How can intelligent machines assess their competencies in completing tasks? This question has come into focus for autonomous systems that algorithmically reason and make decisions under uncertainty. It is argued here that machine self-confidence - a form of meta-reasoning based on self-assessments of an agent's knowledge about the state of the world and itself, as well as its ability to reason about and execute tasks - leads to many eminently computable and useful competency indicators for such agents. This paper presents a culmination of work on this concept in the form of a computational framework called Factorized Machine Self-confidence (FaMSeC), which provides a holistic engineering-focused description of factors driving an algorithmic decision-making process, including: outcome assessment, solver quality, model quality, alignment quality, and past experience. In FaMSeC, self confidence indicators are derived from hierarchical `problem-solving statistics' embedded within broad classes of probabilistic decision-making algorithms such as Markov decision processes. The problem-solving statistics are obtained by evaluating and grading probabilistic exceedance margins with respect to given competency standards, which are specified for each of the various decision-making competency factors by the informee (e.g. a non-expert user or an expert system designer). This approach allows `algorithmic goodness of fit' evaluations to be easily incorporated into the design of many kinds of autonomous agents in the form of human-interpretable competency self-assessment reports. Detailed descriptions and application examples for a Markov decision process agent show how two of the FaMSeC factors (outcome assessment and solver quality) can be computed and reported for a range of possible tasking contexts through novel use of meta-utility functions, behavior simulations, and surrogate prediction models.

We explore the use of quantum generative adversarial networks QGANs for modeling eye movement velocity data. We assess whether the advanced computational capabilities of QGANs can enhance the modeling of complex stochastic distribution beyond the traditional mathematical models, particularly the Markov model. The findings indicate that while QGANs demonstrate potential in approximating complex distributions, the Markov model consistently outperforms in accurately replicating the real data distribution. This comparison underlines the challenges and avenues for refinement in time series data generation using quantum computing techniques. It emphasizes the need for further optimization of quantum models to better align with real-world data characteristics.

Bayesian estimation is a vital tool in robotics as it allows systems to update the belief of the robot state using incomplete information from noisy sensors. To render the state estimation problem tractable, many systems assume that the motion and measurement noise, as well as the state distribution, are all unimodal and Gaussian. However, there are numerous scenarios and systems that do not comply with these assumptions. Existing non-parametric filters that are used to model multimodal distributions have drawbacks that limit their ability to represent a diverse set of distributions. In this paper, we introduce a novel approach to nonparametric Bayesian filtering to cope with multimodal distributions using harmonic exponential distributions. This approach leverages two key insights of harmonic exponential distributions: a) the product of two distributions can be expressed as the element-wise addition of their log-likelihood Fourier coefficients, and b) the convolution of two distributions can be efficiently computed as the tensor product of their Fourier coefficients. These observations enable the development of an efficient and exact solution to the Bayes filter up to the band limit of a Fourier transform. We demonstrate our filter's superior performance compared with established nonparametric filtering methods across a range of simulated and real-world localization tasks.

Recent advancements in machine learning have accelerated its widespread adoption across various real-world applications. However, in safety-critical domains, the deployment of machine learning models is riddled with challenges due to their complexity, lack of interpretability, and absence of formal guarantees regarding their behavior. In this paper, we introduce a verification framework tailored for Bayesian networks, designed to address these drawbacks. Our framework comprises two key components: (1) a two-step compilation and encoding scheme that translates Bayesian networks into Boolean logic literals, and (2) formal verification queries that leverage these literals to verify various properties encoded as constraints. Specifically, we introduce two verification queries: if-then rules (ITR) and feature monotonicity (FMO). We benchmark the efficiency of our verification scheme and demonstrate its practical utility in real-world scenarios.

AI has been dealing with uncertainty to have highly accurate results. This becomes even worse with reasonably small data sets or a variation in the data sets. This has far-reaching effects on decision-making, forecasting and learning mechanisms. This study seeks to unpack the nature of uncertainty that exists within AI by drawing ideas from established works, the latest developments and practical applications and provide a novel total uncertainty definition in AI. From inception theories up to current methodologies, this paper provides an integrated view of dealing with better total uncertainty as well as complexities of uncertainty in AI that help us understand its meaning and value across different domains.

Empirical data can often be considered as samples from a set of probability distributions. Kernel methods have emerged as a natural approach for learning to classify these distributions. Although numerous kernels between distributions have been proposed, applying kernel methods to distribution regression tasks remains challenging, primarily because selecting a suitable kernel is not straightforward. Surprisingly, the question of learning a data-dependent distribution kernel has received little attention. In this paper, we propose a novel objective for the unsupervised learning of data-dependent distribution kernel, based on the principle of entropy maximization in the space of probability measure embeddings. We examine the theoretical properties of the latent embedding space induced by our objective, demonstrating that its geometric structure is well-suited for solving downstream discriminative tasks. Finally, we demonstrate the performance of the learned kernel across different modalities.

We introduce a novel deep operator network (DeepONet) framework that incorporates generalised variational inference (GVI) using R\'enyi's $\alpha$-divergence to learn complex operators while quantifying uncertainty. By incorporating Bayesian neural networks as the building blocks for the branch and trunk networks, our framework endows DeepONet with uncertainty quantification. The use of R\'enyi's $\alpha$-divergence, instead of the Kullback-Leibler divergence (KLD), commonly used in standard variational inference, mitigates issues related to prior misspecification that are prevalent in Variational Bayesian DeepONets. This approach offers enhanced flexibility and robustness. We demonstrate that modifying the variational objective function yields superior results in terms of minimising the mean squared error and improving the negative log-likelihood on the test set. Our framework's efficacy is validated across various mechanical systems, where it outperforms both deterministic and standard KLD-based VI DeepONets in predictive accuracy and uncertainty quantification. The hyperparameter $\alpha$, which controls the degree of robustness, can be tuned to optimise performance for specific problems. We apply this approach to a range of mechanics problems, including gravity pendulum, advection-diffusion, and diffusion-reaction systems. Our findings underscore the potential of $\alpha$-VI DeepONet to advance the field of data-driven operator learning and its applications in engineering and scientific domains.

Multi-agent trajectory prediction is crucial to autonomous driving and understanding the surrounding environment. Learning-based approaches for multi-agent trajectory prediction, such as primarily relying on graph neural networks, graph transformers, and hypergraph neural networks, have demonstrated outstanding performance on real-world datasets in recent years. However, the hypergraph transformer-based method for trajectory prediction is yet to be explored. Therefore, we present a MultiscAle Relational Transformer (MART) network for multi-agent trajectory prediction. MART is a hypergraph transformer architecture to consider individual and group behaviors in transformer machinery. The core module of MART is the encoder, which comprises a Pair-wise Relational Transformer (PRT) and a Hyper Relational Transformer (HRT). The encoder extends the capabilities of a relational transformer by introducing HRT, which integrates hyperedge features into the transformer mechanism, promoting attention weights to focus on group-wise relations. In addition, we propose an Adaptive Group Estimator (AGE) designed to infer complex group relations in real-world environments. Extensive experiments on three real-world datasets (NBA, SDD, and ETH-UCY) demonstrate that our method achieves state-of-the-art performance, enhancing ADE/FDE by 3.9%/11.8% on the NBA dataset. Code is available at https://github.com/gist-ailab/MART.

We propose a system for tracking beats and downbeats with two objectives: generality across a diverse music range, and high accuracy. We achieve generality by training on multiple datasets -- including solo instrument recordings, pieces with time signature changes, and classical music with high tempo variations -- and by removing the commonly used Dynamic Bayesian Network (DBN) postprocessing, which introduces constraints on the meter and tempo. For high accuracy, among other improvements, we develop a loss function tolerant to small time shifts of annotations, and an architecture alternating convolutions with transformers either over frequency or time. Our system surpasses the current state of the art in F1 score despite using no DBN. However, it can still fail, especially for difficult and underrepresented genres, and performs worse on continuity metrics, so we publish our model, code, and preprocessed datasets, and invite others to beat this.

Human groups of all sizes and kinds engage in deliberation, problem solving, strategizing, decision making, and more generally, cognition. Some groups are large, and that setting presents unique challenges. The small-group setting often involves face-to-face dialogue, but group cognition in the large-group setting typically requires some form of online interaction. New approaches are needed to facilitate the kind of rich communication and information processing that are required for effective, functional cognition in the online setting, especially for groups characterized by thousands to millions of participants who wish to share potentially complex, nuanced, and dynamic perspectives. This concept paper proposes the CogNarr (Cognitive Narrative) ecosystem, which is designed to facilitate functional cognition in the large-group setting. The paper's contribution is a novel vision as to how recent developments in cognitive science, artificial intelligence, natural language processing, and related fields might be scaled and applied to large-group cognition, using an approach that itself promotes further scientific advancement. A key perspective is to view a group as an organism that uses some form of cognitive architecture to sense the world, process information, remember, learn, predict, make decisions, and adapt to changing conditions. The CogNarr ecosystem is designed to serve as a component within that architecture.