In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.

Q: This paper presents a theoretical, idealized model of the thinking process with the following characteristics: 1) the model can produce complex thought sequences and can be generalized to new inputs, 2) it can receive and maintain input information indefinitely for the generation of thoughts and later use, and 3) it supports learning while executing. The crux of the model lies within the concept of internal consistency, or the generated thoughts should always be consistent with the inputs from which they are created. Its merit, apart from the capability to generate new creative thoughts from an internal mechanism, depends on the potential to help training to generalize better. This is consequently enabled by separating input information into several parts to be handled by different processing components with a focus mechanism to fetch information for each. This modularized view with the focus binds the model with the computationally capable Turing machines. And as a final remark, this paper constructively shows that the computational complexity of the model is at least, if not surpass, that of a universal Turing machine.

A: (Yet) Another Theoretical Model of Thinking
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Q: Kernel canonical correlation analysis (KCCA) is a nonlinear multi-view representation learning technique with broad applicability in statistics and machine learning. Although there is a closed-form solution for the KCCA objective, it involves solving an N N eigenvalue system where N is the training set size, making its computational requirements in both memory and time prohibitive for large-scale problems. Various approximation techniques have been developed for KCCA. A commonly used approach is to first transform the original inputs to an M -dimensional random feature space so that inner products in the feature space approximate kernel evaluations, and then apply linear CCA to the transformed inputs. In many applications, however, the dimensionality M of the random feature space may need to be very large in order to obtain a sufficiently good approximation; it then becomes challenging to perform the linear CCA step on the resulting very high-dimensional data matrices. We show how to use a stochastic optimization algorithm, recently proposed for linear CCA and its neuralnetwork extension, to further alleviate the computation requirements of approximate KCCA. This approach allows us to run approximate KCCA on a speech dataset with 1.4 million training samples and a random feature space of dimensionality M = 100000 on a typical workstation.

A: LARGE-SCALE APPROXIMATE KERNEL CANONICAL CORRELATION ANALYSIS
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Q: Sparse PCA provides a linear combination of small number of features that maximizes variance across data. Although Sparse PCA has apparent advantages compared to PCA, such as better interpretability, it is generally thought to be computationally much more expensive. In this paper, we demonstrate the surprising fact that sparse PCA can be easier than PCA in practice, and that it can be reliably applied to very large data sets. This comes from a rigorous feature elimination pre-processing result, coupled with the favorable fact that features in real-life data typically have exponentially decreasing variances, which allows for many features to be eliminated. We introduce a fast block coordinate ascent algorithm with much better computational complexity than the existing first-order ones. We provide experimental results obtained on text corpora involving millions of documents and hundreds of thousands of features. These results illustrate how Sparse PCA can help organize a large corpus of text data in a user-interpretable way, providing an attractive alternative approach to topic models.

A:
Large-Scale Sparse Principal Component Analysis with Application to Text Data
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