Papers

Algorithmic mathematical reasoning requires reliable decomposition, computation, and aggregation. Final-answer rewards provide limited guidance on intermediate errors, while successful execution does not guarantee mathematical correctness. This work proposes Function-Structured Graph Reinforcement Learning (FSG-RL), connecting subproblem graphs and Python implementations with multi-verifier feedback. The policy first learns to generate code from function graphs through supervised fine-tuning (SFT). Group Relative Policy Optimization (GRPO) then optimizes the policy using answer-gated rewards and span-level credit assignment. The framework also supports teacher supervision and structured memory. A benchmark curated from Grade School Math 8K (GSM8K), MathQA, MATH, and Omni-MATH pairs public function graphs with private verification specifications. Under a unified evaluation protocol, GRPO improves final-answer accuracy from 43.25% to 67.50% and full solution success from 32.25% to 52.25% over SFT. Continued reinforcement learning (RL) with teacher supervision yields additional gains. The gains extend beyond producing correctly formatted code, supporting verifier-guided reinforcement learning for mathematical reasoning. Code is available at https://github.com/ZihanLiummyycc/FSG-RL.

Understanding loss landscapes is central to explaining neural-network training, yet their structure remains only partially understood even in simple models. We study the Gaussian population loss of shallow, bias-free ReLU networks in the teacher–student setting. This provides a simple model for studying essential aspects such as feature learning and overparameterization. For teacher networks with positive output weights and planar features, we show that including a learned linear skip removes all spurious local minima with non-negative student output weights once the student network is at least as wide as the teacher network. In contrast, without the skip, we construct a fixed teacher network with positive output weights and only three hidden neurons in input dimension two whose spurious local minima persist at every student width at least three. Thus, a learned linear skip can remove spurious minima that persist under arbitrary overparameterization. Furthermore, we show that a positive output weight student network always learns the subspace spanned by the teacher features: student features at local minima with non-negative student output weights lie in the span of the teacher features. For ReLU networks in two dimensions, even heavily overparameterized student networks have effective width controlled by the teacher width: every critical point with positive student output weights has at most twice as many distinct student feature directions as teacher neurons. Finally, we transfer the benignity result to empirical minima over parameter balls of any prescribed radius, with the required sampling accuracy depending on that radius.

Conceptual density functional theory (CDFT) defines chemical reactivity descriptors as derivatives of the electronic energy with respect to the number of electrons and the external potential, or combinations thereof; in practice, however, researchers almost always replace these derivatives with finite-difference and frontier-orbital approximations, and no common software exists for their analytical evaluation. We present PyCDFT, to our knowledge, the first standardized, open-source, and scriptable code that analytically computes the descriptors of conceptual density (matrix) functional theory for ground and excited states up to second order, including the orbital hardness, the Fukui function and Fukui matrix, and the linear response function, from a single converged mean-field wavefunction imported from virtually any electronic-structure package. The descriptors are obtained from matrix-free, preconditioned Krylov-subspace solutions of the coupled-perturbed self-consistent-field equations for both spin-unpolarized and spin-polarized references, with the work distributed over MPI ranks and all data flowing through a single HDF5 checkpoint file that supports restart, post-processing, and the export of real-space descriptors as cube files for visualization. The design delegates integrals, grids, and exchange-correlation kernels to PySCF and Libxc, keeping the library compact, user-friendly, and interoperable. Worked examples on the ground state of H$_2$O and a broken-symmetry $\Delta$SCF excited state of NH$_3$ show that a complete second-order CDFT analysis requires only a few lines of user code.

Enabling robots to estimate the kinematic parameters of articulated objects unlocks a wide range of capabilities for interaction and manipulation. The estimation has to happen from the information the robot currently observes, often just a single RGB image of an object it has never seen before. Current single-image approaches couple articulation part segmentation with articulation estimation, making their predictions vulnerable to missed detections and incorrect part associations, and they regress metric 3D geometry that a single view fixes only up to scale. We present QueryArt, a model that estimates articulation parameters from a single RGB image, a 2D query point, and camera intrinsics. QueryArt is trained to estimate the 3D articulation geometry relative to the queried point and in units of its depth, which keeps its target identifiable from the image alone. A single depth measurement at the query point then supplies the scale and recovers the metric parameters. We train QueryArt on a curated mixture of synthetic and real-world articulation datasets. We evaluate QueryArt on several benchmarks and compare it against recent baselines. QueryArt outperforms recent baselines on most articulation metrics, including on out-of-distribution data. To demonstrate the model's capabilities in real-world settings, we evaluate QueryArt on a mobile manipulator across 57 manipulation trials spanning 16 object parts and five viewpoint classes, achieving a 70.2% success rate. We provide code and videos at: https://abwerby.github.io/queryart/

Tabular foundation models achieve state-of-the-art performance on single-table tasks without any training. Recent work suggests that they are also well-suited for relational learning via deep feature synthesis (DFS), which flattens a relational schema into a single table by adding aggregates of the other tables' columns as features. This approach is appealing because it directly benefits from improvements to or customization of the underlying tabular foundation model. In this paper, we identify two key problems with DFS: feature explosion and interaction blindness. The first problem arises because the number of DFS features grows quickly as the schema becomes more complex, limiting scalability and performance. The second problem arises because column-wise aggregates do not account for feature interactions, limiting performance. We propose and explore an alternative method termed RelICL, which keeps the benefits of DFS but alleviates these two problems. At its heart, RelICL propagates and fuses information step by step through the schema graph, using the same tabular foundation model that is eventually used for prediction to do so. In our experimental study using RelBench tasks, RelICL was on par with the strongest approach based on deep feature synthesis.

For weak solutions to quasilinear degenerate parabolic equations of $p$-Laplace type, a central obstacle in applying the method of intrinsic scaling to prove their Hölder regularity is the derivation of forward-in-time propagation estimate for the spatial measure of level sets. In this paper, we revisit and overcome this difficulty for an inhomogeneous degenerate parabolic $p$-Laplace equation with bounded nonnegative time-independent forcing term and initial data. Our new proof is built upon the temporal Lipschitz estimate that we establish on any time interval separated from the initial time by a positive amount. The strong regularity gain furnished by this estimate allows us to derive the forward propagation of level-set measures directly, thereby bypassing the energy inequality that served as the starting point of the previous approach. Furthermore, we establish space-time $W^{1,\infty}_{x,t}$ estimates away from the initial time and construct counterexamples to demonstrate the sharpness of the positive waiting-time condition under merely bounded initial data.

Text-to-image diffusion models have achieved remarkable progress in image synthesis, yet can exhibit memorization by closely reproducing individual training examples. Effective mitigation must preserve useful prompt information to guide alternative depictions. We introduce a training-free method that redistributes cross-attention with Gaussian smoothing before reinforcing content-token contributions and attenuating padding contributions, without additional denoiser evaluations. With this intervention, stronger content conditioning can improve prompt alignment at comparable training-image similarity. A local analysis identifies when reinforcement preserves shared value information while redistribution reduces localized attention mass. On Stable Diffusion v1.4 and v2.0, all evaluated smoothing widths lie on the empirical Pareto frontiers for training-image similarity versus both prompt alignment and image preference. A configuration selected on Stable Diffusion reduces template reproduction in DeepFloyd IF without further tuning. These findings support jointly controlling conditioning allocation and strength to generate prompt-consistent alternatives.

Bismuth telluride (Bi2Te3) is a prototypical V-VI semiconductor of interest for both thermoelectric and topological applications; however, phase-selective synthesis and thermal stability across the bismuth-telluride homologous series remain poorly understood. We report a facile and phosphine-free colloidal synthesis approach for a phase-selective synthesis of Bi2Te3, BiTe, and Bi4Te5 nanosheets with well-defined hexagonal morphology. By controlling precursor chemistry and reaction temperature, we achieved the selective formation of different phases within the (Bi2)m(Bi2Te3)n homologous series. Based on in situ heating studies, BiTe and Bi4Te5 nanosheets transform into Bi2Te3 at about 340 degree C, followed by preferential Te sublimation under vacuum or oxidation in air at higher temperatures. We discuss plausible mechanisms for these phase transformations. EDS analysis and FFT analysis of STEM images provide direct evidence for the temperature-dependent compositional and structural changes and highlight the close thermal relationship among these phases. These results not only advance fundamental understanding of phase stability and thermal behavior in bismuth-tellurides at the nanoscale but also establish a framework for understanding structural evolution in related homologous series, providing insights into their potential future applications in thermoelectric, spintronic, and topological systems.

Monitoring the Pantograph-Catenary System (PCS) provides insight into the health conditions of the pantograph and the railway infrastructure. Recent industrial solutions trace the pantograph's contact wire height and stagger (PCS height/stagger) using video monitoring through convolutional neural networks. However, these solutions do not account for the train route's geographic location. Therefore, in this paper we propose a novel framework for 1) localization of the PCS height/stagger by alignment with the nominal GPS coordinates of the reference route, and 2) collective anomaly detection to evaluate the health conditions of the PCS. We apply and assess the localization and detection performance of the methodology to a case-study based on a real-world industrial dataset provided by a railway transportation company, which includes the PCS height/stagger of several train journeys across Italian railway routes.

Influential Outlier Detection is developed for mixed-effects models on clustered data. The Influential Outlier Metric is defined as a combination of SHapley Additive exPlanantion (SHAP) values and model residuals, both of which undergo a change of measure transformation. Building on previous work showcasing the suitability of using Normalizing flows to map arbitrary distributions to a flexible base distribution for statistical inference, the Normalizing Flows are constructed to allows contextual information and also provide a goodness of fit diagnostic for model evaluation. The use of SHAP values in the construction moves away from model specific tools and instead provides point-wise model agnostic influential outlier. The advantages and limitations of this approach are examined in several models including the linear model, the random forest, and gradient-boosted trees.

We report thick target yields of $^{65}{\rm Cu}(\alpha,n)^{68}{\rm Ga}$ from $\alpha$ energies $E_{\alpha}$$=$6.5–8~MeV measured via neutron-counting at the Edwards Accelerator Laboratory at Ohio University. Our results agree with prior results based on single-foil irradiations, while disagreeing with thick-target yields inferred from stacked-foil irradiations by up to an order of magnitude. Based on comparisons of our and prior measurements to Hauser-Feshbach calculations, we estimate the thick-target yield for $^{68}{\rm Ga}$ from $E_{\alpha}$=14~MeV impinging on 100%-enriched copper ($^{65}{\rm Cu}$) is 161$^{+5}_{-24}$~MBq/$\mu$Ah (for He$^{++}$), which is in agreement with the current IAEA estimate of 156~MBq/$\mu$Ah. At $E_{\alpha}$$=$8~MeV, where radioimpurity-free production of $^{68}{\rm Ga}$ could be realized with a natural copper target, our yield estimate is nearly 4$\times$ lower than the IAEA estimate. We find that the $^{65}{\rm Cu}(\alpha,n)$ cross section estimates presently employed for neutrino and dark matter detector backgrounds and the $^{65}{\rm Cu}(\alpha,n)$ astrophysical reaction rate recently recommended for nucleosynthesis calculations are in agreement with our measurement results.

Quantum federated learning (QFL) has emerged as a promising approach for collaboratively training compact quantum neural networks (QNNs) over distributed private data on resource-constrained devices. However, differences in device capabilities make a single shared QNN architecture unsuitable for all clients. While personalized quantum neural architecture search (QNAS) allows each client to select a device-specific QNN, averaging parameters across structurally different QNN architectures mixes semantically inconsistent circuit operations. To address this, prototype-guided personalized QNAS for virtual FL (vFedProtoQNAS) is proposed, where model parameters are never aggregated across clients and federated collaboration is achieved through class-wise prototype sharing. Each client independently searches and trains a client-specific QNN, computes class-wise local prototypes from latent representations, and refines them using global prototypes from the server as federated semantic anchors. Experiments demonstrate that vFedProtoQNAS improves accuracy by 3.70% over FedAvg and enhances class-consistent representation alignment.

In a recent paper [Kwaśnicki, Poisson kernels on the half-plane are bell-shaped, Bull. London Math. Soc. 58 (2026), no. e70303], the author proved that Poisson kernels for a class of elliptic operators in the half-plane are bell-shaped. By allowing one-sided barriers, we prove a converse result.

Artificial intelligence presents an unusually difficult problem for global governance. The technology develops rapidly, crosses borders easily, and is shaped by actors whose resources and capabilities may rival those of states. Yet international responses remain fragmented, unevenly representative, and overwhelmingly non-binding. The challenge is therefore not simply to identify appropriate rules or institutions, but to understand who has the capacity and incentive to create, enforce, and adapt them. This review essay examines these questions through Matthijs Maas's Architectures of Global AI Governance. Maas offers an ambitious framework for thinking about AI governance through the lenses of sociotechnical change, governance disruption, and regime complexity. His account usefully resists both technological determinism and the search for a single institutional blueprint, emphasizing instead the possibilities of a fragmented and evolving governance architecture. The essay argues, however, that institutional design cannot be separated from the distribution of power. Maas frequently invokes what "we" should do about AI, but that collective subject obscures important differences among states, international institutions, and technology companies. States retain formidable powers over markets, infrastructure, strategic inputs, and firms themselves. At the same time, many consequential decisions about frontier AI - what is built, how quickly, with what safeguards, and when it is released - are concentrated within a small number of private companies. The central problem of global AI governance may therefore be less architecture without an architect than an emerging architecture shaped by multiple actors possessing different forms of power, divergent incentives, and no common set of plans.

Control of molecular angular momentum orientation enables state-resolved studies of molecular interactions and provides a basis for quantum information processing. Here we propose all-optical Autler-Townes state-selective adiabatic passage (ASAP) to prepare molecules in a single $|J,M\rangle$ sublevel. An Autler-Townes branch created by a strong coupling field is selectively populated and adiabatically mapped onto the target vibrational state. We resolve detuning-dependent rovibrational Autler-Townes splitting in $^{13}$CO$_2$, establishing the spectroscopic basis for the selective excitation of the target dressed branch. The density-matrix model calibrated by these spectra predicts transfer approaching 90%. The scheme can exploit millisecond vibrational radiative lifetimes within the electronic ground state and extend to polar and nonpolar molecules with infrared-active vibrational modes.

We report the synthesis and comprehensive investigation of single-crystalline Tb$_2$IrAl$_4$Ge$_2$ and Er$_2$IrAl$_4$Ge$_2$, the first Ir-based members of the $Ln_2M$Al$_4$Ge$_2$ family. Both compounds crystallize in the tetragonal Tb$_2$NiAl$_4$Ge$_2$-type structure (space group $I4/mmm$) and exhibit easy-axis magnetic anisotropy with the crystallographic $c$ axis as the preferred magnetization direction. Tb$_2$IrAl$_4$Ge$_2$ undergoes antiferromagnetic ordering below $T_N = 25$ K and develops a sequence of field-induced metamagnetic transitions accompanied by pronounced magnetotransport anomalies, including a nonlinear Hall response. In contrast, Er$_2$IrAl$_4$Ge$_2$ exhibits three successive zero-field magnetic transitions and a substantially richer low-temperature magnetic phase diagram comprising multiple competing field-induced phases confined to relatively modest magnetic fields. The differences between the Tb- and Er-based compounds demonstrate the wide range of magnetic behavior that can be realized within the \ce{Tb2NiAl4Ge2}-type structure. More broadly, the successful realization of Ir-based $Ln_2M$Al$_4$Ge$_2$ compounds considerably expands the accessible chemical space of this family and opens a route toward the exploration of related $4d$- and $5d$-based aluminogermanides.

We study complete translating solitons for the mean curvature flow in arbitrary codimension under quadratic pinching of the second fundamental form. We prove a codimension reduction theorem at the Andrews-Baker threshold: if a complete $n$-dimensional connected translator isometrically immersed in $(\mathbb{R}^{n+p},\langle\cdot,\cdot\rangle)$ satisfies \[ |B|^2\leq \left(\frac{4}{3n}-\varepsilon_{0}\right)|H|^2 \] for some $\varepsilon_{0}>0$, then either it is an affine $n$-plane or $|H|>0$ everywhere and the translator is contained in an $(n+1)$-dimensional affine subspace. In particular, this improves in low dimensions the pinching range previously obtained from codimension reduction results for ancient mean curvature flows. Our proof is purely elliptic: viewing translators as weighted minimal submanifolds, we combine Simons-type identities for the drift Laplacian with refined gradient estimates and an Omori-Yau maximum principle. As a consequence, under the stronger pinching condition \[ |B|^2\leq (c_n-\varepsilon_{0})|H|^2,\qquad c_n=\min\left\{\frac{4}{3n},\frac{1}{n-2}\right\} \] for $n\geq3$, with $c_n=2/3$ when $n=2$, we obtain a rigidity theorem: the translator is either an affine plane or a bowl soliton contained in an $(n+1)$-dimensional affine subspace. No entropy assumption is required.

In-context learning (ICL) enables a pretrained model to infer a task from demonstrations without updating its parameters. While much of the existing theory focuses on linear target functions, in this paper we study nonlinear cases by comparing two one-layer attention architectures on the same family of single-index tasks. A kernel learner first maps inputs through a fixed nonlinear feature map and then applies linear attention, whereas a feature learner applies attention to the original input, followed by a learned nonlinear readout. We derive predictions for their memorization and generalization errors using the replica method, retaining the effects of pretraining size, task-pool diversity, and training and inference context lengths. The resulting predictions closely match numerical experiments across a broad range of regimes. Our analysis yields phase diagrams that characterize when each architecture is advantageous as the amount of pretraining data, task diversity, and context lengths vary. We further identify qualitatively different context-length scalings for the two learners. Together, these results clarify how architectural choices interact with the dataset and govern nonlinear in-context learning.

Baxter's classical theorem for orthogonal polynomials on the unit circle establishes that the linear Fourier coefficients of a measure are in $\ell^1$ if and only if the nonlinear coefficients, i.e., the so-called Verblunsky coefficients, are in $\ell^1$. However, this equivalence is purely qualitative. We explore possible formulations of such quantitative theorems with norm and Lipschitz estimates for the $SU(2)$-valued nonlinear Fourier transform, for which the analog of Baxter's theorem has been recently obtained. In particular, the highlight of this paper is a number-theoretic construction for the NLFT which proves some negative results in this direction. We also prove a positive result and discuss the limitations of Baxter's method.

Visual grounding localizes an object described by language with a bounding box. Most multimodal grounding models compress target identification, spatial reasoning, and boundary estimation into one terminal prediction. Free-form rationales make reasoning linguistically explicit but do not necessarily expose measurable, editable spatial states. Intermediate localization errors are therefore difficult to diagnose and correct, allowing incorrect region choices and imprecise boundaries to persist in the final box. We introduce CoEvolve, a construct-to-edit framework that separates grounding into explicit state construction and state editing. Region-Evolution Reinforcement (RER) organizes grounding analysis into a progressive semantic–spatial trajectory, with each reasoning step committing to an explicit candidate region. Bidirectional Denoising Refiner (BDR) treats the reasoning text as fixed semantic context and refines the trajectory's coordinate fields through bidirectional same-position reconstruction. Geometry- and behavior-level objectives provide target geometry and edit-preference signals for consolidating reliable candidates, preserving accurate inputs, or correcting toward annotations. Evaluations cover natural-image and remote-sensing grounding. With a 9B backbone, CoEvolve rivals models up to 241B parameters in grounding accuracy. Under controlled corruption, a single BDR pass improves mean box overlap by over 27 percentage points, demonstrating strong recovery from substantial localization errors. State-source comparisons further support the complementarity of explicit state construction and source-matched editing. The project is at https://sundongwei.github.io/CoEvolve_Project/.

We prove two deterministic results for families of distances arising in the study of canonical processes. The first derives an admissible partition scheme from a growth condition. The second gives a representation in terms of parameterized separation trees and compares it with the corresponding majorizing-measure quantities. The main point is that the proofs do not depend on the distribution of the underlying process: once the initial distance and the family of distances are given, no random variables, independence, tail functions, or moment estimates are used. For canonical processes with regular log-concave tails, the assumptions of the abstract results follow from the usual regularity conditions. One direction of the separation-tree estimate also applies to Bernoulli processes without these additional assumptions, and we prove the reverse estimate for bounded convex unconditional index sets. We also give a version of the growth argument for points which, for finite index sets, leads to a recursive construction of admissible partitions and parameterized separation trees.

The $k$-Schur functions (resp., $K$-$k$-Schur functions) are the symmetric function representatives of Schubert classes in the homology (resp., $K$-homology) of the affine Grassmannian of type $A$. We prove that every $K$-$k$-Schur function is a nonnegative integer linear combination in the basis of $k$-Schur functions. This settles a conjecture by Lam, Schilling and Shimozono. The proof relies on realizations of $k$-Schur and $K$-$k$-Schur functions as Catalan and Katalan functions, respectively.

Mesh extraction from 3D Gaussian Splatting (3DGS) aims to endow 3D Gaussians with accurate geometric structures, enabling explicit and precise 3D occupancy. However, existing methods primarily focus on scene-level mesh extraction, making them unable to represent object-level occupancy and often resulting in non-watertight surfaces. To overcome these limitations, we propose MEGA (\underline{M}esh \underline{E}xtraction from \underline{GA}ussians), a “segment-then-mesh” framework for extracting object-level, watertight meshes from complex 3DGS scenes. At the core of MEGA are Spatial Visual Distillation (SVD) and a mask-guided neural surface reconstruction module. SVD treats the 3DGS model as a teacher, sampling diverse camera poses and rendering the corresponding views of each segmented object. These observations are then used to train a mesh reconstruction model through photometric supervision. Extensive experiments on several widely used benchmarks demonstrate that MEGA achieves state-of-the-art performance in recovering accurate object-level 3D occupancy. Moreover, MEGA enables complex physical interactions by combining high-quality object-level meshes for geometric occupancy with 3DGS representations for photorealistic rendering.

We demonstrate the complete observation of a black-hole lightring resonance in an optical analogue. To do so, we generalize the concept of the photon sphere to non-stationnary systems by showing that the lightring is associated to a spatiotemporal caustic and that its complex frequency is determined by the propagation and divergence of this caustic. For an optical soliton acting as an analogue black-hole potential, we predict a characteristic spectral plateau whose boundaries are set by the real part of the lightring frequency, while its spectral decay is governed by the imaginary part. Using a pump-probe experiment in a 5-km-long dispersion-shifted fiber, we observe these signatures for two distinct pump wavelengths. The measured spectra agree with numerical simulations and with the predicted lightring-mode profile, providing direct access to both the oscillatory and decay properties of the resonance. Our results establish a direct experimental connection between black-hole lightrings, spacetime caustics, and quasinormal-mode spectroscopy in a dispersive analogue system.

LLM-based personal agents are emerging as persistent carriers of user semantics and intermediaries between users and recommendation platforms, maintaining richer user knowledge locally. As agents interact with one another, the conventional User–Platform relation evolves into a User–Agent Web–Platform information pathway, enabling distributed user-side information to complement item-side information. This new pathway, however, defies conventional recommendation: evidence is scattered across mutually opaque agents and reachable only through bounded queries, only a small portion of it is relevant to the current recommendation decision, and the responses returned by different agents are semantically heterogeneous. We therefore recast recommendation over the agent web as a task-time evidence acquisition and fusion problem under a finite evidence budget by deciding what to ask and what to keep, rather than learning from aggregated data. We propose AgentWebRec, a user-agent-oriented framework that progressively acquires and fuses distributed evidence for each user-item decision while keeping underlying agent memories local. It grounds each decision in platform-provided item semantics and task-relevant evidence from the target user agent's private memory, and conditionally queries neighboring user agents for complementary preference patterns when local evidence is insufficient. Experiments on four InstructRec datasets show that AgentWebRec consistently outperforms baseline recommenders, and ablations verify that the evidence layers contribute complementary gains.

Quantum algorithms are usually optimized for gate count or circuit depth. We find on Quantinuum System Model H2 quantum computer that for a tight-binding chain ground state preparation, there is a system size $N$ beyond which the adiabatic evolution reaches significantly lower energies than the Fermionic Fourier Transform (FFT), with the same number of gates, and with the same circuit depth. We attribute this high noise sensitivity of the FFT to its high precision, being able to distinguish momenta by $1/N$. This high resolution in momentum space requires long-range couplings in real space, which propagates errors faster. In contrast, although local and physical circuits such as the adiabatic evolution have a coarser momentum resolution, they also propagate errors more slowly. For physical applications, high momentum resolution is rarely required and is often worth trading for low noise sensitivity. We also introduce a momentum measurement scheme that although less precise than FFT, is less costly and less noisy. We show that it achieves better performance than FFT for spectral function measurement on Quantinuum System Model H2 quantum computer. Our work emphasizes the importance of reducing the noise sensitivity of quantum algorithms, beyond the number of gates or circuit depth.

We study the interplay between local stroboscopic measurements and the unitary quantum circuit dynamics of the deterministic Floquet-quantum East model. We derive exact analytical results for the probability of first detecting a subset of qubits back in their initial state. This is achieved via a renewal equation linking the first-detection probability to the subsystem Loschmidt echo, which encodes the effective open dynamics of the monitored qubits. The resulting statistics exhibit two regimes set by the competition between the measurement probing time and the relaxation timescale of the unitary circuit dynamics: while infrequent monitoring leads to geometric first-detection statistics, frequent monitoring induces correlations that manifest as deviations from this geometric behavior. These results provide a rare exact characterization of how local measurement backaction reshapes detection statistics in an interacting quantum many-body system. In our local protocol, return probabilities are controlled by the size of the monitored subregion and can therefore be accessed on digital quantum simulators via local mid-circuit measurements.

Continual learning (CL) in text classification faces two critical challenges: catastrophic forgetting and negative transfer across sequential tasks. Parameter-Efficient Fine-Tuning (PEFT) methods such as LoRA enable efficient adaptation by learning low-rank updates of the model parameters. However, these compact representations are normally trained in isolation, limiting their reuse across related tasks. We introduce Task-Oriented Rank Adaptation (TORA), a geometric routing framework that leverages the low-rank structure of LoRA adapters to decide whether to transfer knowledge from the most compatible expert (Boosting) or isolate the new task (Shielding) based on structural similarity. Evaluated across 15 diverse text classification benchmarks, TORA consistently avoids harmful routing decisions: compatible tasks exceed their isolated performance while reducing training time, and structurally distant tasks are protected from interference with no loss in accuracy. With a single geometric threshold and no reliance on task identities or predefined sequences, TORA provides a simple and effective approach for dynamic adapter routing in sequential text classification systems.

The smallness of polytropic index $\Gamma_\varepsilon \lesssim 1.75$ and near conformality of sound velocity $c_s^2 \approx 1/3$ in neutron star matter are usually referred to as signals of the emergence of quark matter. We construct a density-resolved nucleonic reference domain in the \((P/P_{\rm free},\Gamma_\varepsilon)\) plane using nucleonic EoSs jointly constrained by nuclear matter properties and neutron star mass, radius and tidal data, and found that the domain extends unambiguously below \(\Gamma_\varepsilon=1.75\). Crucially, the nucleonic domain becomes stable against the truncation order only after \(Z_0\) and \(Z_{sym}\) are included, showing that the higher-order density dependence controls the extrapolation from finite nuclei to neutron-star matter. These findings therefore provide concrete targets for finite-nucleus and heavy-ion experiments, while linking terrestrial nuclear physics directly to multimessenger observations. We compare the domain with smooth equations of state generated by neural networks without phase labels and represented by symbolic regression. Among these reconstructions, \(35.29\%\) have complete trajectories inside the nucleonic domain over \(0.5\leq n/n_0\leq8\). Within the EoS sample obtained after minimizing the multimessenger loss, the smallest value of \(\max_n c_s^2(n)\) is 0.38, above the conformal value $1/3$. In conclusion, we convert microscopic interpretation into a falsifiable, density-resolved null-hypothesis test and show quantitatively that current observations do not reject the nucleonic null over much of the admissible space of equation of state.

We present two particle methods for point set registration in bounded domains based on the Fokker-Planck equation. The first method relies on a moving least squares discretization of the S–formulation, in which moving grid points (particles) are advected by the drift with the target distribution, diffusion is resolved on a dynamically evolving particle cloud. This setting naturally leads to strong compression and expansion of the particle cloud. Obstacles are handled by enforcing reflective boundary conditions through a novel ghost point method. The second method is a Monte Carlo solver for the associated Langevin stochastic differential equation. It relies on a local approximation of the logarithmic gradient of the evolving particle density to extract macroscopic osmotic paths from individual stochastic trajectories. Owing to its inherent parallelism, this method exhibits excellent scalability and is well suited for high-dimensional registration problems. We illustrate the main features and performance of both approaches through extensive numerical experiments.