The seminal work of Bencz\'ur and Karger demonstrated cut sparsifiers of near-linear size, with several applications throughout theoretical computer science. Subsequent extensions have yielded sparsifiers for hypergraph cuts and more recently linear codes over Abelian groups. A decade ago, Kogan and Krauthgamer asked about the sparsifiability of arbitrary constraint satisfaction problems (CSPs). For this question, a trivial lower bound is the size of a non-redundant CSP instance, which admits, for each constraint, an assignment satisfying only that constraint (so that no constraint can be dropped by the sparsifier). For graph cuts, spanning trees are non-redundant instances. Our main result is that redundant clauses are sufficient for sparsification: for any CSP predicate R, every unweighted instance of CSP(R) has a sparsifier of size at most its non-redundancy (up to polylog factors). For weighted instances, we similarly pin down the sparsifiability to the so-called chain length of the predicate. These results precisely determine the extent to which any CSP can be sparsified. A key technical ingredient in our work is a novel application of the entropy method from Gilmer's recent breakthrough on the union-closed sets conjecture. As an immediate consequence of our main theorem, a number of results in the non-redundancy literature immediately extend to CSP sparsification. We also contribute new techniques for understanding the non-redundancy of CSP predicates. In particular, we give an explicit family of predicates whose non-redundancy roughly corresponds to the structure of matching vector families in coding theory. By adapting methods from the matching vector codes literature, we are able to construct an explicit predicate whose non-redundancy lies between $\Omega(n^{1.5})$ and $\widetilde{O}(n^{1.6})$, the first example with a provably non-integral exponent.
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We develop a new efficient method for high-dimensional sampling called Subspace Langevin Monte Carlo. The primary application of these methods is to efficiently implement Preconditioned Langevin Monte Carlo. To demonstrate the usefulness of this new method, we extend ideas from subspace descent methods in Euclidean space to solving a specific optimization problem over Wasserstein space. Our theoretical analysis demonstrates the advantageous convergence regimes of the proposed method, which depend on relative conditioning assumptions common to mirror descent methods. We back up our theory with experimental evidence on sampling from an ill-conditioned Gaussian distribution.
Conditional independence (CI) testing is a fundamental task in modern statistics and machine learning. The conditional randomization test (CRT) was recently introduced to test whether two random variables, $X$ and $Y$, are conditionally independent given a potentially high-dimensional set of random variables, $Z$. The CRT operates exceptionally well under the assumption that the conditional distribution $X|Z$ is known. However, since this distribution is typically unknown in practice, accurately approximating it becomes crucial. In this paper, we propose using conditional diffusion models (CDMs) to learn the distribution of $X|Z$. Theoretically and empirically, it is shown that CDMs closely approximate the true conditional distribution. Furthermore, CDMs offer a more accurate approximation of $X|Z$ compared to GANs, potentially leading to a CRT that performs better than those based on GANs. To accommodate complex dependency structures, we utilize a computationally efficient classifier-based conditional mutual information (CMI) estimator as our test statistic. The proposed testing procedure performs effectively without requiring assumptions about specific distribution forms or feature dependencies, and is capable of handling mixed-type conditioning sets that include both continuous and discrete variables. Theoretical analysis shows that our proposed test achieves a valid control of the type I error. A series of experiments on synthetic data demonstrates that our new test effectively controls both type-I and type-II errors, even in high dimensional scenarios.
In recent years, the enhanced capabilities of ASR models and the emergence of multi-dialect datasets have increasingly pushed Arabic ASR model development toward an all-dialect-in-one direction. This trend highlights the need for benchmarking studies that evaluate model performance on multiple dialects, providing the community with insights into models' generalization capabilities. In this paper, we introduce Open Universal Arabic ASR Leaderboard, a continuous benchmark project for open-source general Arabic ASR models across various multi-dialect datasets. We also provide a comprehensive analysis of the model's robustness, speaker adaptation, inference efficiency, and memory consumption. This work aims to offer the Arabic ASR community a reference for models' general performance and also establish a common evaluation framework for multi-dialectal Arabic ASR models.
We introduce a novel approach for detecting distribution shifts that negatively impact the performance of machine learning models in continuous production environments, which requires no access to ground truth data labels. It builds upon the work of Podkopaev and Ramdas [2022], who address scenarios where labels are available for tracking model errors over time. Our solution extends this framework to work in the absence of labels, by employing a proxy for the true error. This proxy is derived using the predictions of a trained error estimator. Experiments show that our method has high power and false alarm control under various distribution shifts, including covariate and label shifts and natural shifts over geography and time.
Recently, Gaussian splatting has emerged as a robust technique for representing 3D scenes, enabling real-time rasterization and high-fidelity rendering. However, Gaussians' inherent radial symmetry and smoothness constraints limit their ability to represent complex shapes, often requiring thousands of primitives to approximate detailed geometry. We introduce Deformable Radial Kernel (DRK), which extends Gaussian splatting into a more general and flexible framework. Through learnable radial bases with adjustable angles and scales, DRK efficiently models diverse shape primitives while enabling precise control over edge sharpness and boundary curvature. iven DRK's planar nature, we further develop accurate ray-primitive intersection computation for depth sorting and introduce efficient kernel culling strategies for improved rasterization efficiency. Extensive experiments demonstrate that DRK outperforms existing methods in both representation efficiency and rendering quality, achieving state-of-the-art performance while dramatically reducing primitive count.
Interactive Natural Language Processing (iNLP) has emerged as a novel paradigm within the field of NLP, aimed at addressing limitations in existing frameworks while aligning with the ultimate goals of artificial intelligence. This paradigm considers language models as agents capable of observing, acting, and receiving feedback iteratively from external entities. Specifically, language models in this context can: (1) interact with humans for better understanding and addressing user needs, personalizing responses, aligning with human values, and improving the overall user experience; (2) interact with knowledge bases for enriching language representations with factual knowledge, enhancing the contextual relevance of responses, and dynamically leveraging external information to generate more accurate and informed responses; (3) interact with models and tools for effectively decomposing and addressing complex tasks, leveraging specialized expertise for specific subtasks, and fostering the simulation of social behaviors; and (4) interact with environments for learning grounded representations of language, and effectively tackling embodied tasks such as reasoning, planning, and decision-making in response to environmental observations. This paper offers a comprehensive survey of iNLP, starting by proposing a unified definition and framework of the concept. We then provide a systematic classification of iNLP, dissecting its various components, including interactive objects, interaction interfaces, and interaction methods. We proceed to delve into the evaluation methodologies used in the field, explore its diverse applications, scrutinize its ethical and safety issues, and discuss prospective research directions. This survey serves as an entry point for researchers who are interested in this rapidly evolving area and offers a broad view of the current landscape and future trajectory of iNLP.
Minimizing cross-entropy over the softmax scores of a linear map composed with a high-capacity encoder is arguably the most popular choice for training neural networks on supervised learning tasks. However, recent works show that one can directly optimize the encoder instead, to obtain equally (or even more) discriminative representations via a supervised variant of a contrastive objective. In this work, we address the question whether there are fundamental differences in the sought-for representation geometry in the output space of the encoder at minimal loss. Specifically, we prove, under mild assumptions, that both losses attain their minimum once the representations of each class collapse to the vertices of a regular simplex, inscribed in a hypersphere. We provide empirical evidence that this configuration is attained in practice and that reaching a close-to-optimal state typically indicates good generalization performance. Yet, the two losses show remarkably different optimization behavior. The number of iterations required to perfectly fit to data scales superlinearly with the amount of randomly flipped labels for the supervised contrastive loss. This is in contrast to the approximately linear scaling previously reported for networks trained with cross-entropy.
Knowledge graph (KG) embedding encodes the entities and relations from a KG into low-dimensional vector spaces to support various applications such as KG completion, question answering, and recommender systems. In real world, knowledge graphs (KGs) are dynamic and evolve over time with addition or deletion of triples. However, most existing models focus on embedding static KGs while neglecting dynamics. To adapt to the changes in a KG, these models need to be re-trained on the whole KG with a high time cost. In this paper, to tackle the aforementioned problem, we propose a new context-aware Dynamic Knowledge Graph Embedding (DKGE) method which supports the embedding learning in an online fashion. DKGE introduces two different representations (i.e., knowledge embedding and contextual element embedding) for each entity and each relation, in the joint modeling of entities and relations as well as their contexts, by employing two attentive graph convolutional networks, a gate strategy, and translation operations. This effectively helps limit the impacts of a KG update in certain regions, not in the entire graph, so that DKGE can rapidly acquire the updated KG embedding by a proposed online learning algorithm. Furthermore, DKGE can also learn KG embedding from scratch. Experiments on the tasks of link prediction and question answering in a dynamic environment demonstrate the effectiveness and efficiency of DKGE.
Embedding models for deterministic Knowledge Graphs (KG) have been extensively studied, with the purpose of capturing latent semantic relations between entities and incorporating the structured knowledge into machine learning. However, there are many KGs that model uncertain knowledge, which typically model the inherent uncertainty of relations facts with a confidence score, and embedding such uncertain knowledge represents an unresolved challenge. The capturing of uncertain knowledge will benefit many knowledge-driven applications such as question answering and semantic search by providing more natural characterization of the knowledge. In this paper, we propose a novel uncertain KG embedding model UKGE, which aims to preserve both structural and uncertainty information of relation facts in the embedding space. Unlike previous models that characterize relation facts with binary classification techniques, UKGE learns embeddings according to the confidence scores of uncertain relation facts. To further enhance the precision of UKGE, we also introduce probabilistic soft logic to infer confidence scores for unseen relation facts during training. We propose and evaluate two variants of UKGE based on different learning objectives. Experiments are conducted on three real-world uncertain KGs via three tasks, i.e. confidence prediction, relation fact ranking, and relation fact classification. UKGE shows effectiveness in capturing uncertain knowledge by achieving promising results on these tasks, and consistently outperforms baselines on these tasks.
We investigate a lattice-structured LSTM model for Chinese NER, which encodes a sequence of input characters as well as all potential words that match a lexicon. Compared with character-based methods, our model explicitly leverages word and word sequence information. Compared with word-based methods, lattice LSTM does not suffer from segmentation errors. Gated recurrent cells allow our model to choose the most relevant characters and words from a sentence for better NER results. Experiments on various datasets show that lattice LSTM outperforms both word-based and character-based LSTM baselines, achieving the best results.
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