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We provide a comprehensive elaboration of the theoretical foundations of variable instantiation, or grounding, in Answer Set Programming (ASP). Building on the semantics of ASP's modeling language, we introduce a formal characterization of grounding algorithms in terms of (fixed point) operators. A major role is played by dedicated well-founded operators whose associated models provide semantic guidance for delineating the result of grounding along with on-the-fly simplifications. We address an expressive class of logic programs that incorporates recursive aggregates and thus amounts to the scope of existing ASP modeling languages. This is accompanied with a plain algorithmic framework detailing the grounding of recursive aggregates. The given algorithms correspond essentially to the ones used in the ASP grounder gringo.

When training a machine learning classifier on data where one of the classes is intrinsically rare, the classifier will often assign too few sources to the rare class. To address this, it is common to up-weight the examples of the rare class to ensure it isn't ignored. It is also a frequent practice to train on restricted data where the balance of source types is closer to equal for the same reason. Here we show that these practices can bias the model toward over-assigning sources to the rare class. We also explore how to detect when training data bias has had a statistically significant impact on the trained model's predictions, and how to reduce the bias's impact. While the magnitude of the impact of the techniques developed here will vary with the details of the application, for most cases it should be modest. They are, however, universally applicable to every time a machine learning classification model is used, making them analogous to Bessel's correction to the sample variance.

Deep discrete structured models have seen considerable progress recently, but traditional inference using dynamic programming (DP) typically works with a small number of states (less than hundreds), which severely limits model capacity. At the same time, across machine learning, there is a recent trend of using randomized truncation techniques to accelerate computations involving large sums. Here, we propose a family of randomized dynamic programming (RDP) algorithms for scaling structured models to tens of thousands of latent states. Our method is widely applicable to classical DP-based inference (partition, marginal, reparameterization, entropy) and different graph structures (chains, trees, and more general hypergraphs). It is also compatible with automatic differentiation: it can be integrated with neural networks seamlessly and learned with gradient-based optimizers. Our core technique approximates the sum-product by restricting and reweighting DP on a small subset of nodes, which reduces computation by orders of magnitude. We further achieve low bias and variance via Rao-Blackwellization and importance sampling. Experiments over different graphs demonstrate the accuracy and efficiency of our approach. Furthermore, when using RDP for training a structured variational autoencoder with a scaled inference network, we achieve better test likelihood than baselines and successfully prevent posterior collapse. code at: //github.com/FranxYao/RDP

We show that 11-channel sorting networks have at least 35 comparators and that 12-channel sorting networks have at least 39 comparators. This positively settles the optimality of the corresponding sorting networks given in The Art of Computer Programming vol. 3 and closes the two smallest open instances of the Bose-Nelson sorting problem. We obtain these bounds by generalizing a result of Van Voorhis from sorting networks to a more general class of comparator networks. From this we derive a dynamic programming algorithm that computes the optimal size for a sorting network with a given number of channels. From an execution of this algorithm we construct a certificate containing a derivation of the corresponding lower size bound, which we check using a program formally verified using the Isabelle/HOL proof assistant.

It is a well-known fact that there is no complete and discrete invariant on the collection of all multiparameter persistence modules. Nonetheless, many invariants have been proposed in the literature to study multiparameter persistence modules, though each invariant will lose some amount of information. One such invariant is the generalized rank invariant. This invariant is known to be complete on the class of interval decomposable persistence modules in general, under mild assumptions on the indexing poset $P$. There is often a trade-off, where the stronger an invariant is, the more expensive it is to compute in practice. The generalized rank invariant on its own is difficult to compute, whereas the standard rank invariant is readily computable through software implementations such as RIVET. We can interpolate between these two to induce new invariants via restricting the domain of the generalized rank invariant, and this family exhibits the aforementioned trade-off. This work studies the tension which exists between computational efficiency and retaining strength when restricting the domain of the generalized rank invariant. We provide a characterization result on where such restrictions are complete invariants in the setting where $P$ is finite, and furthermore show that such restricted generalized rank invariants are stable.

It is now well known that neural networks can be wrong with high confidence in their predictions, leading to poor calibration. The most common post-hoc approach to compensate for this is to perform temperature scaling, which adjusts the confidences of the predictions on any input by scaling the logits by a fixed value. Whilst this approach typically improves the average calibration across the whole test dataset, this improvement typically reduces the individual confidences of the predictions irrespective of whether the classification of a given input is correct or incorrect. With this insight, we base our method on the observation that different samples contribute to the calibration error by varying amounts, with some needing to increase their confidence and others needing to decrease it. Therefore, for each input, we propose to predict a different temperature value, allowing us to adjust the mismatch between confidence and accuracy at a finer granularity. Furthermore, we observe improved results on OOD detection and can also extract a notion of hardness for the data-points. Our method is applied post-hoc, consequently using very little computation time and with a negligible memory footprint and is applied to off-the-shelf pre-trained classifiers. We test our method on the ResNet50 and WideResNet28-10 architectures using the CIFAR10/100 and Tiny-ImageNet datasets, showing that producing per-data-point temperatures is beneficial also for the expected calibration error across the whole test set. Code is available at: //github.com/thwjoy/adats.

Code summaries help developers comprehend programs and reduce their time to infer the program functionalities during software maintenance. Recent efforts resort to deep learning techniques such as sequence-to-sequence models for generating accurate code summaries, among which Transformer-based approaches have achieved promising performance. However, effectively integrating the code structure information into the Transformer is under-explored in this task domain. In this paper, we propose a novel approach named SG-Trans to incorporate code structural properties into Transformer. Specifically, we inject the local symbolic information (e.g., code tokens and statements) and global syntactic structure (e.g., data flow graph) into the self-attention module of Transformer as inductive bias. To further capture the hierarchical characteristics of code, the local information and global structure are designed to distribute in the attention heads of lower layers and high layers of Transformer. Extensive evaluation shows the superior performance of SG-Trans over the state-of-the-art approaches. Compared with the best-performing baseline, SG-Trans still improves 1.4% and 2.0% in terms of METEOR score, a metric widely used for measuring generation quality, respectively on two benchmark datasets.

The extensive adoption of business analytics (BA) has brought financial gains and increased efficiencies. However, these advances have simultaneously drawn attention to rising legal and ethical challenges when BA inform decisions with fairness implications. As a response to these concerns, the emerging study of algorithmic fairness deals with algorithmic outputs that may result in disparate outcomes or other forms of injustices for subgroups of the population, especially those who have been historically marginalized. Fairness is relevant on the basis of legal compliance, social responsibility, and utility; if not adequately and systematically addressed, unfair BA systems may lead to societal harms and may also threaten an organization's own survival, its competitiveness, and overall performance. This paper offers a forward-looking, BA-focused review of algorithmic fairness. We first review the state-of-the-art research on sources and measures of bias, as well as bias mitigation algorithms. We then provide a detailed discussion of the utility-fairness relationship, emphasizing that the frequent assumption of a trade-off between these two constructs is often mistaken or short-sighted. Finally, we chart a path forward by identifying opportunities for business scholars to address impactful, open challenges that are key to the effective and responsible deployment of BA.

Machine reading comprehension (MRC) aims to teach machines to read and comprehend human languages, which is a long-standing goal of natural language processing (NLP). With the burst of deep neural networks and the evolution of contextualized language models (CLMs), the research of MRC has experienced two significant breakthroughs. MRC and CLM, as a phenomenon, have a great impact on the NLP community. In this survey, we provide a comprehensive and comparative review on MRC covering overall research topics about 1) the origin and development of MRC and CLM, with a particular focus on the role of CLMs; 2) the impact of MRC and CLM to the NLP community; 3) the definition, datasets, and evaluation of MRC; 4) general MRC architecture and technical methods in the view of two-stage Encoder-Decoder solving architecture from the insights of the cognitive process of humans; 5) previous highlights, emerging topics, and our empirical analysis, among which we especially focus on what works in different periods of MRC researches. We propose a full-view categorization and new taxonomies on these topics. The primary views we have arrived at are that 1) MRC boosts the progress from language processing to understanding; 2) the rapid improvement of MRC systems greatly benefits from the development of CLMs; 3) the theme of MRC is gradually moving from shallow text matching to cognitive reasoning.

We present a monocular Simultaneous Localization and Mapping (SLAM) using high level object and plane landmarks, in addition to points. The resulting map is denser, more compact and meaningful compared to point only SLAM. We first propose a high order graphical model to jointly infer the 3D object and layout planes from single image considering occlusions and semantic constraints. The extracted cuboid object and layout planes are further optimized in a unified SLAM framework. Objects and planes can provide more semantic constraints such as Manhattan and object supporting relationships compared to points. Experiments on various public and collected datasets including ICL NUIM and TUM mono show that our algorithm can improve camera localization accuracy compared to state-of-the-art SLAM and also generate dense maps in many structured environments.