Theorem Proving Using Sparse Integer Matrices


Theorem Proving Using Sparse Integer Matrices – This paper addresses the problem of sparse linear regression under natural language models. We show that nonnegative sparse linear regression performs the exact same as one-dimensional regression under standard nonnegative matrix factorization (NMF). The problem is NP-hard for linear regression and finite-time linear regression, which is the classic unsolved problem in statistical physics and computer science. We show that such sparse linear regression has special constraints on the number of variables that make it possible to find the best solution. We formulate such sparse linear regression problems as nonnegative matrix factorization problems, where there are several conditions on the solution matrix. The constraint conditions allow us to approximate the solution matrix in the restricted case. The computational power of our algorithm is compared and compared to that of the standard nonnegative linear regression algorithm. We show that the constraints give good bounds, and the algorithm is able to cope with the restricted case even under sparse linear regression.

In this paper, we propose an end-to-end, fully convolution network which allows for efficient extraction of the low-level information in speech and visual data. The proposed model is a multi-stage, fully convolutional network and utilizes the convolutional layers together to learn a hierarchical representation. After learning, the extracted high-level information is used as a discriminator for inferring the audio patterns to be extracted, and then a sequence of the high-level information is then extracted from the discriminator. Based on the proposed model, the neural network is trained without any additional preprocessing step. To the best of our knowledge, this is the first fully-convolutional neural network that can be used for speech retrieval tasks.

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Theorem Proving Using Sparse Integer Matrices

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  • Explanation-based analysis of taxonomic information in taxonomical text

    Adaptive Sparse Convolutional Features For Deep Neural Network-based Audio ClassificationIn this paper, we propose an end-to-end, fully convolution network which allows for efficient extraction of the low-level information in speech and visual data. The proposed model is a multi-stage, fully convolutional network and utilizes the convolutional layers together to learn a hierarchical representation. After learning, the extracted high-level information is used as a discriminator for inferring the audio patterns to be extracted, and then a sequence of the high-level information is then extracted from the discriminator. Based on the proposed model, the neural network is trained without any additional preprocessing step. To the best of our knowledge, this is the first fully-convolutional neural network that can be used for speech retrieval tasks.


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