Google matrix analysis of directed networks

In past ten years, modern societies developed enormous communication and social networks. Their classification and information retrieval processing become a formidable task for the society. Due to the rapid growth of World Wide Web, social and communication networks, new mathematical methods have been invented to characterize the properties of these networks on a more detailed and precise level. Various search engines are essentially using such methods. It is highly important to develop new tools to classify and rank enormous amount of network information in a way adapted to internal network structures and characteristics. This review describes the Google matrix analysis of directed complex networks demonstrating its efficiency on various examples including World Wide Web, Wikipedia, software architecture, world trade, social and citation networks, brain neural networks, DNA sequences and Ulam networks. The analytical and numerical matrix methods used in this analysis originate from the fields of Markov chains, quantum chaos and Random Matrix theory.Comment: 56 pages, 58 figures. Missed link added in network example of Fig3

Formal Modeling of Connectionism using Concurrency Theory, an Approach Based on Automata and Model Checking

This paper illustrates a framework for applying formal methods techniques, which are symbolic in nature, to specifying and verifying neural networks, which are sub-symbolic in nature. The paper describes a communicating automata [Bowman & Gomez, 2006] model of neural networks. We also implement the model using timed automata [Alur & Dill, 1994] and then undertake a verification of these models using the model checker Uppaal [Pettersson, 2000] in order to evaluate the performance of learning algorithms. This paper also presents discussion of a number of broad issues concerning cognitive neuroscience and the debate as to whether symbolic processing or connectionism is a suitable representation of cognitive systems. Additionally, the issue of integrating symbolic techniques, such as formal methods, with complex neural networks is discussed. We then argue that symbolic verifications may give theoretically well-founded ways to evaluate and justify neural learning systems in the field of both theoretical research and real world applications

On the number of limit cycles in diluted neural networks

We consider the storage properties of temporal patterns, i.e. cycles of finite lengths, in neural networks represented by (generally asymmetric) spin glasses defined on random graphs. Inspired by the observation that dynamics on sparse systems have more basins of attractions than the dynamics of densely connected ones, we consider the attractors of a greedy dynamics in sparse topologies, considered as proxy for the stored memories. We enumerate them using numerical simulation and extend the analysis to large systems sizes using belief propagation. We find that the logarithm of the number of such cycles is a non monotonic function of the mean connectivity and we discuss the similarities with biological neural networks describing the memory capacity of the hippocampus.Comment: 10 pages, 11 figure

Enhancing Stock Movement Prediction with Adversarial Training

This paper contributes a new machine learning solution for stock movement prediction, which aims to predict whether the price of a stock will be up or down in the near future. The key novelty is that we propose to employ adversarial training to improve the generalization of a neural network prediction model. The rationality of adversarial training here is that the input features to stock prediction are typically based on stock price, which is essentially a stochastic variable and continuously changed with time by nature. As such, normal training with static price-based features (e.g. the close price) can easily overfit the data, being insufficient to obtain reliable models. To address this problem, we propose to add perturbations to simulate the stochasticity of price variable, and train the model to work well under small yet intentional perturbations. Extensive experiments on two real-world stock data show that our method outperforms the state-of-the-art solution with 3.11% relative improvements on average w.r.t. accuracy, validating the usefulness of adversarial training for stock prediction task.Comment: IJCAI 201