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We introduce an extension of first-order logic that comes equipped with additional predicates for reasoning about an abstract state. Sequents in the logic comprise a main formula together with pre- and postconditions in the style of Hoare logic, and the axioms and rules of the logic ensure that the assertions about the state compose in the correct way. The main result of the paper is a realizability interpretation of our logic that extracts programs into a mixed functional/imperative language. All programs expressible in this language act on the state in a sequential manner, and we make this intuition precise by interpreting them in a semantic metatheory using the state monad. Our basic framework is very general, and our intention is that it can be instantiated and extended in a variety of different ways. We outline in detail one such extension: A monadic version of Heyting arithmetic with a wellfounded while rule, and conclude by outlining several other directions for future work.

With the increasing demand of intelligent systems capable of operating in different contexts (e.g. users on the move) the correct interpretation of the user-need by such systems has become crucial to give consistent answers to the user questions. The most effective applications addressing such task are in the fields of natural language processing and semantic expansion of terms. These techniques are aimed at estimating the goal of an input query reformulating it as an intent, commonly relying on textual resources built exploiting different semantic relations like \emph{synonymy}, \emph{antonymy} and many others. The aim of this paper is to generate such resources using the labels of a given taxonomy as source of information. The obtained resources are integrated into a plain classifier for reformulating a set of input queries as intents and tracking the effect of each relation, in order to quantify the impact of each semantic relation on the classification. As an extension to this, the best tradeoff between improvement and noise introduction when combining such relations is evaluated. The assessment is made generating the resources and their combinations and using them for tuning the classifier which is used to reformulate the user questions as labels. The evaluation employs a wide and varied taxonomy as a use-case, exploiting its labels as basis for the semantic expansion and producing several corpora with the purpose of enhancing the pseudo-queries estimation.

The field of adversarial textual attack has significantly grown over the last few years, where the commonly considered objective is to craft adversarial examples (AEs) that can successfully fool the target model. However, the imperceptibility of attacks, which is also essential for practical attackers, is often left out by previous studies. In consequence, the crafted AEs tend to have obvious structural and semantic differences from the original human-written text, making them easily perceptible. In this work, we advocate leveraging multi-objectivization to address such issue. Specifically, we reformulate the problem of crafting AEs as a multi-objective optimization problem, where the attack imperceptibility is considered as an auxiliary objective. Then, we propose a simple yet effective evolutionary algorithm, dubbed HydraText, to solve this problem. To the best of our knowledge, HydraText is currently the only approach that can be effectively applied to both score-based and decision-based attack settings. Exhaustive experiments involving 44237 instances demonstrate that HydraText consistently achieves competitive attack success rates and better attack imperceptibility than the recently proposed attack approaches. A human evaluation study also shows that the AEs crafted by HydraText are more indistinguishable from human-written text. Finally, these AEs exhibit good transferability and can bring notable robustness improvement to the target model by adversarial training.

We use Stein characterisations to derive new moment-type estimators for the parameters of several multivariate distributions in the i.i.d. case; we also derive the asymptotic properties of these estimators. Our examples include the multivariate truncated normal distribution and several spherical distributions. The estimators are explicit and therefore provide an interesting alternative to the maximum-likelihood estimator. The quality of these estimators is assessed through competitive simulation studies in which we compare their behaviour to the performance of other estimators available in the literature.

Dynamical systems across the sciences, from electrical circuits to ecological networks, undergo qualitative and often catastrophic changes in behavior, called bifurcations, when their underlying parameters cross a threshold. Existing methods predict oncoming catastrophes in individual systems but are primarily time-series-based and struggle both to categorize qualitative dynamical regimes across diverse systems and to generalize to real data. To address this challenge, we propose a data-driven, physically-informed deep-learning framework for classifying dynamical regimes and characterizing bifurcation boundaries based on the extraction of topologically invariant features. We focus on the paradigmatic case of the supercritical Hopf bifurcation, which is used to model periodic dynamics across a wide range of applications. Our convolutional attention method is trained with data augmentations that encourage the learning of topological invariants which can be used to detect bifurcation boundaries in unseen systems and to design models of biological systems like oscillatory gene regulatory networks. We further demonstrate our method's use in analyzing real data by recovering distinct proliferation and differentiation dynamics along pancreatic endocrinogenesis trajectory in gene expression space based on single-cell data. Our method provides valuable insights into the qualitative, long-term behavior of a wide range of dynamical systems, and can detect bifurcations or catastrophic transitions in large-scale physical and biological systems.

The recent success of neural networks in natural language processing has drawn renewed attention to learning sequence-to-sequence (seq2seq) tasks. While there exists a rich literature that studies classification and regression tasks using solvable models of neural networks, seq2seq tasks have not yet been studied from this perspective. Here, we propose a simple model for a seq2seq task that has the advantage of providing explicit control over the degree of memory, or non-Markovianity, in the sequences -- the stochastic switching-Ornstein-Uhlenbeck (SSOU) model. We introduce a measure of non-Markovianity to quantify the amount of memory in the sequences. For a minimal auto-regressive (AR) learning model trained on this task, we identify two learning regimes corresponding to distinct phases in the stationary state of the SSOU process. These phases emerge from the interplay between two different time scales that govern the sequence statistics. Moreover, we observe that while increasing the integration window of the AR model always improves performance, albeit with diminishing returns, increasing the non-Markovianity of the input sequences can improve or degrade its performance. Finally, we perform experiments with recurrent and convolutional neural networks that show that our observations carry over to more complicated neural network architectures.

Active learning can improve the efficiency of training prediction models by identifying the most informative new labels to acquire. However, non-response to label requests can impact active learning's effectiveness in real-world contexts. We conceptualise this degradation by considering the type of non-response present in the data, demonstrating that biased non-response is particularly detrimental to model performance. We argue that this sort of non-response is particularly likely in contexts where the labelling process, by nature, relies on user interactions. To mitigate the impact of biased non-response, we propose a cost-based correction to the sampling strategy--the Upper Confidence Bound of the Expected Utility (UCB-EU)--that can, plausibly, be applied to any active learning algorithm. Through experiments, we demonstrate that our method successfully reduces the harm from labelling non-response in many settings. However, we also characterise settings where the non-response bias in the annotations remains detrimental under UCB-EU for particular sampling methods and data generating processes. Finally, we evaluate our method on a real-world dataset from e-commerce platform Taobao. We show that UCB-EU yields substantial performance improvements to conversion models that are trained on clicked impressions. Most generally, this research serves to both better conceptualise the interplay between types of non-response and model improvements via active learning, and to provide a practical, easy to implement correction that helps mitigate model degradation.

Rule-based reasoning is an essential part of human intelligence prominently formalized in artificial intelligence research via logic programs. Describing complex objects as the composition of elementary ones is a common strategy in computer science and science in general. The author has recently introduced the sequential composition of logic programs in the context of logic-based analogical reasoning and learning in logic programming. Motivated by these applications, in this paper we construct a qualitative and algebraic notion of syntactic logic program similarity from sequential decompositions of programs. We then show how similarity can be used to answer queries across different domains via a one-step reduction. In a broader sense, this paper is a further step towards an algebraic theory of logic programming.

The remarkable practical success of deep learning has revealed some major surprises from a theoretical perspective. In particular, simple gradient methods easily find near-optimal solutions to non-convex optimization problems, and despite giving a near-perfect fit to training data without any explicit effort to control model complexity, these methods exhibit excellent predictive accuracy. We conjecture that specific principles underlie these phenomena: that overparametrization allows gradient methods to find interpolating solutions, that these methods implicitly impose regularization, and that overparametrization leads to benign overfitting. We survey recent theoretical progress that provides examples illustrating these principles in simpler settings. We first review classical uniform convergence results and why they fall short of explaining aspects of the behavior of deep learning methods. We give examples of implicit regularization in simple settings, where gradient methods lead to minimal norm functions that perfectly fit the training data. Then we review prediction methods that exhibit benign overfitting, focusing on regression problems with quadratic loss. For these methods, we can decompose the prediction rule into a simple component that is useful for prediction and a spiky component that is useful for overfitting but, in a favorable setting, does not harm prediction accuracy. We focus specifically on the linear regime for neural networks, where the network can be approximated by a linear model. In this regime, we demonstrate the success of gradient flow, and we consider benign overfitting with two-layer networks, giving an exact asymptotic analysis that precisely demonstrates the impact of overparametrization. We conclude by highlighting the key challenges that arise in extending these insights to realistic deep learning settings.

Deep learning is usually described as an experiment-driven field under continuous criticizes of lacking theoretical foundations. This problem has been partially fixed by a large volume of literature which has so far not been well organized. This paper reviews and organizes the recent advances in deep learning theory. The literature is categorized in six groups: (1) complexity and capacity-based approaches for analyzing the generalizability of deep learning; (2) stochastic differential equations and their dynamic systems for modelling stochastic gradient descent and its variants, which characterize the optimization and generalization of deep learning, partially inspired by Bayesian inference; (3) the geometrical structures of the loss landscape that drives the trajectories of the dynamic systems; (4) the roles of over-parameterization of deep neural networks from both positive and negative perspectives; (5) theoretical foundations of several special structures in network architectures; and (6) the increasingly intensive concerns in ethics and security and their relationships with generalizability.