Benjamin Englard

Vahid R. Ramezani, Benjamin Englard

Tilted (entropic) risk, obtained by applying a log-exponential transform to a base loss, is a well established tool in statistics and machine learning for emphasizing rare or high loss events while retaining a tractable optimization problem. In this work, our aim is to interpret its structure for Flow Matching (FM). FM learns a velocity field that transports samples from a simple source distribution to data by integrating an ODE. In rectified FM, training pairs are obtained by linearly interpolating between a source sample and a data sample, and a neural velocity field is trained to predict the straight line displacement using a mean squared error loss. This squared loss collapses all velocity targets that reach the same space-time point into a single conditional mean, thereby ignoring higher order conditional information (variance, skewness, multi-modality) that encodes fine geometric structure about the data manifold and minority branches. We apply the standard risk-sensitive (log-exponential) transform to the conditional FM loss and show that the resulting tilted risk loss is a natural upper-bound on a meaningful conditional entropic FM objective defined at each space-time point. Furthermore, we show that a small order expansion of the gradient of this conditional entropic objective yields two interpretable first order corrections: covariance preconditioning of the FM residual, and a skew tail term that favors asymmetric or rare branches. On synthetic data designed to probe ambiguity and tails, the resulting risk-sensitive loss improves statistical metrics and recovers geometric structure more faithfully than standard rectified FM.

Benjamin Englard

The goal of this research was to find a way to extend the capabilities of computers through the processing of language in a more human way, and present applications which demonstrate the power of this method. This research presents a novel approach, Rhetorical Analysis, to solving problems in Natural Language Processing (NLP). The main benefit of Rhetorical Analysis, as opposed to previous approaches, is that it does not require the accumulation of large sets of training data, but can be used to solve a multitude of problems within the field of NLP. The NLP problems investigated with Rhetorical Analysis were the Author Identification problem - predicting the author of a piece of text based on its rhetorical strategies, Election Prediction - predicting the winner of a presidential candidate's re-election campaign based on rhetorical strategies within that president's inaugural address, Natural Language Generation - having a computer produce text containing rhetorical strategies, and Document Summarization. The results of this research indicate that an Author Identification system based on Rhetorical Analysis could predict the correct author 100% of the time, that a re-election predictor based on Rhetorical Analysis could predict the correct winner of a re-election campaign 55% of the time, that a Natural Language Generation system based on Rhetorical Analysis could output text with up to 87.3% similarity to Shakespeare in style, and that a Document Summarization system based on Rhetorical Analysis could extract highly relevant sentences. Overall, this study demonstrated that Rhetorical Analysis could be a useful approach to solving problems in NLP.