100,000-spin coherent Ising machine.

Computers based on physical systems are increasingly anticipated to overcome the impending limitations on digital computer performance. One such computer is a coherent Ising machine (CIM) for solving combinatorial optimization problems. Here, we report a CIM with 100,512 degenerate optical parametric oscillator pulses working as the Ising spins. We show that the CIM delivers fine solutions to maximum cut problems of 100,000-node graphs drastically faster than standard simulated annealing. Moreover, the CIM, when operated near the phase transition point, provides some extremely good solutions and a very broad distribution. This characteristic will be useful for applications that require fast random sampling such as machine learning.

Binary optimization by momentum annealing.

One of the vital roles of computing is to solve large-scale combinatorial optimization problems in a short time. In recent years, methods have been proposed that map optimization problems to ones of searching for the ground state of an Ising model by using a stochastic process. Simulated annealing (SA) is a representative algorithm. However, it is inherently difficult to perform a parallel search. Here we propose an algorithm called momentum annealing (MA), which, unlike SA, updates all spins of fully connected Ising models simultaneously and can be implemented on GPUs that are widely used for scientific computing. MA running in parallel on GPUs is 250 times faster than SA running on a modern CPU at solving problems involving 100 000 spin Ising models.

Experimental investigation of performance differences between coherent Ising machines and a quantum annealer.

Physical annealing systems provide heuristic approaches to solving combinatorial optimization problems. Here, we benchmark two types of annealing machines-a quantum annealer built by D-Wave Systems and measurement-feedback coherent Ising machines (CIMs) based on optical parametric oscillators-on two problem classes, the Sherrington-Kirkpatrick (SK) model and MAX-CUT. The D-Wave quantum annealer outperforms the CIMs on MAX-CUT on cubic graphs. On denser problems, however, we observe an exponential penalty for the quantum annealer [exp(-αDW N 2)] relative to CIMs [exp(-αCIM N)] for fixed anneal times, both on the SK model and on 50% edge density MAX-CUT. This leads to a several orders of magnitude time-to-solution difference for instances with over 50 vertices. An optimal-annealing time analysis is also consistent with a substantial projected performance difference. The difference in performance between the sparsely connected D-Wave machine and the fully-connected CIMs provides strong experimental support for efforts to increase the connectivity of quantum annealers.

Jointly learning word embeddings using a corpus and a knowledge base.

Methods for representing the meaning of words in vector spaces purely using the information distributed in text corpora have proved to be very valuable in various text mining and natural language processing (NLP) tasks. However, these methods still disregard the valuable semantic relational structure between words in co-occurring contexts. These beneficial semantic relational structures are contained in manually-created knowledge bases (KBs) such as ontologies and semantic lexicons, where the meanings of words are represented by defining the various relationships that exist among those words. We combine the knowledge in both a corpus and a KB to learn better word embeddings. Specifically, we propose a joint word representation learning method that uses the knowledge in the KBs, and simultaneously predicts the co-occurrences of two words in a corpus context. In particular, we use the corpus to define our objective function subject to the relational constrains derived from the KB. We further utilise the corpus co-occurrence statistics to propose two novel approaches, Nearest Neighbour Expansion (NNE) and Hedged Nearest Neighbour Expansion (HNE), that dynamically expand the KB and therefore derive more constraints that guide the optimisation process. Our experimental results over a wide-range of benchmark tasks demonstrate that the proposed method statistically significantly improves the accuracy of the word embeddings learnt. It outperforms a corpus-only baseline and reports an improvement of a number of previously proposed methods that incorporate corpora and KBs in both semantic similarity prediction and word analogy detection tasks.

Learning linear transformations between counting-based and prediction-based word embeddings.

Despite the growing interest in prediction-based word embedding learning methods, it remains unclear as to how the vector spaces learnt by the prediction-based methods differ from that of the counting-based methods, or whether one can be transformed into the other. To study the relationship between counting-based and prediction-based embeddings, we propose a method for learning a linear transformation between two given sets of word embeddings. Our proposal contributes to the word embedding learning research in three ways: (a) we propose an efficient method to learn a linear transformation between two sets of word embeddings, (b) using the transformation learnt in (a), we empirically show that it is possible to predict distributed word embeddings for novel unseen words, and

An iterative approach for the global estimation of sentence similarity.

Measuring the similarity between two sentences is often difficult due to their small lexical overlap. Instead of focusing on the sets of features in two given sentences between which we must measure similarity, we propose a sentence similarity method that considers two types of constraints that must be satisfied by all pairs of sentences in a given corpus. Namely, (a) if two sentences share many features in common, then it is likely that the remaining features in each sentence are also related, and (b) if two sentences contain many related features, then those two sentences are themselves similar. The two constraints are utilized in an iterative bootstrapping procedure that simultaneously updates both word and sentence similarity scores. Experimental results on SemEval 2015 Task 2 dataset show that the proposed iterative approach for measuring sentence semantic similarity is significantly better than the non-iterative counterparts.

A coherent Ising machine for 2000-node optimization problems.

The analysis and optimization of complex systems can be reduced to mathematical problems collectively known as combinatorial optimization. Many such problems can be mapped onto ground-state search problems of the Ising model, and various artificial spin systems are now emerging as promising approaches. However, physical Ising machines have suffered from limited numbers of spin-spin couplings because of implementations based on localized spins, resulting in severe scalability problems. We report a 2000-spin network with all-to-all spin-spin couplings. Using a measurement and feedback scheme, we coupled time-multiplexed degenerate optical parametric oscillators to implement maximum cut problems on arbitrary graph topologies with up to 2000 nodes. Our coherent Ising machine outperformed simulated annealing in terms of accuracy and computation time for a 2000-node complete graph.

Uncertain behaviours of integrated circuits improve computational performance.

Improvements to the performance of conventional computers have mainly been achieved through semiconductor scaling; however, scaling is reaching its limitations. Natural phenomena, such as quantum superposition and stochastic resonance, have been introduced into new computing paradigms to improve performance beyond these limitations. Here, we explain that the uncertain behaviours of devices due to semiconductor scaling can improve the performance of computers. We prototyped an integrated circuit by performing a ground-state search of the Ising model. The bit errors of memory cell devices holding the current state of search occur probabilistically by inserting fluctuations into dynamic device characteristics, which will be actualised in the future to the chip. As a result, we observed more improvements in solution accuracy than that without fluctuations. Although the uncertain behaviours of devices had been intended to be eliminated in conventional devices, we demonstrate that uncertain behaviours has become the key to improving computational performance.