Papers

Existing latent world models are typically optimized for future predictability, yet the resulting representations are not necessarily useful for planning in autonomous driving. Predictions are commonly used for pretraining or auxiliary supervision rather than as direct conditioning signals for trajectory generation. We propose ForeDrive, which learns a planning-relevant latent representation and couples it asymmetrically to a Diffusion Transformer (DiT) planner. The planner consumes multi-horizon latent future representations learned with a JEPA-style world model; planning gradients update the shared online encoder, while stop-gradient routing trains the latent predictor with forecasting losses only. Because predicted futures have varying reliability across horizons and BEV trajectories are misaligned with image tokens, we use gated visual fusion, future-status injection, and Trajectory-Adaptive Bias (TAB) to inject future latents as guidance without overriding the current observation. Trained with pure imitation learning and using only the current front-view image as visual input at inference, ForeDrive attains 89.9 PDMS on NAVSIM v1 and 90.0 one-stage EPDMS on NAVSIM v2, without reinforcement learning or an external trajectory scorer.

Spiking Transformers inherit token interaction mechanisms from conventional Transformers, yet their sparse binary representations fundamentally alter how token-to-token communication is established. In particular, spike-based query-key matching produces highly sparse and input-dependent interaction patterns, coupling information propagation to the instantaneous availability of matching spike events. This motivates a different interaction paradigm in which long-range communication does not rely solely on pairwise spike coincidence. We therefore propose Gated Spike Axial Propagation (GSAP), a spike-native token interaction mechanism that decouples information propagation from context selection. Instead of directly determining communication through query-key matching, GSAP first propagates spike-based context along the horizontal and vertical axes, allowing information to reach distant tokens through structured sequential propagation. A receiver-conditioned gate then determines how much of the propagated context is incorporated at each token, while a lightweight local pathway preserves fine-grained neighborhood information. In this way, GSAP reformulates token interaction as a propagate-then-select process, enabling structured long-range communication while retaining the sparse event-driven nature of spiking representations. Code is available at https://github.com/Fancyssc/GSAP.

The mobility sector is undergoing a paradigm shift driven by advances in Generative Artificial Intelligence. With a global market valued at approximately 2.9 trillion dollars annually, considering only cars, the integration of these technologies has the potential to impact more than 1.5 billion vehicles worldwide. As Large Language Models (LLMs) are increasingly adopted in mobility, concerns about cybersecurity, privacy, and reliability emerge. Accordingly, this paper surveys current applications and assesses these challenges. Since the European AI Act classifies transportation AI as high risk, we derive nine technical classes from its requirements to assess current research and future deployments. Our findings show that research mainly studies GPT and Llama models (over 50% of reviewed works) and traffic applications while largely neglecting security, privacy, and reliability. This gap extends to AI Act compliance: among 35 reviewed works, only one includes a partial vulnerability assessment and one a partial risk management system. We identify a clear gap between strong optimization performance and regulatory adherence, suggesting compliance is limited less by technology than by a focus on static performance over lifecycle safety, and underscoring an urgent need for security-by-design in safety-critical intelligent transportation systems.

Learned world models are becoming essential to general-purpose agents: by predicting action consequences, they support planning and decision-making while reducing reliance on costly trial and error. This reliance creates a fundamental ambiguity: when a world-model-guided decision fails, the trajectory alone may not reveal whether the agent's decision rule or the world model caused the loss. We formalize this failure-attribution problem as a counterfactual decomposition of return loss and prove that its components are not identifiable from passive interaction, even for finite-horizon planners. This obstruction motivates Dual-Frontier, a learning principle that admits a world-model-guided decision only when its predicted advantage exceeds a certified bound on decision-relevant world-model error; otherwise, evidence is allocated to world-model verification. Action-conditioned value bounds and a closed-loop extension guarantee non-decreasing return for admitted decisions. Calibrated gates and simultaneous confidence sequences support adaptive evidence reuse, with sufficient and necessary verification bounds. Controlled learned-model experiments validate the predicted failure modes and certification behavior, while cross-backbone tool-use benchmarks instantiate the same verify-then-promote rule in realistic agent world-model pipelines, consistently improving decision quality and reliability.

Physical-condition diversity is largely missing from current benchmarks for robot manipulation. While large-scale simulation benchmarks increasingly incorporate variations in object appearance, scene layout, and visual observations, they typically keep the underlying physical parameters fixed. As a result, important sources of real-world variability, such as changes in mass, friction, and joint dynamics, remain largely untested. We introduce RoboTwin-Phys, a physics-diverse benchmark that treats physical-condition diversity as an explicit dimension of robot manipulation evaluation. The benchmark continuously varies 13 physical attributes within physically plausible ranges, providing a unified setting for evaluating policies across diverse physical operating conditions. We further release more than 5,000 expert demonstrations with ground-truth physical parameters, enabling physical-attribute estimation, condition-aware modeling, and physics-conditioned policy training. Evaluations of representative WAMs and VLAs reveal a substantial robustness gap: models that remain effective under existing visual and layout randomization can degrade markedly under changes in physical conditions. RoboTwin-Phys provides the benchmark, data, and evaluation protocol needed to systematically measure and improve robustness to physical-condition diversity in robot manipulation.

Causal tabular foundation models amortize effect estimation across synthetic mechanisms, but latent-effect supervision rewards posterior shrinkage rather than encoding the repeated-sample response needed in a fixed deployment population. We introduce fluctuation-supervised pretraining (FSP): each synthetic table is labeled by its average treatment effect plus its efficient influence-function fluctuation; deployment remains a frozen forward pass. Along the path $T_{\lambda,P}=\theta(P)+\lambda P_n\psi_P$, we prove an endpoint transition: every fixed $\lambda<1$ retains label ambiguity of order $(1-\lambda)^2/n$, whereas full fluctuation makes the Gaussian label observable and reduces optimal finite-stratum causal label-prediction risk to order $n^{-2}$. A finite-pretraining bound combines label, network, episode-sampling, and optimization errors; its sampling defect controls fixed-mechanism bias, mean squared error, variance, Gaussian approximation, and, with variance-head accuracy, studentized coverage. Complementary lower bounds separate local $n^{-1}$ ATE risk from the $\log N/M$ excess risk of generic finite-dictionary episode learning. Experiments trace the learned sampling response. Across 24 nonlinear continuous-covariate cells at trained context lengths, continuous-row FSP lowers checkpoint-mean macro RMSE by 7.0% versus S-learner and wins all 12 weak-overlap cells; validation-selected Summary FSP deploys $11.6\times$ faster per table in our warm one-thread benchmark. Under effect shift, matched Raw FSP lowers mean-checkpoint RMSE by 54.2% and teacher defect by 99.0% versus latent-effect supervision, and RMSE by 10.2% versus the released CausalPFN-S checkpoint. Known-effect semisynthesis tests coverage; two randomized-study evaluations show that lower RMSE can coexist with residual attenuation.

The manipulation of Deformable Linear Objects (DLOs) such as cables poses a significant challenge for automation due to their infinite degrees of freedom and non-linear dynamics. In this paper we present a machine learning based optimal control approach for the manipulation of DLOs. This approach is divided into two main components: modeling and control. For modeling the dynamics of the DLO, we propose a learning based approach using a bidirectional Long Short-Term Memory (biLSTM) network. The biLSTM network is trained on synthetic data generated by the MuJoCo physics engine. For manipulating the DLO, a model predictive control strategy that employs Model Predictive Path Integral (MPPI) control is selected. The proposed approach is evaluated through simulation and experiments. The results demonstrate the effectiveness of the proposed method in achieving accurate and efficient manipulation of DLOs.

Large Language Models (LLMs) have been used in various industries. However, ensuring their compliance with complex laws and regulatory frameworks remains a great challenge. Existing evaluation paradigms mainly rely on static benchmarks that suffer from three severe limitations: First, the compliance rules being used do not comply with the requirements of Artificial Intelligence (AI) laws and regulations; Second, they only handle apparent, explicit compliance risks, leaving implicit and covert compliance risks undetected; Third, they fail to track the systematic propagation of risks along logical dependency chains or evaluate compliance within nuanced, context-based real-world scenarios. To bridge this critical gap, we introduce EADC, a novel advanced evaluation benchmark of LLMs based on an AI compliance knowledge graph and AI compliance legal experts. By mapping abstract legal rules into structured logical multi-relational graphs, our framework enables automated, evolving agents to distill and synthesize highly sophisticated adversarial scenarios. This compliance benchmark is reviewed and corrected by human AI legal experts throughout the whole process. The resulting dataset (4,435+ QA pairs) provides an extensive, multi-dimensional taxonomy covering critical regulatory frontiers, including bias and discrimination, fairness, personal privacy protection, and values. Crucially, our compliance dataset moves beyond shallow string-matching by incorporating contextual long-horizon interactions and logic-driven hazard chains, capturing deeply embedded compliance anomalies that bypass traditional filters. Experiment evaluations demonstrate that our framework exposes critical regulatory blind spots in state-of-the-art LLMs, offering a rigorous, AI laws and regulations-aligned benchmark to safeguard high-level and deep compliance in the application of LLMs.

Distributed state estimation algorithms have been extended to switching networks, which model unreliable communication networks. Yet existing results apply only to specific classes of systems, such as neutrally stable systems. In this paper, we analyze a distributed observer under the assumption that the system matrix commutes with the coupling matrices. This not only enables a refined analysis that leads to a necessary and sufficient condition for stability over switching networks, but also covers a broader class of systems than existing results, including unstable systems such as vehicular platoons.

We investigate the challenges of enabling effective collaboration between human operators and heterogeneous autonomous agents in complex, dynamic environments by developing an interaction platform that allows study of operator behavior and supports intent inference and decision-making using state-of-the-art frameworks. We demonstrate the extent to which the operator's perception, decisions, and actions could be supported by autonomous systems during search-and-rescue operations with our platform.

This is an essentially derivative note, whose goal is to interpret the 'whole-cube' bound of OpenAI for binary codes in a possibly somewhat more accessible way. This is attained, in part, by connecting it to some previously known results. All of the heavy technical lifting in the interpretation below is also due to the OpenAI language models ChatGPT 5.6 and ChatGPT 6. With that, we hope that the statements of the main results, the ensuing discussion, and the arguments themselves may be of some interest.

Language-model agents often reach a working solution and then fail to consistently deliver it. We study runtime policies: targeted natural-language instructions and action denials applied by the agent harness at states that preceded observed failures, without changing model weights or the user prompt. With this, keeping capability constant, we observe a meaningful unlock in delivered reliability. Across the complete 87-task Terminal-Bench 2.1 suite, with two attempts per task, policies increase repeated success (pass^2) in all three GPT-5.6 tiers: 50.6% to 54.0% for Luna, 55.2% to 60.9% for Terra, and 64.4% to 73.6% for Sol. Sol's best-of-two success changes by 1.2 points while repeated success rises by 9.2, showing that policies chiefly convert reachable solutions into dependable delivery. We further cover 14 tasks under Terra's frozen portfolio. Policy-guided Terra reaches 71.4%, compared with 64.3% for unassisted Sol, at about half the cost, demonstrating how engineering around models could unlock dependability for a use case. To isolate the mechanism we run a randomized five-arm experiment: real policies reach 61% on eligible tasks, versus 39% without a policy, 36% with a timing-matched sham, and 39 to 43% with generic verification or reconsideration. The intended corrective behavior appears in 22 of 24 coded policy attempts, against at most 14 in any other arm. Runtime policies are therefore a practical reliability layer: they make capabilities an agent already possesses substantially more repeatable.

We introduce communication-complexity lifting techniques into the study of recognizable picture languages. As an application, we resolve a long-standing open problem of Anselmo et al. (2006) by constructing a language in UREC whose complement does not belong to REC. Our lower-bound argument is inspired by the communication-complexity approach to unambiguous automata of Göös et al. (2022), although its implementation in the setting of picture languages requires substantially different technical ingredients.

One of the challenges in representational learning is how to encode part-whole hierarchies in a neural net. Prior works rely on flattening tree-like structures into string-like sequences and training a sequence-to-sequence model via autoregression. While such a representation works for parse-trees in NLP, it is not entirely clear how to make it work for images. Thus, we propose a geometric primitive called canonical locks. The key idea is that parts/wholes can be modelled as higher-dimensional vectors ($d \geq 4$), and information can be encoded in their relative phase differences. Inductively, the net consists of positionally-bound bottom-up and top-down neural fields, which drive each other to achieve a state of thermal equilibrium. Additionally, we show the existence of a few symmetrical configurations in the net. The computational iterations taken to break these symmetries depend on the angle between parts/wholes arranged on a disk (or more precisely a ring) in higher dimensions. It also appears to have connections to the psychological phenomenon of mental rotation.

Point cloud generation has emerged as a crucial task for accurately capturing and reproducing the complexity of the physical world. However, existing generative approaches, predominantly relying on Transformers and Variational Autoencoders (VAEs), frequently ignore the continuous, non-grid topologies inherent to 3D spaces. Although the integration of graph-based structures has yielded significant benefits in related discriminative vision tasks, such geometric architectures remain noticeably absent from 3D generative modeling. To address this gap, we introduce EMERGE (Equivariant Multi-scale GNN for Resolution-agnostic point cloud GEneration), the first fully $SE(3)$-equivariant graph-based diffusion backbone explicitly designed to generate point clouds while preserving continuous spatial symmetries. Our framework bypasses the rigid resolution dependencies of standard generative pipelines, enabling zero-shot inference at multiple, arbitrary spatial resolutions. Extensive empirical evaluations demonstrate that EMERGE achieves State-of-the-Art generation quality across standard metrics, while the strong inherent geometric inductive biases enable significantly faster training convergence compared to existing baseline methods.

Compliant arterial wall mechanics, contributing to the Windkessel effect in the carotid artery (CA), have significant impact on hemodynamic patterns and surface shear indicators for cardiovascular diseases, e.g. atherosclerosis. In this study, we extend the linear elastic Fluid-Structure Interaction (FSI) framework to account for nonlinear strain-dependent wall behavior. The model incorporates a Young's modulus generalized from tensile tests on silicone phantoms to capture the nonlinear stress-strain relation of arterial tissue. The final computational model, using a resistance-type boundary condition and in vitro measured stress-strain relation is validated against both, in vitro assessed silicon CA phantom as well as published clinical data on the flow splitting to the daughter branches in CA bifurcations. To better reflect physiological conditions, our model is subsequently extended to incorporate prestress of patient-specific geometries, and clinically measured stress-strain relations, followed by validation against clinical CA data. The present study demonstrates the feasibility of strain-dependent Young's (elastic) modulus as a means to enhance the capacity of the linear elastic framework to accurately represent the physiologically nonlinear mechanics of arterial walls, striking a balance between implementation effort and physiological fidelity. This approach yields realistic strains, volumetric inflation behavior and nonlinear pressure-volume relationships. Furthermore, the study reveals the importance of proper outlet boundary conditions and the shortcomings of resistance-type boundary condition in patient-specific modeling, leading to non-physiological pressure profiles and non-physiological temporal flow splitting.

Explanations are central to causal reasoning, and cognitive science has long established that the human drive to explain is itself a mechanism for learning about causality. Despite this, learning from those abductive signals is largely ignored in artificial intelligence. While explainable AI (XAI) increasingly draws on causal models to generate explanations, the converse direction about what explanations can do for causality remains largely unexplored. To fill this gap, we propose xWhyL, a formal framework connecting causality and XAI by learning causal models from explanations. We develop a mathematical theory that translates explanations into a learning signal complementary to observational data, and demonstrate how it enables overcoming the limits of observational causal discovery. As explanations can be derived from incorrect beliefs and clash with data, a tension we call the Causal Tug-of-War, we prove conditions under which our framework rejects misspecified explanations rather than absorbing them. Our practical instantiation, Causal Interactive Learning (CIL), shows how expert explanations can efficiently support causal discovery and distinguish correct from incorrect explanations.

Conversational agents often express answers in a uniformly confident register. We test whether expressed uncertainty, provenance-aware assertion, and explicit belief revision can be implemented as a behavior layer over a fixed language model; we do not test believability or trust. The layer combines three epistemic states, per-claim confidence and typed provenance, a provenance-gated expression rule, and a persistent revision store with auditable acknowledgments and partial resistance to false corrections. We evaluate it on a constructed, mechanically scored multi-session benchmark using a synthetic model and Qwen2.5-0.5B-Instruct. The synthetic instrument passes all five checks. On the real model, acknowledgment soundness, a by-construction guarantee, holds in 100% of cases, and true corrections are accepted more often than false ones (0.44 vs. 0.15 on held beliefs; 0.875 vs. 0.420 including rule-accepted corrections of unheld facts), but the pre-specified expression-fidelity, contradiction-separation, and provenance margins fail. A disclosed post hoc analysis shows that expression gated on mean answer-token probability ranks correctness below chance end to end (AUC 0.41, conversation-clustered), whereas gating on sampling consistency discriminates (AUC 0.66). A consistency-gated configuration selected from this finding and evaluated under a separately committed protocol meets the conversation-level manipulation and capability-equivalence criteria and replicates on a redrawn conversation set. The manipulation result is selection-dependent, and both criteria remain unresolved when uncertainty is clustered over the 60 facts. The supported conclusions are limited to the by-construction audit guarantee, store-dependent partial correction discrimination, and a benchmark- and model-specific failure of token-probability gating; scaling the fact base is required before human evaluation.

Water treatment research is expanding rapidly, but much of the knowledge acquired from this research remains scattered across unstructured literature. The field still lacks a dedicated language model that can efficiently capture water treatment-specific domain semantics for large-scale literature mining. Here, we address this by developing WaterBERT, a domain-adapted encoder model designed for semantic representation and structured information extraction from water treatment texts. WaterBERT was developed by continual pretraining on a large-scale water treatment corpus comprising about 2.97 billion tokens. Three fine-tuned models based on WaterBERT were systematically evaluated on downstream tasks, achieving the best overall performance among general-purpose and domain-specific BERT models, with F1 scores of 90.12% for multiclass treatment process classification, 79.50% for named entity recognition, and 74.04% for relation extraction. Beyond these benchmark tasks, we further demonstrated WaterBERT's advantages for large-scale literature processing. Applied to 5,144 Environmental Science & Technology articles, WaterBERT-BERTopic identified coherent, diverse, and domain-specific research topics without predefined categories. Building on WaterBERT, we processed 693,211 abstracts at substantially lower cost than commercial LLMs while retaining competitive extraction performance to construct a structured water treatment knowledge graph. The knowledge graph was then integrated with lexical and dense retrieval to develop a Water Knowledge-Enhanced Retrieval System (WaterKERS), which achieved a relevance score of 77.7, substantially outperforming text-based retrieval baselines (54.7-64.5). Through WaterBERT, this study provides a compact and scalable semantic foundation for large-scale information processing and evidence mapping in water treatment research.

We consider the problem of determining if a given two-dimensional nonnegative integer matrix $M$ is the product of two such matrices, excluding trivial units. A matrix $M$ with no such factorisation is called prime and therefore belongs to the minimal (infinite rank) generator of $2 \times 2$ matrices over the natural numbers, otherwise it is called composite. We also consider the problem of finding a (non-unique) factorisation of a composite matrix. Our results have applications in computational group theory and the theory of codes, where such matrices are called incidence matrices. We analyse the complexity of primality and finding a factorisation for a composite matrix, providing a first efficient algorithm.

We construct the first type of non-Euclidean non-autoregressive neural quantum state (NQS) in the form of the hyperbolic Restricted Boltzmann Machine (HRBM), which is studied in the variational Monte-Carlo (VMC) setting of the Quantum Sherrington-Kirkpatrick (QSK) model whose ground state exhibits volume-law entanglement. Across a 512-fold increase in the Hilbert space dimension corresponding to a system size increase from $N=14$ to $N=24$, HRBM NQS robustly outperforms its Euclidean version, the RBM NQS, in terms of better ground state energy optimization as well as lower Renyi-2 $S_2$ and von Neumann $S_{vN}$ absolute entanglement entropy reconstruction errors. More importantly, for all tested QSK system sizes, HRBM NQS demonstrates a superior expressivity in faithfully reproducing the entire entanglement spectrum of the QSK model from the top eigenvalues down to the tail end across 15 orders of magnitude, while RBM NQS consistently overestimates the sub-dominant modes. This work furnishes a proof-of-concept demonstrating that hyperbolic non-autoregressive NQS ansatze, thanks to the exponential volume of the hyperbolic geometry underlying their constructions, might be more natural at representing volume-law quantum systems than conventional Euclidean NQS. Furthermore, an interesting byproduct of this work is the polynomial scaling result of RBM-type NQS ansatze in the QSK volume-law system as the Hilbert space dimension increases exponentially.

Ontology generation from Competency Questions (CQs) is a central yet labor-intensive phase of Ontology Engineering. While large language models (LLMs) offer promising automation capabilities, current evaluations remain fragmented. Task formulations are heterogeneous, gold standards often lack fine-grained CQ provenance, metrics conflate lexical overlap with structural and logical adequacy, and reference ontologies are not always explicitly designed around the evaluation CQs. Here, we address these limitations with CQ4OE, a benchmark for the systematic and reproducible evaluation of LLM-based ontology generation from CQs. For each ontology in the benchmark, we build a CQ-driven gold OWL ontology with explicit provenance linking each CQ to the classes, properties, and axioms required to answer it. From this resource, we define two complementary evaluation tasks. CQ2Term supports term-level evaluation of CQ-specific class and property prediction over 99 CQs, and CQ2Onto supports ontology-level evaluation over 118 CQs, including hierarchy, property modeling, and axiom-level structure. We demonstrate CQ4OE with experiments using nine LLMs under zero-shot, iterative, and multi-agent generation strategies, showing that LLMs recover explicit vocabulary terms more reliably than creating ontologies, particularly in property modeling, hierarchy construction, and axiom generation.

Large audio-language models may mention acoustic events that are absent from the input. A separate audio event detector can verify these mentions, but doing so requires a second audio encoder and a separate forward pass. We propose Reused Encoder States for Verifying Events (REVE), a lightweight method that uses states already computed by the target model. One readout summarizes class scores across audio frames, while another uses pooled states from four consecutive frame intervals. Class-aware score fusion combines their outputs to verify generated event mentions without encoding the audio again. On AudioSet, REVE removes 92.9% of label-unsupported mentions under a faithful-mention recall constraint. With fewer added parameters and no second audio-encoding pass, REVE achieves a reduction comparable to those of CED-Tiny and CED-Base. Its complete verification latency is about 1/18 of the CED-Base path. Results on controlled DESED mixtures and different target-model architectures further confirm the effectiveness of encoder-state reuse.

Human feedback can vary in cost and informativeness. Strong feedback can reveal severe errors but is costly, so cheaper quality ratings can help decide which items to annotate. We propose MICRO (Multi-Fidelity Impact Clustered Rollout), an active search framework that allocates a shared budget to these feedback types to maximise confirmed severe error discoveries. MICRO jointly models ratings and annotation losses conditional on item features to steer acquisition. It clusters acquisitions by their predicted impact on severity probabilities to select diverse candidates, then uses rollout to estimate their discovery value. Experiments on WMT20 English-German show that ratings improve both loss reconstruction and severity prediction. MICRO achieves the highest mean discovery count across four budget and rating cost settings, with similar performance to adapted MF-ENS in one and significant gains over all six comparison policies, including two rollout controls, in the other three $(p<.001)$.

The need for collaboration between diverse fields of research is increasingly recognised as important by research funding agencies. A significant driver of this need is the current revolution in artificial intelligence (AI) and related technologies. There is a growing interest in the potential impact of AI in different fields including the methodologies they use and the resulting advances in new knowledge, new access and enhanced productivity. However, there is also a corresponding increase in concern about the fundamentals of AI technologies and the way in which trans and/or interdisciplinary research is approached. The resulting collaboration too often ends up as a one-way street where the domain partner acts only as an information provider. For example, the contribution of the AHSS partner might be limited to providing insight about ethics and/or the technology partner may only provide a service to build applied AI-based solutions. In response to this problem, we propose a reciprocal approach to collaboration where both partners seek to understand, cooperate and identify jointly significant impacts. In this paper we explore this relationship between cultural heritage institutions (GLAMs), Arts, Humanities & Social Sciences (AHSS) research and technology-led AI research, especially the impact of current technological advances in AI. Drawing from the history of convergence in GLAM studies, we propose five key practices to form a framework for greater understanding across this divide.

We study a finite tiling problem, where tiles are unit squares whose four edges are colored with one of two colors. We ask whether a given rectangle admits a perfect rectangular tiling: every cell of the rectangle is occupied by one tile, neighboring edge colors match, and exactly $n_i$ tiles of type $i$ are used, where rotations of the tiles are allowed. Our problem is related to classical Wang tilings, more general finite tile-placement problems, and edge placement puzzles. But in our problem, the multiplicities of the tile types are part of the input and the tile alphabet is fixed and extremely small; thus the complexity of the problem arises from the interaction between the rectangle dimensions and the prescribed tile multiplicities. We provide a comprehensive study of the perfect rectangular tiling problem. For this we consider all classes of subsets of the six possible tile types for two-colored edges, and we characterize for each class whether multiplicities either always allow a perfect rectangular tiling or whether their existence can be decided efficiently.

Dynamic black-box optimization presents significant challenges for Bayesian Optimization (BO), as the objective function evolves over time, causing optimal locations to shift continuously. Existing dynamic BO (DBO) methods using standard acquisition functions such as Upper Confidence Bound (UCB) fail to explicitly account for temporal variations, leading to suboptimal sample allocation and poor tracking of moving optima. Here, we propose BOBA (Bayesian Optimization through Bayesian Active Inference), a novel acquisition function inspired by free energy principles from active inference that explicitly minimizes predictive uncertainty about future states in dynamic environments. BOBA extends traditional acquisition functions by incorporating a forward-looking uncertainty quantification that estimates uncertainty in function changes, enabling more informed exploration-exploitation trade-offs in non-stationary settings. We evaluate BOBA on synthetic dynamic benchmarks, comparing against state-of-the-art DBO methods. Our experiments demonstrate that BOBA significantly improves regret in query-restricted settings, while remaining competitive in time-limited settings. We further analyze variants of BOBA with different exploration strategies, showing how the exploration-exploitation balance can be tuned for different types of dynamic functions. This work contributes both a free energy-based acquisition function for DBO and insights into how active inference principles can enhance optimization in non-stationary environments, with implications for real-time applications requiring continuous adaptation.

Many learning problems combine a dominant regularity with systematic exceptions. Motivated by U-shaped learning in language acquisition, we study this interaction in controlled quasiregular regression problems where regular and exceptional solutions are explicitly known. Neural networks can partially acquire exceptions, subsequently regress toward the dominant regularity, and finally recover. This overregularization becomes substantially stronger when exceptions are rare, despite their early acquisition, but does not emerge equally across all regularities considered. Our results isolate a simple form of competition between regularities and exceptions during neural learning.

We study prophet inequalities for a random walk reward stopping problem with sample-based information. The goal is to stop as close as possible to the maximum of a random walk with i.i.d. increments, measuring performance by the ratio between the expected reward when stopping and the expected true maximum. We consider a sample-based model in which the increment distribution is unknown and the decision maker has access to $K$ independent sample paths of the reward process. For the infinite-horizon setting, we establish a sharp prophet inequality with constant $(K/(K+1))^{K+1}$. The guarantee is attained by a randomised stopping rule based on the ladder height decomposition of random walks. As $K\to\infty$, this recovers the classical $1/e$ prophet inequality from the full-information setting. For the finite-horizon setting, where the process terminates after $n$ steps, we first prove a tight no-information prophet inequality with constant $1/H_n$, where $H_n$ is the $n$-th harmonic number. For $K\ge1$ samples, we show that a prophet constant of $1/4$ is attainable. Finally, we prove that, with $K$ samples, the prophet constant is at most $(K/(K+1))^{K+1}+(6+6H_K)/H_n$ for $n\ge 2K^2$, implying convergence to the infinite-horizon constant as $n\to\infty$. Our approach combines random walk theory, including ladder heights and Spitzer's identity, with linear programming duality. Our results contribute to random walk stopping theory and to sample-based prophet inequalities for correlated rewards, an area that remains largely unexplored. To the best of our knowledge, our tight sample-based prophet inequalities are the first whose performance is parameterised exactly, rather than only up to constants, by the number of available samples.

We call the object this paper derives and certifies a minimal sufficient governance context: given a finite reachable-state model, a deterministic declared verdict, and candidate observable attributes, we compute sufficient observation sets, distinguish attributes that are individually indispensable from contracts that are jointly sufficient, and select among sufficient contracts under a cardinality or declared-cost objective. An observation contract is a set of candidate attributes whose values determine the declared verdict on every reachable state; an authority contract is one selected under an objective and bound to a gate schema. We synthesize every inclusion-minimal sufficient contract where exhaustive enumeration is affordable, and a minimum-cardinality or minimum-cost contract by SAT/MaxSAT encoding otherwise, checking sufficiency directly. On a constructed code/cloud domain, the individually-indispensable core is not sufficient as an observation contract and two distinct reducts exist; a preregistered cost model separates them exactly. On a second, larger, constructed domain, the same pattern recurs, but that domain's cost model does not separate the alternatives: a fully explained cost tie, reported as found. We measure discernibility-family scaling where exhaustive enumeration is confirmed infeasible within a registered timeout, while SAT/MaxSAT synthesis solves in well under a second; MaxSAT showed no measured cardinality advantage over plain SAT. AuthorityBench compares four baselines across three domains; the declared-only baseline is not exactly sufficient on any. Every selected contract is checked for sufficiency, with a counterexample on failure and a check summary, not a portable certificate, on success – the compiler-focused scope of a two-scope table; an independently specified end-to-end case study is registered follow-up work, not claimed here.