Abstract. We consider the quantum complexities of the following three problems: searching an ordered list, sorting an un-ordered list, and deciding whether the numbers in a list are all distinct. Letting N be the number of elements in the input list, we prove a lower bound of 1 π (ln(N ) − 1) accesses to the list elements for ordered searching, a lower bound of Ω(N log N ) binary comparisons for sorting, and a lower bound of Ω( √ N log N ) binary comparisons for element distinctness. The previously best known lower bounds are 1 12 log 2 (N ) − O(1) due to Ambainis, Ω(N ), and Ω( √ N ), respectively. Our proofs are based on a weighted all-pairs inner product argument.In addition to our lower bound results, we give a quantum algorithm for ordered searching using roughly 0.631 log 2 (N ) oracle accesses. Our algorithm uses a quantum routine for traversing through a binary search tree faster than classically, and it is of a nature very different from a faster algorithm due to Farhi, Goldstone, Gutmann, and Sipser.
Representation or embedding based machine learning models, such as language models or convolutional neural networks have shown great potential for improved performance. However, for complex models on large datasets training time can be extensive, approaching weeks, which is often infeasible in practice. In this work, we present a method to reduce training time substantially by selecting training instances that provide relevant information for training. Selection is based on the similarity of the learned representations over input instances, thus allowing for learning a non-trivial weighting scheme from multi-dimensional representations. We demonstrate the efficiency and effectivity of our approach in several text classification tasks using recursive neural networks. Our experiments show that by removing approximately one fifth of the training data the objective function converges up to six times faster without sacrificing accuracy.
The amount of data for processing and categorization grows at an ever increasing rate. At the same time the demand for collaboration and transparency in organizations, government and businesses, drives the release of data from internal repositories to the public or 3rd party domain. This in turn increase the potential of sharing sensitive information. The leak of sensitive information can potentially be very costly, both financially for organizations, but also for individuals. In this work we address the important problem of sensitive information detection. Specially we focus on detection in unstructured text documents.We show that simplistic, brittle rule sets for detecting sensitive information only find a small fraction of the actual sensitive information. Furthermore we show that previous state-of-the-art approaches have been implicitly tailored to such simplistic scenarios and thus fail to detect actual sensitive content.We develop a novel family of sensitive information detection approaches which only assumes access to labeled examples, rather than unrealistic assumptions such as access to a set of generating rules or descriptive topical seed words. Our approaches are inspired by the current state-of-the-art for paraphrase detection and we adapt deep learning approaches over recursive neural networks to the problem of sensitive information detection. We show that our context-based approaches significantly outperforms the family of previous state-of-the-art approaches for sensitive information detection, so-called keyword-based approaches, on real-world data and with human labeled examples of sensitive and non-sensitive documents.A key challenge in the field of sensitive information detection is the lack of publicly available real-world datasets on which to train and/or benchmark on. This is due to the inherent sensitive nature of the data in question. We address this issue in this work by releasing publicly labeled examples of sensitive and non-sensitive content. We release a total of 8 different types of sensitive information over 2 distinct sets of documents. We utilize efforts by human domain experts in labeling both datasets for 4 complex types of informational content for each set of documents. This release totals 750, 000 labeled sentences with their parse trees for the research community to make use of. i ResuméMaengden af information tilgaengeligt som skal kunne automatisk håndteres og bearbejdes vokser eksplosivt. Dette sker samtidigt med øget fokus på deling af data og krav om transparens. Dette øger risikoen for deling af potentielt følsomme oplysninger som ikke skulle have vaeret delt. Sådanne fejlagtige delinger og afsløringer af følsomme oplysninger er forbundet med høje omkostninger. I denne afhandling adresseres det voksende og komplekse problemområde omkring at finde følsomme informationer ved hjaelp af datalogiske algoritmer. Specifikt fokuseres på at finde følsomme oplysninger i ustrukturerede tekst dokumenter.Vi påviser at simple regelsaet kun finder en relativ lille del af de faktiske f...
We consider the quantum complexities of the following three problems: searching an ordered list, sorting an un-ordered list, and deciding whether the numbers in a list are all distinct. Letting N be the number of elements in the input list, we prove a lower bound of (1/π )(ln(N ) − 1) accesses to the list elements for ordered searching, a lower bound of (N log N ) binary comparisons for sorting, and a lower bound of ( √ N log N ) binary comparisons for element distinctness. The previously best known lower bounds are 1 12 log 2 (N ) − O(1) due to Ambainis, (N ), and ( √ N ), respectively. Our proofs are based on a weighted all-pairs inner product argument.In addition to our lower bound results, we give an exact quantum algorithm for ordered searching using roughly 0.631 log 2 (N ) oracle accesses. Our algorithm uses a quantum routine for traversing through a binary search tree faster than classically, and it is of a nature very different from a faster exact algorithm due to Farhi, Goldstone, Gutmann, and Sipser. Introduction.The speedups of quantum algorithms over classical algorithms have been a main reason for the current interest in quantum computing. One central question regarding the power of quantum computing is: How much speedup is possible? Although dramatic speedups seem possible, as in the case of Shor's [23] algorithms for factoring and finding discrete logarithms, superpolynomial speedups are so far proven only in restricted models such as the black box model.In the black box model the input is given as a black box, so that the only way the algorithm can obtain information about the input is via queries, and the complexity measure is the number of queries. Many problems that allow provable quantum speedups can be formulated in this model, an example being the unordered search problem considered by Grover [18]. Several tight lower bounds are now known for this model, most of them being based on techniques introduced in [6], [4], and [2].
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