A spectral collocation technique based on integrated Chebyshev polynomials for biharmonic problems in irregular domains

In this paper, an integral collocation approach based on Chebyshev polynomials for numerically solving biharmonic equations [N. Mai-Duy, R.I. Tanner, A spectral collocation method based on integrated Chebyshev polynomials for biharmonic boundary-value problems, J. Comput. Appl. Math. 201 (1) (2007) 30–47] is further developed for the case of irregularly shaped domains. The problem domain is embedded in a domain of regular shape, which facilitates the use of tensor product grids. Two relevant important issues, namely the description of the boundary of the domain on a tensor product grid and the imposition of double boundary conditions, are handled effectively by means of integration constants. Several schemes of the integral collocation formulation are proposed, and their performances are numerically investigated through the interpolation of a function and the solution of 1D and 2D biharmonic problems. Results obtained show that they yield spectral accuracy

DemaFormer: Damped Exponential Moving Average Transformer with Energy-Based Modeling for Temporal Language Grounding

Temporal Language Grounding seeks to localize video moments that semantically correspond to a natural language query. Recent advances employ the attention mechanism to learn the relations between video moments and the text query. However, naive attention might not be able to appropriately capture such relations, resulting in ineffective distributions where target video moments are difficult to separate from the remaining ones. To resolve the issue, we propose an energy-based model framework to explicitly learn moment-query distributions. Moreover, we propose DemaFormer, a novel Transformer-based architecture that utilizes exponential moving average with a learnable damping factor to effectively encode moment-query inputs. Comprehensive experiments on four public temporal language grounding datasets showcase the superiority of our methods over the state-of-the-art baselines.Comment: Accepted at EMNLP 2023 (Findings

READ-PVLA: Recurrent Adapter with Partial Video-Language Alignment for Parameter-Efficient Transfer Learning in Low-Resource Video-Language Modeling

Fully fine-tuning pretrained large-scale transformer models has become a popular paradigm for video-language modeling tasks, such as temporal language grounding and video-language summarization. With a growing number of tasks and limited training data, such full fine-tuning approach leads to costly model storage and unstable training. To overcome these shortcomings, we introduce lightweight adapters to the pre-trained model and only update them at fine-tuning time. However, existing adapters fail to capture intrinsic temporal relations among video frames or textual words. Moreover, they neglect the preservation of critical task-related information that flows from the raw video-language input into the adapter's low-dimensional space. To address these issues, we first propose a novel REcurrent ADapter (READ) that employs recurrent computation to enable temporal modeling capability. Second, we propose Partial Video-Language Alignment (PVLA) objective via the use of partial optimal transport to maintain task-related information flowing into our READ modules. We validate our READ-PVLA framework through extensive experiments where READ-PVLA significantly outperforms all existing fine-tuning strategies on multiple low-resource temporal language grounding and video-language summarization benchmarks.Comment: Accepted at AAAI 202