Papers

We study photon conversion into light particles, such as dilatons, axions, and gravitons, induced by background magnetic fields, and formulate the resulting evolution in terms of the Stokes parameters. We show that photon conversion reduces to an effective non-unitary evolution of the photon sector. In the perturbative regime, the Hermitian and anti-Hermitian parts of the effective photon Hamiltonian are related through Kramers–Kronig relations, revealing that the changes in the Stokes parameters are not independent. We apply this general framework to photon evolution in Gaussian stochastic magnetic fields with possible helicity, and derive the ensemble-averaged evolution of the Stokes parameters. We find that two nonzero contributions arise even in the absence of magnetic helicity, which respectively correspond to the overall attenuation of all the Stokes parameters and to an irrelevant overall phase. We also find that magnetic helicity gives rise to two additional contributions, one of which changes the circular polarization while the other induces a rotation of linear polarization. These contributions form two Kramers–Kronig pairs. In particular, photon conversion induced by magnetic helicity is accompanied by both circular-polarization and birefringent responses. The same structure appears in dilaton-photon, axion-photon, and graviton-photon systems, revealing universality of photon conversion in magnetic fields.

Self-evolving LLM agents promise to improve autonomously through continual interaction and learning, reducing their dependence on manually curated supervision. Realizing this promise requires not only updating the agent, but also evolving its training experience as its capabilities change. However, most existing pipelines rely on static datasets or separately updated synthesis models, causing previously useful tasks to become trivial while overly difficult tasks remain uninformative. This growing mismatch between agent capability and training experience limits sustained self-improvement. To address this problem, we propose SynCo, an agentic data synthesis co-training framework for self-evolving LLMs based on multi-agent reinforcement learning. SynCo jointly optimizes two independently parameterized agents: a Synthesizer that constructs training tasks from the Reasoner's evolving capability state, and a Reasoner that learns from the resulting experience. Each synthesized task induces multiple Reasoner rollouts whose outcomes provide complementary rewards to both agents. Correctness feedback improves the Reasoner, while task quality, answer reliability, and outcome-grounded teachability guide the Synthesizer. Their updates are fed back into subsequent synthesis rounds, allowing the task-solving policy and its training distribution to evolve together. Extensive experiments across eight mathematical reasoning benchmarks demonstrate that SynCo substantially outperforms a broad range of existing synthetic-data methods and controlled baselines, achieving the strongest overall performance while deriving most of its gains from previously unsolved problems.

Physics-based models connect scientific explanation with quantitative prediction. Constructing them requires selecting physical processes, defining states and governing equations, specifying couplings, and identifying parameters from experiments. Existing AI systems remain limited in making these model structure decisions autonomously. We introduce EvoSim, a self-evolving AI scientist for physical modeling. It uses experimental discrepancies to drive mechanism and equation revisions and held-out experimental data to test physical plausibility. Exploration traces make updates to knowledge, skills, and multi-agent orchestration. This co-evolution improves physics-based models and EvoSim's ability to select mechanisms, diagnose failures, and coordinate research. We evaluate EvoSim on two industrial battery modeling tasks. It predicts lithium-metal-plating onset from 25 to 45 degrees Celsius and 2 C to 6 C with a mean absolute error of 1.79% in state of charge. Dynamic voltage prediction under vehicle driving conditions achieves a root mean square error of 7.62 mV, surpassing the reported accuracy of models developed by human experts. Self-evolution reduces model and physics errors by approximately 36% relative to baseline, demonstrating improved scientific modeling capability. EvoSim turns experimental observations into validated models and cumulative research expertise.

Estimating covariate-dependent intensity functions from spatial point pattern is challenging when the integrated intensity function cannot be evaluated analytically. This challenge becomes even worse in Bayesian inference due to repeated integration of the intensity function over the high-dimensional covariate space. This paper develops a Bayesian soft-tree Poisson process model that combines adaptive covariate partitioning with smooth intensity function. The key idea is to use soft gating functions to smooth transitions between partition boundaries in a tree generating process while preserving analytic evaluation of integrated intensity. A Bayesian CART prior is adopted to learn the partition structure from data. Given the partition tree, conjugate priors are assigned on leaf parameters to enable analytic marginal likelihood computation. This paper also develops a reversible-jump Markov chain Monte Carlo (RJ-MCMC) algorithm for posterior inference. Posterior consistency is established for the proposed model with respect to the Hellinger distance. Extensive simulation studies and an application to wildfire data confirm the advantages of the proposed method over existing methods.

Synergistically capturing intricate local structures and global contextual dependencies has become a critical challenge in point cloud representation learning. To address this, we introduce PointLearner, a point cloud representation learning network that closely aligns with biological vision which employs an active, foveation-inspired processing strategy, thus enabling local geometric modeling and long-range dependency interactions simultaneously. Specifically, we first design a point-focused attention, which simulates foveal vision at the visual focus through a competitive normalized attention mechanism between local neighbors and spatially downsampled features. The spatially downsampled features are extracted by a pooling method based on learnable inducing points, which can flexibly adapt to the non-uniform distribution of point clouds as the number of inducing points is controlled and they interact directly with point clouds. Second, we propose a context-scan state space that mimics eye's saccade inference, which infers the overall semantic structure and spatial content in the scene through a scan path guided by the Hilbert curve for the bidirectional S6. With this focus-then-context biomimetic design, PointLearner demonstrates remarkable robustness and achieves state-of-the-art performance across multiple point cloud tasks.

Altermagnetic materials, characterized by vanishing net magnetization and momentum-dependent spin splitting, provide a unique platform for realizing unconventional superconducting states without the detrimental stray fields. Here, we demonstrate long-distance Josephson supercurrent transport through epitaxial thin films of the strained altermagnet CrSb. We observe a dissipationless supercurrent across a lateral spacer distance of 150 nm in a CrSb-based Josephson junction, exceeding the conventional spin-singlet coherence length by nearly two orders of magnitude. This supercurrent is further accompanied by a well-defined magnetic-field-induced quantum interference pattern, providing direct evidence for genuine Josephson coupling. Our results reveal altermagnets as a promising route toward generating long-distance supercurrents without macroscopic magnetic stray fields, opening new opportunities for superconducting spintronic applications.

For an almost simple complex algebraic group $G$ of semisimple rank $m$, we prove that a finite family of parabolic subgroups contains a common maximal torus whenever every subfamily of at most $m+2$ members does. We determine the resulting Helly number $(h(G))$ for almost simple groups of types $A$, $B$, $C$, $G_2$, $F_4$, $E_7$, and $E_8$, and obtain bounds differing by one in types $D$ and $E_6$. For general reductive groups of positive semisimple rank, the Helly number is the maximum of those of the almost simple factors. We apply these results to establish a fan-theoretic criterion characterizing smooth toric varieties on which every toric principal $G$-bundle splits equivariantly. In particular, for $d \ge 2$, this splitting property holds on $\mathbb{P}^d$ if and only if $d \ge h(G)$

Global existence of Leray-Hopf (type) weak solutions to the viscous primitive equations in two or three dimensions was established by Lions–Temam–Wang \cite{Lions1,Lions2,Lions3,Lions4} in the 1990s; however, the corresponding uniqueness, no matter in two or three dimensions, has been a long standing open problem since then. In this paper, we solve this open problem in the two-dimensional case. Precisely, we prove the uniqueness of Leray-Hopf weak solutions, with arbitrary $L^2$ initial data, to the viscous primitive equations in a periodic channel, subject to impermeability and stress-free boundary conditions on the solid boundaries.

We prove that for every $N\geq 3$, every solution to the $Q$-curvature-type problem $$ \alpha P_N u + (N-1)!\left(1-\frac{e^{Nu}}{\int_{\mathbb{S}^N} e^{Nu}dw}\right)=0 \ \ \ \ \ \mbox{on} \ \mathbb{S}^N $$ is constant, provided that $ \alpha\ge\frac{1}{2}$ and $\alpha \not =1$. The proof consists of a spectral gap estimate and pointwise estimates of the normalized density $\left(\int_{\mathbb{S}^N} e^{Nu}dw\right)^{-1}e^{Nu}$.

We introduce and study pattern-based tree transformations. As an illustrating example, consider a source pattern $(x \cdot y) + (x \cdot z)$ and a target pattern $x \cdot (y + z)$ as a pair. This source pattern matches any expression $e$ of the form $(e_1 \cdot e_2) + (e_1 \cdot e_3)$ (by substituting $x$ with $e_1$, $y$ with $e_2$, and $z$ with $e_3$) and the pair transforms it into the expression $e_1 \cdot (e_2 + e_3)$ as dictated by the target pattern. Note that in this example, the set of expressions that match the source pattern is not a regular tree language. We propose a model of tree transformations given by a finite representation of a (possibly infinite) set of such (source pattern, target pattern) pairs. The expressive power of this model comes at the cost of undecidability of checking equivalence. Nevertheless, we show that the type-checking problem is decidable for our model of pattern-based tree transformations. The type-checking problem asks whether applying a given transformation to trees having a given regular property (type) preserves the property. Our decision procedure is by a reduction to the emptiness problem of alternating tree automata.

In this article, we derive various weighted p-numerical radius inequalities using the Schatten p-norm with the generalized Aluthge transform for operators in Hilbert spaces. In addition, the article explores classical numerical radius and norm inequalities for operators. The bounds obtained in this work improve upon several well-known previous results. In addition, we provide examples where we calculate and analyze upper bounds for the weighted numerical radius of different types of matrices using generalized Aluthge transformation.

The Belle and Belle II experiments provide a powerful platform for beyond-the-Standard-Model searches, particularly in tau and dark sectors. This summary reports include a measurement of CP violation in $\tau^- \to \pi^- K_S^0 \nu_{\tau}$, a search for $\tau^- \to \ell^- \eta$, a search for axion-like particles via $e^+ e^- \to \gamma a (\to \gamma\gamma)$ using Belle II data, and a search for feebly interacting particles in $B \to h X_{\rm inv}$ decays using Belle data.

In LLM-based agent systems, failures can originate from early steps whose effects propagate through subsequent interactions, making their origins difficult to identify. To trace such failures back to their origin, failure attribution has been formulated as the task of identifying the earliest step responsible for the failure. Recent methods leverage LLM internal signals for failure attribution, typically using hidden states as step representations. We therefore conduct an empirical study to evaluate how effectively these representations distinguish root-cause steps from other steps and find limited separation. Motivated by this observation, we propose ReCast, a step representation learning method that transforms hidden states from a frozen LLM into attribution-oriented step representations. ReCast first selects attribution-relevant layers, then constructs complementary pattern and deviation features, and finally learns contextualized step representations through an encoder trained with contrastive and ranking objectives. We also introduce ReCast-2K, a training dataset for failure attribution. ReCast achieves the best Hit@1 across four benchmarks, surpassing the strongest baseline by 5.65 and 9.19 pp on Who&When Algorithm and Handcrafted, respectively. Code is available at https://anonymous.4open.science/r/ReCast-5FB6 .

AI services incur inference costs during execution, while revenue may arrive later. Changing API prices, limited upfront capital, and service failures can limit operators' ability to sustain or expand their services. Beyond reducing per-request costs, operators need to plan future spending, fund execution before revenue arrives, and obtain compensation for specified losses. This requires clear agreements across services with different pricing and execution conditions. These agreements must distinguish rights to consume services from rights to receive payments, define obligations under uncertain costs and income, and specify which failures qualify for compensation and how much can be paid. We present TokenBank, a financial infrastructure that represents these commitments through structured contracts. It supports service-consumption rights, agreements that settle API-price differences in cash (forwards), financing through limited rights to future service revenue, and protection claims for specified service failures. Contracts specify participants, covered services, validity, ownership, fulfillment conditions, and settlement rules. Evaluation combines replay of 899,441 API requests, real model-driven agent execution, and contract API tests. In a zero-discount rising-price resampling scenario, forwards reduce mean expenditure by USD 304.88 but increase its standard deviation from USD 1,152.45 to USD 1,190.82. A controlled replication with five portfolios per capital condition finds mean contribution differences between financing and self-funding of +1.0635, -0.1406, and -0.2962 experimental USD under low, baseline, and ample capital, respectively. The evaluation distinguishes contract correctness from economic effectiveness under declared economic and failure assumptions; supplier invoices and commercial revenue are unavailable.

Structured pruning reduces the deployment cost of reasoning language models, but the resulting capability degradation can hinder subsequent on-policy distillation (OPD) recovery. Because OPD relies on student-generated trajectories, pruning damage that persists after offline distillation can limit its effectiveness. We propose RECAL, Recovery-Aware Calibration, a simple plug-and-play approach that improves OPD recovery by adjusting calibration before pruning. RECAL uses forward KL between an unpruned teacher and a pruned probe to identify teacher-supported predictions disrupted by pruning, then reweights calibration statistics to guide existing pruning criteria toward preserving these predictions. Across multiple models and pruning methods, RECAL consistently improves mathematical reasoning after OPD, achieving gains of up to 16.7 percentage points on AIME, alongside improvements in most code-generation comparisons. Further analysis shows that RECAL reduces residual damage at heavily affected tokens and establishes performance advantages that persist through recovery. These results demonstrate the value of recovery-aware calibration for improving on-policy distillation recovery of pruned reasoning models.

Our automated analysis of photoelectron yield spectroscopy (PYS) estimates the threshold Ith and the exponent n of a single power law for every spectrum. When this model fits poorly, however, the analysis cannot tell whether the data or the model is at fault. Here we present residual diagnostics that separate the two causes. The exponent is scanned continuously on a 1/n-power fit with an Akaike information criterion (AIC) based on the mean absolute error (MAE), and the spread of the resulting Akaike weights ($P \times \Delta n$) quantifies the uncertainty of the estimate. The normalized MAE (NMAE) and the RMSE-to-MAE ratio (RMR) assess the data quality, the Durbin-Watson (DW) statistic assesses the model adequacy, and the three checks are reported in parallel. With criteria set from an Au reference, the diagnostics were applied to 60 continuous measurements in air of four HF-treated Si samples. For heavily doped p-type Si, DW fell below its criterion, whereas the means of NMAE and RMR remained within their criteria. Prompted by this flag, we fitted the spectrum with a two-component model with fixed exponents (n = 1 and 2.5); the AIC decreased by 56, DW increased from 0.86 to 1.99, and the two components set in at 4.70 and 5.28 eV. For heavily doped n-type Si, the change during air exposure was consistent with a single component. The diagnostics thus identify the spectra that require a multi-component analysis without assuming an emission mechanism.

We provide the first generic exact sampling algorithms with finite expected total cost for uniformly elliptic multivariate diffusions and the corresponding diffusion bridges with bounded coefficients and bounded continuous first derivatives. We formulate a computational cost model that counts work in terms of generation of Gaussian and uniform random variables to execute acceptance–rejection sampling, as well as function evaluations of the drift and diffusion coefficients, together with elementary operations such as sums and multiplications. Our constructions combine randomized parametrix expansions with a finite weighted graph that incorporates both bridge endpoints into the proposal. The exact sampling of the diffusion is minimax optimal jointly in the horizon and number of requested observations, while bridge sampling is minimax optimal in the number of observations for fixed horizon and endpoints.

Pathology vision-language models (VLMs) have shown strong visual perception ability, but their robustness in the language domain remains poorly characterized. Existing pathology VLM benchmarks largely rely on canonical closed-set prompts or perturb only generic templates, treating language as a fixed evaluation component rather than a variable axis of model behavior. In clinical practice, however, diagnostic language varies across reports, institutions, and candidate diagnoses. We introduce PathLang, a language-centered and clinically grounded zero-shot benchmark. PathLang holds the underlying slides, ground-truth labels, and image-text evaluation direction fixed while systematically varying only the diagnostic language, so that performance differences reflect how a diagnosis is phrased rather than what is imaged. The language variation follows how pathologists actually rephrase diagnoses (terminology, specificity, and reporting style), and all prompts and candidate pools are validated by six board-certified pathologists. PathLang covers four task families: (1) zero-shot classification with image-text alignment analysis, (2) cross-modal retrieval, (3) paraphrase robustness, including semantic-equivalence paraphrases, length and reporting-style variation, and prompt ensembling, and (4) open-vocabulary diagnosis retrieval over four candidate pools with distinct forms of semantic competition. Across nine VLMs and five public datasets spanning four organs, we find that performance is highly sensitive to clinically equivalent paraphrases, varies substantially across forms of semantic competition, and that image-text alignment quality does not necessarily translate into inter-class separability. We release the prompt corpus, candidate pools, pre-computed text embeddings, and evaluation code at https://anonymous.4open.science/r/PathLang.

Advances in foundation models are driving efforts to introduce agents to assist people in the physical world. Such agents require agentic spatial intelligence: exploring unfamiliar environments, updating spatial understanding through interaction, and adapting actions based on feedback to sustain progress toward a sequence of goals. Existing benchmarks cover only a limited range of spatial layouts, scales, and traversal requirements. We introduce Mine Odyssey, a benchmark for evaluating agentic spatial intelligence using Minecraft reconstructions of real-world locations. It comprises 180 tasks covering 30 such locations across 20 countries and regions on five continents, including 20 outdoor and 10 indoor settings. These settings span diverse spatial scales, layouts, terrains, and connectivity patterns, from Midtown Manhattan and rural Entrup to Santa Lucía Hill and Buckingham Palace. We select meaningful waypoints, such as landmarks, buildings, and rooms, and manually verify their accessibility. Each task provides a natural-language instruction specifying which waypoints to visit and in what order. Completing these tasks requires agents to find accessible routes and entrances, open doors, and move between levels using stairs and ladders, while monitoring their progress and recovering from navigation errors. Across eight evaluated state-of-the-art models, GPT-6 Astra achieves the highest success rate of 85.6%. However, the second-best model, Claude Opus 5.5, completes 73.9% of tasks, while the strongest evaluated open-weight model, DeepSeek-V4.1-Flash, reaches 23.9%, highlighting substantial room for improvement in the agentic spatial intelligence of current models. Comprehensive analyses and ablation studies on Mine Odyssey reveal current models' limitations and provide insights for advancing agentic spatial intelligence.

Let $M$ be a compact connected oriented smooth manifold, of dimension $n\ge2$. Let $\mathcal T_MG$ be one of the following transformation groups: $Homeo_0(M,\mu)$, $Diff_0(M,\mu)$, $Symp_0(M, \omega)$ (in case $M$ is symplectic) and $Ham(M, \omega )$ (in case $M$ is symplectic). Denote by $\overline{H}_b^d(\mathcal T_M)$ reduced bounded cohomology of $\mathcal T_M$ in degree $d$, and by $\overline{EH}^d(\mathcal T_M)$ reduced exact bounded cohomology of $\mathcal T_M$ in degree $d$. In this paper we prove that if $n=2$ and $M$ is a closed surface $\Sigma_g$ or a disc $\mathbb D$, then for every $d\ge 2$ $$\dim(\overline{H}b^d(\mathcal T_M))=\infty.$$ Moreover, $\dim\overline{EH}^d(\mathcal T_M)=\infty$ if $\mathcal T_M$ is either $Diff_0(\Sigma_g,\mu)$ or $Ham(\Sigma_g, \omega)$, or $Ham(\mathbb{D}, \omega)$; or $g>1$. In case $n>2$, under certain conditions on $\pi_1(M)$, we prove that for every degree $d\ge 2$ $$\dim\overline{EH}^d(\mathcal T_M)=\infty.$$ In particular, these results hold for $\mathcal T_M$ when $M$ is a closed, orientable smooth manifold admitting a Riemannian metric of strictly negative sectional curvature of an arbitrary dimension.

We establish some basic properties of t-flat fine log schemes, i.e., fine log schemes whose underlying schemes are flat over their log structure (in a suitable sense). Notably, we show that the depth of a t-flat fs log scheme is simply determined by its logarithmic stratification. We also show that there is a good theory of log cotangent complexes for t-flat fine log schemes, and use the log cotangent complex to give a homological criterion for t-flatness.

Isotope effects govern fractionation and modulate reactivity, with applications from hydrogen energy to environmental science and catalysis, yet predicting them requires resolving small isotope-dependent free-energy differences that remain very challenging for conventional path-integral simulations in complex systems. Here we introduce iso-EPIGS, a path-integral coarse-graining framework built on a mass-differentiable neural network that reconstructs the mass- and temperature-dependent path integral centroid free-energy surface. Classical molecular dynamics on the learned surface yields rigorous isotope-resolved thermodynamics without explicit path-integral sampling. Benchmarks spanning gas, liquid, and crystalline phases, including liquid water and oxalic acid crystal, reproduce reference path-integral isotope free-energy differences, enthalpies, and lattice parameters at near classical computational cost. Crucially, iso-EPIGS trained solely on all-H and all-D isotopologues retains high accuracy for unseen partially deuterated isotopologues, demonstrating robust transferability across nuclear masses. Iso-EPIGS makes accurate isotope-effect simulations feasible for complex systems and lays the groundwork for foundation models of isotope effects across chemical space.

We resolve Erdős Problem #522, posed in 1961, by proving that for random Littlewood polynomials the proportion of zeros in the closed unit disk converges almost surely to $1/2$. More generally, for partial sums of random power series with i.i.d. coefficients that are bounded, nondegenerate, and centrally symmetric, real Gaussian, or circular complex Gaussian, we prove that the proportion of zeros in the disk of radius $1+x/n$ converges almost surely to $\frac12(1+\coth x-1/x)$, uniformly in $x\in\mathbb{R}$. Thus almost all zeros lie at distance $O(1/n)$ from the unit circle. For random Littlewood polynomials, even with arbitrary dependence between degrees, the convergence at the unit circle holds at the almost-sure rate $O(n^{-1/4}\sqrt{\log n})$. We establish a law-of-the-iterated-logarithm criterion for dependent sequences and, for real Gaussian coefficients, obtain the sharp law of the iterated logarithm over all integer degrees, variance and cross-degree covariance asymptotics, quantitative central limit theorems, joint Gaussian limits, and increment bounds. For symmetric coefficient laws with bounded density and all moments finite, the number of zeros in the closed unit disk has variance $(c_G+\kappa_4/12)n+O_\xi(n^{399/400})$, and for random signs the constant is $c_G-1/6$. Thus the radial law is universal, while the fluctuations depend on the coefficient law through its fourth cumulant $\kappa_4$. All our main results are formally verified in Lean 4, and our proof of Erdős Problem #522 has been accepted as a solution to its formal statement in Google DeepMind's Formal Conjectures project.

We investigate fermionic spectral functions in a two-current Gubser-Rocha background with linear-axion momentum relaxation. Serving as a comparison channel, the dipole coupling $p_1$ is found to produce a soft asymmetric reconstruction without opening a clean hard Mott gap. Our main analysis then focuses on two axion-dependent non-minimal couplings modulated by current mixing. The $p_2$ tensor channel suppresses the zero-energy Fermi peak and shifts the dominant spectral weight to finite frequencies, resulting in a flat-bottom reconstruction. In contrast, the $p_3$ vector channel creates a strong spectral asymmetry in momentum space, generating open, Fermi-arc-like segments. Varying the momentum-relaxation strength $\beta/\mu$ and the doping parameter $\chi$ reveals a channel-dependent response to the two-current background. Increasing $\beta/\mu$ generally broadens the $p_2$ response, whereas the one-sided $p_3$ feature varies non-monotonically under changes of the background parameters. These results clarify how current mixing, axion-induced momentum relaxation, and non-minimal fermion couplings jointly reshape holographic fermionic excitations. These results clarify how current mixing, axion-induced momentum relaxation, and non-minimal fermion couplings jointly reshape holographic fermionic excitations.

Geometrically faithful and functional articulated 3D assets are essential for real-to-sim robot manipulation, where policies trained in simulation must transfer to physical objects. Recent mesh-based methods learn to infer articulation from annotated 3D assets, but deployment remains challenging when real-world objects fall outside the training distribution or their meshes are incomplete or corrupted. To address these limitations, we formulate articulated asset reconstruction as programmatic modeling grounded in partial geometric evidence and introduce USDCraft, a framework in which a pretrained LLM writes and revises executable programs for simulation-ready articulated assets without task-specific training. We propose source geometry analysis, which converts the source mesh into a metric textual description that distinguishes observed surface from unknown space, and iterative geometric rechecking, which re-encodes each candidate in the same representation so that discrepancies point to program edits while unobserved regions remain open to completion. Visual feedback and physical authoring guidance complete the modeling process, which produces articulated USD assets with explicit physical properties that load into Isaac Sim without manual adjustment. Experiments demonstrate leading articulation recovery on two benchmarks and validate USDCraft's effectiveness for real-to-sim-to-real robot manipulation.

Integrated photonic quantum chips have emerged as a promising platform for realizing fault-tolerant photonic quantum computers. Compared with bulk-optics systems, integrated photonics offer compact device footprints, enhanced programmability, and exceptional stability, attributes that are essential for executing large-scale and computationally demanding quantum tasks. In this review, we provide a comprehensive overview of recent advances in both discrete-variable and continuous-variable universal photonic quantum computation. We survey progress in fault-tolerant architectures and state-of-the-art integrated platforms and highlight the key challenges that must be addressed to scale photonic systems toward full fault tolerance. Finally, we outline future opportunities and research directions aimed at bridging the gap between current proof-of-principle demonstrations and fully scalable quantum microprocessors.

Text-to-image models appear to reproduce the habits of the photographs they learned from. Analog clocks are an extreme case: in advertising, watches almost always show 10:10, and generated clocks return to 10:10 even when another time is requested. We measure this bias and test three ways of overcoming it on 52 models available on the Magnific platform, with a replication on Higgsfield. Every image shows three identical clocks that must show 2:35, 6:50 and 11:20. The description of the object is fixed and only the request about the time changes: no time (A), the time in digits (B), the hand positions described by construction relative to the dial numerals (C), or the same description plus a drawn reference dial (D). Two AI readers read all 1,799 images blind from coded copies, with a third reader and the author settling disagreements (dial-level agreement 96.0% and 97.3%). With no time requested, 67% of the images have all three clocks at 10:10. On the 20 current models, all three clocks are correct in 34% of the images with digits, 30% with the hands described in words and 75% with the reference dial (D-B: +37 points, 95% CI +28 to +45); we found no evidence that describing the hands in words beats the digits (C-B: -4 points, CI -10 to +1). The replication on the 12 models shared by both platforms gives the same picture (B 54%, C 50%, D 81%). Writing the time reduces the bias but leaves two thirds of the images of the 20 current models with at least one wrong clock; adding a drawn reference raises full accuracy to three quarters and almost eliminates images entirely at 10:10. We release all images, prompts, raw readings and a script that recomputes every result.

While both neutrino propagation in photons and ultrarelativistic plasmas and neutrino oscillations in curved spacetimes have been studied extensively, their combination in a self-gravitating geometry appears not to have been considered previously. In this paper, we will investigate neutrino oscillations inside a static spherically symmetric spacetime, derived self-consistently from Einstein's equations, supported by ultrarelativistic matter. By relying on the geodesic motion and geometrical symmetries of the configuration, we will compute analytically the neutrino eikonal and spinoptics phase oscillations. Next, we will relate resonance phenomena to the physical interpretation of the background material inside which neutrinos travel for disentangling gravitational versus electroweak effects. We will inspect the effects of the pure gravitational and pure matter fields, and of the temperature in the neutrino oscillations; we will explain why our results are not coordinate artifacts, and we will certify our heuristic method by comparing with the asymptotic behaviours predicted by thermal field theory approaches. We will raise awareness on the relevance of the spinoptics phase shift entering the flavor conversion probability, should the neutrinos hit a curvature singularity. Theoretically, we will scrutinize the separate roles of geometrical symmetries versus physical features of the configuration, while astrophysically we will qualitatively discuss neutrino oscillations inside stars and in the Cosmic Microwave Background at different temperature and density conditions. Our research puts forward, in the context of the Tolman VI metric, an observational method for identifying naked singularities in our Universe: neutrinos would simultaneously be physically overlapped, in flavor-equilibrium and quantum-mechanically scrambled.

Single-cell snapshot data can resolve a continuum of cellular states but do not uniquely determine the dynamics governing transitions between them. However, additional dynamical information can often be encoded in a cell-cell Markov transition kernel. Existing generative approaches for single cell trajectory inference either infer transport only from population marginals, impose a symmetric geometry on the state space, or incorporate directionality through a single velocity vector at each observed state. We introduce Finsler Flow Matching (FFM), a framework for learning continuous stochastic dynamics from discrete Markov transition graphs. We use the first and second local moments to construct a Finsler structure motivated by the Freidlin–Wentzell action, where the second moment determines anisotropic accessibility and the first moment introduces a preferred direction of motion. We learn neural approximations of the resulting directed geodesics, use their Finsler cost to construct source-target couplings, and define geometry-aware stochastic conditional paths that can be distilled into a continuous generative process through simulation-free score and flow matching. Across synthetic and single-cell trajectory inference benchmarks, FFM improves recovery of withheld intermediate populations, particularly when the transition dynamics are strongly directional or anisotropic. Our results provide a principled route from discrete transition probabilities to continuous generative dynamics while retaining both directional and diffusive structure.

Mixture-of-Experts (MoE) architectures have become essential for scaling large language models, with recent work demonstrating the benefits of fine-grained expert designs. Training such models from scratch is expensive, and sparse upcycling from pre-trained dense models is an attractive alternative. However, we identify a structural pathology of fine-grained upcycling: when fine-grained experts are derived from a single source model, naive routing collapses and downstream accuracy drops to near-random (e.g., on Qwen3-1.7B, Drop-Upcycling-fine-grained reaches only 23.2% average accuracy across 15 benchmarks, essentially matching from-scratch training at 22.2%, while the same method's coarse-grained variant reaches 50.2%). We propose DivMoE, the first framework achieving fine-grained MoE Upcycling with structurally-balanced routing. DivMoE introduces domain-specialized fine-grained expert initialization, deriving experts from dense models that have undergone domain-adaptive continual pre-training, and diversity-constrained routing, a hard structural constraint guaranteeing that each token activates experts from distinct domain groups. Across two base models and 15 benchmarks, DivMoE consistently outperforms six upcycling baselines (55.6% vs. 51.6% for the strongest baseline on Qwen3-1.7B) and strictly improves over the dense base model on every benchmark after Stage 2 continual pre-training – closing the regression gap that has plagued prior fine-grained upcycling. After supervised fine-tuning on a public reasoning mixture, our 12B-parameter DivMoE model matches Moonlight-MoE (16B) at 64.5% average accuracy while outperforming a controlled NVIDIA-Upcycling baseline by 6.1 percentage points.