Numerical Strategies of Computing the Luminosity Distance

We propose two efficient numerical methods of evaluating the luminosity distance in the spatially flat {\Lambda}CDM universe. The first method is based on the Carlson symmetric form of elliptic integrals, which is highly accurate and can replace numerical quadratures. The second method, using a modified version of Hermite interpolation, is less accurate but involves only basic numerical operations and can be easily implemented. We compare our methods with other numerical approximation schemes and explore their respective features and limitations. Possible extensions of these methods to other cosmological models are also discussed.Comment: 4 pages, 2 figures. v2: A minor error in the last equation has been corrected (conclusions are not affected). v3: Accepted by MNRA

Masked Images Are Counterfactual Samples for Robust Fine-tuning

Deep learning models are challenged by the distribution shift between the training data and test data. Recently, the large models pre-trained on diverse data demonstrate unprecedented robustness to various distribution shifts. However, fine-tuning on these models can lead to a trade-off between in-distribution (ID) performance and out-of-distribution (OOD) robustness. Existing methods for tackling this trade-off do not explicitly address the OOD robustness problem. In this paper, based on causal analysis on the aforementioned problems, we propose a novel fine-tuning method, which use masked images as counterfactual samples that help improving the robustness of the fine-tuning model. Specifically, we mask either the semantics-related or semantics-unrelated patches of the images based on class activation map to break the spurious correlation, and refill the masked patches with patches from other images. The resulting counterfactual samples are used in feature-based distillation with the pre-trained model. Extensive experiments verify that regularizing the fine-tuning with the proposed masked images can achieve a better trade-off between ID and OOD performance, surpassing previous methods on the OOD performance. Our code will be publicly available.Comment: Accepted by CVPR 2023 (v2: improve the clarity

Exploring Format Consistency for Instruction Tuning

Instruction tuning has emerged as a promising approach to enhancing large language models in following human instructions. It is shown that increasing the diversity and number of instructions in the training data can consistently enhance generalization performance, which facilitates a recent endeavor to collect various instructions and integrate existing instruction tuning datasets into larger collections. However, different users have their unique ways of expressing instructions, and there often exist variations across different datasets in the instruction styles and formats, i.e., format inconsistency. In this work, we study how format inconsistency may impact the performance of instruction tuning. We propose a framework called "Unified Instruction Tuning" (UIT), which calls OpenAI APIs for automatic format transfer among different instruction tuning datasets. We show that UIT successfully improves the generalization performance on unseen instructions, which highlights the importance of format consistency for instruction tuning. To make the UIT framework more practical, we further propose a novel perplexity-based denoising method to reduce the noise of automatic format transfer. We also train a smaller offline model that achieves comparable format transfer capability than OpenAI APIs to reduce costs in practice

Wave interaction and energy absorption from arrays of complex-shaped point absorbers

Water wave interactions with arrays of wave energy converters are numerically investigated based on the interaction theory. The converter is a heaving point absorber that can harness the ocean wave energy through up-and-down movements. A semi-analytical hybrid method is developed that combines the boundary element method and the interaction theory. The developed numerical method is verified against theoretical solutions for arrays of truncated vertical circular cylinders. Three different array layouts are studied in detail. It is found that trapped waves exist at critical wave numbers just below the cutoff values, and the peak load on the middle device increases with the number of devices in head waves. With the increase in the complexity of the array layout, significant wave force enhancement is observed, leading to a broader range of magnitude and stronger variations over the frequency band in beam waves. Moreover, variations of the q-factor show that there are some remarkable "bright spot"regions, indicating that the wave energy absorption there is locally optimized against wave conditions. By arranging the layout in a more randomized way, the optimal conditions for maximized power output can be hard to achieve, but the maximum power output can increase to a higher level