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We develop a denotational semantics of muLL, a version of propositional Linear Logic with least and greatest fixed points extending David Baelde's propositional muMALL with exponentials. Our general categorical setting is based on the notion of Seely category and on strong functors acting on them. We exhibit two simple instances of this setting. In the first one, which is based on the category of sets and relations, least and greatest fixed points are interpreted in the same way. In the second one, based on a category of sets equipped with a notion of totality (non-uniform totality spaces) and relations preserving them, least and greatest fixed points have distinct interpretations. This latter model shows that muLL enjoys a denotational form of normalization of proofs.

We develop an approach to choice principles and their contrapositive bar-induction principles as extensionality schemes connecting an "intensional" or "effective" view of respectively ill-and well-foundedness properties to an "extensional" or "ideal" view of these properties. After classifying and analysing the relations between different intensional definitions of ill-foundedness and well-foundedness, we introduce, for a domain A, a codomain B and a "filter" T on finite approximations of functions from A to B, a generalised form GDC(A,B,T) of the axiom of dependent choice and dually a generalised bar induction principle GBI(A,B,T) such that: - GDC(A,B,T) intuitionistically captures the strength of $\bullet$ the general axiom of choice expressed as $\forall$a $\exists$b R(a, b) $\Rightarrow$ $\exists$$\alpha$ $\forall$a R(a, $\alpha$(a))) when T is a filter that derives point-wise from a relation R on A x B without introducing further constraints, $\bullet$ the Boolean Prime Filter Theorem / Ultrafilter Theorem if B is the two-element set Bool (for a constructive definition of prime filter), $\bullet$ the axiom of dependent choice if A = $\mathbb{N}$, $\bullet$ Weak K\"onig's Lemma if A = $\mathbb{N}$ and B = Bool (up to weak classical reasoning) - GBI(A,B,T) intuitionistically captures the strength of $\bullet$ G\"odel's completeness theorem in the form validity implies provability for entailment relations if B = Bool, $\bullet$ bar induction when A = $\mathbb{N}$, $\bullet$ the Weak Fan Theorem when A = $\mathbb{N}$ and B = Bool. Contrastingly, even though GDC(A,B,T) and GBI(A,B,T) smoothly capture several variants of choice and bar induction, some instances are inconsistent, e.g. when A is Bool^$\mathbb{N}$ and B is $\mathbb{N}$.

Fusemate is a logic programming system that implements the possible model semantics for disjunctive logic programs. Its input language is centered around a weak notion of stratification with comprehension and aggregation operators on top of it. Fusemate is implemented as a shallow embedding in the Scala programming language. This enables using Scala data types natively as terms, a tight interface with external systems, and it makes model computation available as an ordinary container data structure constructor. The paper describes the above features and demonstrates them with a non-trivial use-case, the embedding of the description logic $\cal ALCIF$ into Fusemate's input language This version of the paper corrects an error in the published version, which used an unsuitable version of "blocking" in the $\cal ALCIF$ embedding.

Educational technologies, and the systems of schooling in which they are deployed, enact particular ideologies about what is important to know and how learners should learn. As artificial intelligence technologies -- in education and beyond -- have led to inequitable outcomes for marginalized communities, various approaches have been developed to evaluate and mitigate AI systems' disparate impact. However, we argue in this paper that the dominant paradigm of evaluating fairness on the basis of performance disparities in AI models is inadequate for confronting the structural inequities that educational AI systems (re)produce. We draw on a lens of structural injustice informed by critical theory and Black feminist scholarship to critically interrogate several widely-studied and widely-adopted categories of educational AI systems and demonstrate how educational AI technologies are bound up in and reproduce historical legacies of structural injustice and inequity, regardless of the parity of their models' performance. We close with alternative visions for a more equitable future for educational AI research.

Rankings, especially those in search and recommendation systems, often determine how people access information and how information is exposed to people. Therefore, how to balance the relevance and fairness of information exposure is considered as one of the key problems for modern IR systems. As conventional ranking frameworks that myopically sorts documents with their relevance will inevitably introduce unfair result exposure, recent studies on ranking fairness mostly focus on dynamic ranking paradigms where result rankings can be adapted in real-time to support fairness in groups (i.e., races, genders, etc.). Existing studies on fairness in dynamic learning to rank, however, often achieve the overall fairness of document exposure in ranked lists by significantly sacrificing the performance of result relevance and fairness on the top results. To address this problem, we propose a fair and unbiased ranking method named Maximal Marginal Fairness (MMF). The algorithm integrates unbiased estimators for both relevance and merit-based fairness while providing an explicit controller that balances the selection of documents to maximize the marginal relevance and fairness in top-k results. Theoretical and empirical analysis shows that, with small compromises on long list fairness, our method achieves superior efficiency and effectiveness comparing to the state-of-the-art algorithms in both relevance and fairness for top-k rankings.

We introduce GQA, a new dataset for real-world visual reasoning and compositional question answering, seeking to address key shortcomings of previous VQA datasets. We have developed a strong and robust question engine that leverages scene graph structures to create 22M diverse reasoning questions, all come with functional programs that represent their semantics. We use the programs to gain tight control over the answer distribution and present a new tunable smoothing technique to mitigate question biases. Accompanying the dataset is a suite of new metrics that evaluate essential qualities such as consistency, grounding and plausibility. An extensive analysis is performed for baselines as well as state-of-the-art models, providing fine-grained results for different question types and topologies. Whereas a blind LSTM obtains mere 42.1%, and strong VQA models achieve 54.1%, human performance tops at 89.3%, offering ample opportunity for new research to explore. We strongly hope GQA will provide an enabling resource for the next generation of models with enhanced robustness, improved consistency, and deeper semantic understanding for images and language.

We explore the use of a knowledge graphs, that capture general or commonsense knowledge, to augment the information extracted from images by the state-of-the-art methods for image captioning. The results of our experiments, on several benchmark data sets such as MS COCO, as measured by CIDEr-D, a performance metric for image captioning, show that the variants of the state-of-the-art methods for image captioning that make use of the information extracted from knowledge graphs can substantially outperform those that rely solely on the information extracted from images.

Classification tasks are usually analysed and improved through new model architectures or hyperparameter optimisation but the underlying properties of datasets are discovered on an ad-hoc basis as errors occur. However, understanding the properties of the data is crucial in perfecting models. In this paper we analyse exactly which characteristics of a dataset best determine how difficult that dataset is for the task of text classification. We then propose an intuitive measure of difficulty for text classification datasets which is simple and fast to calculate. We show that this measure generalises to unseen data by comparing it to state-of-the-art datasets and results. This measure can be used to analyse the precise source of errors in a dataset and allows fast estimation of how difficult a dataset is to learn. We searched for this measure by training 12 classical and neural network based models on 78 real-world datasets, then use a genetic algorithm to discover the best measure of difficulty. Our difficulty-calculating code ( //github.com/Wluper/edm ) and datasets ( //data.wluper.com ) are publicly available.

Autoencoders provide a powerful framework for learning compressed representations by encoding all of the information needed to reconstruct a data point in a latent code. In some cases, autoencoders can "interpolate": By decoding the convex combination of the latent codes for two datapoints, the autoencoder can produce an output which semantically mixes characteristics from the datapoints. In this paper, we propose a regularization procedure which encourages interpolated outputs to appear more realistic by fooling a critic network which has been trained to recover the mixing coefficient from interpolated data. We then develop a simple benchmark task where we can quantitatively measure the extent to which various autoencoders can interpolate and show that our regularizer dramatically improves interpolation in this setting. We also demonstrate empirically that our regularizer produces latent codes which are more effective on downstream tasks, suggesting a possible link between interpolation abilities and learning useful representations.

While neural machine translation (NMT) models provide improved translation quality in an elegant, end-to-end framework, it is less clear what they learn about language. Recent work has started evaluating the quality of vector representations learned by NMT models on morphological and syntactic tasks. In this paper, we investigate the representations learned at different layers of NMT encoders. We train NMT systems on parallel data and use the trained models to extract features for training a classifier on two tasks: part-of-speech and semantic tagging. We then measure the performance of the classifier as a proxy to the quality of the original NMT model for the given task. Our quantitative analysis yields interesting insights regarding representation learning in NMT models. For instance, we find that higher layers are better at learning semantics while lower layers tend to be better for part-of-speech tagging. We also observe little effect of the target language on source-side representations, especially with higher quality NMT models.