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The saturation-based reasoning methods are among the most theoretically developed ones and are used by most of the state-of-the-art first-order logic reasoners. In the last decade there was a sharp increase in performance of such systems,…
In many real-world applications, a model provider provides probabilistic forecasts to downstream decision-makers who use them to make decisions under diverse payoff objectives. The provider may have access to multiple predictive models,…
This paper studies the underlying combinatorial structure of a class of object rearrangement problems, which appear frequently in applications. The problems involve multiple, similar-geometry objects placed on a flat, horizontal surface,…
We present a reinforcement learning (RL) based guidance system for automated theorem proving geared towards Finding Longer Proofs (FLoP). Unlike most learning based approaches, we focus on generalising from very little training data and…
Retrieval tasks typically require a ranking of items given a query. Collaborative filtering tasks, on the other hand, learn to model user's preferences over items. In this paper we study the joint problem of recommending items to a user…
Statistical discoveries are often obtained through multiple hypothesis testing. A variety of procedures exists to evaluate multiple hypotheses, for instance the ones of Benjamini-Hochberg, Bonferroni, Holm or Sidak. We are particularly…
Scientists form hypotheses and experimentally test them. If a hypothesis fails (is refuted), scientists try to explain the failure to eliminate other hypotheses. The more precise the failure analysis the more hypotheses can be eliminated.…
We learn mathematics subjectively and must apply it objectively. But sometimes, we apply it subjectively by using wrong intuitions which may be elusive to our eyes. The aim of this note is to disclose the secretes of two kinds of these…
Existing self-supervised learning methods learn representation by means of pretext tasks which are either (1) discriminating that explicitly specify which features should be separated or (2) aligning that precisely indicate which features…
For many applications of probabilistic classifiers it is important that the predicted confidence vectors reflect true probabilities (one says that the classifier is calibrated). It has been shown that common models fail to satisfy this…
We consider the problem faced by a service platform that needs to match limited supply with demand but also to learn the attributes of new users in order to match them better in the future. We introduce a benchmark model with heterogeneous…
First-order knowledge compilation techniques have proven efficient for lifted inference. They compile a relational probability model into a target circuit on which many inference queries can be answered efficiently. Early methods used data…
Our study contributes to the debate on the evolution of cooperation in the single-shot Prisoner's Dilemma (PD) played on networks. We construct a model in which individuals are connected with positive and negative ties. Some agents play…
The data scarcity of user preferences and the cold-start problem often appear in real-world applications and limit the recommendation accuracy of collaborative filtering strategies. Leveraging the selections of social friends and foes can…
Punishment is a common tactic to sustain cooperation and has been extensively studied for a long time. While most of previous game-theoretic work adopt the imitation learning where players imitate the strategies who are better off, the…
The development of logic has largely been through the 'deductive' paradigm: conclusions are inferred from established premisses. However, the use of logic in the context of both human and machine reasoning is typically through the dual…
Current Large Language Models (LLMs) excel in general reasoning yet struggle with specialized tasks requiring proprietary or domain-specific knowledge. Fine-tuning large models for every niche application is often infeasible due to…
Given a model of a system and an objective, the model-checking question asks whether the model satisfies the objective. We study polynomial-time problems in two classical models, graphs and Markov Decision Processes (MDPs), with respect to…
The $\lambda$-calculus is a handy formalism to specify the evaluation of higher-order programs. It is not very handy, however, when one interprets the specification as an execution mechanism, because terms can grow exponentially with the…
Proof search has been used to specify a wide range of computation systems. In order to build a framework for reasoning about such specifications, we make use of a sequent calculus involving induction and co-induction. These proof principles…