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Reinforcement learning of real-world tasks is very data inefficient, and extensive simulation-based modelling has become the dominant approach for training systems. However, in human-robot interaction and many other real-world settings, there is no appropriate one-model-for-all due to differences in individual instances of the system (e.g. different people) or necessary oversimplifications in the simulation models. This requires two approaches: 1. either learning the individual system's dynamics approximately from data which requires data-intensive training or 2. using a complete digital twin of the instances, which may not be realisable in many cases. We introduce two approaches: co-kriging adjustments (CKA) and ridge regression adjustment (RRA) as novel ways to combine the advantages of both approaches. Our adjustment methods are based on an auto-regressive AR1 co-kriging model that we integrate with GP priors. This yield a data- and simulation-efficient way of using simplistic simulation models (e.g., simple two-link model) and rapidly adapting them to individual instances (e.g., biomechanics of individual people). Using CKA and RRA, we obtain more accurate uncertainty quantification of the entire system's dynamics than pure GP-based and AR1 methods. We demonstrate the efficiency of co-kriging adjustment with an interpretable reinforcement learning control example, learning to control a biomechanical human arm using only a two-link arm simulation model (offline part) and CKA derived from a small amount of interaction data (on-the-fly online). Our method unlocks an efficient and uncertainty-aware way to implement reinforcement learning methods in real world complex systems for which only imperfect simulation models exist.

With the increasing availability of large scale datasets, computational power and tools like automatic differentiation and expressive neural network architectures, sequential data are now often treated in a data-driven way, with a dynamical model trained from the observation data. While neural networks are often seen as uninterpretable black-box architectures, they can still benefit from physical priors on the data and from mathematical knowledge. In this paper, we use a neural network architecture which leverages the long-known Koopman operator theory to embed dynamical systems in latent spaces where their dynamics can be described linearly, enabling a number of appealing features. We introduce methods that enable to train such a model for long-term continuous reconstruction, even in difficult contexts where the data comes in irregularly-sampled time series. The potential for self-supervised learning is also demonstrated, as we show the promising use of trained dynamical models as priors for variational data assimilation techniques, with applications to e.g. time series interpolation and forecasting.

In recent years, there has been an intense debate about how learning in biological neural networks (BNNs) differs from learning in artificial neural networks. It is often argued that the updating of connections in the brain relies only on local information, and therefore a stochastic gradient-descent type optimization method cannot be used. In this paper, we study a stochastic model for supervised learning in BNNs. We show that a (continuous) gradient step occurs approximately when each learning opportunity is processed by many local updates. This result suggests that stochastic gradient descent may indeed play a role in optimizing BNNs.

The (modern) arbitrary derivative (ADER) approach is a popular technique for the numerical solution of differential problems based on iteratively solving an implicit discretization of their weak formulation. In this work, focusing on an ODE context, we investigate several strategies to improve this approach. Our initial emphasis is on the order of accuracy of the method in connection with the polynomial discretization of the weak formulation. We demonstrate that precise choices lead to higher-order convergences in comparison to the existing literature. Then, we put ADER methods into a Deferred Correction (DeC) formalism. This allows to determine the optimal number of iterations, which is equal to the formal order of accuracy of the method, and to introduce efficient $p$-adaptive modifications. These are defined by matching the order of accuracy achieved and the degree of the polynomial reconstruction at each iteration. We provide analytical and numerical results, including the stability analysis of the new modified methods, the investigation of the computational efficiency, an application to adaptivity and an application to hyperbolic PDEs with a Spectral Difference (SD) space discretization.

We present a constant-factor approximation algorithm for the Nash social welfare maximization problem with subadditive valuations accessible via demand queries. More generally, we propose a template for NSW optimization by solving a configuration-type LP and using a rounding procedure for (utilitarian) social welfare as a blackbox, which could be applicable to other variants of the problem.

We consider the linear lambda-calculus extended with the sup type constructor, which provides an additive conjunction along with a non-deterministic destructor. The sup type constructor has been introduced in the context of quantum computing. In this paper, we study this type constructor within a simple linear logic categorical model, employing the category of semimodules over a commutative semiring. We demonstrate that the non-deterministic destructor finds a suitable model in a "weighted" codiagonal map. This approach offers a valid and insightful alternative to interpreting non-determinism, especially in instances where the conventional Powerset Monad interpretation does not align with the category's structure, as is the case with the category of semimodules. The validity of this alternative relies on the presence of biproducts within the category.

Over the past decades, cognitive neuroscientists and behavioral economists have recognized the value of describing the process of decision making in detail and modeling the emergence of decisions over time. For example, the time it takes to decide can reveal more about an agent's true hidden preferences than only the decision itself. Similarly, data that track the ongoing decision process such as eye movements or neural recordings contain critical information that can be exploited, even if no decision is made. Here, we argue that artificial intelligence (AI) research would benefit from a stronger focus on insights about how decisions emerge over time and incorporate related process data to improve AI predictions in general and human-AI interactions in particular. First, we introduce a highly established computational framework that assumes decisions to emerge from the noisy accumulation of evidence, and we present related empirical work in psychology, neuroscience, and economics. Next, we discuss to what extent current approaches in multi-agent AI do or do not incorporate process data and models of decision making. Finally, we outline how a more principled inclusion of the evidence-accumulation framework into the training and use of AI can help to improve human-AI interactions in the future.

This paper introduces a prognostic method called FLASH that addresses the problem of joint modelling of longitudinal data and censored durations when a large number of both longitudinal and time-independent features are available. In the literature, standard joint models are either of the shared random effect or joint latent class type. Combining ideas from both worlds and using appropriate regularisation techniques, we define a new model with the ability to automatically identify significant prognostic longitudinal features in a high-dimensional context, which is of increasing importance in many areas such as personalised medicine or churn prediction. We develop an estimation methodology based on the EM algorithm and provide an efficient implementation. The statistical performance of the method is demonstrated both in extensive Monte Carlo simulation studies and on publicly available real-world datasets. Our method significantly outperforms the state-of-the-art joint models in predicting the latent class membership probability in terms of the C-index in a so-called ``real-time'' prediction setting, with a computational speed that is orders of magnitude faster than competing methods. In addition, our model automatically identifies significant features that are relevant from a practical perspective, making it interpretable.

A general class of the almost instantaneous fixed-to-variable-length (AIFV) codes is proposed, which contains every possible binary code we can make when allowing finite bits of decoding delay. The contribution of the paper lies in the following. (i) Introducing $N$-bit-delay AIFV codes, constructed by multiple code trees with higher flexibility than the conventional AIFV codes. (ii) Proving that the proposed codes can represent any uniquely-encodable and uniquely-decodable variable-to-variable length codes. (iii) Showing how to express codes as multiple code trees with minimum decoding delay. (iv) Formulating the constraints of decodability as the comparison of intervals in the real number line. The theoretical results in this paper are expected to be useful for further study on AIFV codes.

Graph representation learning for hypergraphs can be used to extract patterns among higher-order interactions that are critically important in many real world problems. Current approaches designed for hypergraphs, however, are unable to handle different types of hypergraphs and are typically not generic for various learning tasks. Indeed, models that can predict variable-sized heterogeneous hyperedges have not been available. Here we develop a new self-attention based graph neural network called Hyper-SAGNN applicable to homogeneous and heterogeneous hypergraphs with variable hyperedge sizes. We perform extensive evaluations on multiple datasets, including four benchmark network datasets and two single-cell Hi-C datasets in genomics. We demonstrate that Hyper-SAGNN significantly outperforms the state-of-the-art methods on traditional tasks while also achieving great performance on a new task called outsider identification. Hyper-SAGNN will be useful for graph representation learning to uncover complex higher-order interactions in different applications.