arXiv:2606.25975v1 Announce Type: new Abstract: Common first-order optimizers, such as Adam, implicitly treat each parameter block as an unstructured vector, which disregards the multilinear weight structure present in many modern machine learning models. Recent work has shown that exploiting matrix structure can improve optimization dynamics. A notable example is Muon, which performs steepest descent under the spectral norm constraint. We take the next step and introduce Tensorion, a tensor-aware optimizer that extends Muon's constrained optimization perspective from matrices to higher-order tensors. Tensorion is built around a linear minimization oracle (LMO) over a tensor norm ball. The norm is carefully chosen to balance two objectives: tightly bounding the tensor spectral norm, while still keeping the LMO tractable. This LMO becomes computable because it reduces to operations on adaptively selected unfolding matrices. Notably, when restricted to order-2 tensors (i.e., matrices), Tensorion recovers Muon exactly. Experiments on tensor-based computer vision problems suggest that Tensorion can offer improved convergence behavior and more stable gradient updates compared with Adam-based and existing tensor-aware baselines in the evaluated settings.
Science Journals
arXiv:2606.24971v1 Announce Type: cross Abstract: Unfolding observed $\gamma$-ray spectra is an ill-conditioned Poisson inverse problem. Detector response effects and finite energy resolution make distinct non-negative emitted $\gamma$-ray spectra nearly indistinguishable after forward mapping, so direct inversion can strongly amplify statistical fluctuations. Here, we present an empirical-Bayes hierarchical unfolding method that preserves the Poisson counting structure, enforces non-negativity, and incorporates background through a joint ON/OFF likelihood. The prior on the emitted spectrum is centered on an automatically selected Richardson-Lucy reference spectrum, with an adaptive width that remains broad in weakly constrained regions. Posterior inference is performed with the No-U-Turn Sampler, and simultaneous uncertainty bands are reported for the resolution-limited unfolded spectrum. Our Bayesian method provides a robust and extensible framework for uncertainty quantification in unfolding, and a direct comparison with a recent frequentist regularized maximum-likelihood method gives highly consistent unfolded spectra in representative high- and low-statistics cases.
arXiv:2606.24987v1 Announce Type: cross Abstract: Optimal transport (OT) has become a central language for comparing probability measures, but exact balanced OT is often both too rigid for data with missing, created, or destroyed mass and subject to unfavorable high-dimensional sample complexity. Entropic regularization and unbalanced relaxations address these limitations in complementary ways. Entropy smooths the geometry, improves statistical behavior, and enables fast Sinkhorn-type algorithms, while unbalanced marginal penalties replace hard conservation constraints by divergence terms adapted to noisy empirical data. This paper studies the sample complexity of entropic unbalanced OT at the level of the optimal coupling, rather than only the scalar transport value. We develop a translation-invariant dual formulation, prove compactness and strong convexity properties for the intrinsic dual variables, and convert these geometric estimates into high-probability finite-sample bounds for empirical couplings. The results clarify why regularization is a practical necessity in machine learning applications: it softens the curse of dimensionality, reduces the number of samples needed for stable transport estimation, and keeps the resulting estimators compatible with scalable Sinkhorn-type solvers.
arXiv:2606.25072v1 Announce Type: cross Abstract: A popular view in the foundations of diffeomorphism-invariant theories is that their physical content is encoded in correlations or `observables': a set of phase space functions that have vanishing Poisson brackets with the constraints related to diffeomorphisms. In this article I study the phase space structure of models with a temporal diffeomorphism invariance and prove a series of formal results that challenge this view in a few ways. First, I show how this view is not applicable to all the phase space trajectories of every diffeomorphism-invariant theory. Second, I show how correlations can be proved to be invariant only in a way that generalizes the standard definition of invariance and in a way that does not provide smooth phase space functions. Third, I prove that spatiotemporal relations are also invariant. Fourth, I prove that spatiotemporal structures are indispensable for defining the invariant content of diffeomorphism-invariant models. Finally, I comment that these results are expected to be generalizable for models invariant under $d$-dimensional diffeomorphisms, which represents a challenge for some views in the foundations of general relativity and quantum gravity.
arXiv:2606.25229v1 Announce Type: cross Abstract: Chemical potentials are among the most important properties that can be obtained from a molecular simulation since they define many technologically relevant collective properties. The chemical potential of a species in solution is obtained by computing the free energy change of adding that species into a bulk system, a calculation typically very expensive for systems such as electrolytes, due to the lack of phase space overlap between "not-inserted" and "inserted" states. Recently, normalizing flows have been introduced as a way to accelerate free energy computations by learning a bijective function, constructed to be as expressive as possible, that maps the configuration space of one Boltzmann distribution onto another. This expressivity makes them difficult to train, limiting their ability to be generated "on-the-fly" for any new system, and in practice these mappings have shown only modest sampling improvements for liquids. We address these issues by introducing a "minimal" normalizing flow (MNF). This is a trainable bijective mapping that is intentionally limited in expressivity, and instead applies low-dimensional, physically informed transformations. Useful MNFs can be trained in 1 minute of GPU time due to their simplicity and our introduction of a novel training strategy. We show how calculations of chemical potentials of Lennard-Jones particle systems can be accelerated by at least 10 times with a simple radial mapping. We also apply a radial and orientational mapping to ion solvation in water, showing that MNFs can increase the effective sample size by 3 times for charging free energy calculations and 8 times for calculating free energy changes due to force field perturbations. This provides the foundation for the development of physically-informed mappings that can accelerate complex free energy calculations while retaining low training costs.
arXiv:2606.25283v1 Announce Type: cross Abstract: Some orbital locations are crowded while others remain unoccupied. We explain why using the geostationary orbit as a near-ideal laboratory: a mature, one-dimensional orbit in which satellite operators compete for position under first-come first-served allocation rules. Using the complete ITU registry and a simple competitive entry model, we predict the observed distribution of active GEO satellites with $R^2 = 0.64$. In walk-forward tests, the structural model also predicts individual slot choices out of sample better than a fitted conditional-logit discrete-choice model. Our model also predicts the distribution of inactive payloads in GEO with $R^2 = 0.44$, showing that the geography of debris risk can be predicted when it is a function of satellite launches. Surprisingly, we find that the current satellite distribution in GEO is relatively fair: driven by population rather than income and placing satellites in economically efficient locations. However, our model shows that this is only the case for mature slots.
arXiv:2606.25333v1 Announce Type: cross Abstract: This paper presents a dual-algebraic framework for control barrier functions (CBFs) that guarantees deterministic execution using exclusively elementary arithmetic. We develop this deterministic approach to solve a fundamental bottleneck in safety-critical control: pointwise minima naturally compose intersecting safe sets, but generate non-smooth boundaries where standard Lie derivatives fail. Existing mathematical workarounds inject approximation bias, probabilistic non-determinism, or combinatorial execution delays that strictly impede hard real-time hardware certification. By embedding the system state and vector field into the dual-number ring, our method extracts both the composite barrier value and its exact directional derivative in a single evaluation. The standard floating-point minimum deterministically isolates a single vertex of the Clarke generalized gradient for the quadratic-program solver. We prove this selected vertex constitutes a valid Clarke subgradient and the resulting simultaneous-enforcement safety filter guarantees forward invariance. The arithmetic overhead remains a fixed constant factor, strictly independent of state dimension or constraint count. We extend this framework to arbitrary $\min$/$\max$ Boolean compositions and systems of higher relative degree, validating the computational scaling on three physical examples.
arXiv:2606.25403v1 Announce Type: cross Abstract: Accent conversion and controllability remain fundamental challenges in cross-lingual text-to-speech (TTS), particularly for low-resource and phonetically diverse Indic languages. While recent large language model (LLM)-based TTS systems exhibit strong cross-lingual generalization, they provide limited explicit control over accent characteristics and intensity. In this paper, we propose CrossAccentTTS, a framework that enables both accent control and conversion while preserving speaker identity. Specifically, we introduce an Accent Intensity Controller (AIC) that injects weighted language embeddings into the accent subspace, allowing smooth interpolation between accents and fine-grained modulation of accent strength at inference time. Experiments on the Indic Multilingual and L2-arctic datasets shows that CrossAccent-TTS achieves precise control of accent intensity, outperforming strong baselines in accent similarity and controllability by maintaining speaker similarity and naturalness.
arXiv:2606.25811v1 Announce Type: cross Abstract: Commodity futures can be represented hierarchically, with underlying assets at the upper level and individual futures contracts at the lower level. Entities at each level can be connected by edges reflecting inherent correlations, with cross-level edges capturing contract-to-underlying asset connections. Building on our observations of these structures, we propose a hierarchical graph learning approach for calendar spread (CS) strategies in commodity futures markets, addressing two significant gaps in the machine-learning literature: (i) the absence of learning-based methods for CS strategies in futures markets, and (ii) the lack of consideration of maturity-dependent interrelationships across commodity futures. We first establish the efficacy of CS strategies by analytically showing that CS strategies can possess higher risk-adjusted returns, measured by the information ratio, and lower risk, measured by variance and delta, than long-only strategies. We then introduce a method to convert learning-based predictions into CS positions. Next, we develop a hierarchical graph learning method that predicts futures price movements by utilizing the maturity-dependent interrelationships, thereby yielding a CS trading algorithm. Empirical results on commodity futures markets traded on the Chicago Mercantile Exchange Group demonstrate that our method outperforms benchmark models in both prediction and trading performance. We find that maturity-dependent interrelationships across commodity futures are instrumental in prediction and that CS trading based on hierarchical graph learning is effective for statistical arbitrage.
arXiv:2606.25862v1 Announce Type: cross Abstract: The critical current of a type-II superconductor is controlled by vortex pinning, whose microscopic input is the elementary pinning force. Scanning tunneling spectroscopy has shown that a defect pins a vortex by reorganizing the Caroli-de Gennes-Matricon (CdGM) states in its core, but why this spectral reorganization amounts to a pinning force has lacked a quantum-mechanical, first-principles account. Here we establish a transferable first-principles computational framework for elementary vortex pinning, in which defect-resolved DFT/Wannier electronic structures are embedded into a finite-box projected Bogoliubov-de Gennes free-energy formalism to convert quasiparticle spectral reorganization into vortex-pinning energies and forces. Using this framework, we confirm that the defect-induced reorganization of the vortex-core spectrum is the microscopic origin of the elementary pinning force. The force is evaluated as a finite-box vortex-insertion free energy whose four-configuration subtraction isolates the meV-scale interaction from much larger backgrounds. With the superconducting gap scale and vortex-core profile fixed from experiments, the FeSe Fe-site vacancy reproduces the microscopic STM value together with the measured spectral reorganization. All five point defects in FeSe and FeTe pin attractively, with FeTe Te-site vacancy strongest. Elementary vortex pinning thereby becomes a computable electronic-structure quantity, opening the first-principles screening of point defects toward higher critical currents.
arXiv:2606.26023v1 Announce Type: cross Abstract: The altermagnetic nature of rutile RuO2 remains under active debate: bulk measurements indicate a nearly nonmagnetic ground state, whereas thin-film studies have reported symmetry-dependent transport signatures consistent with altermagnetism. Here, we provide experimental evidence that altermagnetic spin splitting in RuO2 is a strain-stabilized emergent state rather than an intrinsic bulk property. Angular-resolved spin-torque measurements reveal a symmetry-selected spin Hall response characteristic of altermagnetic spin splitting, which is strongest in the strained regime but progressively suppressed as the lattice relaxes toward the bulk limit. Complementary magnetic measurements further reveal enhanced coercivity and exchange-bias behavior exclusively in strained films, indicating the emergence of a strain-stabilized magnetic state. First-principles calculations reproduce the strain-dependent evolution of the Neel order and spin-split electronic structure, supporting the experimental observations. Together, these results establish altermagnetic spin splitting in RuO2 as a strain-stabilized emergent state and provide a unified explanation for the long-standing discrepancy between bulk and thin-film observations.
arXiv:2606.26037v1 Announce Type: cross Abstract: Federated learning has emerged as the foremost approach for decentralized model training with privacy preservation. The global class imbalance and cross-client data heterogeneity naturally coexist, and the mismatch between local and global imbalances exacerbates the performance degradation of the aggregated model. The agnosticism of global class distribution poses significant challenges for data-level methods, especially under extreme conditions with severe class absence across clients. In this paper, we propose FedReLa, a novel data-level approach that tackles the coexistence of data heterogeneity and class imbalance in federated learning. By re-labeling samples with a feature-dependent label re-allocator, FedReLa corrects biased global decision boundaries without requiring knowledge of the global class distribution. This modular, model-agnostic approach can be integrated with algorithmic methods to deliver consistent improvements without additional communication overhead. Through extensive experiments, our method significantly improves the accuracy of minority classes and the overall accuracy on stepwise-imbalanced and long-tailed datasets, outperforming the previous state of the art.
arXiv:2606.26053v1 Announce Type: cross Abstract: Synthetic data augmentation is widely used to mitigate class imbalance, but its theoretical effects on score-based classification remain poorly understood. This paper develops a framework for characterizing when synthetic minority augmentation can improve threshold-integrated and threshold-optimized metrics, including AUROC, AUPRC, best-threshold balanced accuracy, and best-threshold \(\F_1\) score. We separate the effect of augmentation into two components: a change in effective class weighting and a discrepancy between the synthetic and true minority distributions. Under well-specified score models, the raw estimator already targets the likelihood-ratio ordering, which is population-optimal for the metrics considered. Consequently, augmentation cannot provide a fundamental population-level improvement beyond possible finite-sample variance reduction, and may introduce additional bias through synthetic distributional error. We further establish minimax lower bounds showing that the raw estimator already achieves the optimal metric-regret rate in the well-specified regime. Under misspecification, however, augmentation can play a qualitatively different role: by changing the effective class balance, it can alter the restricted-class projection and correct ranking errors induced by the raw imbalanced objective. We provide explicit improvement bounds quantifying the roles of approximation error, finite-sample estimation error, and synthetic distributional error. Simulation studies corroborate the theory, demonstrating limited gains under well-specification and nontrivial but nonmonotone improvements under misspecification.
arXiv:2507.00028v2 Announce Type: replace Abstract: The representation of urban trajectory data plays a critical role in effectively analyzing spatial movement patterns. Despite considerable progress, the challenge of designing trajectory representations that can capture diverse and complementary information remains an open research problem. Existing methods struggle in incorporating trajectory fine-grained details and high-level summary in a single model, limiting their ability to attend to both long-term dependencies while preserving local nuances. To address this, we propose HiT-JEPA (Hierarchical Interactions of Trajectory Semantics via a Joint Embedding Predictive Architecture), a unified framework for learning multi-scale urban trajectory representations across semantic abstraction levels. HiT-JEPA adopts a three-layer hierarchy that progressively captures point-level fine-grained details, intermediate patterns, and high-level trajectory abstractions, enabling the model to integrate both local dynamics and global semantics in one coherent structure. Extensive experiments on multiple real-world datasets for trajectory similarity computation show that HiT-JEPA's hierarchical design yields richer, multi-scale representations. Code is available at: https://anonymous.4open.science/r/HiT-JEPA.
arXiv:2602.04109v2 Announce Type: replace Abstract: Conversational AI agents are increasingly explored as creative partners, yet how conversation design shapes child-AI dialogue in co-creative settings remains underexplored. We present Tinker Tales, a tangible dialogue system for child-AI collaborative storytelling, in which educational frameworks (narrative development and social-emotional learning) are instantiated as conversation design, shaping how the agent engages children across four narrative stages. The system combines a physical storytelling board, NFC-embedded toys, and a mobile app mediating multimodal interaction through tangible manipulation and voice-based dialogue. We conducted a home-based user study with 10 children (ages 6-8) across two conversation design conditions varying in how the agent structured elaboration, with and without educational scaffolding. Our findings show that prompt framing shapes the form and consistency of children's narrative contributions, structuring how they participate in co-creative dialogue with AI.
arXiv:2602.05977v2 Announce Type: replace Abstract: We introduce Clifford Kolmogorov-Arnold Network (ClKAN), a flexible and efficient architecture for function approximation in arbitrary Clifford Algebra spaces. We propose the use of Randomized Quasi-Monte Carlo grid generation as a solution to the exponential scaling associated with higher-dimensional algebras. Our ClKAN also introduces new batch normalization strategies to deal with variable domain input. ClKAN finds application in scientific discovery and engineering, and is validated in synthetic and physics-inspired tasks.
arXiv:2602.11933v2 Announce Type: replace Abstract: End-to-End Speech Translation (E2E-ST) has seen significant advancements, yet current models are primarily benchmarked on curated, "clean" datasets. This overlooks critical real-world challenges, such as morphological robustness to inflectional variations common in non-native or dialectal speech. In this work, we adapt a text-based adversarial attack targeting inflectional morphology to the speech domain and demonstrate that state-of-the-art E2E-ST models are highly vulnerable it. While adversarial training effectively mitigates such risks in text-based tasks, generating high-quality adversarial speech data remains computationally expensive and technically challenging. To address this, we propose Cross-Modal Robustness Transfer (CMRT), a framework that transfers adversarial robustness from the text modality to the speech modality. Our method eliminates the requirement for adversarial speech data during training. Extensive experiments across four language pairs demonstrate that CMRT improves adversarial robustness by an average of more than 3 BLEU points, establishing a new baseline for robust E2E-ST without the overhead of generating adversarial speech.
arXiv:2602.12390v2 Announce Type: replace Abstract: We study neural networks with trainable low-degree rational activation functions and show that they are more expressive and parameter-efficient than modern piecewise-linear and smooth activations such as ELU, LeakyReLU, LogSigmoid, PReLU, ReLU, SELU, CELU, Sigmoid, SiLU, Mish, Softplus, Tanh, Softmin, Softmax, and LogSoftmax. For an error target of $\varepsilon>0$, we establish approximation-theoretic separations: Any network built from standard fixed activations can be uniformly approximated on compact domains by a rational-activation network with only $\mathrm{poly}(\log\log(1/\varepsilon))$ overhead in size, while the converse provably requires $\Omega(\log(1/\varepsilon))$ parameters in the worst case. This exponential gap persists at the level of full networks and extends to gated activations and transformer-style nonlinearities. In practice, rational activations integrate seamlessly into standard architectures and training pipelines, allowing rationals to match or outperform fixed activations under identical architectures and optimizers.
arXiv:2602.20359v3 Announce Type: replace Abstract: We present StochasticBarrier.jl, an open-source Julia-based toolbox for generating Stochastic Barrier Functions (SBFs) for safety verification of discrete-time stochastic systems with additive Gaussian noise. StochasticBarrier.jl certifies linear, polynomial, and piecewise affine (PWA) systems. The latter enables verification for a wide range of system dynamics, including general nonlinear types. The toolbox implements a Sum-of-Squares (SOS) optimization approach, as well as methods based on piecewise constant (PWC) functions. For SOS-based SBFs, StochasticBarrier.jl leverages semi-definite programming solvers, while for PWC SBFs, it offers three engines: two using linear programming (LP) and one based on gradient descent (GD). Benchmarking StochasticBarrier.jl against the state-of-the-art shows that the tool outperforms existing tools in computation time, safety probability bounds, and scalability across over 30 case studies. Compared to its closest competitor, StochasticBarrier.jl is up to four orders of magnitude faster, achieves significant safety probability improvements, and supports higher-dimensional systems.
arXiv:2602.20960v3 Announce Type: replace Abstract: Capturing ultrafast spin and charge photocurrents on nanoscopic scales is essential for fundamental research in physics and engineering, as well as for future applications, such as novel spinorbitronic devices. Accessing the fundamental dynamics driven by changes in electronic energy, linear momentum, and angular momentum requires probing at its native spatiotemporal scales: femtoseconds and nanometers. However, experimental approaches achieving this simultaneous resolution remain scarce and instrumentally demanding. Near-field probing offers promising platforms to combine ultrafast and nanometer resolution typically with high sensitivity to out-of-plane electric fields. However, applying this technique to in-plane ultrafast coupled spin and charge currents is largely unexplored, although being highly application-relevant - from ultrafast spin transport in 2D materials to spin-to-charge conversion in spintronic terahertz emitters (STEs). Here, we fill this gap by performing spatiotemporal terahertz (THz) emission nanoscopy (TEN) of a photoexcited fiber-coupled STE using a scanning-probe microscope. We uncover a counterintuitive, dipolar spatial evolution of the near-field THz signal, which we show originates from the out-of-plane electric fields emerging from the in-plane spin-driven charge currents. Our findings explain why TEN is sensitive to ultrafast spin-driven in-plane charge currents, paving the way for TEN to become a fully vectorial probe for the spatiotemporal mapping of coupled nanoscale THz charge and spin dynamics.
arXiv:2602.21151v3 Announce Type: replace Abstract: Understanding the locality of high-temperature plasma energy deposition on material surfaces in fusion reactors is critical for design. Here, we utilize the Gyrokinetic ElectroMagnetic turbulence including X-points (GEMX) simulation, together with SOLPS-ITER solutions for the background equilibrium electric field including drifts, to model the heat flux at the divertor plate and characterize the heat load width using realistic X-point geometry. We use a theory-based blobby transport model called the "Coherent Structure Transport" (CST) model to include the effect of plasma transport in the edge scrape-off layer. The CST model is extremely fast and can be used to quickly analyze any SOLPS-ITER solution. SOLPS-ITER provides the steady state, or equilibrium on which we superimpose blobby turbulence characterized by blob size, amplitude and frequency. We obtain the $1/B_p$ scaling of the heat load exponential decay width $\lambda_q$, in agreement with the Eich empirical scaling and with the Goldston heuristic theory. When including blobby turbulence in combination with the SOLPS-ITER electric field, we find a secondary peak in the heat flux radial profile, outwardly displaced from the strike point radius, with a relative amplitude that increases with the initial blob density. We describe the CST model in detail and provide initial investigations of the scaling of $\lambda_q$ and the secondary heat flux peak with blob size and amplitude.
arXiv:2602.21996v3 Announce Type: replace Abstract: Numerical simulations of contaminant dispersion after a gas leakage incident on a chemical plant can provide valuable insights for both emergency response and preparedness. Simulation approaches combine incompressible Navier-Stokes (INS) equations with advection-diffusion (AD) processes to model wind and concentration field. However, the computational cost of such high-fidelity simulations increases rapidly for complex geometries like urban environments, making them unfeasible in time-critical or multi-query "what-if" scenarios. Therefore, this study focuses on the application of model order reduction (MOR) techniques enabling fast yet accurate predictions. To this end, a thorough comparison of intrusive and non-intrusive MOR methods is performed for the computationally more demanding parametric INS problem with varying wind velocities. Based on these insights, a non-intrusive reduced-order model (ROM) is constructed accounting for both wind velocity and direction. The study is conducted on a two-dimensional domain derived from real-world building footprints, preserving key features for analyzing passive transport across urban areas. The resulting ROM enables faster than real-time predictions of spatio-temporal contaminant dispersion from an instantaneous source under varying wind conditions. This capability allows assessing wind measurement uncertainties by a Monte Carlo analysis. To demonstrate the practical applicability, an interactive dashboard provides intuitive access to simulation results.
arXiv:2603.29591v2 Announce Type: replace Abstract: Every day, many people die under violent circumstances, whether from crimes, war, migration, or climate disasters. Medico-legal and law enforcement institutions document many portraits of the deceased for evidence, but cannot immediately carry out identification on them. While traditional image editing tools can process these photos for public release, the workflow is lengthy and produces suboptimal results. In this work, we leverage advances in image generation models, which can now produce photorealistic human portraits, to introduce FlowID, an identity-preserving facial reconstruction method. Our approach combines single-image fine-tuning, which adapts the generative model to out-of-distribution injured faces, with attention-based masking that localizes edits to damaged regions while preserving identity-critical features. Together, these components enable the removal of artifacts from violent death while retaining sufficient identity information to support identification. To evaluate our method, we introduce InjuredFaces, a novel benchmark for identity-preserving facial reconstruction under severe facial damage. Beyond serving as an evaluation tool for this work, InjuredFaces provides a standardized resource for the community to study and compare methods addressing facial reconstruction in extreme conditions. Experimental results show that FlowID outperforms state-of-the-art open-source methods while maintaining low memory requirements, making it suitable for local deployment without compromising data privacy.
arXiv:2603.29919v2 Announce Type: replace Abstract: LLM-based coding agents rely on \emph{skills}, pre-packaged instruction sets that extend agent capabilities, yet every token of skill content injected into the context window incurs both monetary cost and attention dilution. To understand the severity of this problem, we conduct a large-scale empirical study of 55,315 publicly available skills and find systemic inefficiencies: 26.4\% lack routing descriptions entirely, over 60\% of body content is non-actionable, and reference files can inject tens of thousands of tokens per invocation. Motivated by these findings, we present \textsc{SkillReducer}, a two-stage optimization framework. Stage~1 optimizes the routing layer by compressing verbose descriptions and generating missing ones via adversarial delta debugging. Stage~2 restructures skill bodies through taxonomy-driven classification and progressive disclosure, separating actionable core rules from supplementary content loaded on demand, validated by faithfulness checks and a self-correcting feedback loop. Evaluated on 600 skills and the SkillsBench benchmark, \textsc{SkillReducer} achieves 48\% description compression and 39\% body compression while improving functional quality by 2.8\%, revealing a \emph{less-is-more} effect where removing non-essential content reduces distraction in the context window. These benefits transfer across five models from four families with a mean retention of 0.965, and generalize to an independent agent framework.
arXiv:2605.02831v3 Announce Type: replace Abstract: We develop a unified analytical and computational framework for the generalized Abel ordinary differential equation $y^{\prime }(x)=a_n(x)\bigl(% y^n+\lambda_{n-1}(x)y^{n-1}+\dots+\lambda_0(x)\bigr)$ of arbitrary degree $% n\ge1$ on the unbounded interval $[x_0,\infty)$. Under mild structural hypotheses on the coefficients and on the existence of a stable moving equilibrium branch $E(x)$, we prove a new \emph{Asymptotic Plateau Theorem} establishing that the solution issued from $y(x_0)=0$ is globally defined, strictly monotone, trapped between zero and $E(x)$, and converges to a finite positive limit $L=\lim_{x\to\infty}E(x)$. We further obtain an explicit, computable rate of convergence and a degree-reduction principle that generalizes the classical Liouville substitution. The theory is complemented by a high-order Radau IIA implementation whose output reproduces the predicted plateaus to nine significant digits. A detailed application to a generalized Merton structural credit-risk model derives an Abel-type equation for the long-maturity state profile of the credit spread and illustrates the economic relevance of the framework.