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arXiv2026

Re-interpreting the GRS 1915+105 observations within the variable TADAF scenario

The Galactic microquasar GRS 1915+105 is one of the most interesting X-ray binary systems, exhibiting an exceptionally diverse range of observational phenomena. It displays the most complicated and variable X-ray light curves and carries superluminal radio jets. Its X-ray and radio fluxes change on very different timescales, from seconds to minutes to days and even longer. In recent years, its jet has also displayed large position angle shifts. We find that most of the observational phenomena can be well explained within our newly developed variable turbulent ADAF (TADAF) model. The accretion disk is composed of an outer thin disk and an unstable inner TADAF torus whose size is variable. The previously suggested 'disappearance' and regain of the inner disk is understood as the transition between the thick TADAF and the thin disk. Some types of QPOs are understood in terms of the radius change of the TADAF torus. The jet position angle shift is understood as the direct sideways frame-dragging on the jet by the Lense-Thirring effect from a tilted, spinning black hole. The slower the outshooting jet, the larger the angle shift. We note that such an effect also applies to other sources, such as V404 Cygni and the AGN M87. This mechanism may also be applicable to the famous 'precessing' jet in SS 433.

astro-ph.HE↗
arXiv2026

Chondrule size averaging in two and three dimensions

Chondrule sizes are an important discriminant of chondrite groups and chondrule formation theories. Yet most studies report 2D sizes without attempting the somewhat tedious corrections to 3D proposed in the past literature. I show here that 3D size averages can be simply calculated directly from 2D averages of appropriate powers of sizes (and vice-versa), without having to reconstruct 3D distributions, although explicit formulas to that end are also provided. This illuminates the comparison between 3D and 2D arithmetic size averages, which are confirmed to be little different for the published datasets. Yet I suggest another type of average, the "sphere-weighted average" (i.e. weighted by the chondrule equal-volume sphere area), a measure of the surface/volume ratio of the chondrule population, which is more robust against omission of small chondrules. While larger than the arithmetic averages, it is best in line with previous literature estimates based on less exhaustive surveys of chondrules.

astro-ph.EP↗
arXiv2026

On an infinite family of cubic fields with explicit fundamental units

For an integer $b\neq0,1$ let $θ$ be the unique real root of $f_b(x)=x^3-3bx-b^3$ and let $K_b=\mathbb{Q}(θ)$. We exhibit an explicit set of $b$ of positive density for which $η_b=-1/(θ-(b+1))$ is the fundamental unit of $K_b$, and we determine the set of $b$ for which $η_b$ is the square of a unit: it is parametrized by the Pell equation $D^2-3E^2=1$, hence infinite, and under an explicit mild condition on the field discriminant it accounts for all $b$ for which $η_b$ is not the fundamental unit. That condition fails for only four $b$ with $|b|\le3000$, and at one of them, $b=3$, the conclusion itself fails. In the order $\mathbb{Z}[η_b]$ generated by $η_b$, by contrast, $η_b$ is the fundamental unit for every $b$, so these exceptions are a phenomenon of the maximal order. As an application we construct infinitely many biquadratic fields whose $3$-class field tower has length greater than $1$.

math.NT↗
arXiv2026

FedSocket: Recipient-Executable Knowledge Exchange for Heterogeneous Multimodal Federated Learning

Federated knowledge must remain usable by recipients with different modalities, private architectures, and tasks. We present FedSocket, which makes recipient execution a design requirement of the exchanged model. A shared Q combines recipient-computable inputs, task-owned outputs, and ownership-aware aggregation, connecting heterogeneous private models through a common prediction interface. Private models teach local Q copies; the returned Q supports local learning and Joint inference, with only Q parameters and counts exchanged. Across six datasets, FedSocket improves missing-modality recipient accuracy over Local by 14.44 and 15.51 percentage points on MELD and UCF-51. Under matched inference capacity, Joint exceeds independent ensembles by 11.06 points in UCF-51 accuracy and 4.87 points in mean bidirectional Flickr30k R@1. Joint also improves over Q alone on all four heterogeneous endpoints, demonstrating the value of combining local and exchanged predictions. Teacher controls, sharing-path interventions, and component factorials identify the roles of supervision, sharing, and deployment. FedSocket makes exchanged knowledge directly usable from federated training to recipient inference.

cs.CV↗
arXiv2026

RLTLDR: Self-improvement by Internalizing Self-generated Feedback

The common paradigm of reinforcement learning with verifiable rewards (RLVR) is to let agents make multiple attempts at a task, and optimize towards the successful ones. This becomes problematic in the realms of self-improvement, where tasks are so difficult that the agent has a low or even no chance of success, and where there are no teacher models or example solutions to distill from. In this paper, we introduce RLTLDR. After each failed attempt, we show the policy the verifier outputs and let it write its own feedback, in the form of a single TL;DR insight. The next rollout is conditioned on all previous insights, and we sequentially sample rollouts until a solution is found. Moreover, we enable backpropagation on the in-context insights to internalize a direct task to insight mapping. On challenging tool-calling and coding datasets (filtered to Pass@128=0), standard GRPO training of a Qwen 3.5 9B Thinking policy stays flat at a Pass@1 of 0% to 1%. RLTLDR breaks through this learning barrier, achieving a Pass@1 of 14-31% with insights in context during training and, crucially, 12-13% when no insight is in context at eval time. We identify that the key is the task to insight internalization. To study this further, we reduce our approach to SFTLDR, training only on (task, insight) tuples, without showing or backpropagating on any rollouts. Training on only 4k of these tuples recovers almost the full performance of RLTLDR and classical SFT on full rollouts. This demonstrates a promising compacted training paradigm of the form "on this sort of task, keep this sort of thing in mind", which we hope to inspire future research on.

cs.LG↗
arXiv2026

Mutual Information Constrained Chernoff Bottleneck

The classical information bottleneck (IB) measures the relevance of a representation $U$ of $X$ to a target $Y$ by $I(U;Y)$, which does not directly characterize the error of downstream decisions. For a binary hypothesis $Y$ inferred from many separately encoded observations, the optimal error exponent is the Chernoff information between the two conditional distributions of $U$ given $Y$. We study the mutual information constrained Chernoff bottleneck, which seeks an encoder that maximizes this Chernoff information subject to a rate constraint $I(U;X) \leq R$. We show that its optimal value $C(R)$ increases strictly up to $R = H(V)$, where $V$ merges the symbols of $X$ with equal likelihood ratio, remains at the uncompressed exponent beyond, and, unlike the IB curve, need not be concave. We further show that $k+1$ outputs suffice to attain $C(R)$, where $k$ is the cardinality of $V$. We propose an alternating algorithm that updates the encoder via a generalized Blahut--Arimoto algorithm and the Chernoff parameter $s$ via a nonlinear equation, and prove that its iterates remain feasible, with nondecreasing and convergent Chernoff information. Comparing with the classical IB for $n$ samples, we show that, whenever the two objectives disagree, the IB encoder has the smaller equivocation $H(Y|U^{n})$ at $n = 1$, whereas the Chernoff bottleneck has the smaller error probability and equivocation for all large $n$. Numerical experiments confirm the theory, and on real topic-detection data from the 20 Newsgroups corpus, compressing each word to only $17\%$ of its entropy retains $90\%$ of the error exponent and nearly the accuracy of the uncompressed classifier.

cs.IT↗
arXiv2026

Retargeting Motions to Diverse Skeletons via Learnable Flattening

Cross-structural motion retargeting aims to transfer motion between different skeletal topologies. Despite recent progress, existing state-of-the-art models struggle with reliability in zero-shot settings, i.e. skeletons with different topologies which were unseen during training, and recent Transformer-based attempts have failed to outperform specialized geometric methods. We bridge this gap with a Transformer Autoencoder that learns a topology- and translation-invariant latent space. Our core contribution is a learnable flattening of skeletal graphs that captures both local dependencies and global structure. Unlike the standard transformer architecture, which adds positional information to token content, we integrate graph-based positional encodings multiplicatively, a design choice that follows directly from our flattening formulation. The resulting model handles diverse skeletal topologies within a single unified architecture and trains in a fully unsupervised manner, requiring no paired retargeting data. Ablation studies show, that the graph encodings, multiplicative formulation, and Transformer backbone is critical for the performance. In zero-shot evaluations, our method reduces global joint position error by $43-47\%$ over current benchmarks. A user study ($n = 37$), including expert animators, further ranks our approach highest in motion alignment and physical plausibility ($p < 0.05$). These results demonstrate that our model design is key to making transformer architectures effective for motion retargeting, outperforming existing approaches.

cs.CV↗
arXiv2026

Generalized Fiducial Inference for Hybrid Discrete-Continuous Count Data: Theory and Application

High-frequency athlete-tracking data can be summarized as quantile cubes (Thomas and Hannig, 2026): counts of time spent in bins of velocity, acceleration, and movement angle. In our application, each athlete-match session has 100 such bins, with counts ranging from under a hundred to several thousand. Whether a bin's negative binomial distribution is well approximated by a normal distribution depends on its shape parameter, the product of its mean and dispersion, rather than on the count alone. We develop a hybrid generalized fiducial framework that uses exact negative binomial structural equations where the estimated shape is small and moment-matched normal approximations where it is large. This approach provides uncertainty quantification for hundreds of regression and dispersion parameters without specifying a prior distribution. Only the normal components contribute to the fiducial Jacobian, which has a closed-form block-diagonal structure, and we prove a Bernstein-von Mises theorem for the correctly specified hybrid model. Simulations show near-nominal coverage, agreement with a flat-prior Bayesian analysis, and the importance of partitioning by estimated shape rather than by the mean or observed responses. In 216 sessions from 17 professional women's soccer athletes, the estimated position effects concentrate at the velocity extremes, while the estimated age effects follow an acceleration gradient. However, an athlete-level permutation check indicates that these patterns are not distinguishable from those obtained under athlete-label permutations.

stat.ME↗
arXiv2026

Marking Contour Tones in Yorùbá: A Typographic and Computational Proposal

Yorùbá is a tonal language in which contour tones pose persistent orthographic challenges. These are especially notable for personal names and lexical items whose conventional spellings avoid vowel lengthening that would otherwise provide a host syllable for the second tone. A particular concern is a class of names in which the conventional spelling does not just omit tonal information but inverts the meaning of said name, sometimes asserting the opposite of what the name intends. This paper describes the problem, illustrates the inadequacy of current solutions, and proposes the adoption of the caron and circumflex marks. These are symbols with precedent in Yorùbá phonological scholarship since Olmsted (1951), used as orthographic conventions on single vowels to encode rising and falling contour tones, making them accessible for the first time through standard keyboard input and computational text processing. The proposal is supported by an implementation in the WriteYoruba keyboard and the TTSYoruba speech synthesizer, whose architecture and listener evaluation are reported separately (Tubosun et al., 2026).

cs.CL↗
arXiv2026

Distill the Visual Evidence, Not Just the Answer: Cross-World On-Policy Distillation for Vision-Language Models

A central goal of vision-language model (VLM) distillation is to transfer both the teacher's language capabilities and its visual understanding. However, existing methods primarily supervise the student's output, leaving visual understanding implicit. Our analysis reveals that a student can match the teacher's answer without relying on the same visual evidence, raising the question: how can we ensure the student responds to the visual information that actually determines the answer? To this end, we propose \textbf{Cross-World On-Policy Distillation (CW-OPD)}, which explicitly supervises the student's response to changes in visual evidence. For each example, CW-OPD constructs two visual worlds that share the question and scene context but differ in answer-critical evidence, yielding different answers. We perform on-policy distillation in both worlds and distill the teacher's cross-world belief transition, encouraging the student to match not only \emph{what} the teacher predicts but also \emph{why} its prediction changes with the evidence. A gradient analysis shows that this term is invariant to errors shared by both worlds and supplies a corrective signal invisible to endpoint matching alone. In this way, CW-OPD makes reliance on the relevant visual evidence an explicit distillation target rather than an implicit consequence of output matching. To diagnose whether a model truly grounds its answers in visual evidence, we introduce CWBench, which measures cross-world consistency via Cross-World Pair Accuracy (CWPA). Experiments on Qwen3.5-4B show that CW-OPD outperforms the strongest baseline by \textbf{1.2} points on average, and the 4B student exceeds DeepSeek-V4.1 (552B) by \textbf{22.4} CWPA points on CWBench. Code is released in https://github.com/baokou-fw2/CWAD.

cs.CV↗
arXiv2026

MADGRAV: a multilevel anomaly-detection pipeline for gravitational-wave searches applied to LIGO data

We present the results of \textbf{MADGRAV}, a deep-learning-based search for high-mass compact binary coalescences, applied to the data collected by the LIGO interferometers during the third observing run and during the first and second part of the fourth observing run. The \textbf{MADGRAV} pipeline consists of a series of sequential convolutional neural networks that perform anomaly detection, glitch classification, coherence testing, and signal ranking. Data from the Hanford and Livingston LIGO detectors are studied (both individually and in coherence) by way of 1 second Q-transform windows. Of the candidates that survive every stage of the pipeline, 48 reach the significance threshold, and we report 47 gravitational wave detections characterised by a false alarm rate below $1\,{\rm yr}^{-1}$ with a probability of astrophysical origin $p_{\rm astro}>0.9$. Of the 47 detections, 44 are shared with the minimally modelled coherent WaveBurst search. The observed total source-frame masses, extracted from official gravitational wave transient catalogues, are in the $14-236 M_{\odot}$ range with a median of $69 M_{\odot}$, and a median SNR of 16. We note that the recovered fraction of confident detections rises with mass: for LIGO detectors network SNR $>10$ the pipeline recovers $8.1\%$ of confident catalog events below $30 M_{\odot}$, $39.8\%$ between $30$ and $100 M_{\odot}$, and $53.3\%$ above $100 M_{\odot}$, corresponding to $33.3\%$, $45.5\%$ and $53.3\%$ of the events detected by coherent WaveBurst in the same bins. These results suggest that anomaly detection pipelines can serve as an independent detection channel complementary to matched filtering in the high-mass high-SNR regime.

gr-qc↗
arXiv2026

Quantum--classical break-even in electronic dynamics of macrocyclic molecules

Here we demonstrate quantum--classical break-even for chemical dynamics applications, reaching useful accuracy with a quantum-hardware wall-clock time comparable to that estimated for practical classical computing resources. To this end, we develop a workflow for problems that are hardware-native but classically hard. We target large ring-shaped molecules that map naturally onto quantum hardware with neighboring connections. Exploiting the spatial locality of interactions, we compress short-time evolution within a small region using tensor networks. We then use rotational symmetry to replicate the compressed circuit in space and time, enabling long-time dynamics of large systems with practical classical processing times. We apply the workflow to conjugated macrocycles with rotational periodicity, 12-qubit benzene and 120-qubit [60]annulene, by embedding their electronic structure onto loops of IBM quantum processors. For the annulene, we compared the quantum-processing-unit (QPU) wall-clock times for hole-doped nonequilibrium dynamics to the estimated wall-clock time of two state-of-the-art classical methods, Majorana propagation and matrix-product-state time evolution based on the time-dependent variational principle. We show a situation in which a hybrid quantum--classical strategy is comparable to a classical-only counterpart in terms of both accuracy and computational time for a conventional high-performance computing system under ideal parallelization. These results show that quantum hardware can become a realistic computational option for chemical simulations for practitioners in chemical science and engineering.

quant-ph↗
arXiv2026

On a question of Jones on tracelike vectors, cusp forms, and von Neumann algebras

Using the theory of von Neumann algebras, Vaughan Jones showed abstractly that there is a bridge between holomorphic cusp forms and random matrices. This bridge is supplied by a distinguished function he called a {\it tracelike vector}. He posed the following problem: construct a tracelike vector to make this bridge explicit. We carry out Jones' vision for the full modular group. We construct holomorphic tracelike vectors for every finite-covolume Fuchsian group throughout the permissible Bergman range. For the modular group at the critical parameter $s=13$, we use the resulting unit tracelike vector to assign explicit group coefficients to cusp form multiplication operators, and form positive finite random matrices from a shared Haar-distributed unitary matrix. Almost surely, their normalised traces recover all joint operator moments, first as the matrix size tends to infinity, and then as the group-word cutoff tends to infinity. We also identify the limiting mixed second moment with a series of Petersson norms that involve Maass-Shimura operators of cusp forms. The exact nature of our use of AI is detailed in the introduction.

math.NT↗
arXiv2026

Towards breaking the degeneracy between stellar ages and unresolved multiplicity

Stellar age is the central desirable parameter we need to disentangle different Galactic formation scenarios. Nevertheless, no stellar age dating method is completely model-independent. Even in the best-case scenarios, present-day stellar age estimates are only precise to $\sim7\%$ and accurate to $\sim10-15\%$. A main drawback of state-of-the-art stellar parameter inference codes like {\tt StarHorse} is that they do not take into account unresolved stellar multiplicity. Especially in the case of nearly equal-mass binaries or higher-order systems on the main sequence, properly taking into account unresolved multiplicity is imperative for the next generation of stellar surveys. Simulation-based inference (SBI) is a robust and flexible approach for dealing with complex models where traditional likelihood-based methods become unfeasible. Here we sketch how SBI can be used to obtain precise stellar ages, masses, binary mass ratios, and other stellar parameters from spectroscopic, photometric, and astrometric measurements.

astro-ph.SR↗
arXiv2026

Spectra of Random Polynomial Matrices: the Petaloid Law

We study the distribution of the zeros of $\det P_N(z)$ where $P_N(z)$ is a random monic polynomial matrix, i.e., $P_N(z)=z^dI-\sum_{j=0}^{d-1}A_{j,N}z^j$ for possibly coupled random matrices $A_{j,N}$, scaled to have entrywise variance $O(1/N)$. We provide general conditions under which this distribution almost-surely weakly converges as $N\to\infty$ to a deterministic measure, depending on just the variance and covariance of the entries of the $A_j$. This generalizes the circular, elliptic, and semicircle laws, which concern the special case of this question where $d=1$. Unlike those classical laws, these measures can combine nonuniform two-dimensional densities with singular components supported on curves, producing a variety of petal-shaped regions, inspiring our name ``the petaloid law''. We give explicit formulas for the limiting densities and supports. Under a Gaussianity assumption, we also show that there are almost surely no eigenvalues outside small neighborhoods of the limiting support.

math.PR↗
arXiv2026

Sharp Fresh-Gradient Complexity of Nonconvex-Strongly-Concave Minimax Optimization

We characterize the fresh-gradient oracle complexity of smooth nonconvex-strongly-concave minimax optimization, with matching upper and lower bounds up to logarithmic factors. Let $Φ(x)=\max_y f(x,y)$, where $f$ is jointly $L$-smooth and $μ$-strongly concave in $y$ on unconstrained Euclidean domains, and set $κ=L/μ$. Each query returns a fresh unbiased joint gradient with conditional variance at most $σ^2$. Given initial primal gap at most $Δ$ and dual residual $\|\nabla_y f(x_0,y_0)\|\le G$, the fixed-budget complexity of finding $\|\nablaΦ(\widehat x)\|\leε$ with probability at least $2/3$ is $\widetildeΘ(\sqrtκLΔ/ε^2+κLΔσ^2/ε^4+κ^2σ^2/ε^2+\sqrtκ\log_+(G/(ε\sqrtκ)))$, where $\log_+u=\log\max\{1,u\}$. This characterization holds when $κ$ and $LΔ/ε^2$ exceed universal constants, uniformly over finite dimensions, and the suppressed logarithms are independent of $G$. It establishes the necessity of linear condition-number dependence in the global stochastic cost and identifies a separate statistical refinement cost. A proximal method separates coarse primal progress from one final refinement, while the lower bounds apply to arbitrary adaptive randomized algorithms. Dual initialization contributes only an additive logarithmic cost, yet removing its control eliminates every finite dimension-free complexity bound, even with exact gradients.

math.OC↗
arXiv2026

Matching Lower Bounds for Randomized First-Order Methods in Hessian-Lipschitz Nonconvex Optimization

We establish a randomized first-order lower bound for finding an $ε$-stationary point, $\|\nabla f(x)\|\le ε$, of a nonconvex function with initial gap at most $Δ$, $L_1$-Lipschitz gradient, and $L_2$-Lipschitz Hessian. Each oracle call returns the exact function value and gradient. Let $Q_{\mathrm{rand},\mathrm{FO}}^{\infty}(ε;Δ,L_1,L_2)$ denote the minimax number of calls, maximized over finite dimensions, for arbitrary adaptive randomized algorithms with per-instance success probability at least $2/3$. In the regime $ε\lesssim L_1^2/L_2$ and $ΔL_2^{1/2}ε^{-3/2}\gtrsim 1$, we prove $ Q_{\mathrm{rand},\mathrm{FO}}^{\infty}(ε;Δ,L_1,L_2) \ge c\,ΔL_1^{1/2}L_2^{1/4}ε^{-7/4}, $ where $c>0$ is an absolute constant. This matches the deterministic restarted accelerated-gradient upper bound of Li and Lin (2023) and extends the sharp deterministic lower bound of Zhou (2026) to unrestricted randomized algorithms. Thus, randomization does not improve the high-dimensional worst-case query rate. The construction keeps quadratic curvature visible while revealing the forcing directions sequentially. Large eigenspaces limit preprocessing, and a scheduled-disclosure coupling makes each fresh direction incur a separate cost.

math.OC↗
arXiv2026

Sharp High-Probability Statistical Rates for Heavy-Tailed Nonsmooth Convex Optimization

We establish sharp high-probability statistical rates for nonsmooth stochastic convex optimization under heavy-tailed noise, closing the confidence-dependence gap in both general convex and strongly convex settings. We consider composite objectives with a Lipschitz convex loss and a known proximal regularizer, accessed through fresh unbiased stochastic subgradients. The centered noise has conditional norm and directional $p$th moments bounded by $L^p$ and $s^p$, respectively, where $1<p\le2$ and $0<s\le L$. For $T$ oracle calls and failure probability $0<δ<1/10$, set $q=1-1/p$, $\ell=\log(3/δ)$, and $A=s(L^2/s^2)^q$. With initial distance bound $D$, the minimax objective error is $Θ(D(A+s\ell^q)/T^q)$ in the nonsaturated statistical regime. For a $μ$-strongly convex regularizer, the corresponding quadratic-regime rate is $Θ((A^2+s^2\ell^{2q})/(μT^{2q}))$. These rates require domination of the deterministic and finite-variance terms; matching lower bounds require $d\ge\lceil L^2/s^2\rceil$, while the upper bounds hold in every finite dimension. The new upper bounds attain known statistical lower-bound orders, replacing the previous confidence coefficient $s^{1/p}L^{1-1/p}$ by $s$, and its square by $s^2$ under strong convexity. The key is an online inequality that separates directional fluctuations from the total second moment created by rejection sampling. Localization preserves this separation under strong convexity without additional horizon logarithms. The results characterize oracle complexity with unrestricted internal computation.

math.OC↗