We introduce a novel geometric framework for optimal experimental design (OED). Traditional OED approaches, such as those based on mutual information, rely explicitly on probability densities, leading to restrictive invariance properties. To address these limitations, we propose the mutual transport dependence (MTD), a measure of statistical dependence grounded in optimal transport theory which provides a geometric objective for optimizing designs. Unlike conventional approaches, the MTD can be tailored to specific downstream estimation problems by choosing appropriate geometries on the underlying spaces. We demonstrate that our framework produces high-quality designs while offering a flexible alternative to standard information-theoretic techniques.

Autonomous drone racing (ADR) systems have recently achieved champion-level performance, yet remain highly specific to drone racing. While end-to-end vision-based methods promise broader applicability, no system to date simultaneously achieves full sim-to-real transfer, onboard execution, and champion-level performance. In this work, we present SkyDreamer, to the best of our knowledge, the first end-to-end vision-based ADR policy that maps directly from pixel-level representations to motor commands. SkyDreamer builds on informed Dreamer, a model-based reinforcement learning approach where the world model decodes to privileged information only available during training. By extending this concept to end-to-end vision-based ADR, the world model effectively functions as an implicit state and parameter estimator, greatly improving interpretability. SkyDreamer runs fully onboard without external aid, resolves visual ambiguities by tracking progress using the state decoded from the world model's hidden state, and requires no extrinsic camera calibration, enabling rapid deployment across different drones without retraining. Real-world experiments show that SkyDreamer achieves robust, high-speed flight, executing tight maneuvers such as an inverted loop, a split-S and a ladder, reaching speeds of up to 21 m/s and accelerations of up to 6 g. It further demonstrates a non-trivial visual sim-to-real transfer by operating on poor-quality segmentation masks, and exhibits robustness to battery depletion by accurately estimating the maximum attainable motor RPM and adjusting its flight path in real-time. These results highlight SkyDreamer's adaptability to important aspects of the reality gap, bringing robustness while still achieving extremely high-speed, agile flight.

In blockchain networks, the strategic ordering of transactions within blocks has emerged as a significant source of profit extraction, known as Maximal Extractable Value (MEV). The transition from spam-based Priority Gas Auctions to structured auction mechanisms like Polygon Atlas has transformed MEV extraction from public bidding wars into sealed-bid competitions under extreme time constraints. While this shift reduces network congestion, it introduces complex strategic challenges where searchers must make optimal bidding decisions within a sub-second window without knowledge of competitor behavior or presence. Traditional game-theoretic approaches struggle in this high-frequency, partially observable environment due to their reliance on complete information and static equilibrium assumptions. We present a reinforcement learning framework for MEV extraction on Polygon Atlas and make three contributions: (1) A novel simulation environment that accurately models the stochastic arrival of arbitrage opportunities and probabilistic competition in Atlas auctions; (2) A PPO-based bidding agent optimized for real-time constraints, capable of adaptive strategy formulation in continuous action spaces while maintaining production-ready inference speeds; (3) Empirical validation demonstrating our history-conditioned agent captures 49\% of available profits when deployed alongside existing searchers and 81\% when replacing the market leader, significantly outperforming static bidding strategies. Our work establishes that reinforcement learning provides a critical advantage in high-frequency MEV environments where traditional optimization methods fail, offering immediate value for industrial participants and protocol designers alike.

Neuro-symbolic (NeSy) AI aims to develop deep neural networks whose predictions comply with prior knowledge encoding, e.g. safety or structural constraints. As such, it represents one of the most promising avenues for reliable and trustworthy AI. The core idea behind NeSy AI is to combine neural and symbolic steps: neural networks are typically responsible for mapping low-level inputs into high-level symbolic concepts, while symbolic reasoning infers predictions compatible with the extracted concepts and the prior knowledge. Despite their promise, it was recently shown that - whenever the concepts are not supervised directly - NeSy models can be affected by Reasoning Shortcuts (RSs). That is, they can achieve high label accuracy by grounding the concepts incorrectly. RSs can compromise the interpretability of the model's explanations, performance in out-of-distribution scenarios, and therefore reliability. At the same time, RSs are difficult to detect and prevent unless concept supervision is available, which is typically not the case. However, the literature on RSs is scattered, making it difficult for researchers and practitioners to understand and tackle this challenging problem. This overview addresses this issue by providing a gentle introduction to RSs, discussing their causes and consequences in intuitive terms. It also reviews and elucidates existing theoretical characterizations of this phenomenon. Finally, it details methods for dealing with RSs, including mitigation and awareness strategies, and maps their benefits and limitations. By reformulating advanced material in a digestible form, this overview aims to provide a unifying perspective on RSs to lower the bar to entry for tackling them. Ultimately, we hope this overview contributes to the development of reliable NeSy and trustworthy AI models.

Causal discovery algorithms often perform poorly with limited samples. While integrating expert knowledge (including from LLMs) as constraints promises to improve performance, guarantees for existing methods require perfect predictions or uncertainty estimates, making them unreliable for practical use. We propose the Guess2Graph (G2G) framework, which uses expert guesses to guide the sequence of statistical tests rather than replacing them. This maintains statistical consistency while enabling performance improvements. We develop two instantiations of G2G: PC-Guess, which augments the PC algorithm, and gPC-Guess, a learning-augmented variant designed to better leverage high-quality expert input. Theoretically, both preserve correctness regardless of expert error, with gPC-Guess provably outperforming its non-augmented counterpart in finite samples when experts are "better than random."

Iterative retrieval-augmented generation (RAG) enables large language models to answer complex multi-hop questions, but each additional loop increases latency, costs, and the risk of introducing distracting evidence, motivating the need for an efficient stopping strategy. Existing methods either use a predetermined number of iterations or rely on confidence proxies that poorly reflect whether more retrieval will actually help. We cast iterative RAG as a finite-horizon Markov decision process and introduce Stop-RAG, a value-based controller that adaptively decides when to stop retrieving. Trained with full-width forward-view Q($λ$) targets from complete trajectories, Stop-RAG learns effective stopping policies while remaining compatible with black-box APIs and existing pipelines. On multi-hop question-answering benchmarks, Stop-RAG consistently outperforms both fixed-iteration baselines and prompting-based stopping with LLMs. These results highlight adaptive stopping as a key missing component in current agentic systems, and demonstrate that value-based control can improve the accuracy of RAG systems.

Diffusion models enable the synthesis of highly accurate samples from complex distributions and have become foundational in generative modeling. Recently, they have demonstrated significant potential for solving Bayesian inverse problems by serving as priors. This review offers a comprehensive overview of current methods that leverage \emph{pre-trained} diffusion models alongside Monte Carlo methods to address Bayesian inverse problems without requiring additional training. We show that these methods primarily employ a \emph{twisting} mechanism for the intermediate distributions within the diffusion process, guiding the simulations toward the posterior distribution. We describe how various Monte Carlo methods are then used to aid in sampling from these twisted distributions.

We introduce an action-centric graph representation framework for learning to guide planning in Partially Observable Markov Decision Processes (POMDPs). Unlike existing approaches that require domain-specific neural architectures and struggle with scalability, GammaZero leverages a unified graph-based belief representation that enables generalization across problem sizes within a domain. Our key insight is that belief states can be systematically transformed into action-centric graphs where structural patterns learned on small problems transfer to larger instances. We employ a graph neural network with a decoder architecture to learn value functions and policies from expert demonstrations on computationally tractable problems, then apply these learned heuristics to guide Monte Carlo tree search on larger problems. Experimental results on standard POMDP benchmarks demonstrate that GammaZero achieves comparable performance to BetaZero when trained and tested on the same-sized problems, while uniquely enabling zero-shot generalization to problems 2-4 times larger than those seen during training, maintaining solution quality with reduced search requirements. Partially observable Markov decision processes (POMDPs) provide a principled framework for sequential decision-making under uncertainty, where agents must act based on incomplete information about the true state of the environment Kaelbling et al. (1998). This partial observability arises naturally in many real-world applications, from autonomous driving where sensors provide limited field-of-view Hoel et al. (2019), to robotic manipulation where object properties must be inferred through interaction Lauri et al. (2022), to subsurface exploration where underground structures can only be observed at sparse drilling locations Mern & Caers (2023).

The Rashomon set of decision trees (DTs) finds importance uses. Recent work showed that DTs computing the same classification function, i.e. predictive equivalent DTs, can represent a significant fraction of the Rashomon set. Such redundancy is undesirable. For example, feature importance based on the Rashomon set becomes inaccurate due the existence of predictive equivalent DTs, i.e. DTs with the same prediction for every possible input. In recent work, McTavish et al. proposed solutions for several computational problems related with DTs, including that of deciding predictive equivalent DTs. The approach of McTavish et al. consists of applying the well-known method of Quine-McCluskey (QM) for obtaining minimum-size DNF (disjunctive normal form) representations of DTs, which are then used for comparing DTs for predictive equivalence. Furthermore, the minimum-size DNF representation was also applied to computing explanations for the predictions made by DTs, and to finding predictions in the presence of missing data. However, the problem of formula minimization is hard for the second level of the polynomial hierarchy, and the QM method may exhibit worst-case exponential running time and space. This paper first demonstrates that there exist decision trees that trigger the worst-case exponential running time and space of the QM method. Second, the paper shows that the QM method may incorrectly decide predictive equivalence, if two key constraints are not respected, and one may be difficult to formally guarantee. Third, the paper shows that any of the problems to which the smallest DNF representation has been applied to can be solved in polynomial time, in the size of the DT. The experiments confirm that, for DTs for which the worst-case of the QM method is triggered, the algorithms proposed in this paper are orders of magnitude faster than the ones proposed by McTavish et al.

Causal discovery methods can identify valid adjustment sets for causal effect estimation for a pair of target variables, even when the underlying causal graph is unknown. Global causal discovery methods focus on learning the whole causal graph and therefore enable the recovery of optimal adjustment sets, i.e., sets with the lowest asymptotic variance, but they quickly become computationally prohibitive as the number of variables grows. Local causal discovery methods offer a more scalable alternative by focusing on the local neighborhood of the target variables, but are restricted to statistically suboptimal adjustment sets. In this work, we propose Local Optimal Adjustments Discovery (LOAD), a sound and complete causal discovery approach that combines the computational efficiency of local methods with the statistical optimality of global methods. First, LOAD identifies the causal relation between the targets and tests if the causal effect is identifiable by using only local information. If it is identifiable, it then finds the optimal adjustment set by leveraging local causal discovery to infer the mediators and their parents. Otherwise, it returns the locally valid parent adjustment sets based on the learned local structure. In our experiments on synthetic and realistic data LOAD outperforms global methods in scalability, while providing more accurate effect estimation than local methods.