Parametric Markov chains (pMC) are used to model probabilistic systems with unknown or partially known probabilities. Although (universal) pMC verification for reachability properties is known to be coETR-complete, there have been efforts to approach it using potentially easier-to-check properties such as asking whether the pMC is monotonic in certain parameters. In this paper, we first reduce monotonicity to asking whether the reachability probability from a given state is never less than that of another given state. Recent results for the latter property imply an efficient algorithm to collapse same-value equivalence classes, which in turn preserves verification results and monotonicity. We implement our algorithm to collapse "trivial" equivalence classes in the pMC and show empirical evidence for the following: First, the collapse gives reductions in size for some existing benchmarks and significant reductions on some custom benchmarks; Second, the collapse speeds up existing algorithms to check monotonicity and parameter lifting, and hence can be used as a fast pre-processing step in practice.

--This work presents a novel method for leveraging intercepted Radio Frequency (RF) signals to inform a constrained Reinforcement Learning (RL) policy for robust control of a satellite operating in contested environments. Uncooperative satellite engagements with nation-state actors prompts the need for enhanced maneuverability and agility on-orbit. However, robust, autonomous and rapid adversary avoidance capabilities for the space environment is seldom studied. Further, the capability constrained nature of many space vehicles does not afford robust space situational awareness capabilities that can be used for well informed maneuvering. We present a "Cat & Mouse" system for training optimal adversary avoidance algorithms using RL. We propose the novel approach of utilizing intercepted radio frequency communication and dynamic spacecraft state as multi-modal input that could inform paths for a mouse to outmaneuver the cat satellite. Given the current ubiquitous use of RF communications, our proposed system can be applicable to a diverse array of satellites. In addition to providing a comprehensive framework for training and implementing a constrained RL policy capable of providing control for robust adversary avoidance, we also explore several optimization based methods for adversarial avoidance. These methods were then tested on real-world data obtained from the Space Surveillance Network (SSN) to analyze the benefits and limitations of different avoidance methods. In March of 2025, Chinese satellites exhibited dog-fighting capabilities [1], following years of both Russian [2] and Chinese [3] satellites approaching dangerously close to US satellites in geosynchronous orbit. Such uncooperative activity prompts the need for satellite agility and maneuverability which can be facilitated through edge-based autonomy. To achieve this, appropriate sensing would be required to properly characterize the contested environment. Not all satellites have precise space domain awareness (SDA) sensing suites onboard, despite having powerful buses and flight controllers that can facilitate autonomous operations. We propose leveraging an uncooperative space vehicle's communication systems as a means to evaluate safe flight control policies to carefully navigate contested domains in situations where support from the ground is not feasible.

This paper addresses the challenge of navigation in large, visually complex environments with sparse rewards. We propose a method that uses object-oriented macro actions grounded in a topological map, allowing a simple Deep Q-Network (DQN) to learn effective navigation policies. The agent builds a map by detecting objects from RGBD input and selecting discrete macro actions that correspond to navigating to these objects. This abstraction drastically reduces the complexity of the underlying reinforcement learning problem and enables generalization to unseen environments. We evaluate our approach in a photorealistic 3D simulation and show that it significantly outperforms a random baseline under both immediate and terminal reward conditions. Our results demonstrate that topological structure and macro-level abstraction can enable sample-efficient learning even from pixel data.

Identification of defects or anomalies in 3D objects is a crucial task to ensure correct functionality. In this work, we combine Bayesian learning with recent developments in quantum and quantum-inspired machine learning, specifically orthogonal neural networks, to tackle this anomaly detection problem for an industrially relevant use case. Bayesian learning enables uncertainty quantification of predictions, while orthogonality in weight matrices enables smooth training. We develop orthogonal (quantum) versions of 3D convolutional neural networks and show that these models can successfully detect anomalies in 3D objects. To test the feasibility of incorporating quantum computers into a quantum-enhanced anomaly detection pipeline, we perform hardware experiments with our models on IBM's 127-qubit Brisbane device, testing the effect of noise and limited measurement shots.

Large Language Models (LLMs) are known to produce very high-quality tests and responses to our queries. But how much can we trust this generated text? In this paper, we study the problem of uncertainty quantification in LLMs. We propose a novel Random-Set Large Language Model (RSLLM) approach which predicts finite random sets (belief functions) over the token space, rather than probability vectors as in classical LLMs. In order to allow so efficiently, we also present a methodology based on hierarchical clustering to extract and use a budget of "focal" subsets of tokens upon which the belief prediction is defined, rather than using all possible collections of tokens, making the method scalable yet effective. RS-LLMs encode the epistemic uncertainty induced in their generation process by the size and diversity of its training set via the size of the credal sets associated with the predicted belief functions. The proposed approach is evaluated on CoQA and OBQA datasets using Llama2-7b, Mistral-7b and Phi-2 models and is shown to outperform the standard model in both datasets in terms of correctness of answer while also showing potential in estimating the second level uncertainty in its predictions and providing the capability to detect when its hallucinating.

We develop a geometric account of sequence modelling that links patterns in the data to measurable properties of the loss landscape in transformer networks. First, we cast conditional sequence distributions into a Hilbert-space framework and apply tensor decompositions to identify their principal modes. Truncating the small-amplitude modes yields an effective data distribution that preserves dominant structure while discarding statistical detail. Second, we show theoretically that Local Learning Coefficient (LLC) estimates are insensitive to modes below a data-dependent threshold. Consequently, the LLC calculated in practice characterises the geometry of the effective rather than the true distribution. This insight clarifies why reliable LLC estimates can be obtained even when a network parameter is not a strict minimiser of the population loss, and it highlights how the inverse temperature in SGLD acts as a resolution dial on the landscape structure.

Do We Need Transformers to Play FPS Video Games? Abstract --In this paper, we explore the Transformer based architectures for reinforcement learning in both online and offline settings within the Doom game environment. Our investigation focuses on two primary approaches: Deep Transformer Q-learning Networks (DTQN) for online learning [1] and Decision Transformers (DT) for offline reinforcement learning [2]. DTQN leverages the sequential modelling capabilities of Transformers to enhance Q-learning in partially observable environments,while Decision Transformers repurpose sequence modelling techniques to enable offline agents to learn from past trajectories without direct interaction with the environment. We conclude that while Transformers might have performed well in Atari games, more traditional methods perform better than Transformer based method in both the settings in the VizDoom environment [3] Q-networks traditionally have been used in various Atari game environments [4] and in partially observable environments like in the Doom 1993 game [5].

Kernel mean embeddings -- integrals of a kernel with respect to a probability distribution -- are essential in Bayesian quadrature, but also widely used in other computational tools for numerical integration or for statistical inference based on the maximum mean discrepancy. These methods often require, or are enhanced by, the availability of a closed-form expression for the kernel mean embedding. However, deriving such expressions can be challenging, limiting the applicability of kernel-based techniques when practitioners do not have access to a closed-form embedding. This paper addresses this limitation by providing a comprehensive dictionary of known kernel mean embeddings, along with practical tools for deriving new embeddings from known ones. We also provide a Python library that includes minimal implementations of the embeddings.

Integrating various data modalities brings valuable insights into underlying phenomena. Multimodal factor analysis (FA) uncovers shared axes of variation underlying different simple data modalities, where each sample is represented by a vector of features. However, FA is not suited for structured data modalities, such as text or single cell sequencing data, where multiple data points are measured per each sample and exhibit a clustering structure. To overcome this challenge, we introduce FACTM, a novel, multi-view and multi-structure Bayesian model that combines FA with correlated topic modeling and is optimized using variational inference. Additionally, we introduce a method for rotating latent factors to enhance interpretability with respect to binary features. On text and video benchmarks as well as real-world music and COVID-19 datasets, we demonstrate that FACTM outperforms other methods in identifying clusters in structured data, and integrating them with simple modalities via the inference of shared, interpretable factors.

We study regret minimization under privacy constraints in episodic inhomogeneous linear Markov Decision Processes (MDPs), motivated by the growing use of reinforcement learning (RL) in personalized decision-making systems that rely on sensitive user data. In this setting, both transition probabilities and reward functions are assumed to be linear in a feature mapping $\phi(s, a)$, and we aim to ensure privacy through joint differential privacy (JDP), a relaxation of differential privacy suited to online learning. Prior work has established suboptimal regret bounds by privatizing the LSVI-UCB algorithm, which achieves $\widetilde{O}(\sqrt{d^3 H^4 K})$ regret in the non-private setting. Building on recent advances that improve this to near minimax optimal regret $\widetilde{O}(d\sqrt{H^{3}K})$ via LSVI-UCB++ with Bernstein-style bonuses, we design a new differentially private algorithm by privatizing LSVI-UCB++ and adapting techniques for variance-aware analysis from offline RL. Our algorithm achieves a regret bound of $\widetilde{O}(d \sqrt{H^3 K} + H^{15/4} d^{7/6} K^{1/2} / \epsilon)$, improving over previous private methods. Empirical results show that our algorithm retains near-optimal utility compared to non-private baselines, indicating that privacy can be achieved with minimal performance degradation in this setting.