In pioneering work from 2019, Barceló and coauthors identified logics that precisely match the expressive power of constant iteration-depth graph neural networks (GNNs) relative to properties definable in first-order logic. In this article, we give exact logical characterizations of recurrent GNNs in two scenarios: (1) in the setting with floating-point numbers and (2) with reals. For floats, the formalism matching recurrent GNNs is a rule-based modal logic with counting, while for reals we use a suitable infinitary modal logic, also with counting. These results give exact matches between logics and GNNs in the recurrent setting without rel-ativising to a background logic in either case, but using some natural assumptions about floating-point arithmetic. Applying our characterizations, we also prove that, relative to graph properties definable in monadic second-order logic (MSO), our infinitary and rule-based logics are equally expressive. This implies that recurrent GNNs with reals and floats have the same expressive power over MSO-definable properties and shows that, for such properties, also recurrent GNNs with reals are characterized by a (finitary!)

This simple generative task requires a model to copy binary symbols over long-range dependencies, ignoring the tokens in between. We find that Transformer FFLMs suffer from a long tail of sporadic reasoning errors, some of which we can eliminate using various regularization techniques.

This simple generative task requires a model to copy binary symbols over long-range dependencies, ignoring the tokens in between. We find that Transformer FFLMs suffer from a long tail of sporadic reasoning errors, some of which we can eliminate using various regularization techniques.

RDPs are the subclass of Non-Markov Decision Processes where the dependency on the history of past events can be captured by a finite-state automaton. We consider a setting where the automaton that underlies the RDP is unknown, and a learner strives to learn a near-optimal policy using pre-collected data, in the form of non-Markov sequences of observations, without further exploration. We present RegORL, an algorithm that suitably combines automata learning techniques and state-of-the-art algorithms for offline RL in MDPs. RegORL has a modular design allowing one to use any off-the-shelf offline RL algorithm in MDPs. We report a non-asymptotic high-probability sample complexity bound for RegORL to yield an $\varepsilon$-optimal policy, which makes appear a notion of concentrability relevant for RDPs. Furthermore, we present a sample complexity lower bound for offline RL in RDPs. To our best knowledge, this is the first work presenting a provably efficient algorithm for offline learning in RDPs.

Real-world robotic tasks often require agents to achieve sequences of goals while respecting time-varying safety constraints. However, standard Reinforcement Learning (RL) paradigms are fundamentally limited in these settings. A natural approach to these problems is to combine RL with Linear-time Temporal Logic (LTL), a formal language for specifying complex, temporally extended tasks and safety constraints. Yet, existing RL methods for LTL objectives exhibit poor empirical performance in complex and continuous environments. As a result, no scalable methods support both temporally ordered goals and safety simultaneously, making them ill-suited for realistic robotics scenarios. We propose Automaton Constrained Q-Learning (ACQL), an algorithm that addresses this gap by combining goal-conditioned value learning with automaton-guided reinforcement. ACQL supports most LTL task specifications and leverages their automaton representation to explicitly encode stage-wise goal progression and both stationary and non-stationary safety constraints. We show that ACQL outperforms existing methods across a range of continuous control tasks, including cases where prior methods fail to satisfy either goal-reaching or safety constraints. We further validate its real-world applicability by deploying ACQL on a 6-DOF robotic arm performing a goal-reaching task in a cluttered, cabinet-like space with safety constraints. Our results demonstrate that ACQL is a robust and scalable solution for learning robotic behaviors according to rich temporal specifications.

Nowadays, social networks are becoming a popular way of analyzing tourist behavior, thanks to the digital traces left by travelers during their stays on these networks. The massive amount of data generated; by the propensity of tourists to share comments and photos during their trip; makes it possible to model their journeys and analyze their behavior. Predicting the next movement of tourists plays a key role in tourism marketing to understand demand and improve decision support. In this paper, we propose a method to understand and to learn tourists' movements based on social network data analysis to predict future movements. The method relies on a machine learning grammatical inference algorithm. A major contribution in this paper is to adapt the grammatical inference algorithm to the context of big data. Our method produces a hidden Markov model representing the movements of a group of tourists. The hidden Markov model is flexible and editable with new data. The capital city of France, Paris is selected to demonstrate the efficiency of the proposed methodology.

Automata extraction is a method for synthesising interpretable surrogates for black-box neural models that can be analysed symbolically. Existing techniques assume a finite input alphabet, and thus are not directly applicable to data sequences drawn from continuous domains. We address this challenge with deterministic register automata (DRAs), which extend finite automata with registers that store and compare numeric values. Our main contribution is a framework for robust DRA extraction from black-box models: we develop a polynomial-time robustness checker for DRAs with a fixed number of registers, and combine it with passive and active automata learning algorithms. This combination yields surrogate DRAs with statistical robustness and equivalence guarantees. As a key application, we use the extracted automata to assess the robustness of neural networks: for a given sequence and distance metric, the DRA either certifies local robustness or produces a concrete counterexample. Experiments on recurrent neural networks and transformer architectures show that our framework reliably learns accurate automata and enables principled robustness evaluation. Overall, our results demonstrate that robust DRA extraction effectively bridges neural network interpretability and formal reasoning without requiring white-box access to the underlying network.