Papers

A Hsiang cubic is a cubic form on $\mathbb{R}^{n}$ whose zero set is a minimal cone; equivalently, it is the cubic form of a commutative nonassociative metrized algebra satisfying a single identity of degree four. We show that the intrinsic geometry of such an algebra, encoded in its idempotents and their Peirce decompositions, is the geometry of a Chebyshev-type extremal problem on the sphere. A Hsiang cubic equioscillates on $S^{n-1}$: its maximum set is the set of normalized idempotents, and on suitable great circles through an idempotent it restricts to the Chebyshev polynomial $T_3$. For the spherical analogue of the problem of least deviation, the minimization of $\|p\|_\infty^2/\|p\|_2^2$ over harmonic cubics, a sharp lower bound based on Kellogg's inequality shows that Cartan's isoparametric cubics are the global minimizers in dimensions $5$, $8$, $14$ and $26$. In general, we compute the ratio of every Hsiang cubic in terms of the Killing form and characterize stationarity by a Kolmogorov criterion: it amounts to a positive measure on the idempotent variety. Such measures are given explicitly in several cases which together cover every Hsiang cubic known to exist; in particular, all of them are stationary. These measures give quadrature identities on the idempotent variety whose moments are invariants of the algebra; they are spherical designs exactly in the Einstein (Killing metrized) case, i.e.\ when the Killing form is proportional to the inner product. Distinguished low-dimensional Hsiang cubics are strict local minimizers, whereas a polar Hsiang cubic is a stationary non-minimizer.

We study the zeros of the spectrogram of complex white noise analyzed with Hermite windows of order n, extending the classical Gaussian-window correspondence with Gaussian Analytic Functions to the polyanalytic setting. Using the polyanalytic Bargmann transform, these zeros split into two families according to the sign of the local Jacobian, giving rise to a natural notion of charge, and we show that these zeros are almost surely simple, isolated, and form a translation and rotation-invariant point process. We derive closed-form expressions for the one-point intensity, decomposed by charge, and also for the unsigned, signed, and hybrid two-point intensities. Besides, we prove that unlike the total repulsion observed with a Gaussian window, the Hermite window of order n generates a pair correlation function that converges at the origin to a strictly positive constant depending on n. Finally, we propose a numerical method for detecting spectrogram zeros via the winding number around candidate local minima.

A permutation is $n$-universal if it contains every permutation of length $n$ as a pattern. We prove that a uniformly random permutation of length $32n^2$ is $n$-universal with probability at least $1-\exp(-c n/\log n)$, for an absolute constant $c>0$ and all sufficiently large $n$. This removes a $\log\log n$ factor from an earlier result of He and Kwan~\cite{He-Kwan} and resolves an open problem of Alon~\cite{Alon2016}. The proof was found by GPT-6 Pro.

Digital platforms provide increasingly detailed traces of collaborative activity, yet these traces do not directly reveal whether contributions remain largely independent or whether more structured forms of collective work emerge through interaction. This paper addresses the methodological problem of measuring such organization when the collective being studied is not defined as a team in advance. We propose a trace-based method for measuring teamness, understood as the degree to which collaborative activity expresses properties associated with teamwork. The method translates established dimensions of teamwork into behavioral indicators that can be recovered from digital traces. These indicators can be examined separately and summarized through a composite measure of their joint expression. It does not require predefined team membership and is designed to be adapted across collaborative settings. We illustrate the method using revision histories from 52,437 articles in the English Wikipedia's Medicine WikiProject, comprising more than 10 million human-authored edits. Using article-months as observation units, the application shows that different dimensions of teamlike organization display distinct patterns and that their joint expression can vary within the same articles over time. The contribution is a general measurement framework for examining graded and dynamic forms of collective organization directly from behavioral traces.

For every smooth projective generalised Markoff surface $X_m$, every hyperplane section $H$, and every integer $n\ge2$, we establish Campana strong approximation with the Brauer–Manin obstruction for $\bigl(X_m,(1-1/n)H\bigr)$.

Multimodal language models (MLLMs) exhibit promising spatial reasoning capabilities, yet the internal mechanisms supporting them remain poorly understood. We uncover S-Space, a linear representation subspace in which object-token representations encode continuous coordinates along horizontal, vertical, and distance axes. Although we identify these axes by differentiating spatial-answer scores with respect to object-token activations, S-Space is intrinsic rather than induced by specific data or prompts, remaining readable under non-spatial questions. We show that S-Space functions as an internal spatial workspace of MLLMs. Perception encodes object locations into it, forming spatial representations that can be directly read out to support accurate spatial judgments. Internal reasoning transforms it for changing viewpoints. Verbal responses selectively access it, evidenced by causal interventions that alter spatial judgments while largely preserving non-spatial responses. Case studies further show that S-Space assigns locations to unseen entities and the observer, and connects physical directions with abstract linguistic meanings, suggesting both the capabilities and limitations of large-scale language training. Finally, we use S-Space as a diagnostic tool for spatial reasoning failures. Direction-word readouts reveal systematic coupling between cardinal and image-relative reference frames. More importantly, a perception-computation decomposition exposes a key bottleneck: MLLMs can form capable spatial representations, yet fall short in the spatial transformations required to reason reliably across viewpoint changes.

Low Earth Orbit (LEO) satellite constellations are expected to play a key role in future 6G Non-Terrestrial Networks (NTNs), where dense deployments enable cooperative multi-satellite processing for communication and positioning. While existing works have addressed communication and localization objectives separately, the correlation and alignment between these objectives remain largely unexplored. In this paper, we investigate the correlation between Spectral Efficiency (SE) and positioning accuracy in cooperative multi-LEO satellite clusters. We consider an uplink direct-to-device scenario in which multiple satellites jointly process user signals and evaluate cluster performance using SE and Position Error Bound (PEB) metrics. We derive Time-of-Arrival (TOA)-based and Doppler-based PEBs, while communication performance is quantified through the achievable SE under joint signal processing. Using realistic LEO constellation simulations, we demonstrate that for clusters of seven satellites, SE exhibits a strong negative correlation with Doppler-based PEB (correlation coefficient of $-0.72$). In contrast, its correlation with TOA-based PEB is notably weaker, ranging between $-0.55$ and $-0.37$. These findings suggest that communication-oriented LEO clusters are largely compatible with Doppler-based positioning, but not necessarily with TOA-based positioning.

This paper proposes and analyzes a compact fluorescence-photometer lab-on-a-chip that is simpler than a fluorescence spectrometer, and that does not require spectrum reconstruction by a computer. An on-chip AlGaN VCSEL lasing at 280 nm, or at 310 nm, pumps an on-chip sample in the form of liquid or solid or tissue, thereby exciting signature fluorescence in the 300 to 540 nm wavelength range. This emission signal is detected and read out by an on-chip UV-enhanced Silicon photodiode. The 2 cm x 5 cm chip consists of C-plane (0001) Sapphire, and no lenses, prisms, or mirrors are utilized in the photometer. The chip is opto-electronic and features co-packaged electronics using tiny electronic chiplets that are bonded to the sapphire. These consist of an LD driver and transimpedance amplifier for the UV photonics, together with ASICs, ADC, microcontroller, micro-battery and RF-wireless or Ethernet chiplets. The mission of this self-contained cost-effective chip is sensing targeted medical-chemical-biological (MCB) agents in a local or network setting. Eight significant MCB applications are detailed here.

Intermittent “spikes” in loss, during the pre-training of Large Language Models (LLMs), remains a mysterious phenomenon both theoretically and empirically. In this paper, we show that simple quadratic models with heavy-tailed, power-law distributed inputs can replicate these spikes. We introduce a theoretical framework and simulation algorithm to model per-layer training dynamics of Deep Neural Networks (DNNs), using such quadratic models. In a case study on an Adam hyperparameter configuration (where $\beta_2$ is set close to $1$) known to induce spikes in Transformer LMs, our simulation successfully predicts bumps indicating spiky behavior from a given checkpoint. Furthermore, we derive an appropriate $\beta_2$ schedule from observed metrics, which empirically improves performance.

The pronounced chiral asymmetry of biomolecules is a defining feature of living systems, yet the mechanisms by which such asymmetry emerged remain unresolved. Chiral symmetry breaking may have occurred under prebiotic conditions in systems with sufficiently small molecular populations for intrinsic fluctuations to play an important role. Here, we investigate how finite-population fluctuations affect chiral-state selection, the characteristic time for symmetry breaking, and stochastic switching between chiral states in a system driven by autocatalysis and mutual antagonism. We determine how these dynamical processes scale with particle number and derive an analytical expression for the probability of selecting either chiral state as a function of the initial enantiomeric bias. We further calculate the mean selection time for different initial biases and show that, for weak mutual antagonism, fluctuations can induce transitions between opposite chiral states. These results characterize how finite-population fluctuations control both the emergence and stability of molecular chirality in autocatalytic chemical systems.

Action-conditioned world models offer a promising foundation for generalist robotic intelligence by predicting the consequences of actions. However, existing robotic datasets provide limited coverage of the diverse interaction dynamics required for generalizable world modeling. Large-scale egocentric human videos offer complementary interaction experience, yet the embodiment gap between human hands and robotic manipulators hinders effective cross-embodiment learning. Meanwhile, the predominance of successful demonstrations leaves failure dynamics substantially underrepresented, limiting the ability of world models to anticipate unsuccessful executions. To address these limitations, we introduce HF-WM, an action-conditioned world model that combines Human interaction learning with Failure-aware post-training. To bridge the embodiment gap, we develop a dual-branch framework that couples video generation with auxiliary pointflow prediction, using stabilized pointflow as a unified motion representation across human and robot interactions while suppressing egocentric camera motion. To improve failure modeling, we further perform Group Relative Policy Optimization (GRPO) post-training on perturbed actions derived from successful demonstrations, guided by action alignment and physical plausibility rewards, enabling the model to learn plausible failure dynamics without paired ground-truth videos. Extensive experiments demonstrate that HF-WM achieves state-of-the-art performance in action-conditioned video generation and exhibits strong utility for policy evaluation in downstream robotic tasks.

Multi-teacher on-policy distillation (MOPD) extends on-policy distillation (OPD) by routing domain-specific data to specialized teachers, integrating their capabilities through dense token-level supervision on student-generated trajectories. However, domain routing only distinguishes the supervision sources for different domains; updates from all domains still act on shared parameters. When teachers differ substantially in response style and domain expertise, supervision that is effective in isolation may still lead to persistent gradient conflicts and capability degradation during joint optimization. To address this challenge, we propose Cross-Teacher Guarding for MOPD (Road MOPD), which introduces non-routed teachers as auxiliary cross-domain critics on the same student trajectories and coordinates multi-teacher supervision through token-level credit assignment and gradient updates. Specifically, cross-teacher-guided credit assignment uses teacher agreement to strengthen token-level corrections jointly supported by the teachers and attenuate conflicting signals; preventive multi-teacher gradient projection uses auxiliary gradients from the same trajectories to constrain potentially conflicting updates and adaptively controls projection strength to retain target-domain learning signals. In experiments, Road MOPD mitigates degradation in the disadvantaged domain, gains over 5 percentage points under high conflict, and improves overall performance in low-conflict and three-domain settings.

Identifying causal effects from observational data typically requires a fully specified causal graph, an assumption that is often unrealistic in complex or high-dimensional settings. Causal abstractions address this limitation by retaining only partial causal information, thereby defining equivalence classes of compatible causal graphs. In this paper, we study causal effect identifiability directly at the level of these graph collections, rather than at the level of individual causal diagrams. We formalize several notions of identifiability in this setting and organize them into a hierarchy that clarifies their relationships and differences. In particular, we establish that a causal effect may be identified over a collection of graphs without admitting a single causal derivation that holds uniformly across all compatible graphs. These results help reveal gaps and clarify ambiguities in the existing literature.

The structure of high-entropy alloys, which include 5 or more components in equimolar proportions, is proposed to be described in the mathematical language of Latin squares. This model is fundamentally discrete and allows for a quantitative description of ideal mixing, in which any given alloy element is guaranteed not to have an identical element as its nearest neighbor. For the two-dimensional case, the model possesses four axes of translational symmetry, which makes it possible to tile the plane with a single Latin square and, based on the properties of this square, describe the properties of macroscopic material samples. The model makes it possible to make quantitative estimates of the suitability of a particular atomic structure (configuration) for implementation in a perfectly mixed high-entropy alloy with maximum mixing entropy. A condition has been obtained for acceptable fluctuations in the concentration of components at which the thermodynamic stability of the alloy is maintained. The possibility of identifying superstructures in high-entropy alloys based on group theory, as applied to the description and construction of Latin squares, is discussed. Based on the proposed model, the probability of forming a multicomponent alloy with ideal mixing is estimated. For a five-component alloy, this probability is no more than 2.6*10^{-10}.

In machine learning, a self-attention dynamics describes the attention mechanism of transformers, and is obtained treating the layer index of a transformer as time index. Even though naturally discrete-time, this dynamical system is most often studied in continuous-time. Scope of this paper is to provide a thorough investigation of the discrete-time version of the self-attention dynamics: a complete classification of its equilibria is given, and their stability properties are studied, in both the single-head and the multihead case. We show that in both cases the main attractor of the dynamics is a consensus equilibrium aligned with the principal eigenvector of the value matrix (in the single-head case, a corresponding matrix of weights in the multihead case), even though other locally asymptotically stable bipartite equilibria can be show to exist at least in the single-head situation. The behavior is confirmed by looking at the learned weight matrices of a real transformer.

Tidally-locked planets express a range of climate regimes distinct from those found in our solar system. Their atmospheres are often dominated by planetary-wide overturning circulations and super- rotating jets. In this paper we explore the hydrological cycle of such planets and how it might depend on the total inventory of condensate. To this end we use a set of idealised GCM simulations to probe the response of the hydrological cycle to the surface moisture budget in their atmospheres. We find that for low moisture inventories the climate quickly develops a barren day side and a moist night side where the moisture is trapped, as might be expected. For higher moisture inventories the drying of the day side is significantly delayed by the development of a substellar lake just east of the substellar point, which is sustained by the presence of a local thunderstorm-like convective system that persists even after the lake disappears. The timescales for the lake to disappear are millennia, suggesting that even a weak transfer of moisture through surface processes could maintain a moist day side. We also find that adjusting the threshold at which the evaporative rate becomes constrained by the remaining surface liquid depth modifies the longevity of the lake and surrounding day side conditions. These findings have implications for understanding a diverse range of planetary climates and habitability, given the distribution of moisture and presence of a substellar lake.

Runtime failure monitors for robot policies are typically evaluated by how accurately they distinguish failed from successful executions. Yet an accurate alarm may arrive too late for recovery, while an unnecessary intervention may disrupt an execution that would otherwise succeed. We introduce RESCUE, a counterfactual framework for evaluating whether a monitor's alarms enable useful interventions. By restoring simulator and policy states at execution checkpoints, RESCUE compares alternative actions, identifies the latest checkpoint satisfying a specified recovery criterion, and evaluates whether acting on alarms reduces expected task-completion cost. We evaluate RESCUE with OpenVLA-OFT and $\pi_{0.5}$ over LIBERO-Spatial and LIBERO-Plus using 128,340 counterfactual branches. Recoverability depends on the state–intervention pair rather than on robot state alone: at $\tau=0.5$, 14 of 66 OpenVLA-OFT/LIBERO-Plus failures contain a recoverable checkpoint under continuation, compared with 34 of 66 under continuation or scripted recovery, while recovery reduces recoverability in other conditions. On the primary strong-policy conditions, favourable detection scores do not establish lower intervention cost. Under the evaluated stop-and-reset model, even an idealised detector can afford only a 2.0–3.3% false-alarm rate before unnecessary resets outweigh the savings from stopping failures early. These results show that monitor value depends jointly on the intervention available and the workload in which it is deployed.

In this paper, we investigate the weak invariance principle in some Besov spaces for strictly stationary sequences. In particular, we provide sufficient conditions on the moments and the dependence of a strictly stationary sequence to guaranty the weak invariance principle in these Besov spaces. Several dependence structures are considered, including projective conditions, $\alpha$-dependent, $\rho$-mixing, and $\tau$ -dependent conditions. The main tools in the proofs are martingale approximation and deviation inequalities for weakly dependent sequences. Our results cover a large range of strictly stationary sequences that were not treated previously in the literature. Moreover, the presented conditions are sharp.

Understanding the gravitational interaction is one of the great scientific endeavors of the 21st century. The Nobel Prize-winning discovery of gravitational waves in 2015, and subsequent detections by the LIGO-Virgo-KAGRA Collaboration, have marked a revolutionary step forward in physics and astrophysics by opening an entirely new window for exploring the Universe. Future upgrades to these detectors, along with upcoming facilities such as LISA, the Einstein Telescope, and radio and optical instruments, promise other breakthrough discoveries that the next generation of scientists will need to interpret. The School on Gravity (22–26 June 2026, Copenhagen) aimed to introduce junior scientists–graduate students and advanced undergraduates with a background in general relativity–to a wide range of foundational topics in the exciting new field of gravitational-wave physics. Topics spanned from the theory of motion, to new challenges introduced by quantum physics, to the astrophysics of black holes and source modeling for gravitational-wave detectors. The School on Gravity took place at the legendary Auditorium A of the Niels Bohr Institute, inviting students and lecturers to challenge current paradigms in gravitational physics in the spirit of the quantum revolution that unfolded in this very room. These lecture notes aim at opening up those new ideas presented in Auditorium A to the rest of the scientific community.

We study the asymptotic behavior of eigenvalues of nonlocal convolution-type operators $$L_\varepsilon\rho=-\frac{1}{\varepsilon^{d}}\int_\Omega J\left({\frac{|x-y|^2}{\varepsilon^2}}\right)\rho(y)dy+a(x)\rho(x),$$ (with a continuous sufficiently fast decaying at infinity function $J\geq 0$) when the scaling parameter $\varepsilon>0$ tends to zero. Assuming that the minimum of the function $a(x)$ is attained at a point $x_0\in \overline{\Omega}\subset \mathbb{R}^d$ and is non-degenerate, we establish several terms in the asymptotic expansion of the first eigenvalues $\lambda_\varepsilon^{(k)}$ of $L_\varepsilon$. If $x_0$ is an interior point of the domain $\Omega$, we show that $\lambda_\varepsilon^{(k)}=a(x_0)-1+\varepsilon\mu^{(k)}+\overline{o}(\varepsilon)$, where $\mu^{(k)}$ are eigenvalues of a harmonic oscillator (obtained by the blow up analysis), the corresponding eigenfunctions of $\mathcal{L}_\varepsilon$ are concentrated near $x_0$ on the scale $\varepsilon^{1/2}$. If $x_0\in\partial \Omega$ then the asymptotic expansion of the eigenvalues of $L_\varepsilon$ has the form $\lambda_\varepsilon^{(k)}=a(x_0)-1+\varepsilon^{2/3}\Lambda_0+\varepsilon(\mu^{(k)}+\alpha p_0)+\overline{o}(\varepsilon)$. The corresponding eigenfunctions are represented as the product of a function depending on the distance to $\partial\Omega$ and concentrated on the scale $\varepsilon^{2/3}$, and functions localized on the scale $\varepsilon^{1/2}$ and asymptotically independent of the distance to $\partial\Omega$. The latter functions converge (after rescaling) to eigenfunctions of a harmonic oscillator (in tangential variables), $\mu^{(k)}$ being their eigenvalues. The former function is given, to the leading term, by the scaled Airy function, and $\Lambda_0$, $\alpha$ and $p_0$ depend on $J(|x|^2)$ and $a(x)$.

The recently developed concept of germ graphs (P. Kurasov et al., Phys. Rev. Research 7, L022071 (2025)) is employed to construct families of isocattering, non-isospectral graphs that exhibit dissipation. More specifically, a new pair of isoscattering non-isospectral graphs is constructed by connecting the existing isoscattering non-isospectral graphs, so called attachments, to the different contact vertices of the germ graph. The existing isoscattering non-isospectral graphs contained a two-loop graph labelled $\Gamma_{A2}$ and a three-loop graph labelled $\Gamma_{A3}$. These graphs have an equal total metric length, but different topologies. The resulting graphs $\Gamma_3$ and $\Gamma_4$ are verified as non-isospectral using their Euler characteristics, while their isoscattering properties are investigated by calculating the one-port scattering matrices numerically.

A useful thermodynamic model predicts what a device will do without tracking its full microscopic state. For a finite quantum working medium, the difficult question is which quantities should actually be measured. We develop a task-based method that keeps exact energy accounting separate from calibrated macroscopic prediction. Operator geometry identifies what a measured record determines and bounds what remains uncertain. We then compare direct measurements of dynamical observables with earlier measurements of the same coarse record, selecting the representation together with its measurement cost. A Bose–Hubbard example yields a compact response table tested over a continuous operating region and on unseen microscopic trajectories. A driven Ising chain shows why history is not always the cheaper choice. The result is a way to turn detailed quantum dynamics into a small, reusable, and explicitly qualified thermodynamic description.

Clinical prognosis requires integrating structured measurements, physiological waveforms, longitudinal history, and population context. We introduce PRISM (Population-Retrieved Inference for Structured Multimodal Prognosis), a multimodal language model that combines per-feature numerical tokenization, recency-weighted aggregation of longitudinal ECGs, and a dual-modality population memory bank. Retrieval operates in representation space: the model receives mean-pooled embeddings of similar training-cohort encounters, while no individual retrieved record enters the prompt. On the 1,443-task MDS-ED benchmark, PRISM achieves AUROCs of 86.2% for diagnosis, 93.1% for deterioration, 91.8% for ICU admission, and 92.8% for mortality. These results use a 96-hour pre-arrival window unavailable to reported baselines. With benchmark-window inputs only, PRISM reaches 0.8895 AUROC, compared with 0.8937 for UniPACT and 0.8889 for MDS-ED. A matched-input compact fusion model using the same five evidence streams and frozen encoders reaches 0.7652 AUROC, versus 0.9092 for PRISM. Replacing numerical EHR encoding with text serialization reduces AUROC by 3.66 points; removing pre-arrival history reduces it by 1.97 points; and zeroing retrieval reduces it by 0.99 points. Genuine retrieval outperforms random-neighbor retrieval by 0.97 macro-average points, although a paired task-level sign test does not establish a uniform advantage (p=0.067). On the external MC-MED cohort, supervised fine-tuning reaches 0.8611 AUROC, compared with 0.8227 for locally trained gradient boosting and 0.7841 for source-only PRISM. These results support structure-aware multimodal integration and supervised external adaptation.

Helium incorporation during magnetron sputtering can strongly affect thin film growth and lead to the formation of gas/solid nanocomposites and nanoporous structures. Here, molecular dynamics (MD) simulations are used to investigate the trapping mechanism of helium atoms (He) and the subsequent formation of He bubbles during the sputter deposition of aluminum (Al) and titanium (Ti) thin films. The simulations account for the kinetic energy distributions of sputtered metal atoms and backscattered gas species. Results indicate that He is efficiently incorporated into the growing films, leading to the formation of high-pressure, dense He bubbles, with a much higher He-to-metal atomic ratio in Ti ($\sim$ 60%) than in Al ($\sim$ 12%). More importantly, the simulations reveal a clear energy dependence of He trapping in Ti: background He atoms at thermal energies are essentially not incorporated, whereas efficient trapping starts at an incident energy of approximately 20 eV and increases up to a saturation regime near 100 eV. Simulated thermal desorption spectroscopy (TDS) further reveals distinct release mechanisms in the two investigated metals: He desorption from Al occurs at higher temperatures and is preceded by the removal of surface Al atoms, whereas He and Ti atom desorption starts continuously around 950 K, leading to a porous structure. Comparative simulations with argon (Ar) demonstrate negligible trapping even at comparable kinetic energy or momentum, showing that neither parameter alone accounts for the strong He incorporation observed in Ti. The above results are in very good agreement with what is reported in literature for low-kinetic energy He ion implantation in metal surfaces, suggesting similar insertion mechanisms. They clarify the atomistic conditions governing noble gas trapping during film growth and provide a basis for controlling He incorporation and porosity in films synthesized by magnetron sputtering.

Federated learning (FL) seeks to optimize a shared global model from decentralized client data. While effective for average performance, this process can produce unfair performance across clients, particularly under statistically heterogeneous data distributions. Existing fairness-aware and multi-objective FL methods address this through client re-weighting, gradient correction, or common-descent formulations, but often change the global optimization direction or treat client objectives symmetrically. We propose FedPCD, a priority-constrained federated optimization framework that separates the global optimization objective from client protection. FedPCD preserves the conventional federated aggregate as the primary objective, while allowing only the minimum correction necessary to meet client performance constraints. Across heterogeneous FL benchmarks, FedPCD consistently outperforms state-of-the-art baselines, achieving the highest global accuracy across all configurations and leading worst-10% client accuracy in nearly all. FedPCD further preserves competitive trade-offs between global accuracy and client performance variability. Beyond this trade-off, FedPCD demonstrates faster empirical convergence, reaching matching or superior performance in substantially fewer communication rounds.

On the Riemannian Schwarzschild–Tangherlini metric of dimension $n\geq 4$, we show that the destabilizing TT tensor of Ozuch lies in the image of the “TT-tensor machine”. By continuity, it can then be approximated, in suitable weighted Sobolev spaces, by smooth compactly supported TT tensors, on which the stability quadratic form is still negative. This proves instability in the usual sense for noncompact manifolds. To our knowledge, no exact smooth compactly supported destabilizing TT tensor was known before, even in 4D.

Autoregressive Transformer and Conformer models have achieved state-of-the-art performance in automatic speech recognition (ASR). However, their sequential token generation mechanism imposes a significant bottleneck during decoding, resulting in substantial inference latency. While speculative decoding has emerged as a promising lossless acceleration technique, existing ASR-oriented approaches either suffer from low draft acceptance rates due to suboptimal draft quality or rely on specially designed external draft models, which limit their generality and practicality. To overcome these limitations, we propose EAGLE-ASR, a novel framework that accelerates ASR inference via EAGLE-style speculative decoding while strictly preserving lossless output quality. Specifically, we introduce Speech-Draft, a lightweight autoregressive module that serves as a universal draft model by jointly leveraging encoder acoustic features and hierarchical decoder representations from the target ASR model. Furthermore, we adopt a multi-step generation strategy with self-distilled data to train the Speech-Draft, enabling it to better approximate the target model's output distribution and maintain causal consistency during multi-token generation. Extensive experiments on representative Whisper and Conformer AED models demonstrate that EAGLE-ASR achieves significant lossless speedups of up to $1.9\times$ and $2.4\times$, respectively, consistently outperforming existing speculative decoding baselines for ASR. Our proposed framework further generalizes effectively to multilingual ASR and speech translation tasks, establishing EAGLE-ASR as a practical and universally applicable solution for accelerating modern ASR systems without compromising recognition accuracy.

Semi-Markov networks provide a natural framework for describing stochastic transitions between coarse-grained states with non-exponential dwell times, with applications ranging from biophysics and neuroscience to epidemiology and finance. Here, it is shown that finite semi-Markov networks admit explicit combinatorial representations of their Laplace-transformed occupation probabilities and hitting-time distributions as sums over weighted spanning trees and forests of an augmented graph. These representations yield asymptotic results, including a generalization of the Markov Chain Tree Theorem to semi-Markov networks, in which the rate constants replaced by pseudo-rates given by the inverse mean sojourn time weighted by the exit probability through this channel, as well as the long-time scaling of hitting-time survival probabilities in the presence of infinite-mean sojourn times. They also extend recently derived combinatorial formulas for hitting-time moments to the semi-Markov setting. In particular, the mean hitting-time formula coincides with that of a Markov network with the corresponding pseudo-rates, which also yields a short proof of the constancy of Kemeny's constant for finite-mean semi-Markov networks. Finally, we use the same framework to show that weak ergodicity breaking occurs generically for time-additive state observables that are nonconstant on the support of the limiting distribution in heavy-tailed semi-Markov networks.

Generative Recommenders increasingly use Reinforcement Learning (RL) to optimize outcomes that may appear hundreds or thousands of interactions after a decision. Standard RL propagates reward according to temporal proximity rather than explicit relevance, attenuating the signal assigned to distant but important actions and creating a source of sample inefficiency. We introduce Explanatory World Models (EWM), an attribution framework that uses explanations to identify the earlier events that plausibly contributed to a realized outcome. We instantiate EWM with a frontier language model and use its explanations as learning signals using a conservative hierarchical operator that recursively redistributes reward while preserving the undiscounted episode return. To investigate what constitutes a useful explanation, we operationalize three complementary variants inspired by Halpern's actual causation, Lombrozo's explanatory simplicity, and Deutsch's hard-to-vary explanations. We evaluate EWM on two controlled long-horizon RL benchmarks, a public sequential-recommendation benchmark, and an industry-scale generative recommender. On Crafter and WordCraft, EWM substantially outperforms PPO and LaRe, with its largest gains when rewards are most delayed. On KuaiRand, EWM outperforms SFT and LaRe offline and A2C online. Finally, in an offline evaluation of an industry generative recommender, EWM considerably improves Recall and increases behavioral proxies. These results suggest that explanations can provide structured and reusable credit for learning from delayed outcomes.

Existing 3D Gaussian Splatting (3DGS) pruning methods primarily rely on global Top-K selection based on independent importance scores, lacking regional budget control and ignoring joint deletion effects. Consequently, they cannot ensure balanced reconstruction quality across a scene. We propose SplatQ, a combinatorial pruning algorithm that coordinates regional budget allocation and joint Gaussian selection under a fixed budget. SplatQ partitions Gaussians by spatial proximity and appearance similarity into size-limited blocks, decomposing global selection into subproblems of a specific size. It then smooths importance-based block retention quotas to prevent excessive budget concentration. Finally, it constructs a quadratic approximation of joint deletion effects using the responses of representative pixel colors to changes in Gaussian opacity. Individual responses, pairwise interactions, and quota penalties are incorporated into a quadratic unconstrained binary optimization (QUBO) objective, solved using simulated annealing (SA) or a coherent Ising machine (CIM) to jointly select Gaussians. Experiments on 5 benchmarks demonstrate that SplatQ outperforms state-of-the-art pruning methods in aggregate reconstruction quality, spatial quality balance, and rendering speed. Ablations confirm that budget smoothing improves local detail reconstruction, while interaction modeling improves Gaussian selection quality under a fixed budget.