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Numerical solution of discrete PDEs corresponding to saddle point problems is highly relevant to physical systems such as Stokes flow. However, scaling up numerical solvers for such systems is often met with challenges in efficiency and convergence. Multigrid is an approach with excellent applicability to elliptic problems such as the Stokes equations, and can be a solution to such challenges of scalability and efficiency. The degree of success of such methods, however, is highly contingent on the design of key components of a multigrid scheme, including the hierarchy of discretizations, and the relaxation scheme used. Additionally, in many practical cases, it may be more effective to use a multigrid scheme as a preconditioner to an iterative Krylov subspace solver, as opposed to striving for maximum efficacy of the relaxation scheme in all foreseeable settings. In this paper, we propose an efficient symmetric multigrid preconditioner for the Stokes Equations on a staggered finite-difference discretization. Our contribution is focused on crafting a preconditioner that (a) is symmetric indefinite, matching the property of the Stokes system itself, (b) is appropriate for preconditioning the SQMR iterative scheme, and (c) has the requisite symmetry properties to be used in this context. In addition, our design is efficient in terms of computational cost and facilitates scaling to large domains.

The success of deep learning hinges on enormous data and large models, which require labor-intensive annotations and heavy computation costs. Subset selection is a fundamental problem that can play a key role in identifying smaller portions of the training data, which can then be used to produce similar models as the ones trained with full data. Two prior methods are shown to achieve impressive results: (1) margin sampling that focuses on selecting points with high uncertainty, and (2) core-sets or clustering methods such as k-center for informative and diverse subsets. We are not aware of any work that combines these methods in a principled manner. To this end, we develop a novel and efficient factor 3-approximation algorithm to compute subsets based on the weighted sum of both k-center and uncertainty sampling objective functions. To handle large datasets, we show a parallel algorithm to run on multiple machines with approximation guarantees. The proposed algorithm achieves similar or better performance compared to other strong baselines on vision datasets such as CIFAR-10, CIFAR-100, and ImageNet.

In supervised learning, automatically assessing the quality of the labels before any learning takes place remains an open research question. In certain particular cases, hypothesis testing procedures have been proposed to assess whether a given instance-label dataset is contaminated with class-conditional label noise, as opposed to uniform label noise. The existing theory builds on the asymptotic properties of the Maximum Likelihood Estimate for parametric logistic regression. However, the parametric assumptions on top of which these approaches are constructed are often too strong and unrealistic in practice. To alleviate this problem, in this paper we propose an alternative path by showing how similar procedures can be followed when the underlying model is a product of Local Maximum Likelihood Estimation that leads to more flexible nonparametric logistic regression models, which in turn are less susceptible to model misspecification. This different view allows for wider applicability of the tests by offering users access to a richer model class. Similarly to existing works, we assume we have access to anchor points which are provided by the users. We introduce the necessary ingredients for the adaptation of the hypothesis tests to the case of nonparametric logistic regression and empirically compare against the parametric approach presenting both synthetic and real-world case studies and discussing the advantages and limitations of the proposed approach.

While coresets have been growing in terms of their application, barring few exceptions, they have mostly been limited to unsupervised settings. We consider supervised classification problems, and non-decomposable evaluation measures in such settings. We show that stratified uniform sampling based coresets have excellent empirical performance that are backed by theoretical guarantees too. We focus on the F1 score and Matthews Correlation Coefficient, two widely used non-decomposable objective functions that are nontrivial to optimize for and show that uniform coresets attain a lower bound for coreset size, and have good empirical performance, comparable with ``smarter'' coreset construction strategies.

The prevalence of the powerful multilingual models, such as Whisper, has significantly advanced the researches on speech recognition. However, these models often struggle with handling the code-switching setting, which is essential in multilingual speech recognition. Recent studies have attempted to address this setting by separating the modules for different languages to ensure distinct latent representations for languages. Some other methods considered the switching mechanism based on language identification. In this study, a new attention-guided adaptation is proposed to conduct parameter-efficient learning for bilingual ASR. This method selects those attention heads in a model which closely express language identities and then guided those heads to be correctly attended with their corresponding languages. The experiments on the Mandarin-English code-switching speech corpus show that the proposed approach achieves a 14.2% mixed error rate, surpassing state-of-the-art method, where only 5.6% additional parameters over Whisper are trained.

The development of autonomous agents which can interact with other agents to accomplish a given task is a core area of research in artificial intelligence and machine learning. Towards this goal, the Autonomous Agents Research Group develops novel machine learning algorithms for autonomous systems control, with a specific focus on deep reinforcement learning and multi-agent reinforcement learning. Research problems include scalable learning of coordinated agent policies and inter-agent communication; reasoning about the behaviours, goals, and composition of other agents from limited observations; and sample-efficient learning based on intrinsic motivation, curriculum learning, causal inference, and representation learning. This article provides a broad overview of the ongoing research portfolio of the group and discusses open problems for future directions.

Recent contrastive representation learning methods rely on estimating mutual information (MI) between multiple views of an underlying context. E.g., we can derive multiple views of a given image by applying data augmentation, or we can split a sequence into views comprising the past and future of some step in the sequence. Contrastive lower bounds on MI are easy to optimize, but have a strong underestimation bias when estimating large amounts of MI. We propose decomposing the full MI estimation problem into a sum of smaller estimation problems by splitting one of the views into progressively more informed subviews and by applying the chain rule on MI between the decomposed views. This expression contains a sum of unconditional and conditional MI terms, each measuring modest chunks of the total MI, which facilitates approximation via contrastive bounds. To maximize the sum, we formulate a contrastive lower bound on the conditional MI which can be approximated efficiently. We refer to our general approach as Decomposed Estimation of Mutual Information (DEMI). We show that DEMI can capture a larger amount of MI than standard non-decomposed contrastive bounds in a synthetic setting, and learns better representations in a vision domain and for dialogue generation.

We present a large-scale study on unsupervised spatiotemporal representation learning from videos. With a unified perspective on four recent image-based frameworks, we study a simple objective that can easily generalize all these methods to space-time. Our objective encourages temporally-persistent features in the same video, and in spite of its simplicity, it works surprisingly well across: (i) different unsupervised frameworks, (ii) pre-training datasets, (iii) downstream datasets, and (iv) backbone architectures. We draw a series of intriguing observations from this study, e.g., we discover that encouraging long-spanned persistency can be effective even if the timespan is 60 seconds. In addition to state-of-the-art results in multiple benchmarks, we report a few promising cases in which unsupervised pre-training can outperform its supervised counterpart. Code is made available at //github.com/facebookresearch/SlowFast

Few-shot Knowledge Graph (KG) completion is a focus of current research, where each task aims at querying unseen facts of a relation given its few-shot reference entity pairs. Recent attempts solve this problem by learning static representations of entities and references, ignoring their dynamic properties, i.e., entities may exhibit diverse roles within task relations, and references may make different contributions to queries. This work proposes an adaptive attentional network for few-shot KG completion by learning adaptive entity and reference representations. Specifically, entities are modeled by an adaptive neighbor encoder to discern their task-oriented roles, while references are modeled by an adaptive query-aware aggregator to differentiate their contributions. Through the attention mechanism, both entities and references can capture their fine-grained semantic meanings, and thus render more expressive representations. This will be more predictive for knowledge acquisition in the few-shot scenario. Evaluation in link prediction on two public datasets shows that our approach achieves new state-of-the-art results with different few-shot sizes.

Multi-relation Question Answering is a challenging task, due to the requirement of elaborated analysis on questions and reasoning over multiple fact triples in knowledge base. In this paper, we present a novel model called Interpretable Reasoning Network that employs an interpretable, hop-by-hop reasoning process for question answering. The model dynamically decides which part of an input question should be analyzed at each hop; predicts a relation that corresponds to the current parsed results; utilizes the predicted relation to update the question representation and the state of the reasoning process; and then drives the next-hop reasoning. Experiments show that our model yields state-of-the-art results on two datasets. More interestingly, the model can offer traceable and observable intermediate predictions for reasoning analysis and failure diagnosis.