Completing low-rank matrices from subsampled measurements has received much attention in the past decade. Existing works indicate that $\mathcal{O}(nr\log^2(n))$ datums are required to theoretically secure the completion of an $n \times n$ noisy matrix of rank $r$ with high probability, under some quite restrictive assumptions: (1) the underlying matrix must be incoherent; (2) observations follow the uniform distribution. The restrictiveness is partially due to ignoring the roles of the leverage score and the oracle information of each element. In this paper, we employ the leverage scores to characterize the importance of each element and significantly relax assumptions to: (1) not any other structure assumptions are imposed on the underlying low-rank matrix; (2) elements being observed are appropriately dependent on their importance via the leverage score. Under these assumptions, instead of uniform sampling, we devise an ununiform/biased sampling procedure that can reveal the ``importance'' of each observed element. Our proofs are supported by a novel approach that phrases sufficient optimality conditions based on the Golfing Scheme, which would be of independent interest to the wider areas. Theoretical findings show that we can provably recover an unknown $n\times n$ matrix of rank $r$ from just about $\mathcal{O}(nr\log^2 (n))$ entries, even when the observed entries are corrupted with a small amount of noisy information. The empirical results align precisely with our theories.
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Replication crises have shaken the scientific landscape during the last decade. As potential solutions, open science practices were heavily discussed and have been implemented with varying success in different disciplines. We argue that computational-x disciplines such as computational social science, are also susceptible for the symptoms of the crises, but in terms of reproducibility. We expand the binary definition of reproducibility into a tier system which allows increasing levels of reproducibility based on external verfiability to counteract the practice of open-washing. We provide solutions for barriers in Computational Social Science that hinder researchers from obtaining the highest level of reproducibility, including the use of alternate data sources and considering reproducibility proactively.
The interaction of fibers in a viscous (Stokes) fluid plays a crucial role in industrial and biological processes, such as sedimentation, rheology, transport, cell division, and locomotion. Numerical simulations generally rely on slender body theory (SBT), an asymptotic, nonconvergent approximation whose error blows up as fibers approach each other. Yet convergent boundary integral equation (BIE) methods which completely resolve the fiber surface have so far been impractical due to the prohibitive cost of layer-potential quadratures in such high aspect-ratio 3D geometries. We present a high-order Nystr\"om quadrature scheme with aspect-ratio independent cost, making such BIEs practical. It combines centerline panels (each with a small number of poloidal Fourier modes), toroidal Green's functions, generalized Chebyshev quadratures, HPC parallel implementation, and FMM acceleration. We also present new BIE formulations for slender bodies that lead to well conditioned linear systems upon discretization. We test Laplace and Stokes Dirichlet problems, and Stokes mobility problems, for slender rigid closed fibers with (possibly varying) circular cross-section, at separations down to $1/20$ of the slender radius, reporting convergence typically to at least 10 digits. We use this to quantify the breakdown of numerical SBT for close-to-touching rigid fibers. We also apply the methods to time-step the sedimentation of 512 loops with up to $1.65$ million unknowns at around 7 digits of accuracy.
Generative modeling has recently undergone remarkable advancements, primarily propelled by the transformative implications of Diffusion Probabilistic Models (DPMs). The impressive capability of these models, however, often entails significant computational overhead during both training and inference. To tackle this challenge, we present Diff-Pruning, an efficient compression method tailored for learning lightweight diffusion models from pre-existing ones, without the need for extensive re-training. The essence of Diff-Pruning is encapsulated in a Taylor expansion over pruned timesteps, a process that disregards non-contributory diffusion steps and ensembles informative gradients to identify important weights. Our empirical assessment, undertaken across several datasets highlights two primary benefits of our proposed method: 1) Efficiency: it enables approximately a 50\% reduction in FLOPs at a mere 10\% to 20\% of the original training expenditure; 2) Consistency: the pruned diffusion models inherently preserve generative behavior congruent with their pre-trained models. Code is available at \url{//github.com/VainF/Diff-Pruning}.
3D speech enhancement can effectively improve the auditory experience and plays a crucial role in augmented reality technology. However, traditional convolutional-based speech enhancement methods have limitations in extracting dynamic voice information. In this paper, we incorporate a dual-path recurrent neural network block into the U-Net to iteratively extract dynamic audio information in both the time and frequency domains. And an attention mechanism is proposed to fuse the original signal, reference signal, and generated masks. Moreover, we introduce a loss function to simultaneously optimize the network in the time-frequency and time domains. Experimental results show that our system outperforms the state-of-the-art systems on the dataset of ICASSP L3DAS23 challenge.
When training powerful AI systems to perform complex tasks, it may be challenging to provide training signals which are robust to optimization. One concern is \textit{measurement tampering}, where the AI system manipulates multiple measurements to create the illusion of good results instead of achieving the desired outcome. In this work, we build four new text-based datasets to evaluate measurement tampering detection techniques on large language models. Concretely, given sets of text inputs and measurements aimed at determining if some outcome occurred, as well as a base model able to accurately predict measurements, the goal is to determine if examples where all measurements indicate the outcome occurred actually had the outcome occur, or if this was caused by measurement tampering. We demonstrate techniques that outperform simple baselines on most datasets, but don't achieve maximum performance. We believe there is significant room for improvement for both techniques and datasets, and we are excited for future work tackling measurement tampering.
With the rapid development of deep learning, training Big Models (BMs) for multiple downstream tasks becomes a popular paradigm. Researchers have achieved various outcomes in the construction of BMs and the BM application in many fields. At present, there is a lack of research work that sorts out the overall progress of BMs and guides the follow-up research. In this paper, we cover not only the BM technologies themselves but also the prerequisites for BM training and applications with BMs, dividing the BM review into four parts: Resource, Models, Key Technologies and Application. We introduce 16 specific BM-related topics in those four parts, they are Data, Knowledge, Computing System, Parallel Training System, Language Model, Vision Model, Multi-modal Model, Theory&Interpretability, Commonsense Reasoning, Reliability&Security, Governance, Evaluation, Machine Translation, Text Generation, Dialogue and Protein Research. In each topic, we summarize clearly the current studies and propose some future research directions. At the end of this paper, we conclude the further development of BMs in a more general view.
Graph Neural Networks (GNNs) have shown promising results on a broad spectrum of applications. Most empirical studies of GNNs directly take the observed graph as input, assuming the observed structure perfectly depicts the accurate and complete relations between nodes. However, graphs in the real world are inevitably noisy or incomplete, which could even exacerbate the quality of graph representations. In this work, we propose a novel Variational Information Bottleneck guided Graph Structure Learning framework, namely VIB-GSL, in the perspective of information theory. VIB-GSL advances the Information Bottleneck (IB) principle for graph structure learning, providing a more elegant and universal framework for mining underlying task-relevant relations. VIB-GSL learns an informative and compressive graph structure to distill the actionable information for specific downstream tasks. VIB-GSL deduces a variational approximation for irregular graph data to form a tractable IB objective function, which facilitates training stability. Extensive experimental results demonstrate that the superior effectiveness and robustness of VIB-GSL.
Weakly supervised phrase grounding aims at learning region-phrase correspondences using only image-sentence pairs. A major challenge thus lies in the missing links between image regions and sentence phrases during training. To address this challenge, we leverage a generic object detector at training time, and propose a contrastive learning framework that accounts for both region-phrase and image-sentence matching. Our core innovation is the learning of a region-phrase score function, based on which an image-sentence score function is further constructed. Importantly, our region-phrase score function is learned by distilling from soft matching scores between the detected object class names and candidate phrases within an image-sentence pair, while the image-sentence score function is supervised by ground-truth image-sentence pairs. The design of such score functions removes the need of object detection at test time, thereby significantly reducing the inference cost. Without bells and whistles, our approach achieves state-of-the-art results on the task of visual phrase grounding, surpassing previous methods that require expensive object detectors at test time.
Properly handling missing data is a fundamental challenge in recommendation. Most present works perform negative sampling from unobserved data to supply the training of recommender models with negative signals. Nevertheless, existing negative sampling strategies, either static or adaptive ones, are insufficient to yield high-quality negative samples --- both informative to model training and reflective of user real needs. In this work, we hypothesize that item knowledge graph (KG), which provides rich relations among items and KG entities, could be useful to infer informative and factual negative samples. Towards this end, we develop a new negative sampling model, Knowledge Graph Policy Network (KGPolicy), which works as a reinforcement learning agent to explore high-quality negatives. Specifically, by conducting our designed exploration operations, it navigates from the target positive interaction, adaptively receives knowledge-aware negative signals, and ultimately yields a potential negative item to train the recommender. We tested on a matrix factorization (MF) model equipped with KGPolicy, and it achieves significant improvements over both state-of-the-art sampling methods like DNS and IRGAN, and KG-enhanced recommender models like KGAT. Further analyses from different angles provide insights of knowledge-aware sampling. We release the codes and datasets at //github.com/xiangwang1223/kgpolicy.
Learning from a few examples remains a key challenge in machine learning. Despite recent advances in important domains such as vision and language, the standard supervised deep learning paradigm does not offer a satisfactory solution for learning new concepts rapidly from little data. In this work, we employ ideas from metric learning based on deep neural features and from recent advances that augment neural networks with external memories. Our framework learns a network that maps a small labelled support set and an unlabelled example to its label, obviating the need for fine-tuning to adapt to new class types. We then define one-shot learning problems on vision (using Omniglot, ImageNet) and language tasks. Our algorithm improves one-shot accuracy on ImageNet from 87.6% to 93.2% and from 88.0% to 93.8% on Omniglot compared to competing approaches. We also demonstrate the usefulness of the same model on language modeling by introducing a one-shot task on the Penn Treebank.
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