Knowledge Graph (KG) completion is the problem of extending an incomplete KG with missing facts. A key feature of Machine Learning approaches for KG completion is their ability to learn inference patterns, so that the predicted facts are the results of applying these patterns to the KG. Standard completion benchmarks, however, are not well-suited for evaluating models' abilities to learn patterns, because the training and test sets of these benchmarks are a random split of a given KG and hence do not capture the causality of inference patterns. We propose a novel approach for designing KG completion benchmarks based on the following principles: there is a set of logical rules so that the missing facts are the results of the rules' application; the training set includes both premises matching rule antecedents and the corresponding conclusions; the test set consists of the results of applying the rules to the training set; the negative examples are designed to discourage the models from learning rules not entailed by the rule set. We use our methodology to generate several benchmarks and evaluate a wide range of existing KG completion systems. Our results provide novel insights on the ability of existing models to induce inference patterns from incomplete KGs.

In the past decades, various forms of structured prediction have been used extensively across many fields, including computer vision, natural language processing, network analysis, computational chemistry, to name a few. In these fields, examples of structured prediction problems include foreground / background detection in a digital image [Nowozin et al., 2011], grammatical partof-speech tagging in an English sentence [Weiss and Taskar, 2010], community identification and clustering in social networks [Kelley et al., 2012], and identifying representative subsets of millions of chemical compounds [Downs and Barnard, 2002]. On a higher level, all of the structured prediction inference problems mentioned above seek to maximize some score function over the space of labels. In other words, a common goal in inference tasks is to recover the label of each entity, such that the prediction matches the observation as much as possible. Suppose we represent the structured prediction inference problem using an undirected graph G = (V, E), where each node represents an entity, and each edge represents the interaction between two nodes.

Persistent homology (PH) provides topological descriptors for geometric data, such as weighted graphs, which are interpretable, stable to perturbations, and invariant under, e.g., relabeling. Most applications of PH focus on the one-parameter case -- where the descriptors summarize the changes in topology of data as it is filtered by a single quantity of interest -- and there is now a wide array of methods enabling the use of one-parameter PH descriptors in data science, which rely on the stable vectorization of these descriptors as elements of a Hilbert space. Although the multiparameter PH (MPH) of data that is filtered by several quantities of interest encodes much richer information than its one-parameter counterpart, the scarceness of stability results for MPH descriptors has so far limited the available options for the stable vectorization of MPH. In this paper, we aim to bring together the best of both worlds by showing how the interpretation of signed barcodes -- a recent family of MPH descriptors -- as signed measures leads to natural extensions of vectorization strategies from one parameter to multiple parameters. The resulting feature vectors are easy to define and to compute, and provably stable. While, as a proof of concept, we focus on simple choices of signed barcodes and vectorizations, we already see notable performance improvements when comparing our feature vectors to state-of-the-art topology-based methods on various types of data.

Hyperbolic neural networks can effectively capture the inherent hierarchy of graph datasets, and consequently a powerful choice of GNNs. However, they entangle multiple incongruent (gyro-)vector spaces within a layer, which makes them limited in terms of generalization and scalability. In this work, we propose the Poincare disk model as our search space, and apply all approximations on the disk (as if the disk is a tangent space derived from the origin), thus getting rid of all inter-space transformations. Such an approach enables us to propose a hyperbolic normalization layer and to further simplify the entire hyperbolic model to a Euclidean model cascaded with our hyperbolic normalization layer. We applied our proposed nonlinear hyperbolic normalization to the current state-of-the-art homogeneous and multi-relational graph networks. We demonstrate that our model not only leverages the power of Euclidean networks such as interpretability and efficient execution of various model components, but also outperforms both Euclidean and hyperbolic counterparts on various benchmarks. Our code is made publicly available at https://github.com/oom-debugger/ijcai23.

The representation space of pretrained Language Models (LMs) encodes rich information about words and their relationships (e.g., similarity, hypernymy, polysemy) as well as abstract semantic notions (e.g., intensity). In this paper, we demonstrate that lexical stylistic notions such as complexity, formality, and figurativeness, can also be identified in this space. We show that it is possible to derive a vector representation for each of these stylistic notions from only a small number of seed pairs. Using these vectors, we can characterize new texts in terms of these dimensions by performing simple calculations in the corresponding embedding space. We conduct experiments on five datasets and find that static embeddings encode these features more accurately at the level of words and phrases, whereas contextualized LMs perform better on sentences. The lower performance of contextualized representations at the word level is partially attributable to the anisotropy of their vector space, which can be corrected to some extent using techniques like standardization.

We study the fundamental mistake bound and sample complexity in the strategic classification, where agents can strategically manipulate their feature vector up to an extent in order to be predicted as positive. For example, given a classifier determining college admission, student candidates may try to take easier classes to improve their GPA, retake SAT and change schools in an effort to fool the classifier. Ball manipulations are a widely studied class of manipulations in the literature, where agents can modify their feature vector within a bounded radius ball. Unlike most prior work, our work considers manipulations to be personalized, meaning that agents can have different levels of manipulation abilities (e.g., varying radii for ball manipulations), and unknown to the learner. We formalize the learning problem in an interaction model where the learner first deploys a classifier and the agent manipulates the feature vector within their manipulation set to game the deployed classifier. We investigate various scenarios in terms of the information available to the learner during the interaction, such as observing the original feature vector before or after deployment, observing the manipulated feature vector, or not seeing either the original or the manipulated feature vector. We begin by providing online mistake bounds and PAC sample complexity in these scenarios for ball manipulations. We also explore non-ball manipulations and show that, even in the simplest scenario where both the original and the manipulated feature vectors are revealed, the mistake bounds and sample complexity are lower bounded by $\Omega(|\mathcal{H}|)$ when the target function belongs to a known class $\mathcal{H}$.

As believers reflect on the lessons gained during Lent, many consider how they may more fully live out their faith each and every day. As 1 Peter 3:18 reminds the faithful, "For Christ also suffered for sins once, the righteous for the sake of the unrighteous, that he might lead you to God. Put to death in the flesh, he was brought to life in the spirit." This Bible verse comes from the First Epistle of Peter, a letter to a persecuted group of Christians. The epistle is believed to have been written by the apostle Peter in the mid-first century, says the website Bible Study Tools.

Recent studies have experimentally shown that we can achieve in non-Euclidean metric space effective and efficient graph embedding, which aims to obtain the vertices' representations reflecting the graph's structure in the metric space. Specifically, graph embedding in hyperbolic space has experimentally succeeded in embedding graphs with hierarchical-tree structure, e.g., data in natural languages, social networks, and knowledge bases. However, recent theoretical analyses have shown a much higher upper bound on non-Euclidean graph embedding's generalization error than Euclidean one's, where a high generalization error indicates that the incompleteness and noise in the data can significantly damage learning performance. It implies that the existing bound cannot guarantee the success of graph embedding in non-Euclidean metric space in a practical training data size, which can prevent non-Euclidean graph embedding's application in real problems. This paper provides a novel upper bound of graph embedding's generalization error by evaluating the local Rademacher complexity of the model as a function set of the distances of representation couples. Our bound clarifies that the performance of graph embedding in non-Euclidean metric space, including hyperbolic space, is better than the existing upper bounds suggest. Specifically, our new upper bound is polynomial in the metric space's geometric radius $R$ and can be $O(\frac{1}{S})$ at the fastest, where $S$ is the training data size. Our bound is significantly tighter and faster than the existing one, which can be exponential to $R$ and $O(\frac{1}{\sqrt{S}})$ at the fastest. Specific calculations on example cases show that graph embedding in non-Euclidean metric space can outperform that in Euclidean space with much smaller training data than the existing bound has suggested.

We develop a categorical compositional distributional semantics for Lambek Calculus with a Relevant Modality !L*, which has a limited edition of the contraction and permutation rules. The categorical part of the semantics is a monoidal biclosed category with a coalgebra modality, very similar to the structure of a Differential Category. We instantiate this category to finite dimensional vector spaces and linear maps via "quantisation" functors and work with three concrete interpretations of the coalgebra modality. We apply the model to construct categorical and concrete semantic interpretations for the motivating example of !L*: the derivation of a phrase with a parasitic gap. The effectiveness of the concrete interpretations are evaluated via a disambiguation task, on an extension of a sentence disambiguation dataset to parasitic gap phrases, using BERT, Word2Vec, and FastText vectors and Relational tensors.

The lack of comprehensive sources of accurate vulnerability data represents a critical obstacle to studying and understanding software vulnerabilities (and their corrections). In this paper, we present an approach that combines heuristics stemming from practical experience and machine-learning (ML) - specifically, natural language processing (NLP) - to address this problem. Our method consists of three phases. First, an advisory record containing key information about a vulnerability is extracted from an advisory (expressed in natural language). Second, using heuristics, a subset of candidate fix commits is obtained from the source code repository of the affected project by filtering out commits that are known to be irrelevant for the task at hand. Finally, for each such candidate commit, our method builds a numerical feature vector reflecting the characteristics of the commit that are relevant to predicting its match with the advisory at hand. The feature vectors are then exploited for building a final ranked list of candidate fixing commits. The score attributed by the ML model to each feature is kept visible to the users, allowing them to interpret the predictions. We evaluated our approach using a prototype implementation named FixFinder on a manually curated data set that comprises 2,391 known fix commits corresponding to 1,248 public vulnerability advisories. When considering the top-10 commits in the ranked results, our implementation could successfully identify at least one fix commit for up to 84.03% of the vulnerabilities (with a fix commit on the first position for 65.06% of the vulnerabilities). In conclusion, our method reduces considerably the effort needed to search OSS repositories for the commits that fix known vulnerabilities.