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Cluster Editing, also known as Correlation Clustering, is a well-studied graph modification problem. In this problem, one is given a graph and the task is to perform up to $k$ edge additions or deletions to transform it into a cluster graph, i.e., a graph consisting of a disjoint union of cliques. However, in real-world networks, clusters are often overlapping. For example in social networks, a person might belong to several communities - e.g. those corresponding to work, school, or neighborhood. Other strong motivations come from biological network analysis and from language networks. Trying to cluster words with similar usage in the latter can be confounded by homonyms, that is, words with multiple meanings like "bat." In this paper, we introduce a new variant of Cluster Editing whereby a vertex can be split into two or more vertices. First used in the context of graph drawing, this operation allows a vertex $v$ to be replaced by two vertices whose combined neighborhood is the neighborhood of $v$ (and thus $v$ can belong to more than one cluster). We call the new problem Cluster Editing with Vertex Splitting and we initiate the study of it. We show that it is NP-complete and fixed-parameter tractable when parameterized by the total number $k$ of allowed vertex-splitting and edge-editing operations. In particular, we obtain an $O(2^{9k log k} + n + m)$-time algorithm and a $6k$-vertex kernel.

Data pruning, which aims to downsize a large training set into a small informative subset, is crucial for reducing the enormous computational costs of modern deep learning. Though large-scale data collections invariably contain annotation noise and numerous robust learning methods have been developed, data pruning for the noise-robust learning scenario has received little attention. With state-of-the-art Re-labeling methods that self-correct erroneous labels while training, it is challenging to identify which subset induces the most accurate re-labeling of erroneous labels in the entire training set. In this paper, we formalize the problem of data pruning with re-labeling. We first show that the likelihood of a training example being correctly re-labeled is proportional to the prediction confidence of its neighborhood in the subset. Therefore, we propose a novel data pruning algorithm, Prune4Rel, that finds a subset maximizing the total neighborhood confidence of all training examples, thereby maximizing the re-labeling accuracy and generalization performance. Extensive experiments on four real and one synthetic noisy datasets show that \algname{} outperforms the baselines with Re-labeling models by up to 9.1% as well as those with a standard model by up to 21.6%.

Challenges to reproducibility and replicability have gained widespread attention over the past decade, driven by a number of large replication projects with lukewarm success rates. A nascent work has emerged developing algorithms to estimate, or predict, the replicability of published findings. The current study explores ways in which AI-enabled signals of confidence in research might be integrated into literature search. We interview 17 PhD researchers about their current processes for literature search and ask them to provide feedback on a prototype replicability estimation tool. Our findings suggest that information about replicability can support researchers throughout literature review and research design processes. However, explainability and interpretability of system outputs is critical, and potential drawbacks of AI-enabled confidence assessment need to be further studied before such tools could be widely accepted and deployed. We discuss implications for the design of technological tools to support scholarly activities and advance reproducibility and replicability.

The block Kaczmarz method and its variants are designed for solving the over-determined linear system. They involve iteratively projecting the current point onto the solution space of a subset of constraints. In this work, by alternately dealing with two subproblems (i.e., linear system with multiple right-hand sides) using the block Kaczmarz method, we propose the {\it Alternating Randomized Block Kaczmarz} (ARBK) method to solve the linear matrix equation $AXB=F$, which incorporates a randomized index selection scheme to determine the subset of constraints. The convergence analysis reveals that the ARBK method has a linear convergence rate bounded by an explicit expression. Several numerical studies have been conducted to validate the theoretical findings.

Manifold learning flows are a class of generative modelling techniques that assume a low-dimensional manifold description of the data. The embedding of such a manifold into the high-dimensional space of the data is achieved via learnable invertible transformations. Therefore, once the manifold is properly aligned via a reconstruction loss, the probability density is tractable on the manifold and maximum likelihood can be used to optimize the network parameters. Naturally, the lower-dimensional representation of the data requires an injective-mapping. Recent approaches were able to enforce that the density aligns with the modelled manifold, while efficiently calculating the density volume-change term when embedding to the higher-dimensional space. However, unless the injective-mapping is analytically predefined, the learned manifold is not necessarily an efficient representation of the data. Namely, the latent dimensions of such models frequently learn an entangled intrinsic basis, with degenerate information being stored in each dimension. Alternatively, if a locally orthogonal and/or sparse basis is to be learned, here coined canonical intrinsic basis, it can serve in learning a more compact latent space representation. Toward this end, we propose a canonical manifold learning flow method, where a novel optimization objective enforces the transformation matrix to have few prominent and non-degenerate basis functions. We demonstrate that by minimizing the off-diagonal manifold metric elements $\ell_1$-norm, we can achieve such a basis, which is simultaneously sparse and/or orthogonal. Canonical manifold flow yields a more efficient use of the latent space, automatically generating fewer prominent and distinct dimensions to represent data, and a better approximation of target distributions than other manifold flow methods in most experiments we conducted, resulting in lower FID scores.

Enumeration problems aim at outputting, without repetition, the set of solutions to a given problem instance. However, outputting the entire solution set may be prohibitively expensive if it is too big. In this case, outputting a small, sufficiently diverse subset of the solutions would be preferable. This leads to the Diverse-version of the original enumeration problem, where the goal is to achieve a certain level d of diversity by selecting k solutions. In this paper, we look at the Diverse-version of the query answering problem for Conjunctive Queries and extensions thereof. That is, we study the problem if it is possible to achieve a certain level d of diversity by selecting k answers to the given query and, in the positive case, to actually compute such k answers.

Advances in artificial intelligence are driven by technologies inspired by the brain, but these technologies are orders of magnitude less powerful and energy efficient than biological systems. Inspired by the nonlinear dynamics of neural networks, new unconventional computing hardware has emerged with the potential to exploit natural phenomena and gain efficiency, in a similar manner to biological systems. Physical reservoir computing demonstrates this with a variety of unconventional systems, from optical-based to memristive systems. Reservoir computers provide a nonlinear projection of the task input into a high-dimensional feature space by exploiting the system's internal dynamics. A trained readout layer then combines features to perform tasks, such as pattern recognition and time-series analysis. Despite progress, achieving state-of-the-art performance without external signal processing to the reservoir remains challenging. Here we perform an initial exploration of three magnetic materials in thin-film geometries via microscale simulation. Our results reveal that basic spin properties of magnetic films generate the required nonlinear dynamics and memory to solve machine learning tasks (although there would be practical challenges in exploiting these particular materials in physical implementations). The method of exploration can be applied to other materials, so this work opens up the possibility of testing different materials, from relatively simple (alloys) to significantly complex (antiferromagnetic reservoirs).

We present an alternative approach to decompose non-negative tensors, called many-body approximation. Traditional decomposition methods assume low-rankness in the representation, resulting in difficulties in global optimization and target rank selection. We avoid these problems by energy-based modeling of tensors, where a tensor and its mode correspond to a probability distribution and a random variable, respectively. Our model can be globally optimized in terms of the KL divergence minimization by taking the interaction between variables (that is, modes), into account that can be tuned more intuitively than ranks. Furthermore, we visualize interactions between modes as tensor networks and reveal a nontrivial relationship between many-body approximation and low-rank approximation. We demonstrate the effectiveness of our approach in tensor completion and approximation.

Collaborative learning techniques have significantly advanced in recent years, enabling private model training across multiple organizations. Despite this opportunity, firms face a dilemma when considering data sharing with competitors -- while collaboration can improve a company's machine learning model, it may also benefit competitors and hence reduce profits. In this work, we introduce a general framework for analyzing this data-sharing trade-off. The framework consists of three components, representing the firms' production decisions, the effect of additional data on model quality, and the data-sharing negotiation process, respectively. We then study an instantiation of the framework, based on a conventional market model from economic theory, to identify key factors that affect collaboration incentives. Our findings indicate a profound impact of market conditions on the data-sharing incentives. In particular, we find that reduced competition, in terms of the similarities between the firms' products, and harder learning tasks foster collaboration.

Although measuring held-out accuracy has been the primary approach to evaluate generalization, it often overestimates the performance of NLP models, while alternative approaches for evaluating models either focus on individual tasks or on specific behaviors. Inspired by principles of behavioral testing in software engineering, we introduce CheckList, a task-agnostic methodology for testing NLP models. CheckList includes a matrix of general linguistic capabilities and test types that facilitate comprehensive test ideation, as well as a software tool to generate a large and diverse number of test cases quickly. We illustrate the utility of CheckList with tests for three tasks, identifying critical failures in both commercial and state-of-art models. In a user study, a team responsible for a commercial sentiment analysis model found new and actionable bugs in an extensively tested model. In another user study, NLP practitioners with CheckList created twice as many tests, and found almost three times as many bugs as users without it.