With advances in the quality of text-to-image (T2I) models has come interest in benchmarking their prompt faithfulness --the semantic coherence of generated images to the prompts they were conditioned on. A variety of T2I faithfulness metrics have been proposed, leveraging advances in cross-modal embeddings and vision-language models (VLMs).

We consider the problem of prediction with expert advice for ``easy'' sequences. We show that a variant of NormalHedge enjoys a second-order $ε$-quantile regret bound of $O\big(\sqrt{V_T \log(V_T/ε)}\big) $ when $V_T > \log N$, where $V_T$ is the cumulative second moment of instantaneous per-expert regret averaged with respect to a natural distribution determined by the algorithm. The algorithm is motivated by a continuous time limit using Stochastic Differential Equations. The discrete time analysis uses self-concordance techniques.

To explore topologically complex free spaces and identify critical pathways, task-space topology analysis is employed to explicitly model free space connectivity and find critical regions. Due to the sampling inefficiency encountered when planning through narrow passages in high-dimensional C-space, a keyframe-guided sampling-based planner is developed that leverages topological insights from high-level analysis to explore C-space. Experimental validation is conducted demonstrating the effectiveness and efficiency of proposed method compared to state-of-the-art planning baselines on manipulation tasks involving elongated objects and narrow passages. Remainder of the article is organized as follows. Section II formally defines the planning problem. Section III details the proposed topology-aware high-level planning approach. In Section IV, the method for low-level path generation is presented. Section V describes experimental setup and results used to evaluate the performance of proposed method. Finally, Section VI provides a brief summary of the work and discusses directions for future research.

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The input image was cropped into a fix size of 512 512 using zero padding if needed.