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Sep 1

High-order finite element method for atomic structure calculations

We introduce featom, an open source code that implements a high-order finite element solver for the radial Schr\"odinger, Dirac, and Kohn-Sham equations. The formulation accommodates various mesh types, such as uniform or exponential, and the convergence can be systematically controlled by increasing the number and/or polynomial order of the finite element basis functions. The Dirac equation is solved using a squared Hamiltonian approach to eliminate spurious states. To address the slow convergence of the kappa=pm1 states due to divergent derivatives at the origin, we incorporate known asymptotic forms into the solutions. We achieve a high level of accuracy (10^{-8} Hartree) for total energies and eigenvalues of heavy atoms such as uranium in both Schr\"odinger and Dirac Kohn-Sham solutions. We provide detailed convergence studies and computational parameters required to attain commonly required accuracies. Finally, we compare our results with known analytic results as well as the results of other methods. In particular, we calculate benchmark results for atomic numbers (Z) from 1 to 92, verifying current benchmarks. We demonstrate significant speedup compared to the state-of-the-art shooting solver dftatom. An efficient, modular Fortran 2008 implementation, is provided under an open source, permissive license, including examples and tests, wherein particular emphasis is placed on the independence (no global variables), reusability, and generality of the individual routines.

  • 8 authors
·
Jul 11, 2023 1

MM-SpuBench: Towards Better Understanding of Spurious Biases in Multimodal LLMs

Spurious bias, a tendency to exploit spurious correlations between superficial input attributes and prediction targets, has revealed a severe robustness pitfall in classical machine learning problems. Multimodal Large Language Models (MLLMs), which leverage pretrained vision and language models, have recently demonstrated strong capability in joint vision-language understanding. However, both the presence and severity of spurious biases in MLLMs remain poorly understood. In this work, we address this gap by analyzing the spurious biases in the multimodal setting and uncovering the specific inference-time data patterns that can manifest this problem. To support this analysis, we introduce MM-SpuBench, a comprehensive, human-verified benchmark dataset consisting of image-class pairs annotated with core and spurious attributes, grounded in our taxonomy of nine distinct types of spurious correlations. The benchmark is constructed using human-interpretable attribute information to capture a wide range of spurious patterns reflective of real-world knowledge. Leveraging this benchmark, we conduct a comprehensive evaluation of the state-of-the-art open-source and proprietary MLLMs with both standard accuracy and the proposed Conditional Generation Likelihood Advantage (CGLA). Our findings highlight the persistence of reliance on spurious correlations and the difficulty of mitigation on our benchmark. We hope this work can inspire new technical strides to mitigate these biases. Our benchmark is publicly available at https://huggingface.co/datasets/mmbench/MM-SpuBench.

  • 9 authors
·
Jun 24, 2024

Beyond Question-Based Biases: Assessing Multimodal Shortcut Learning in Visual Question Answering

We introduce an evaluation methodology for visual question answering (VQA) to better diagnose cases of shortcut learning. These cases happen when a model exploits spurious statistical regularities to produce correct answers but does not actually deploy the desired behavior. There is a need to identify possible shortcuts in a dataset and assess their use before deploying a model in the real world. The research community in VQA has focused exclusively on question-based shortcuts, where a model might, for example, answer "What is the color of the sky" with "blue" by relying mostly on the question-conditional training prior and give little weight to visual evidence. We go a step further and consider multimodal shortcuts that involve both questions and images. We first identify potential shortcuts in the popular VQA v2 training set by mining trivial predictive rules such as co-occurrences of words and visual elements. We then introduce VQA-CounterExamples (VQA-CE), an evaluation protocol based on our subset of CounterExamples i.e. image-question-answer triplets where our rules lead to incorrect answers. We use this new evaluation in a large-scale study of existing approaches for VQA. We demonstrate that even state-of-the-art models perform poorly and that existing techniques to reduce biases are largely ineffective in this context. Our findings suggest that past work on question-based biases in VQA has only addressed one facet of a complex issue. The code for our method is available at https://github.com/cdancette/detect-shortcuts.

  • 4 authors
·
Aug 31, 2021