A formal definition and meta-model for a machine theory of mind

This paper proposes, for the first time, a rigorous formal definition of the concept of Machine Theory of Mind, based on principles supported by evidence from cognitive psychology, neuroscience and artificial intelligence, and uses the above as a lens to examine state-of-the-art and current efforts in the field, driving a potential agenda for further research there able to "crack" the problem. It also advances a general holistic meta-model for Machine Theory of Mind, and examines the state of the art when it comes to empirically benchmarking such models.

Random-Set Graph Neural Networks

Uncertainty quantification has become an important factor in understanding the data representations produced by Graph Neural Networks (GNNs). Despite their predictive capabilities being ever useful across industrial workspaces, the inherent uncertainty induced by the nature of the data is a huge mitigating factor to GNN performance. While aleatoric uncertainty is the result of noisy and incomplete stochastic data such as missing edges or over-smoothing, epistemic uncertainty arises from lack of knowledge about a system or model (e.g., a graph's topology or node feature representation), which can be reduced by gathering more data and information. In this paper, we propose an original new framework in which node-level epistemic uncertainty is modelled in a belief function (finite random set) formalism. The resulting Random-Set Graph Neural Networks have a belief-function head predicting a random set over the list of classes, from which both a precise probability prediction and a measure of epistemic uncertainty can be obtained. Extensive experiments on 9 different graph learning datasets, including real-world autonomous driving benchmarks as such Nuscene and ROAD, demonstrate RS-GNN's superior uncertainty quantification capabilities

Direct Interval Propagation Methods using Neural-Network Surrogates for Uncertainty Quantification in Physical Systems Surrogate Model

In engineering, uncertainty propagation aims to characterise system outputs under uncertain inputs. For interval uncertainty, the goal is to determine output bounds given interval-valued inputs, which is critical for robust design optimisation and reliability analysis. However, standard interval propagation relies on solving optimisation problems that become computationally expensive for complex systems. Surrogate models alleviate this cost but typically replace only the evaluator within the optimisation loop, still requiring many inference calls. To overcome this limitation, we reformulate interval propagation as an interval-valued regression problem that directly predicts output bounds. We present a comprehensive study of neural network-based surrogate models, including multilayer perceptrons (MLPs) and deep operator networks (DeepONet), for this task. Three approaches are investigated: (i) naive interval propagation through standard architectures, (ii) bound propagation methods such as Interval Bound Propagation (IBP) and CROWN, and (iii) interval neural networks (INNs) with interval weights. Results show that these methods significantly improve computational efficiency over traditional optimisation-based approaches while maintaining accurate interval estimates. We further discuss practical limitations and open challenges in applying interval-based propagation methods.

Epistemic Generative Adversarial Networks

Generative models, particularly Generative Adversarial Networks (GANs), often suffer from a lack of output diversity, frequently generating similar samples rather than a wide range of variations. This paper introduces a novel generalization of the GAN loss function based on Dempster-Shafer theory of evidence, applied to both the generator and discriminator. Additionally, we propose an architectural enhancement to the generator that enables it to predict a mass function for each image pixel. This modification allows the model to quantify uncertainty in its outputs and leverage this uncertainty to produce more diverse and representative generations. Experimental evidence shows that our approach not only improves generation variability but also provides a principled framework for modeling and interpreting uncertainty in generative processes.

Set-based v.s. Distribution-based Representations of Epistemic Uncertainty: A Comparative Study

Epistemic uncertainty in neural networks is commonly modeled using two second-order paradigms: distribution-based representations, which rely on posterior parameter distributions, and set-based representations based on credal sets (convex sets of probability distributions). These frameworks are often regarded as fundamentally non-comparable due to differing semantics, assumptions, and evaluation practices, leaving their relative merits unclear. Empirical comparisons are further confounded by variations in the underlying predictive models. To clarify this issue, we present a controlled comparative study enabling principled, like-for-like evaluation of the two paradigms. Both representations are constructed from the same finite collection of predictive distributions generated by a shared neural network, isolating representational effects from predictive accuracy. Our study evaluates each representation through the lens of 3 uncertainty measures across 8 benchmarks, including selective prediction and out-of-distribution detection, spanning 6 underlying predictive models and 10 independent runs per configuration. Our results show that meaningful comparison between these seemingly non-comparable frameworks is both feasible and informative, providing insights into how second-order representation choices impact practical uncertainty-aware performance.

Learning Credal Ensembles via Distributionally Robust Optimization

Credal predictors are models that are aware of epistemic uncertainty and produce a convex set of probabilistic predictions. They offer a principled way to quantify predictive epistemic uncertainty (EU) and have been shown to improve model robustness in various settings. However, most state-of-the-art methods mainly define EU as disagreement caused by random training initializations, which mostly reflects sensitivity to optimization randomness rather than uncertainty from deeper sources. To address this, we define EU as disagreement among models trained with varying relaxations of the i.i.d. assumption between training and test data. Based on this idea, we propose CreDRO, which learns an ensemble of plausible models through distributionally robust optimization. As a result, CreDRO captures EU not only from training randomness but also from meaningful disagreement due to potential distribution shifts between training and test data. Empirical results show that CreDRO consistently outperforms existing credal methods on tasks such as out-of-distribution detection across multiple benchmarks and selective classification in medical applications.

Credal Ensemble Distillation for Uncertainty Quantification

Deep ensembles (DE) have emerged as a powerful approach for quantifying predictive uncertainty and distinguishing its aleatoric and epistemic components, thereby enhancing model robustness and reliability. However, their high computational and memory costs during inference pose significant challenges for wide practical deployment. To overcome this issue, we propose credal ensemble distillation (CED), a novel framework that compresses a DE into a single model, CREDIT, for classification tasks. Instead of a single softmax probability distribution, CREDIT predicts class-wise probability intervals that define a credal set, a convex set of probability distributions, for uncertainty quantification. Empirical results on out-of-distribution detection benchmarks demonstrate that CED achieves superior or comparable uncertainty estimation compared to several existing baselines, while substantially reducing inference overhead compared to DE.

Uncertainty-Aware Autonomous Vehicles: Predicting the Road Ahead

Autonomous Vehicle (AV) perception systems have advanced rapidly in recent years, providing vehicles with the ability to accurately interpret their environment. Perception systems remain susceptible to errors caused by overly-confident predictions in the case of rare events or out-of-sample data. This study equips an autonomous vehicle with the ability to 'know when it is uncertain', using an uncertainty-aware image classifier as part of the AV software stack. Specifically, the study exploits the ability of Random-Set Neural Networks (RS-NNs) to explicitly quantify prediction uncertainty. Unlike traditional CNNs or Bayesian methods, RS-NNs predict belief functions over sets of classes, allowing the system to identify and signal uncertainty clearly in novel or ambiguous scenarios. The system is tested in a real-world autonomous racing vehicle software stack, with the RS-NN classifying the layout of the road ahead and providing the associated uncertainty of the prediction. Performance of the RS-NN under a range of road conditions is compared against traditional CNN and Bayesian neural networks, with the RS-NN achieving significantly higher accuracy and superior uncertainty calibration. This integration of RS-NNs into Robot Operating System (ROS)-based vehicle control pipeline demonstrates that predictive uncertainty can dynamically modulate vehicle speed, maintaining high-speed performance under confident predictions while proactively improving safety through speed reductions in uncertain scenarios. These results demonstrate the potential of uncertainty-aware neural networks - in particular RS-NNs - as a practical solution for safer and more robust autonomous driving.

Position: Epistemic Artificial Intelligence is Essential for Machine Learning Models to Know When They Do Not Know

Despite the impressive achievements of AI, including advancements in generative models and large language models, there remains a significant gap in the ability of AI to handle uncertainty and generalize beyond the training data. We argue that AI models, especially in autonomous systems, fail to make robust predictions when faced with unfamiliar or adversarial data, as evidenced by incidents with autonomous vehicles. Traditional machine learning approaches struggle to address these issues due to an overemphasis on data fitting and domain adaptation. This position paper posits a paradigm shift towards epistemic artificial intelligence, emphasizing the need for models to learn not only from what they know but also from their ignorance. This approach, which focuses on recognizing and managing uncertainty, offers a potential solution to improve the resilience and robustness of AI systems, ensuring that they can better handle unpredictable real-world environments.

Epistemic Wrapping for Uncertainty Quantification

Uncertainty estimation is pivotal in machine learning, especially for classification tasks, as it improves the robustness and reliability of models. We introduce a novel `Epistemic Wrapping' methodology aimed at improving uncertainty estimation in classification. Our approach uses Bayesian Neural Networks (BNNs) as a baseline and transforms their outputs into belief function posteriors, effectively capturing epistemic uncertainty and offering an efficient and general methodology for uncertainty quantification. Comprehensive experiments employing a Bayesian Neural Network (BNN) baseline and an Interval Neural Network for inference on the MNIST, Fashion-MNIST, CIFAR-10 and CIFAR-100 datasets demonstrate that our Epistemic Wrapper significantly enhances generalisation and uncertainty quantification.