Flow-based generative models have shown promise in various machine learning applications, but they often face challenges in handling noise and ensuring robustness in trajectory estimation. In this work, we propose NRFlow, a novel extension to flow-based generative modeling that incorporates second-order dynamics through acceleration fields. We develop a comprehensive theoretical framework to analyze the regularization effects of high-order terms and derive noise robustness guarantees. Our method leverages a two-part loss function to simultaneously train first-order velocity fields and high-order acceleration fields, enhancing both smoothness and stability in learned transport trajectories. These results highlight the potential of high-order flow matching for robust generative modeling in complex and noisy environments.

We introduce a new neural network based similarity model for learning document relevance under a query. The main idea is to use the binomial distribution to model the proportion of people who clicked document d under query q among the users who viewed d under q. Our model is a generalization of existing neural network based latent semantic models in that both its objective function and its parametrization of the user click probability generalizes the existing ones. Compared with the existing models, our new objective function distinguishes the clicked (query, document)-pairs with different relevance information, and our new parametrization of the user click probability considers both the semantic similarity and the term or lexical match information as the reasons for click(s). We tested our model on the media search logs of a commercial search engine and obtained superior performance under several metrics for relevance ranking.

Lack of high quality relevance labels is a common challenge in the early stage of search engine development. In media search, due to the high recruiting and training cost, the labeling process is usually conducted by a small number of human judges. Consequently, the generated labels are often limited and biased. On the contrary, the click data that is extracted from a large population of real users is massive and less biased. However, the click data also contains considerable noise. Therefore, more and more researchers have begun to focus on combining those two resources to generate a better ground-truth approximation. In this paper, we present a novel method of generating the relevance labels for media search. The method is based on a generative model that considers human judgment, position, and click status as observations generated from a hidden relevance with multinomial prior. The model considers the position bias with a requirement that the click status depends on both the hidden relevance and the position. We infer the model parameters by using a Gibbs sampling procedure with hyper-parameter optimization. From experiments on the Xbox's data, the newly inferred relevance labels significantly increase the data volume for ranker training and have demonstrated superior performance compared to using the limited human labels only, the click-through-rates only, and the heuristic combination of the two.

MOTIVATION: Pairwise protein sequence alignments are generally evaluated using scores defined as the sum of substitution scores for aligning amino acids to one another, and gap scores for aligning runs of amino acids in one sequence to null characters inserted into the other. Protein profiles may be abstracted from multiple alignments of protein sequences, and substitution and gap scores have been generalized to the alignment of such profiles either to single sequences or to other profiles. Although there is widespread agreement on the general form substitution scores should take for profile-sequence alignment, little consensus has been reached on how best to construct profile-profile substitution scores, and a large number of these scoring systems have been proposed. Here, we assess a variety of such substitution scores. For this evaluation, given a gold standard set of multiple alignments, we calculate the probability that a profile column yields a higher substitution score when aligned to a related than to an unrelated column. We also generalize this measure to sets of two or three adjacent columns. This simple approach has the advantages that it does not depend primarily upon the gold-standard alignment columns with the weakest empirical support, and that it does not need to fit gap and offset costs for use with each substitution score studied. RESULTS: A simple symmetrization of mean profile-sequence scores usually performed the best. These were followed closely by several specific scoring systems constructed using a variety of rationales. CONTACT: [email protected] SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.