Skeleton-based hand gesture recognition plays a crucial role in enabling intuitive human-computer interaction. Traditional methods have primarily relied on hand-crafted features--such as distances between joints or positional changes across frames--to alleviate issues from viewpoint variation or body proportion differences. However, these hand-crafted features often fail to capture the full spatio-temporal information in raw skeleton data, exhibit poor interpretability, and depend heavily on dataset-specific preprocessing, limiting generalization. In addition, normalization strategies in traditional methods, which rely on training data, can introduce domain gaps between training and testing environments, further hindering robustness in diverse real-world settings. To overcome these challenges, we exclude traditional hand-crafted features and propose Skeleton Kinematics Extraction Through Coordinated grapH (SKETCH), a novel framework that directly utilizes raw four-dimensional (time, x, y, and z) skeleton sequences and transforms them into intuitive visual graph representations.

Human intelligence effortlessly interprets visual scenes along a rich spectrum of semantic dimensions. However, existing approaches to language-grounded visual concept learning are limited to a few predefined primitive axes, such as color and shape, and are typically explored in synthetic datasets. In this work, we propose a scalable framework that adaptively identifies image-related concept axes and grounds visual concepts along these axes in real-world scenes. Leveraging a pretrained vision-language model and our universal prompting strategy, our framework identifies a diverse image-related axes without any prior knowledge. Our universal concept encoder adaptively binds visual features to the discovered axes without introducing additional model parameters for each concept. To ground visual concepts along the discovered axes, we optimize a compositional anchoring objective, which ensures that each axis can be independently manipulated without affecting others. We demonstrate the effectiveness of our framework on subsets of ImageNet, CelebA-HQ, and AFHQ, showcasing superior editing capabilities across diverse real-world concepts that are too varied to be manually predefined. Our method also exhibits strong compositional generalization, outperforming existing visual concept learning and text-based editing methods.

The advent of foundation models in AI has significantly advanced general-purpose learning, enabling remarkable capabilities in zero-shot inference and in-context learning. However, training such models on physics data, including solutions to partial differential equations (PDEs), poses a unique challenge due to varying dimensionalities across different systems. Traditional approaches either fix a maximum dimension or employ separate encoders for different dimensionalities, resulting in inefficiencies. To address this, we propose a dimension-agnostic neural network architecture, the Axial Neural Network (XNN), inspired by parametersharing structures such as Deep Sets and Graph Neural Networks.

Dexterous robotic hands are essential for performing complex manipulation tasks, yet remain difficult to train due to the challenges of demonstration collection and high-dimensional control. While reinforcement learning (RL) can alleviate the data bottleneck by generating experience in simulation, it typically relies on carefully designed, task-specific reward functions, which hinder scalability and generalization. Thus, contemporary works in dexterous manipulation have often bootstrapped from reference trajectories. These trajectories specify target hand poses that guide the exploration of RL policies and object poses that enable dense, task-agnostic rewards. However, sourcing suitable trajectories--particularly for dexterous hands--remains a significant challenge. Yet, the precise details in explicit reference trajectories are often unnecessary, as RL ultimately refines the motion.

Einsum expressions specify an output tensor in terms of several input tensors. They offer a simple yet expressive abstraction for many computational tasks in artificial intelligence and beyond. However, evaluating einsum expressions poses hard algorithmic problems that depend on the representation of the tensors. Two popular representations are multidimensional arrays and coordinate lists. The latter is a more compact representation for sparse tensors, that is, tensors where a significant proportion of the entries are zero. So far, however, most of the popular einsum implementations use the multidimensional array representation for tensors. Here, we show on a non-trivial example that, when evaluating einsum expressions, coordinate lists can be exponentially more efficient than multidimensional arrays. In practice, however, coordinate lists can also be significantly less efficient than multidimensional arrays, but it is hard to decide from the input tensors whether this will be the case.

Large language models (LLMs) can sometimes report the strategies they actually use to solve tasks, yet at other times seem unable to recognize those strategies that govern their behavior. This suggests a limited degree of metacognition -- the capacity to monitor one's own cognitive processes for subsequent reporting and self-control. Metacognition enhances LLMs' capabilities in solving complex tasks but also raises safety concerns, as models may obfuscate their internal processes to evade neural-activation-based oversight (e.g., safety detector). Given society's increased reliance on these models, it is critical that we understand their metacognitive abilities. To address this, we introduce a neuroscience-inspired neurofeedback paradigm that uses in-context learning to quantify metacognitive abilities of LLMs to report and control their activation patterns. We demonstrate that their abilities depend on several factors: the number of in-context examples provided, the semantic interpretability of the neural activation direction (to be reported/controlled), and the variance explained by that direction. These directions span a "metacognitive space" with dimensionality much lower than the model's neural space, suggesting LLMs can monitor only a small subset of their neural activations. Our paradigm provides empirical evidence to quantify metacognition in LLMs, with significant implications for AI safety (e.g., adversarial attack and defense).

Recent large language models (LLMs) with long-chain-of-thought reasoning--such as DeepSeek-R1--have achieved impressive results on Olympiad-level mathematics benchmarks. However, they often rely on a narrow set of strategies and struggle with problems that require a novel way of thinking. To systematically investigate these limitations, we introduce OMEGA--Out-of-distribution Math Problems Evaluation with 3 Generalization Axes--a controlled yet diverse benchmark designed to evaluate three axes of out-of-distribution generalization, inspired by Boden's typology of creativity: (1) Exploratory--applying known problem-solving skills to more complex instances within the same problem domain; (2) Compositional--combining distinct reasoning skills, previously learned in isolation, to solve novel problems that require integrating these skills in new and coherent ways; and (3) Transformative--adopting novel, often unconventional strategies by moving beyond familiar approaches to solve problems more effectively. OMEGA consists of programmatically generated training-test pairs derived from templated problem generators across geometry, number theory, algebra, combinatorics, logic, and puzzles, with solutions verified using symbolic, numerical, or graphical methods. We evaluate frontier (or top-tier) LLMs and observe sharp performance degradation as problem complexity increases. Moreover, we fine-tune the Qwen-series models across all generalization settings and observe notable improvements in exploratory generalization, while compositional generalization remains limited, and transformative reasoning shows little to no improvement. By isolating and quantifying these fine-grained failures, OMEGA lays the groundwork for advancing LLMs toward genuine mathematical creativity beyond mechanical proficiency.

We present a covariance-aware sampler that improves the quality of pixel-space Diffusion Model (DM) sampling in the few-step regime. We hypothesize that in the few-step regime samplers fail because they rely solely on the predicted mean of the reverse distribution, while our solution explicitly models the reverse-process covariance. Our method combines Tweedie's formula to estimate the covariance with an efficient, structured Fourier-space decomposition of the covariance matrix. Implemented as an extension of DDIM, our method requires only a minimal overhead: one extra Jacobian-Vector Product (JVP) per step. We demonstrate that for pixel-based DMs, our method consistently produces superior samples compared to state-of-the-art second order samplers (Heun, DPM-Solver++) and the recent aDDIM sampler, at an identical number of function evaluations (NFE).

The Brier score conflates two distinct properties of probabilistic predictions: reliability (calibration error) and resolution (discriminatory power). We introduce the Manokhin Probability Matrix, a BCG-style two-dimensional diagnostic framework that separates them. Classifiers are placed on a 2x2 grid by Spiegelhalter Z-statistic and AUC-ROC expected rank, then assigned to one of four archetypes: Eagle (good on both axes), Bull (strong discrimination, poor calibration), Sloth (well-calibrated, weak discriminator), and Mole (poor on both). Each archetype carries a distinct prescription. We populate the matrix from a large-scale empirical study spanning 21 classifiers, 5 post-hoc calibrators, and 30 real-world binary classification tasks from the TabArena-v0.1 suite. The assignment is unambiguous. CatBoost, TabICL, EBM, TabPFN, GBC, and Random Forest are Eagles. XGBoost, LightGBM, and HGB are Bulls; Venn-Abers calibration cuts log-loss by 6.5 to 12.6% on Bulls but degrades Eagles by 2.1%. SVM, LR, LDA, and the empirical base-rate predictor are Sloths. MLP, KNN, Naive Bayes, and ExtraTrees are Moles. A theoretical asymmetry follows: no order-preserving post-hoc calibrator can add discriminatory power (Proposition 1), so calibration is the fixable part and discrimination is the hard part. The practical rule is direct: do not optimise aggregate Brier score without first decomposing it; optimise discrimination first, then fix calibration post-hoc. Code and raw experimental data are available at https://github.com/valeman/classifier_calibration.