Controlled generation with pre-trained Diffusion and Flow Matching models has vast applications. One strategy for guiding ODE-based generative models is through optimizing a target loss $R(x_1)$ while staying close to the prior distribution. Along this line, some recent work showed the effectiveness of guiding flow model by differentiating through its ODE sampling process. Despite the superior performance, the theoretical understanding of this line of methods is still preliminary, leaving space for algorithm improvement. Moreover, existing methods predominately focus on Euclidean data manifold, and there is a compelling need for guided flow methods on complex geometries such as SO(3), which prevails in high-stake scientific applications like protein design. We present OC-Flow, a general and theoretically grounded training-free framework for guided flow matching using optimal control. Building upon advances in optimal control theory, we develop effective and practical algorithms for solving optimal control in guided ODE-based generation and provide a systematic theoretical analysis of the convergence guarantee in both Euclidean and SO(3). We show that existing backprop-through-ODE methods can be interpreted as special cases of Euclidean OC-Flow. OC-Flow achieved superior performance in extensive experiments on text-guided image manipulation, conditional molecule generation, and all-atom peptide design.

Understanding the contribution of the inputs on the output is useful across many tasks.This work provides an information-theoretic framework to analyse the influence of inputs for text classification tasks.Natural language processing (NLP) tasks take either a single or multiple text elements to predict an output variable.Each text element has two components: the semantic meaning and a linguistic realization.Multiple-choice reading comprehension (MCRC) and sentiment classification (SC) are selected to showcase the framework.For MCRC, it is found that the relative context influence on the output reduces on more challenging datasets.In particular, more challenging contexts allows greater variation in the question complexity.Hence, test creators need to carefully consider the choice of the context when designing multiple-choice questions for assessment.For SC, it is found the semantic meaning of the input dominates compared to its linguistic realization when determining the sentiment.The framework is made available at: https://github.com/WangLuran/n lp-element-influence.

This small qualitative study evaluates UCL Engineering students’ experiences and perceptions of online PBL during the 2020-21 academic year. Study findings suggest that although the transition to online learning was not smooth, most students ultimately became agile online PBL learners. The study suggests that PBL in the post-COVID-19 era is likely to be blended, with some aspects best delivered in-person and some aspects best delivered online.