Order is one of the main instruments to measure the relationship between objects in (empirical) data. However, compared to methods that use numerical properties of objects, the amount of ordinal methods developed is rather small. One reason for this is the limited availability of computational resources in the last century that would have been required for ordinal computations. Another reason -- particularly important for this line of research -- is that order-based methods are often seen as too mathematically rigorous for applying them to real-world data. In this paper, we will therefore discuss different means for measuring and 'calculating' with ordinal structures -- a specific class of directed graphs -- and show how to infer knowledge from them. Our aim is to establish Ordinal Data Science as a fundamentally new research agenda. Besides cross-fertilization with other cornerstone machine learning and knowledge representation methods, a broad range of disciplines will benefit from this endeavor, including, psychology, sociology, economics, web science, knowledge engineering, scientometrics.

Intelligent agents use internal world models to reason and make predictions about different courses of their actions at many scales [22]. Devising learning paradigms and architectures that allow machines to learn world models that operate at multiple levels of temporal abstractions while dealing with complex uncertainty predictions is a major technical hurdle [18]. In this work, we propose a probabilistic formalism to learn multi-time scale world models which we call the Multi Time Scale State Space (MTS3) model. Our model uses a computationally efficient inference scheme on multiple time scales for highly accurate long-horizon predictions and uncertainty estimates over several seconds into the future. Our experiments, which focus on action conditional long horizon future predictions, show that MTS3 outperforms recent methods on several system identification benchmarks including complex simulated and real-world dynamical systems. Code is available at this repository: https://github.com/ALRhub/MTS3.

In recent years, several machine learning models have been proposed. They are trained with a language modelling objective on large-scale text-only data. With such pretraining, they can achieve impressive results on many Natural Language Understanding and Generation tasks. However, many facets of meaning cannot be learned by ``listening to the radio" only. In the literature, many Vision+Language (V+L) tasks have been defined with the aim of creating models that can ground symbols in the visual modality. In this work, we provide a systematic literature review of several tasks and models proposed in the V+L field. We rely on Wittgenstein's idea of `language games' to categorise such tasks into 3 different families: 1) discriminative games, 2) generative games, and 3) interactive games. Our analysis of the literature provides evidence that future work should be focusing on interactive games where communication in Natural Language is important to resolve ambiguities about object referents and action plans and that physical embodiment is essential to understand the semantics of situations and events. Overall, these represent key requirements for developing grounded meanings in neural models.

Unlike most reinforcement learning agents which require an unrealistic amount of environment interactions to learn a new behaviour, humans excel at learning quickly by merely observing and imitating others. This ability highly depends on the fact that humans have a model of their own embodiment that allows them to infer the most likely actions that led to the observed behaviour. In this paper, we propose Action Inference by Maximising Evidence (AIME) to replicate this behaviour using world models. AIME consists of two distinct phases. In the first phase, the agent learns a world model from its past experience to understand its own body by maximising the ELBO. While in the second phase, the agent is given some observation-only demonstrations of an expert performing a novel task and tries to imitate the expert's behaviour. AIME achieves this by defining a policy as an inference model and maximising the evidence of the demonstration under the policy and world model. Our method is "zero-shot" in the sense that it does not require further training for the world model or online interactions with the environment after given the demonstration. We empirically validate the zero-shot imitation performance of our method on the Walker and Cheetah embodiment of the DeepMind Control Suite and find it outperforms the state-of-the-art baselines. Code is available at: https://github.com/argmax-ai/aime.

In the noisy intermediate-scale quantum era, variational quantum algorithms (VQAs) have emerged as a promising avenue to obtain quantum advantage. However, the success of VQAs depends on the expressive power of parameterised quantum circuits, which is constrained by the limited gate number and the presence of barren plateaus. In this work, we propose and numerically demonstrate a novel approach for VQAs, utilizing randomised quantum circuits to generate the variational wavefunction. We parameterize the distribution function of these random circuits using artificial neural networks and optimize it to find the solution. This random-circuit approach presents a trade-off between the expressive power of the variational wavefunction and time cost, in terms of the sampling cost of quantum circuits. Given a fixed gate number, we can systematically increase the expressive power by extending the quantum-computing time. With a sufficiently large permissible time cost, the variational wavefunction can approximate any quantum state with arbitrary accuracy. Furthermore, we establish explicit relationships between expressive power, time cost, and gate number for variational quantum eigensolvers. These results highlight the promising potential of the random-circuit approach in achieving a high expressive power in quantum computing.

Modelling human cognition can provide key insights into behavioral dynamics under changing conditions. This enables synthetic data generation and guides adaptive interventions for cognitive regulation. Challenges arise when environments are highly dynamic, obscuring stimulus-behavior relationships. We propose a cognitive agent integrating drift-diffusion with deep reinforcement learning to simulate granular stress effects on logical reasoning process. Leveraging a large dataset of 21,157 logical responses, we investigate performance impacts of dynamic stress. This prior knowledge informed model design and evaluation. Quantitatively, the framework improves cognition modelling by capturing both subject-specific and stimuli-specific behavioural differences. Qualitatively, it captures general trends in human logical reasoning under stress. Our approach is extensible to examining diverse environmental influences on cognition and behavior. Overall, this work demonstrates a powerful, data-driven methodology to simulate and understand the vagaries of human logical reasoning process in dynamic contexts.

Contemporary artificial intelligence systems exhibit rapidly growing abilities accompanied by the growth of required resources, expansive datasets and corresponding investments into computing infrastructure. Although earlier successes predominantly focus on constrained settings, recent strides in fundamental research and applications aspire to create increasingly general systems. This evolving landscape presents a dual panorama of opportunities and challenges in refining the generalisation and transfer of knowledge - the extraction from existing sources and adaptation as a comprehensive foundation for tackling new problems. Within the domain of reinforcement learning (RL), the representation of knowledge manifests through various modalities, including dynamics and reward models, value functions, policies, and the original data. This taxonomy systematically targets these modalities and frames its discussion based on their inherent properties and alignment with different objectives and mechanisms for transfer. Where possible, we aim to provide coarse guidance delineating approaches which address requirements such as limiting environment interactions, maximising computational efficiency, and enhancing generalisation across varying axes of change. Finally, we analyse reasons contributing to the prevalence or scarcity of specific forms of transfer, the inherent potential behind pushing these frontiers, and underscore the significance of transitioning from designed to learned transfer.

Search and planning algorithms have been a cornerstone of artificial intelligence since the field's inception. Giving reinforcement learning agents the ability to plan during execution time has resulted in significant performance improvements in various domains. However, in real-world environments, the model with respect to which the agent plans has been constrained to be grounded in the real environment itself, as opposed to a more abstract model which allows for planning over compound actions and behaviors. We propose a new method, called PiZero, that gives an agent the ability to plan in an abstract search space that the agent learns during training, which is completely decoupled from the real environment. Unlike prior approaches, this enables the agent to perform high-level planning at arbitrary timescales and reason in terms of compound or temporally-extended actions, which can be useful in environments where large numbers of base-level micro-actions are needed to perform relevant macro-actions. In addition, our method is more general than comparable prior methods because it seamlessly handles settings with continuous action spaces, combinatorial action spaces, and partial observability. We evaluate our method on multiple domains, including the traveling salesman problem, Sokoban, 2048, the facility location problem, and Pacman. Experimentally, it outperforms comparable prior methods without assuming access to an environment simulator at execution time.

While language models are powerful and versatile, they often fail to address highly complex problems. This is because solving complex problems requires deliberate thinking, which has been only minimally guided during training. In this paper, we propose a new method called Cumulative Reasoning (CR), which employs language models in a cumulative and iterative manner to emulate human thought processes. By decomposing tasks into smaller components, CR streamlines the problem-solving process, rendering it both more manageable and effective. For logical inference tasks, CR consistently outperforms existing methods with an improvement up to 9.3%, and achieves an accuracy of 98.04% on the curated FOLIO wiki dataset. In the context of the Game of 24, CR achieves an accuracy of 98%, which signifies a substantial enhancement of 24% over the previous state-of-the-art method. Finally, on the MATH dataset, we establish new state-of-the-art results with 58.0% overall accuracy, surpassing the previous best approach by a margin of 4.2%, and achieving 43% relative improvement on the hardest level 5 problems (22.4% to 32.1%). Additionally, we expand the concept of Cumulative Reasoning to incorporate a Python code environment, deliberately omitting external aids such as retrieval and web browsing and focusing solely on the LLM's intrinsic reasoning capabilities within a Python code environment. Our experiments in this setting yielded impressive results, with an overall accuracy of 72.2% on the MATH dataset, significantly outperforming the PAL method with 38.8% relative improvement. Code is available at https://github.com/iiis-ai/cumulative-reasoning.

Human behavior is inherently hierarchical, resulting from the decomposition of a task into subtasks or an abstract action into concrete actions. However, behavior is typically measured as a sequence of actions, which makes it difficult to infer its hierarchical structure. In this paper, we explore how people form hierarchically-structured plans, using an experimental paradigm that makes hierarchical representations observable: participants create programs that produce sequences of actions in a language with explicit hierarchical structure. This task lets us test two well-established principles of human behavior: utility maximization (i.e. using fewer actions) and minimum description length (MDL; i.e. having a shorter program). We find that humans are sensitive to both metrics, but that both accounts fail to predict a qualitative feature of human-created programs, namely that people prefer programs with reuse over and above the predictions of MDL. We formalize this preference for reuse by extending the MDL account into a generative model over programs, modeling hierarchy choice as the induction of a grammar over actions. Our account can explain the preference for reuse and provides the best prediction of human behavior, going beyond simple accounts of compressibility to highlight a principle that guides hierarchical planning.