Intercepting fast moving objects, by its very nature, is challenging because of its tight time constraints. This problem becomes further complicated in the presence of sensor noise because noisy sensors provide, at best, incomplete information, which results in a distribution over target states to be intercepted. Since time is of the essence, to hit the target, the planner must begin directing the interceptor, in this case a robot arm, while still receiving information. We introduce an tree-like structure, which is grown using kinodynamic motion primitives in state-time space. This tree-like structure encodes reachability to multiple goals from a single origin, while enabling real-time value updates as the target belief evolves and seamless transitions between goals. We evaluate our framework on an interception task on a 6 DOF industrial arm (ABB IRB-1600) with an onboard stereo camera (ZED 2i). A robust Innovation-based Adaptive Estimation Adaptive Kalman Filter (RIAE-AKF) is used to track the target and perform belief updates.

The principle of minimal change in belief revision theory requires that, when accepting new information, one keeps one's belief state as close to the initial belief state as possible. This is precisely what the method known as minimal revision does. However, unlike less conservative belief revision methods, minimal revision falls short in learning power: It cannot learn everything that can be learned by other learning methods. We begin by showing that, despite this limitation, minimal revision is still a successful learning method in a wide range of situations. Firstly, it can learn any problem that is finitely identifiable. Secondly, it can learn with positive and negative data, as long as one considers finitely many possibilities. We then characterize the prior plausibility assignments (over finitely many possibilities) that enable one to learn via minimal revision, and do the same for conditioning and lexicographic upgrade. Finally, we show that not all of our results still hold when learning from possibly erroneous information.

The idea of using belief bases as formal semantics for multi-agent epistemic logic was first introduced in [26] and further developed in [27, 28]. This approach aligns with the sentential (or syntactic) perspective on knowledge representation [21, 13, 33, 20], which holds th at an agent's body of knowledge should be represented as a set of sentences in a formal language. The key novelty of belief base semantics, compared to traditional epistemic logic semantics based on multi-relational Kripke models [31, 12], lies in two main aspects. First, a possible world (or state) in a mo del is not treated as a primitive entity but is instead composed of the agents' belief bases and a valu ation of propositional atoms. Second, the agents' accessibility relations are not explicitly par t of the model but are determined a posteriori from their belief bases.

State resetting is a fundamental but often overlooked capability of simulators. It supports sample-based planning by allowing resets to previously encountered simulation states, and enables calibration of simulators using real data by resetting to states observed in real-system traces. While often taken for granted, state resetting in complex simulators can be nontrivial: when the simulator comes with latent variables (states), state resetting requires sampling from the posterior over the latent state given the observable history, a.k.a. the belief state (Silver and Veness, 2010). While exact sampling is often infeasible, many approximate belief-state samplers can be constructed, raising the question of how to select among them using only sampling access to the simulator. In this paper, we show that this problem reduces to a general conditional distribution-selection task and develop a new algorithm and analysis under sampling-only access. Building on this reduction, the belief-state selection problem admits two different formulations: latent state-based selection, which directly targets the conditional distribution of the latent state, and observation-based selection, which targets the induced distribution over the observation. Interestingly, these formulations differ in how their guarantees interact with the downstream roll-out methods: perhaps surprisingly, observation-based selection may fail under the most natural roll-out method (which we call Single-Reset) but enjoys guarantees under the less conventional alternative (which we call Repeated-Reset). Together with discussion on issues such as distribution shift and the choice of sampling policies, our paper reveals a rich landscape of algorithmic choices, theoretical nuances, and open questions, in this seemingly simple problem.

The core premise of AI debate as a scalable oversight technique is that it is harder to lie convincingly than to refute a lie, enabling the judge to identify the correct position. Yet, existing debate experiments have relied on datasets with ground truth, where lying is reduced to defending an incorrect proposition. This overlooks a subjective dimension: lying also requires the belief that the claim defended is false. In this work, we apply debate to subjective questions and explicitly measure large language models' prior beliefs before experiments. Debaters were asked to select their preferred position, then presented with a judge persona deliberately designed to conflict with their identified priors. This setup tested whether models would adopt sycophantic strategies, aligning with the judge's presumed perspective to maximize persuasiveness, or remain faithful to their prior beliefs. We implemented and compared two debate protocols, sequential and simultaneous, to evaluate potential systematic biases. Finally, we assessed whether models were more persuasive and produced higher-quality arguments when defending positions consistent with their prior beliefs versus when arguing against them. Our main findings show that models tend to prefer defending stances aligned with the judge persona rather than their prior beliefs, sequential debate introduces significant bias favoring the second debater, models are more persuasive when defending positions aligned with their prior beliefs, and paradoxically, arguments misaligned with prior beliefs are rated as higher quality in pairwise comparison. These results can inform human judges to provide higher-quality training signals and contribute to more aligned AI systems, while revealing important aspects of human-AI interaction regarding persuasion dynamics in language models.

Despite the explosive growth of AI and the technologies built upon it, predicting and inferring the sub-optimal behavior of users or human collaborators remains a critical challenge. In many cases, such behaviors are not a result of irrationality, but rather a rational decision made given inherent cognitive bounds and biased beliefs about the world. In this paper, we formally introduce a class of computational-rational (CR) user models for cognitively-bounded agents acting optimally under biased beliefs. The key novelty lies in explicitly modeling how a bounded memory process leads to a dynamically inconsistent and biased belief state and, consequently, sub-optimal sequential decision-making. We address the challenge of identifying the latent user-specific bound and inferring biased belief states from passive observations on the fly. We argue that for our formalized CR model family with an explicit and parameterized cognitive process, this challenge is tractable. To support our claim, we propose an efficient online inference method based on nested particle filtering that simultaneously tracks the user's latent belief state and estimates the unknown cognitive bound from a stream of observed actions. We validate our approach in a representative navigation task using memory decay as an example of a cognitive bound. With simulations, we show that (1) our CR model generates intuitively plausible behaviors corresponding to different levels of memory capacity, and (2) our inference method accurately and efficiently recovers the ground-truth cognitive bounds from limited observations ($\le 100$ steps). We further demonstrate how this approach provides a principled foundation for developing adaptive AI assistants, enabling adaptive assistance that accounts for the user's memory limitations.

Boolean equivalence allows Boolean networks with identical functionality to exhibit diverse graph structures. This gives more room for exploration in logic optimization, while also posing a challenge for tasks involving consistency between Boolean networks. To tackle this challenge, we introduce BoolSkeleton, a novel Boolean network skeletonization method that improves the consistency and reliability of design-specific evaluations. BoolSkeleton comprises two key steps: preprocessing and reduction. In preprocessing, the Boolean network is transformed into a defined Boolean dependency graph, where nodes are assigned the functionality-related status. Next, the homogeneous and heterogeneous patterns are defined for the node-level pattern reduction step. Heterogeneous patterns are preserved to maintain critical functionality-related dependencies, while homogeneous patterns can be reduced. Parameter K of the pattern further constrains the fanin size of these patterns, enabling fine-tuned control over the granularity of graph reduction. To validate BoolSkeleton's effectiveness, we conducted four analysis/downstream tasks around the Boolean network: compression analysis, classification, critical path analysis, and timing prediction, demonstrating its robustness across diverse scenarios. Furthermore, it improves above 55% in the average accuracy compared to the original Boolean network for the timing prediction task. These experiments underscore the potential of BoolSkeleton to enhance design consistency in logic synthesis.

As AI grows more powerful, it will increasingly shape how we understand the world. But with this influence comes the risk of amplifying misinformation and deepening social divides-especially on consequential topics where factual accuracy directly impacts well-being. Scalable Oversight aims to ensure AI systems remain truthful even when their capabilities exceed those of their evaluators. Yet when humans serve as evaluators, their own beliefs and biases can impair judgment. We study whether AI debate can guide biased judges toward the truth by having two AI systems debate opposing sides of controversial factuality claims on COVID-19 and climate change where people hold strong prior beliefs. We conduct two studies. Study I recruits human judges with either mainstream or skeptical beliefs who evaluate claims through two protocols: debate (interaction with two AI advisors arguing opposing sides) or consultancy (interaction with a single AI advisor). Study II uses AI judges with and without human-like personas to evaluate the same protocols. In Study I, debate consistently improves human judgment accuracy and confidence calibration, outperforming consultancy by 4-10% across COVID-19 and climate change claims. The improvement is most significant for judges with mainstream beliefs (up to +15.2% accuracy on COVID-19 claims), though debate also helps skeptical judges who initially misjudge claims move toward accurate views (+4.7% accuracy). In Study II, AI judges with human-like personas achieve even higher accuracy (78.5%) than human judges (70.1%) and default AI judges without personas (69.8%), suggesting their potential for supervising frontier AI models. These findings highlight AI debate as a promising path toward scalable, bias-resilient oversight in contested domains.

Thanks to the remarkable human-like capabilities of machine learning (ML) models in perceptual and cognitive tasks, frameworks integrating ML within rational agent architectures are gaining traction. Yet, the landscape remains fragmented and incoherent, often focusing on embedding ML into generic agent containers while overlooking the expressive power of rational architectures--such as Belief-Desire-Intention (BDI) agents. This paper presents a fine-grained systematisation of existing approaches, using the BDI paradigm as a reference. Our analysis illustrates the fast-evolving literature on rational agents enhanced by ML, and identifies key research opportunities and open challenges for designing effective rational ML agents.

Proof autoformalization, the task of translating natural language theorems and proofs into machine-verifiable code, is a critical step for integrating large language models into rigorous mathematical workflows. Current approaches focus on producing executable code, but they frequently fail to preserve the semantic meaning and logical structure of the original human-written argument. To address this, we introduce ProofFlow, a novel pipeline that treats structural fidelity as a primary objective. ProofFlow first constructs a directed acyclic graph (DAG) to map the logical dependencies between proof steps. Then, it employs a novel lemma-based approach to systematically formalize each step as an intermediate lemma, preserving the logical structure of the original argument. To facilitate evaluation, we present a new benchmark of 184 undergraduate-level problems, manually annotated with step-by-step solutions and logical dependency graphs, and introduce ProofScore, a new composite metric to evaluate syntactic correctness, semantic faithfulness, and structural fidelity. Experimental results show our pipeline sets a new state-of-the-art for autoformalization, achieving a ProofScore of 0.545, substantially exceeding baselines like full-proof formalization (0.123), which processes the entire proof at once, and step-proof formalization (0.072), which handles each step independently. Our pipeline, benchmark, and score metric are open-sourced to encourage further progress at https://github.com/Huawei-AI4Math/ProofFlow.