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Optimization over the set of matrices $X$ that satisfy $X^\top B X = I_p$, referred to as the generalized Stiefel manifold, appears in many applications involving sampled covariance matrices such as the canonical correlation analysis (CCA), independent component analysis (ICA), and the generalized eigenvalue problem (GEVP). Solving these problems is typically done by iterative methods that require a fully formed $B$. We propose a cheap stochastic iterative method that solves the optimization problem while having access only to random estimates of $B$. Our method does not enforce the constraint in every iteration; instead, it produces iterations that converge to critical points on the generalized Stiefel manifold defined in expectation. The method has lower per-iteration cost, requires only matrix multiplications, and has the same convergence rates as its Riemannian optimization counterparts that require the full matrix $B$. Experiments demonstrate its effectiveness in various machine learning applications involving generalized orthogonality constraints, including CCA, ICA, and the GEVP.

Lifelong few-shot customization for text-to-image diffusion aims to continually generalize existing models for new tasks with minimal data while preserving old knowledge. Current customization diffusion models excel in few-shot tasks but struggle with catastrophic forgetting problems in lifelong generations. In this study, we identify and categorize the catastrophic forgetting problems into two folds: relevant concepts forgetting and previous concepts forgetting. To address these challenges, we first devise a data-free knowledge distillation strategy to tackle relevant concepts forgetting. Unlike existing methods that rely on additional real data or offline replay of original concept data, our approach enables on-the-fly knowledge distillation to retain the previous concepts while learning new ones, without accessing any previous data. Second, we develop an In-Context Generation (ICGen) paradigm that allows the diffusion model to be conditioned upon the input vision context, which facilitates the few-shot generation and mitigates the issue of previous concepts forgetting. Extensive experiments show that the proposed Lifelong Few-Shot Diffusion (LFS-Diffusion) method can produce high-quality and accurate images while maintaining previously learned knowledge.

Recent advances have demonstrated that large language models (LLMs) excel as listwise rerankers, but their high computational demands remain a barrier to widespread adoption. Further, the traditional language modeling (LM) objective is not ideally suited for reranking tasks. FIRST is a novel approach that addresses these challenges by integrating a learning-to-rank objective and leveraging the logits of only the first generated token, thereby significantly reducing inference latency compared to traditional LLM rerankers. In this study, we extend the evaluation of FIRST to the TREC Deep Learning datasets (DL19-22), validating its robustness across diverse domains. We investigate the influence of different first-stage retrievers on FIRST rerankers, observing diminishing returns and patterns consistent with traditional LLM rerankers. Through applying the FIRST objective to a broader range of backbone models, we achieve effectiveness surpassing the original implementation. Our experiments confirm that fast reranking with single-token logits does not compromise out-of-domain reranking quality. To better quantify the computational savings in the original study, we measure and compare latency to find a 21%-42% gain across various models and benchmarks. Moreover, while LM training implicitly improves zero-shot single-token reranking, our experiments also raise questions about whether LM pre-training may hinder subsequent fine-tuning with the FIRST objective. These findings pave the way for more efficient and effective listwise reranking in future applications.

This paper analyzes the impact of causal manner in the text encoder of text-to-image (T2I) diffusion models, which can lead to information bias and loss. Previous works have focused on addressing the issues through the denoising process. However, there is no research discussing how text embedding contributes to T2I models, especially when generating more than one object. In this paper, we share a comprehensive analysis of text embedding: i) how text embedding contributes to the generated images and ii) why information gets lost and biases towards the first-mentioned object. Accordingly, we propose a simple but effective text embedding balance optimization method, which is training-free, with an improvement of 125.42% on information balance in stable diffusion. Furthermore, we propose a new automatic evaluation metric that quantifies information loss more accurately than existing methods, achieving 81% concordance with human assessments. This metric effectively measures the presence and accuracy of objects, addressing the limitations of current distribution scores like CLIP's text-image similarities.

In this paper, we investigate $C^2$ super-smoothness of the full $C^1$ cubic spline space on a Powell-Sabin refined triangulation, for which a B-spline basis can be constructed. Blossoming is used to identify the $C^2$ smoothness conditions between the functionals of the dual basis. Some of these conditions can be enforced without difficulty on general triangulations. Others are more involved but greatly simplify if the triangulation and its corresponding Powell-Sabin refinement possess certain symmetries. Furthermore, it is shown how the $C^2$ smoothness constraints can be integrated into the spline representation by reducing the set of basis functions. As an application of the super-smooth basis functions, a reduced spline space is introduced that maintains the cubic precision of the full $C^1$ spline space.

The development of large language models (LLMs) has expanded to multi-modal systems capable of processing text, images, and speech within a unified framework. Training these models demands significantly larger datasets and computational resources compared to text-only LLMs. To address the scaling challenges, we introduce Mixture-of-Transformers (MoT), a sparse multi-modal transformer architecture that significantly reduces pretraining computational costs. MoT decouples non-embedding parameters of the model by modality -- including feed-forward networks, attention matrices, and layer normalization -- enabling modality-specific processing with global self-attention over the full input sequence. We evaluate MoT across multiple settings and model scales. In the Chameleon 7B setting (autoregressive text-and-image generation), MoT matches the dense baseline's performance using only 55.8\% of the FLOPs. When extended to include speech, MoT reaches speech performance comparable to the dense baseline with only 37.2\% of the FLOPs. In the Transfusion setting, where text and image are trained with different objectives, a 7B MoT model matches the image modality performance of the dense baseline with one third of the FLOPs, and a 760M MoT model outperforms a 1.4B dense baseline across key image generation metrics. System profiling further highlights MoT's practical benefits, achieving dense baseline image quality in 47.2\% of the wall-clock time and text quality in 75.6\% of the wall-clock time (measured on AWS p4de.24xlarge instances with NVIDIA A100 GPUs).

We introduce a simple, stochastic, a-posteriori, turbulence closure model based on a reduced subgrid scale term. This subgrid scale term is tailor-made to capture the statistics of a small set of spatially-integrate quantities of interest (QoIs), with only one unresolved scalar time series per QoI. In contrast to other data-driven surrogates the dimension of the "learning problem" is reduced from an evolving field to one scalar time series per QoI. We use an a-posteriori, nudging approach to find the distribution of the scalar series over time. This approach has the advantage of taking the interaction between the solver and the surrogate into account. A stochastic surrogate parametrization is obtained by random sampling from the found distribution for the scalar time series. Compared to an a-priori trained convolutional neural network, evaluating the new method is computationally much cheaper and gives similar long-term statistics.

In the current Video-based Dynamic Mesh Coding (V-DMC) standard, inter-frame coding is restricted to mesh frames with constant topology. Consequently, temporal redundancy is not fully leveraged, resulting in suboptimal compression efficacy. To address this limitation, this paper introduces a novel coarse-to-fine scheme to generate anchor meshes for frames with time-varying topology. Initially, we generate a coarse anchor mesh using an octree-based nearest neighbor search. Motion estimation compensates for regions with significant motion changes during this process. However, the quality of the coarse mesh is low due to its suboptimal vertices. To enhance details, the fine anchor mesh is further optimized using the Quadric Error Metrics (QEM) algorithm to calculate more precise anchor points. The inter-frame anchor mesh generated herein retains the connectivity of the reference base mesh, while concurrently preserving superior quality. Experimental results show that our method achieves 7.2% ~ 10.3% BD-rate gain compared to the existing V-DMC test model version 7.

Commit Message Generation (CMG) approaches aim to automatically generate commit messages based on given code diffs, which facilitate collaboration among developers and play a critical role in Open-Source Software (OSS). Very recently, Large Language Models (LLMs) have demonstrated extensive applicability in diverse code-related task. But few studies systematically explored their effectiveness using LLMs. This paper conducts the first comprehensive experiment to investigate how far we have been in applying LLM to generate high-quality commit messages. Motivated by a pilot analysis, we first clean the most widely-used CMG dataset following practitioners' criteria. Afterward, we re-evaluate diverse state-of-the-art CMG approaches and make comparisons with LLMs, demonstrating the superior performance of LLMs against state-of-the-art CMG approaches. Then, we further propose four manual metrics following the practice of OSS, including Accuracy, Integrity, Applicability, and Readability, and assess various LLMs accordingly. Results reveal that GPT-3.5 performs best overall, but different LLMs carry different advantages. To further boost LLMs' performance in the CMG task, we propose an Efficient Retrieval-based In-Context Learning (ICL) framework, namely ERICommiter, which leverages a two-step filtering to accelerate the retrieval efficiency and introduces semantic/lexical-based retrieval algorithm to construct the ICL examples. Extensive experiments demonstrate the substantial performance improvement of ERICommiter on various LLMs for code diffs of different programming languages. Meanwhile, ERICommiter also significantly reduces the retrieval time while keeping almost the same performance. Our research contributes to the understanding of LLMs' capabilities in the CMG field and provides valuable insights for practitioners seeking to leverage these tools in their workflows.

Pre-trained Language Models (PLMs) which are trained on large text corpus via self-supervised learning method, have yielded promising performance on various tasks in Natural Language Processing (NLP). However, though PLMs with huge parameters can effectively possess rich knowledge learned from massive training text and benefit downstream tasks at the fine-tuning stage, they still have some limitations such as poor reasoning ability due to the lack of external knowledge. Research has been dedicated to incorporating knowledge into PLMs to tackle these issues. In this paper, we present a comprehensive review of Knowledge-Enhanced Pre-trained Language Models (KE-PLMs) to provide a clear insight into this thriving field. We introduce appropriate taxonomies respectively for Natural Language Understanding (NLU) and Natural Language Generation (NLG) to highlight these two main tasks of NLP. For NLU, we divide the types of knowledge into four categories: linguistic knowledge, text knowledge, knowledge graph (KG), and rule knowledge. The KE-PLMs for NLG are categorized into KG-based and retrieval-based methods. Finally, we point out some promising future directions of KE-PLMs.