On the Equivalence of Forward Mode Automatic Differentiation and Symbolic Differentiation

We show that forward mode automatic differentiation and symbolic differentiation are equivalent in the sense that they both perform the same operations when computing derivatives. This is in stark contrast to the common claim that they are substantially different. The difference is often illustrated by claiming that symbolic differentiation suffers from "expression swell" whereas automatic differentiation does not. Here, we show that this statement is not true. "Expression swell" refers to the phenomenon of a much larger representation of the derivative as opposed to the representation of the original function

Text Summarization Techniques: A Brief Survey

In recent years, there has been a explosion in the amount of text data from a variety of sources. This volume of text is an invaluable source of information and knowledge which needs to be effectively summarized to be useful. In this review, the main approaches to automatic text summarization are described. We review the different processes for summarization and describe the effectiveness and shortcomings of the different methods.Comment: Some of references format have update

Knowledge-rich Image Gist Understanding Beyond Literal Meaning

We investigate the problem of understanding the message (gist) conveyed by images and their captions as found, for instance, on websites or news articles. To this end, we propose a methodology to capture the meaning of image-caption pairs on the basis of large amounts of machine-readable knowledge that has previously been shown to be highly effective for text understanding. Our method identifies the connotation of objects beyond their denotation: where most approaches to image understanding focus on the denotation of objects, i.e., their literal meaning, our work addresses the identification of connotations, i.e., iconic meanings of objects, to understand the message of images. We view image understanding as the task of representing an image-caption pair on the basis of a wide-coverage vocabulary of concepts such as the one provided by Wikipedia, and cast gist detection as a concept-ranking problem with image-caption pairs as queries. To enable a thorough investigation of the problem of gist understanding, we produce a gold standard of over 300 image-caption pairs and over 8,000 gist annotations covering a wide variety of topics at different levels of abstraction. We use this dataset to experimentally benchmark the contribution of signals from heterogeneous sources, namely image and text. The best result with a Mean Average Precision (MAP) of 0.69 indicate that by combining both dimensions we are able to better understand the meaning of our image-caption pairs than when using language or vision information alone. We test the robustness of our gist detection approach when receiving automatically generated input, i.e., using automatically generated image tags or generated captions, and prove the feasibility of an end-to-end automated process