Multiscale mixed methods based on non-overlapping domain decompositions can efficiently handle the solution of significant subsurface flow problems in very heterogeneous formations of interest to the industry, especially when implemented on multi-core supercomputers. Efficiency in obtaining numerical solutions is dictated by the choice of interface spaces that are selected: the smaller the dimension of these spaces, the better, in the sense that fewer multiscale basis functions need to be computed, and smaller interface linear systems need to be solved. Thus, in solving large computational problems, it is desirable to work with piecewise constant or linear polynomials for interface spaces. However, for these choices of interface spaces, it is well known that the flux accuracy is of the order of 10-1. This study is dedicated to advancing an efficient and accurate multiscale mixed method aimed at addressing industry-relevant problems. A distinctive feature of our approach involves subdomains with overlapping regions, a departure from conventional methods. We take advantage of the overlapping decomposition to introduce a computationally highly efficient smoothing step designed to rectify small-scale errors inherent in the multiscale solution. The effectiveness of the proposed solver, which maintains a computational cost very close to its predecessors, is demonstrated through a series of numerical studies. Notably, for scenarios involving modestly sized overlapping regions and employing just a few smoothing steps, a substantial enhancement of two orders of magnitude in flux accuracy is achieved with the new approach.
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The evaluation of English text embeddings has transitioned from evaluating a handful of datasets to broad coverage across many tasks through benchmarks such as MTEB. However, this is not the case for multilingual text embeddings due to a lack of available benchmarks. To address this problem, we introduce the Scandinavian Embedding Benchmark (SEB). SEB is a comprehensive framework that enables text embedding evaluation for Scandinavian languages across 24 tasks, 10 subtasks, and 4 task categories. Building on SEB, we evaluate more than 26 models, uncovering significant performance disparities between public and commercial solutions not previously captured by MTEB. We open-source SEB and integrate it with MTEB, thus bridging the text embedding evaluation gap for Scandinavian languages.
Music generation schemes using language modeling rely on a vocabulary of audio tokens, generally provided as codes in a discrete latent space learnt by an auto-encoder. Multi-stage quantizers are often employed to produce these tokens, therefore the decoding strategy used for token prediction must be adapted to account for multiple codebooks: either it should model the joint distribution over all codebooks, or fit the product of the codebook marginal distributions. Modelling the joint distribution requires a costly increase in the number of auto-regressive steps, while fitting the product of the marginals yields an inexact model unless the codebooks are mutually independent. In this work, we introduce an independence-promoting loss to regularize the auto-encoder used as the tokenizer in language models for music generation. The proposed loss is a proxy for mutual information based on the maximum mean discrepancy principle, applied in reproducible kernel Hilbert spaces. Our criterion is simple to implement and train, and it is generalizable to other multi-stream codecs. We show that it reduces the statistical dependence between codebooks during auto-encoding. This leads to an increase in the generated music quality when modelling the product of the marginal distributions, while generating audio much faster than the joint distribution model.
Text-to-video generation has lagged behind text-to-image synthesis in quality and diversity due to the complexity of spatio-temporal modeling and limited video-text datasets. This paper presents I4VGen, a training-free and plug-and-play video diffusion inference framework, which enhances text-to-video generation by leveraging robust image techniques. Specifically, following text-to-image-to-video, I4VGen decomposes the text-to-video generation into two stages: anchor image synthesis and anchor image-guided video synthesis. Correspondingly, a well-designed generation-selection pipeline is employed to achieve visually-realistic and semantically-faithful anchor image, and an innovative Noise-Invariant Video Score Distillation Sampling is incorporated to animate the image to a dynamic video, followed by a video regeneration process to refine the video. This inference strategy effectively mitigates the prevalent issue of non-zero terminal signal-to-noise ratio. Extensive evaluations show that I4VGen not only produces videos with higher visual realism and textual fidelity but also integrates seamlessly into existing image-to-video diffusion models, thereby improving overall video quality.
Mixed linear regression is a well-studied problem in parametric statistics and machine learning. Given a set of samples, tuples of covariates and labels, the task of mixed linear regression is to find a small list of linear relationships that best fit the samples. Usually it is assumed that the label is generated stochastically by randomly selecting one of two or more linear functions, applying this chosen function to the covariates, and potentially introducing noise to the result. In that situation, the objective is to estimate the ground-truth linear functions up to some parameter error. The popular expectation maximization (EM) and alternating minimization (AM) algorithms have been previously analyzed for this. In this paper, we consider the more general problem of agnostic learning of mixed linear regression from samples, without such generative models. In particular, we show that the AM and EM algorithms, under standard conditions of separability and good initialization, lead to agnostic learning in mixed linear regression by converging to the population loss minimizers, for suitably defined loss functions. In some sense, this shows the strength of AM and EM algorithms that converges to ``optimal solutions'' even in the absence of realizable generative models.
We propose a novel nonparametric sequential test for composite hypotheses for means of multiple data streams. Our proposed method, \emph{peeking with expectation-based averaged capital} (PEAK), builds upon the testing-by-betting framework and provides a non-asymptotic $\alpha$-level test across any stopping time. Our contributions are two-fold: (1) we propose a novel betting scheme and provide theoretical guarantees on type-I error control, power, and asymptotic growth rate/$e$-power in the setting of a single data stream; (2) we introduce PEAK, a generalization of this betting scheme to multiple streams, that (i) avoids using wasteful union bounds via averaging, (ii) is a test of power one under mild regularity conditions on the sampling scheme of the streams, and (iii) reduces computational overhead when applying the testing-as-betting approaches for pure-exploration bandit problems. We illustrate the practical benefits of PEAK using both synthetic and real-world HeartSteps datasets. Our experiments show that PEAK provides up to an 85\% reduction in the number of samples before stopping compared to existing stopping rules for pure-exploration bandit problems, and matches the performance of state-of-the-art sequential tests while improving upon computational complexity.
Although recent generative image compression methods have demonstrated impressive potential in optimizing the rate-distortion-perception trade-off, they still face the critical challenge of flexible rate adaption to diverse compression necessities and scenarios. To overcome this challenge, this paper proposes a Controllable Generative Image Compression framework, Control-GIC, the first capable of fine-grained bitrate adaption across a broad spectrum while ensuring high-fidelity and generality compression. We base Control-GIC on a VQGAN framework representing an image as a sequence of variable-length codes (i.e. VQ-indices), which can be losslessly compressed and exhibits a direct positive correlation with the bitrates. Therefore, drawing inspiration from the classical coding principle, we naturally correlate the information density of local image patches with their granular representations, to achieve dynamic adjustment of the code quantity following different granularity decisions. This implies we can flexibly determine a proper allocation of granularity for the patches to acquire desirable compression rates. We further develop a probabilistic conditional decoder that can trace back to historic encoded multi-granularity representations according to transmitted codes, and then reconstruct hierarchical granular features in the formalization of conditional probability, enabling more informative aggregation to improve reconstruction realism. Our experiments show that Control-GIC allows highly flexible and controllable bitrate adaption and even once compression on an entire dataset to fulfill constrained bitrate conditions. Experimental results demonstrate its superior performance over recent state-of-the-art methods.
Large Language Models (LLMs) have highlighted the necessity of effective unlearning mechanisms to comply with data regulations and ethical AI practices. LLM unlearning aims at removing undesired data influences and associated model capabilities without compromising utility out of the scope of unlearning. While interest in studying LLM unlearning is growing,the impact of the optimizer choice for LLM unlearning remains under-explored. In this work, we shed light on the significance of optimizer selection in LLM unlearning for the first time, establishing a clear connection between {second-order optimization} and influence unlearning (a classical approach using influence functions to update the model for data influence removal). This insight propels us to develop a second-order unlearning framework, termed SOUL, built upon the second-order clipped stochastic optimization (Sophia)-based LLM training method. SOUL extends the static, one-shot model update using influence unlearning to a dynamic, iterative unlearning process. Our extensive experiments show that SOUL consistently outperforms conventional first-order methods across various unlearning tasks, models, and metrics, suggesting the promise of second-order optimization in providing a scalable and easily implementable solution for LLM unlearning.
The increasing size of deep neural networks necessitates effective model compression to improve computational efficiency and reduce their memory footprint. Sparsity and quantization are two prominent compression methods that have individually demonstrated significant reduction in computational and memory footprints while preserving model accuracy. While effective, the interplay between these two methods remains an open question. In this paper, we investigate the interaction between these two methods and assess whether their combination impacts final model accuracy. We mathematically prove that applying sparsity before quantization is the optimal sequence for these operations, minimizing error in computation. Our empirical studies across a wide range of models, including OPT and Llama model families (125M-8B) and ViT corroborate these theoretical findings. In addition, through rigorous analysis, we demonstrate that sparsity and quantization are not orthogonal; their interaction can significantly harm model accuracy, with quantization error playing a dominant role in this degradation. Our findings extend to the efficient deployment of large models in resource-limited compute platforms and reduce serving cost, offering insights into best practices for applying these compression methods to maximize efficacy without compromising accuracy.
As machine learning tasks continue to evolve, the trend has been to gather larger datasets and train increasingly larger models. While this has led to advancements in accuracy, it has also escalated computational costs to unsustainable levels. Addressing this, our work aims to strike a delicate balance between computational efficiency and model accuracy, a persisting challenge in the field. We introduce a novel method that employs core subset selection for reweighting, effectively optimizing both computational time and model performance. By focusing on a strategically selected coreset, our approach offers a robust representation, as it efficiently minimizes the influence of outliers. The re-calibrated weights are then mapped back to and propagated across the entire dataset. Our experimental results substantiate the effectiveness of this approach, underscoring its potential as a scalable and precise solution for model training.
This work considers the question of how convenient access to copious data impacts our ability to learn causal effects and relations. In what ways is learning causality in the era of big data different from -- or the same as -- the traditional one? To answer this question, this survey provides a comprehensive and structured review of both traditional and frontier methods in learning causality and relations along with the connections between causality and machine learning. This work points out on a case-by-case basis how big data facilitates, complicates, or motivates each approach.
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