-Memory (CIM) SoC with a 2.25MB RRAM-based accelerator and an embedded Cortex M3 core. The collaborative SNN swarm can fully exploit the specialty of CIM accelerator in matrix and vector multiplications. Compared to previous works, such an algorithm-hardware synergized solver exhibits advantageous speed and energy efficiency for edge devices. 

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4. The (Un)Scalability of Informed Heuristic Function Estimation in NP-Hard Search Problems

   Pendurkar, Sumedh; Huang, Taoan; Juba, Brendan; Zhang, Jiapeng; Koenig, Sven; Sharon, Guni (November 2023, Transactions on Machine Learning Research)

   The A* algorithm is commonly used to solve NP-hard combinatorial optimization problems. When provided with a completely informed heuristic function, A* can solve such problems in time complexity that is polynomial in the solution cost and branching factor. In light of this fact, we examine a line of recent publications that propose fitting deep neural networks to the completely informed heuristic function. We assert that these works suffer from inherent scalability limitations since --- under the assumption of NP P/poly --- such approaches result in either (a) network sizes that scale super-polynomially in the instance sizes or (b) the accuracy of the fitted deep neural networks scales inversely with the instance sizes. Complementing our theoretical claims, we provide experimental results for three representative NP-hard search problems. The results suggest that fitting deep neural networks to informed heuristic functions requires network sizes that grow quickly with the problem instance size. We conclude by suggesting that the research community should focus on scalable methods for integrating heuristic search with machine learning, as opposed to methods relying on informed heuristic estimation. 

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5. Machine Learning Framework for Quantum Sampling of Highly-Constrained, Continuous Optimization Problems

   B. Wilson, Z. Kudyshev (May 2021, ArXivorg)

   null (Ed.)

   In the recent years, there is a growing interest in using quantum computers for solving combinatorial optimization problems. In this work, we developed a generic, machine learning-based framework for mapping continuous-space inverse design problems into surrogate quadratic unconstrained binary optimization (QUBO) problems by employing a binary variational autoencoder and a factorization machine. The factorization machine is trained as a low-dimensional, binary surrogate model for the continuous design space and sampled using various QUBO samplers. Using the D-Wave Advantage hybrid sampler and simulated annealing, we demonstrate that by repeated resampling and retraining of the factorization machine, our framework finds designs that exhibit figures of merit exceeding those of its training set. We showcase the framework’s performance on two inverse design problems by optimizing (i) thermal emitter topologies for thermophotovoltaic applications and (ii) diffractive meta-gratings for highly efficient beam steering. This technique can be further scaled to leverage future developments in quantum optimization to solve advanced inverse design problems for science and engineering applications. 

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