Unsupervised Generative Modeling Using Matrix Product States

Generative modeling, which learns joint probability distribution from data and generates samples according to it, is an important task in machine learning and artificial intelligence. Inspired by probabilistic interpretation of quantum physics, we propose a generative model using matrix product states, which is a tensor network originally proposed for describing (particularly one-dimensional) entangled quantum states. Our model enjoys efficient learning analogous to the density matrix renormalization group method, which allows dynamically adjusting dimensions of the tensors and offers an efficient direct sampling approach for generative tasks. We apply our method to generative modeling of several standard datasets including the Bars and Stripes, random binary patterns and the MNIST handwritten digits to illustrate the abilities, features and drawbacks of our model over popular generative models such as Hopfield model, Boltzmann machines and generative adversarial networks. Our work sheds light on many interesting directions of future exploration on the development of quantum-inspired algorithms for unsupervised machine learning, which are promisingly possible to be realized on quantum devices.Comment: 11 pages, 12 figures (not including the TNs) GitHub Page: https://congzlwag.github.io/UnsupGenModbyMPS

Towards correct-by-construction product variants of a software product line: GFML, a formal language for feature modules

Software Product Line Engineering (SPLE) is a software engineering paradigm that focuses on reuse and variability. Although feature-oriented programming (FOP) can implement software product line efficiently, we still need a method to generate and prove correctness of all product variants more efficiently and automatically. In this context, we propose to manipulate feature modules which contain three kinds of artifacts: specification, code and correctness proof. We depict a methodology and a platform that help the user to automatically produce correct-by-construction product variants from the related feature modules. As a first step of this project, we begin by proposing a language, GFML, allowing the developer to write such feature modules. This language is designed so that the artifacts can be easily reused and composed. GFML files contain the different artifacts mentioned above.The idea is to compile them into FoCaLiZe, a language for specification, implementation and formal proof with some object-oriented flavor. In this paper, we define and illustrate this language. We also introduce a way to compose the feature modules on some examples.Comment: In Proceedings FMSPLE 2015, arXiv:1504.0301

Computational Batik Motif Generation: Innovation of Traditional Heritage by Fractal Computation\ud

Human-computer interaction has been the cause of the emerging innovations in many fields, including in design and art, architectural, technological artifacts, and even traditional heritage. In the case of Indonesian traditional heritages, the computation of fractal designs has been introduced to develop batik design – the genuine textile art and skill that becomes a symbol of Indonesian culture. The uniqueness of Batik, which depicted in the richness of its motifs, is regarded as one of interesting aspect to be researched and innovated using computational techniques. Recent studies of batik motifs have discovered conjecture to the existence of fractal geometry in batik designs. This finding has given some inspiration of implementing certain fractal concepts, such escape-time fractal (complex plane) and iterated function system to generate batik motifs. We develop motif generator based upon the Collage Theorem by using Java TM platform. This software is equipped by interface that can be used by user to generate basic patterns, which could be interpreted and painted as batik motif. Experimentally, we found that computationally generated fractal motifs are appropriated to be implemented as batik motif. However, human made batik motifs are less detail and some of them differ significantly with the computationally generated ones for tools used to draw batik and human aesthetic constraints

Tensor Monte Carlo: particle methods for the GPU era

Multi-sample, importance-weighted variational autoencoders (IWAE) give tighter bounds and more accurate uncertainty estimates than variational autoencoders (VAE) trained with a standard single-sample objective. However, IWAEs scale poorly: as the latent dimensionality grows, they require exponentially many samples to retain the benefits of importance weighting. While sequential Monte-Carlo (SMC) can address this problem, it is prohibitively slow because the resampling step imposes sequential structure which cannot be parallelised, and moreover, resampling is non-differentiable which is problematic when learning approximate posteriors. To address these issues, we developed tensor Monte-Carlo (TMC) which gives exponentially many importance samples by separately drawing $K$ samples for each of the $n$ latent variables, then averaging over all $K^n$ possible combinations. While the sum over exponentially many terms might seem to be intractable, in many cases it can be computed efficiently as a series of tensor inner-products. We show that TMC is superior to IWAE on a generative model with multiple stochastic layers trained on the MNIST handwritten digit database, and we show that TMC can be combined with standard variance reduction techniques

Pathophysiology, histopathology and therapeutic of SARS-CoV-2

The rapid transmission of SARS-CoV-2 through the world has induced the scientist to understand the histopathology of the virus and then to find an effective drug. However, many of the point associated with the virus pathogenicity still unknown and need more studies. In this chapter the pathophysiology, histopathology and therapeutic of SARS-CoV-2 has been reviewed. It was appeared that pathogenicity of SARS-CoV-2 is belonging to the viral with genome structure which acting by blocking the host innate immune response. Both chloroquine and hydroxyl-chloroquine have similar structure and mechanism action and they are among the most effective antiviral for treating the patents with the SARS-CoV-2. Chloroquine works by inhibition the intracellular organism by increasing the pH