Standard Vision Transformers flatten 2D images into 1D sequences, disrupting the natural spatial topology. While Rotary Positional Embedding (RoPE) excels in 1D, it inherits this limitation, often treating spatially distant patches (e.g., at row edges) as sequence neighbors. Existing 2D approaches typically treat spatial axes independently, failing to decouple this false sequential proximity from true spatial distance. To restore the 2D spatial manifold, we introduce Geometric Positional Embedding (GeoPE), a framework that extends rotations to 3D Euclidean space using quaternions. To overcome non-commutativity and ensure symmetry, GeoPE constructs a unified rotational operator by computing the geometric mean in the Lie algebra. This creates a geometrically coupled encoding that effectively separates spatial dimensions. Extensive experiments on image classification, object detection, and 3D semantic segmentation demonstrate that GeoPE consistently outperforms existing 2D RoPE variants and significantly enhances shape bias, confirming its ability to capture true geometric structure.

Large language models (LLMs) demonstrate remarkable potential across diverse language-related tasks, yet whether they capture deeper linguistic properties--such as syntactic structure, phonetic cues, and metrical patterns--from raw text remains unclear. To analysis whether LLMs can learn these features effectively and apply them to important nature language related tasks, we introduce a novel multilingual genre classification dataset derived from Project Gutenberg, a large-scale digital library offering free access to thousands of public domain literary works, comprising thousands of sentences per binary task (poetry vs. novel; drama vs. poetry; drama vs. novel) in six languages (English, French, German, Italian, Spanish, and Portuguese). We augment each with three explicit linguistic feature sets (syntactic tree structures, metaphor counts, and phonetic metrics) to evaluate their impact on classification performance. Experiments demonstrate that although LLM classifiers can learn latent linguistic structures either from raw text or from explicitly provided features, different features contribute unevenly across tasks, which underscores the importance of incorporating more complex linguistic signals during model training.

Across diverse domains--from complex systems and finance to high-energy physics and astrophysics--scientific inquiry often relies on deriving theoretical parameters from observational data [1]. At the core of this challenge lies the inverse problem: inferring the posterior distribution of theoretical parameters given a set of observables [2]. Traditional approaches for posterior estimation rely on sampling algorithms such as Markov Chain Monte Carlo (MCMC) [3, 4] and Nested Sampling (NS) [5]. In astrophysics and cosmology, implementations like emcee [6] and dynesty [7] have become standard tools. While these frameworks are statistically robust, they suffer significantly from the curse of dimensionality. In real-world scenarios, where the parameter space is high-dimensional and the likelihood function relies on computationally expensive simulators (e.g., in particle physics phenomenology [8]), convergence can take weeks or even months. Recent advances in machine learning have introduced Normalizing Flows (NFs) as a powerful alternative for probabilistic modelling [9, 10]. By learning a bijective mapping between a simple base distribution (e.g., a Gaussian) and the complex target distribution, NFs allow for exact density estimation and efficient sampling [11] from the target distribution. Modern architectures, such as RealNVP [12] and Neural Spline Flows [13], offer enough expressivity to model highly complex distributions.

Agents capable of accomplishing complex tasks through multiple interactions with the environment have emerged as a popular research direction. However, in such multi-step settings, the conventional group-level policy optimization algorithm becomes suboptimal because of its underlying assumption that each action holds equal contribution, which deviates significantly from reality. Our analysis reveals that only a small fraction of actions are critical in determining the final outcome. Building on this insight, we propose CARL, a critical-action-focused reinforcement learning algorithm tailored for multi-step agents. CARL achieves focused training through providing action-level optimization signals for high-criticality actions while excluding low-criticality actions from model update. Extensive experiments demonstrate that CARL achieves both stronger performance and higher efficiency during training and inference across diverse evaluation settings.

Patients with rare neurological diseases report cognitive symptoms--"brain fog"--invisible to traditional tests. Proof-of-concept in phenylketonuria (PKU) shows speech-derived "Proficiency in Verbal Discourse" correlates Success would transform episodic neurology into continuous personalized monitoring for millions globally. In phenylketonuria (PKU), adults describe "brain fog" and working memory deficits [ We envision smartphone-based speech analysis integrated with medical databases via RELGT, enabling continuous neurocog-nitive monitoring--transforming reactive episodic care into proactive precision neurology. Parkinson's disease involves hypophonia and speech fluctuations tied to medication Huntington's disease reflects CAG-repeat-driven degrneration and progressive motor-cognitive decline. Wilson's disease presents with dysarthria linked to copper accumulation.

Initial challenges, such as grade-school mathematics (GSM8K) and standard competition math (MATH dataset), have largely been surmounted, pushing the frontier of AI reasoning toward "grand challenge" problems, such as those found in the International Mathematical Olympiad (IMO). These problems, renowned for their demand for deep insight, creativity, and rigorous proof, expose a fascinating weakness in modern LLMs. While a model's performance on a single attempt (termed pass@1) may be very low, its ability to produce a correct answer within k attempts (pass@k) can be significantly higher. This pass@1 versus pass@k gap, especially pronounced when sampling with high temperature to produce diverse outputs, suggests that models possess a vast, latent capability that is not accessible in a single, high-confidence generation. Interestingly, to recover the full power of the model it is not sufficient to simply use multiple attempts. In fact, even the pass@k metric fails to capture the full story. On the most difficult problems, simply sampling k times and selecting the best answer (e.g., "best-of-32") still yields poor results. For instance, Huang and Yang (2025) report that a best-of-32 baseline on the IMO 2025 problems achieved an accuracy of only 31.6-38.1% for leading models [HY25]. This paradox lies at the heart of our work: the latent capability of LLMs is not merely a matter of selection (finding one correct needle in a haystack of k attempts), but one of synthesis.

This work investigates how disturbance-aware, robustness-embedded reference trajectories translate into driving performance when executed by professional drivers in a dynamic simulator. Three planned reference trajectories are compared against a free-driving baseline (NOREF) to assess trade-offs between lap time (LT) and steering effort (SE): NOM, the nominal time-optimal trajectory; TLC, a track-limit-robust trajectory obtained by tightening margins to the track edges; and FLC, a friction-limit-robust trajectory obtained by tightening against axle and tire saturation. All trajectories share the same minimum lap-time objective with a small steering-smoothness regularizer and are evaluated by two professional drivers using a high-performance car on a virtual track. The trajectories derive from a disturbance-aware minimum-lap-time framework recently proposed by the authors, where worst-case disturbance growth is propagated over a finite horizon and used to tighten tire-friction and track-limit constraints, preserving performance while providing probabilistic safety margins. LT and SE are used as performance indicators, while RMS lateral deviation, speed error, and drift angle characterize driving style. Results show a Pareto-like LT-SE trade-off: NOM yields the shortest LT but highest SE; TLC minimizes SE at the cost of longer LT; FLC lies near the efficient frontier, substantially reducing SE relative to NOM with only a small LT increase. Removing trajectory guidance (NOREF) increases both LT and SE, confirming that reference trajectories improve pace and control efficiency. Overall, the findings highlight reference-based and disturbance-aware planning, especially FLC, as effective tools for training and for achieving fast yet stable trajectories.

In general, approximating classes of functions defined over high-dimensional input spaces by linear combinations of a fixed set of basis functions or ``features'' is known to be hard. Typically, the worst-case error of the best basis set decays only as fast as $Θ\(n^{-1/d}\)$, where $n$ is the number of basis functions and $d$ is the input dimension. However, there are many examples of high-dimensional pattern recognition problems (such as face recognition) where linear combinations of small sets of features do solve the problem well. Hence these function classes do not suffer from the ``curse of dimensionality'' associated with more general classes. It is natural then, to look for characterizations of high-dimensional function classes that nevertheless are approximated well by linear combinations of small sets of features. In this paper we give a general result relating the error of approximation of a function class to the covering number of its ``convex core''. For one-hidden-layer neural networks, covering numbers of the class of functions computed by a single hidden node upper bound the covering numbers of the convex core. Hence, using standard results we obtain upper bounds on the approximation rate of neural network classes.

This paper presents a novel approach to automated stripboard circuit layout design using Answer Set Programming (ASP). The work formulates the layout problem as both a synthesis and multi-objective optimization task that simultaneously generates viable layouts while minimizing board area and component strip crossing. By leveraging ASP's declarative nature, this work expresses complex geometric and electrical constraints in a natural and concise manner. The two-phase solving methodology first ensures feasibility before optimizing layout quality. Experimental results demonstrate that this approach generates compact, manufacturable layouts for a range of circuit complexities. This work represents a significant advancement in automated stripboard layout, offering a practical tool for electronics prototyping and education while showcasing the power of declarative programming for solving complex design automation problems.

Multimodal Artificial Intelligence (AI) systems, particularly Vision-Language Models (VLMs), have become integral to critical applications ranging from autonomous decision-making to automated document processing. As these systems scale, they rely heavily on preprocessing pipelines to handle diverse inputs efficiently. However, this dependency on standard preprocessing operations, specifically image downscaling, creates a significant yet often overlooked security vulnerability. While intended for computational optimization, scaling algorithms can be exploited to conceal malicious visual prompts that are invisible to human observers but become active semantic instructions once processed by the model. Current adversarial strategies remain largely static, failing to account for the dynamic nature of modern agentic workflows. To address this gap, we propose Chameleon, a novel, adaptive adversarial framework designed to expose and exploit scaling vulnerabilities in production VLMs. Unlike traditional static attacks, Chameleon employs an iterative, agent-based optimization mechanism that dynamically refines image perturbations based on the target model's real-time feedback. This allows the framework to craft highly robust adversarial examples that survive standard downscaling operations to hijack downstream execution. We evaluate Chameleon against Gemini 2.5 Flash model. Our experiments demonstrate that Chameleon achieves an Attack Success Rate (ASR) of 84.5% across varying scaling factors, significantly outperforming static baseline attacks which average only 32.1%. Furthermore, we show that these attacks effectively compromise agentic pipelines, reducing decision-making accuracy by over 45% in multi-step tasks. Finally, we discuss the implications of these vulnerabilities and propose multi-scale consistency checks as a necessary defense mechanism.