Papers

We consider a generalization of the Gaussian information bottleneck problem to jointly stable variables $X$ and $Y$. Specifically, for $X = Y + A$, where $A$ is stable and independent of $Y$, we find optimal stable linear encoders of the form $T = kX + N$, with $N$ stable and independent of $X$. We characterize the linear stable information bottleneck in closed-form and its critical value. Furthermore, we show that, except for the Gaussian case, such stochastic linear encoders are strictly suboptimal, while becoming asymptotically optimal at large compression rates. Our linear solution recovers the Gaussian information bottleneck for jointly Gaussian variables as a special case.

We investigate modified gravity with quadratic curvature terms ($R^2$, $R_{AB}R^{AB}$, and $R_{ABCD}R^{ABCD}$). In this framework, the geometry of the extra dimensions is determined by the higher-dimensional field equations together with auxiliary conditions. For inhomogeneous metrics, we derive new stability conditions under radion excitations. The central result is that stable solutions satisfying these conditions are not isolated: a typical stable regular metric belongs to a continuous family of stable metrics in its immediate neighbourhood. Since the effective four-dimensional physical parameters depend on the extra-dimensional geometry, this geometrical landscape of stable metrics induces a continuous landscape of effective four-dimensional parameters. Transitions between distinct static solutions within the landscape cannot be induced by spatially localized perturbations, whose asymptotic decay ($|x|\to\infty$) preserves the boundary data distinguishing the states. We also note a possible topological transition from a two-brane to a one-brane configuration, associated with a change in the number of regular zeros of the metric function $r(u)$.

The possibility of generating light in a squeezed quantum state during saturated light amplification in a semiconductor amplifier is theoretically analyzed. Due to four-wave mixing process during amplification, weak components of the spontaneous emission of the medium with symmetric frequency shifts relative to the strong amplified wave acquire the quantum properties of two-mode squeezed light. The squeezing of quadrature components occurs in the range of frequency shifts of several GHz ($\sim$ the inverse relaxation time of the charge carrier density) and can reach 10 dB or more under optimal conditions. The formation of a two-mode squeezing phase facilitates the observation of the squeezing effect, in which a strong wave, playing the role of a local wave, exhibits quadrature noise suppression without additional homodyne detection.

This study examines whether universities shape the regional innovation effects of public R&D expenditure and whether this role varies across regional development trajectories. We analyse a panel of 1166 EU NUTS 3 regions over the period 2007-2020, combining data on European public R&D funding, patenting performance, university presence and regional development traps. Toa ddress the endogeneity of public R&D expenditure, we employ a control function aproach. The results show that public r&D expendirue positively affects patenting performance in both university and non-university, but the difference between them is not statistically significant. University presence therefore does not sistematically amplify the returns to public R&D. However, its moderating role becomes more pronounced in regions exposed to development trap risk and in regions experiencing persistent stagnation, while evidence is weaker for trap intensity. These fundings suggest that universities act as contingent rather than unviersal catalyst of public R&D. Their contribution appears particularly relevant in vulnerable and persistently stagnant regional trajectories, but less able to offset sever structural constraints. The study contributes to debates on the geography of public R&D and regional development traps by showing that the effectiveness of research funding depends not only on institutional presence, bu also on the development rajectory in which that institutional capacity is embedded.

When humans hand each other objects, they incorporate both geometric and semantic information into this process. For example, passing a knife with the handle towards the recipient, rather than the blade, is both more ergonomic and safer. Recent state-of-the-art methods for task-oriented robot-human handovers have progressed from modeling object geometry to incorporating object affordances. However, they often forgo predicting the explicit, task-specific hand poses a human selects to utilize an object. Since many objects support multiple interaction modalities, e.g., a claw hammer used to strike or pull nails, this variability must be modeled to achieve robust task-oriented handovers. To tackle this, we propose a novel approach, GENESIS-Handover (GENErative HypotheSIS), which leverages VLM image generation to produce a variety of task-specific hand-object interaction hypotheses. These hypotheses are matched in real time to the observed human hand pose, enabling inference of the most suitable handover configuration. By leveraging VLMs as priors of plausible hand-object interactions, the method produces task-conditioned handover strategies for previously unseen object-task pairs. We evaluate the standalone interaction proposal module before deploying the full system on a mobile manipulator. In a user study with 12 participants across five task-object pairs, 83.3% perceived our method to have better task understanding than the previous state of the art.

Solving the strong CP problem with spontaneous CP violation (SCPV) in SUSY requires that the constant term of the superpotential and the SUSY-breaking F-term be real to high accuracy. When both are generated dynamically, by gaugino condensation and by dynamical SUSY breaking (DSB), their phases need not vanish even if every theta-angle vanishes and every coupling is real; e.g., the multivalued non-perturbative superpotential may sit on a branch with a complex phase. In fact, gaugino condensation, in pure SUSY Yang-Mills theory and in its Affleck-Dine-Seiberg generalization, is safe only for N_c - N_f in {1,2} (N_c = 2 for pure SYM); otherwise the phase of the constant term reaches the gluino mass through anomaly mediation. The SUSY-breaking F-term is the main source of the MSSM soft masses, including the gluino mass, so its phase reaches theta-bar as well. In the framework of global SUSY, the 3-2 model introduces no phase. The ISS model is safe in that sector as long as the quark-mass splittings exceed the messenger-loop corrections; when they fall below, a complex vacuum orientation can generate an O(1) phase. The IYIT model can generate a purely imaginary F-term: for half of the real Yukawa parameter space, the meson VEV is purely imaginary and CP is spontaneously broken. In all three, the vacuum of the field coupled to the messengers is aligned with the constant term, so a complex constant term generates a strong CP phase through a second route, separate from anomaly mediation.

Temporal oscillations arise naturally in biological systems with feedback loops or explicit delays. When incorporating spatial effects, the travel times of propagating signals can also generate intrinsic delays, and this behaviour is complicated further in the presence of spatial heterogeneity. In this work, we investigate the mechanistic origin and dynamics of spatiotemporal oscillations driven by intrinsic diffusive delays in a representative activator-inhibitor system with spatial heterogeneity using a combination of mathematical modelling, simulations and numerical methods. In contrast to delay-differential equation models where delays are explicitly prescribed, in the partial differential equation system we consider here delays are an intrinsic consequence of signal travel time through space. We demonstrate that undamped oscillations can arise as a result of spatially heterogeneous feedback when the system size increases through a critical length. At this critical length the time for systems to reach steady-state diverges, and the systems first exhibit an eigenvalue with a positive real part and non-zero imaginary part, corresponding to a Hopf bifurcation. We infer that this critical length could define a theoretical upper limit for the size of systems where oscillations hinder function. The analysis pipeline derived in this work offers a novel route for understanding the onset of spatiotemporal oscillations and Hopf bifurcations in a diverse array of biological systems where interactions are mediated by diffusive species.

We construct an explicit rational \(\mathrm{SL}_2(\mathbb C)\)-action on the underlying vector space of the rank-two \(\beta\gamma\)-system. The construction is motivated by Creutzig's branching decomposition with respect to \(L_{-1}(\mathfrak{sl}_2)\) and a rank-one Heisenberg vertex algebra. We realize the raising and lowering operators as residues of lattice-type fields, prove that they preserve the original \(\beta\gamma\)-system despite being defined on localizations, and establish their commutation relations and integrability. The resulting action commutes with the affine \(L_{-1}(\mathfrak{sl}_2)\)-action and all nonzero Heisenberg modes, while the Heisenberg zero mode serves as its Cartan operator. Each affine multiplicity space is thereby identified with \(V_n\otimes\mathcal F_{\mathrm{osc}}\), where \(V_n\) is the irreducible \(\mathrm{SL}_2(\mathbb C)\)-module of highest weight \(n\) and \(\mathcal F_{\mathrm{osc}}\) is the Heisenberg oscillator Fock space. Thus the Heisenberg charge decomposition is realized as the weight decomposition of \(V_n\). The infinitesimal action is not by vertex algebra derivations and does not preserve the symmetric conformal grading.

We study the integer sequence that enumerates cokernel-closed, idempotent split, full, additive subcategories of the category of finite dimensional complex representations of a uniformly oriented $A_n$ quiver. Using a combinatorial model, we describe a non-obvious connection of this sequence to Catalan numbers and derive an implicit recurrence. We also describe some basic properties of the lattice underlying the sequences, in particular, we give an explicit description of the meet irreducible elements of that lattice.

Cell permeability is a key bottleneck for PROTAC development, and public data available to model it is scarce and inconsistent. We adapt an expert-in-the-loop LLM extraction workflow to mine PAMPA measurements from the primary literature, recovering image-only structures by optical chemical structure recognition and hand-verifying every record, expanding the public record from 31 PROTACs to 87. Ridge models trained on PROTAC-DB 3.0 reach $R^2 = 0.67$ within that resource but collapse on the newly extracted chemistry ($\rho = 0.12$), while models trained on the new compounds transfer back successfully ($\rho = 0.80$). We conclude that the current composition of the published records, and not dataset size, is limiting the construction of more generalizable models, and we outline what would need to change in reporting practices for better data-driven permeability models.

Molecular encoders contrastively pretrained on paired molecule-morphology data, such as CLOOME and CellCLIP, have been proposed as cheap surrogates for phenotypic prediction, avoiding the need to run a Cell Painting assay. We evaluate this idea for these molecular encoders under a protocol designed to control for two confounds that can inflate apparent performance: leakage across an encoder's own pretraining boundary, and the correlation between phenotypic activity and cytotoxicity. Testing six representations, including a non-pretrained MLP control matching CLOOME's input and layer count, on two distinct Cell Painting screens, we find that once these confounds are controlled for, the pretrained molecular encoders show no clear advantage over plain physicochemical descriptors, and that toxicity is generally easier to predict than phenotypic activity across representations. Our results suggest leakage-aware, confound-controlled evaluation should be standard practice before phenotype-pretrained encoders are trusted as surrogates for phenotypic drug discovery.

Tabular foundation models (TFMs) achieve strong predictive performance by conditioning on labeled demonstrations provided in context, without any parameter update. Yet how individual demonstrations shape a given prediction remains poorly understood. This gap matters in practice: the context is often assembled from whatever labeled data is available, potentially leading to the inclusion of mislabeled, redundant, or low-quality examples that degrade performance. Standard data attribution methods do not transfer to the TFM setting: resampling-based approaches such as DemoShapley require a combinatorial number of forward passes, and gradient-based estimators such as influence functions require computing training point's effect on the model parameters, which in-context learning never updates. We introduce TICDA, a method that measures the influence of every demonstration in the context directly from linear surrogates trained on TFM latent embeddings, in a single forward pass and at negligible cost. We show that TICDA offers the best compromise against competitors across four tasks: detecting labeling errors, curating context to preserve predictive accuracy while lowering inference cost, producing attribution scores that transfer across TFMs, and supporting an acquisition strategy for efficient active learning.

A local measurement of a critical many-body state produces exponentially many microscopic outcomes, each defining a different conditioned quantum state. We ask how much information from one such outcome is actually needed to predict the entanglement that remains between two unmeasured regions. We show that, in critical quantum chains, the universal outcome-resolved Rényi entropy is asymptotically determined by a single compact conformal coordinate extracted directly from the measurement record. Compact-boson theory explains this compression: the universal entropy is insensitive to all spatially varying components of the boundary profile, retaining only a single relative compact zero mode. At the free-fermion XX point, exact lattice identities expose the microscopic structure underlying the decoder, while large-scale outcome-by-outcome calculations confirm its scaling prediction across different subsystem geometries and Rényi indices. Numerical calculations in interacting XXZ chains further show that the same microscopic coordinate continues to decode the conditional entropy without interaction-dependent retuning. Thus an exponentially large space of measurement outcomes is reduced, for this universal observable, to a single conformal degree of freedom, revealing an emergent Luttinger-liquid mechanism for outcome-resolved postmeasurement entanglement.

This paper studies waveform-level security for Integrated Sensing and Communication (ISAC). Instead of relying on spatial beamforming or power allocation, we randomize the sensing waveform itself using phase keys and tangent Artificial Noise (AN) applied to a Fourier-curve constellation. Coordinated legitimate nodes know the key and recover the sensing reference, while Eve observes only a randomized waveform and cannot construct the correct coherent matched reference. We consider an Unmanned Aerial Vehicle (UAV)-mounted Eve with a dominant Line-of-Sight (LOS) link who fully exploits favorable geometry, including a bypass scenario where Eve listens to both the direct and echo sides to circumvent our design. We further consider a stronger Eve that attempts phase-key reconstruction from long-term observations; even then, residual key mismatch structurally degrades correlation and AN cancellation, while accurate key recovery incurs high computational complexity. Numerical results show that the proposed design reduces Eve's probability of detecting the sensing reference using non-coherent detection and, in the bypass case, substantially suppresses her correct-delay lock probability, while the legitimate receiver reliably locks onto the reference through echo accumulation.

We study sparse locally private discrete mechanisms generated by a nonnegative kernel and an input-dependent admissible output support. The support set is intentionally small relative to the ambient alphabet and acts as a mechanism-design parameter. This formulation covers metric-ball supports, sparse exponential mechanisms, sparse staircase mechanisms, sparse randomized response, sparse additive kernels such as Skellam perturbations, and Poisson-binomial-inspired bounded-support channels. We give a general exact characterization of pure and approximate local differential privacy for this sparse-kernel class. Pure local differential privacy forces all supports to coincide, so genuinely input-dependent sparse supports are incompatible with pure privacy. In the approximate regime, the privacy defect decomposes exactly into support leakage and overlap excess loss. We instantiate the formula for several discrete mechanism families. For sparse staircase mechanisms, a shell-ratio condition eliminates overlap excess loss. For graph-metric supports, overlap of metric balls is necessary for nontrivial privacy. For sparse randomized response, the support-leakage term has a closed form in terms of support mismatch. For generic radius-truncated additive kernels and, in particular, sparse Skellam mechanisms, we obtain exact finite-support formulas in terms of the Skellam CDF and an exact Bessel-ratio overlap condition. Numerical evaluations illustrate how support radius and kernel shape separately affect support leakage and overlap excess loss.

For every integer $N\ge4$, we construct a fixed smooth, non-locally-conformally-flat metric on the $n$-dimensional unit sphere $\mathbb{S}^n$ for which the constant $Q_{2N}$-curvature equation admits an $L^\infty$-unbounded sequence of positive solutions. The construction applies for $n\ge2N+20$ when $N=4,5$, $n\ge2N+19$ when $6\le N\le8$, $n\ge2N+18$ when $9\le N\le17$, and $n\ge2N+17$ when $N\ge18$. For each $L \in \mathbb{N} \cup \{0\}$, the metric can be chosen arbitrarily close to the round metric in the $C^L$ norm. Together with the known cases $N=1,2,3$, this establishes noncompactness at every order, with dimension bounds that we expect to be optimal. We derive an explicit formula for the fixed-volume Hessian of total $Q_{2N}$-curvature in transverse-traceless (TT) directions at closed Einstein metrics satisfying $\operatorname{Ric}=(n-1)g$. Building on Juhl's formulas, we identify this Hessian, for every $N\in\mathbb{N}$ and $n>2N$, as a degree-$N$ polynomial in the Lichnerowicz Laplacian. For the metric perturbations generated by algebraic Weyl tensors in the construction, the quadratic reduced energy with fixed bubble center is a positive multiple of this Hessian restricted to a four-dimensional TT space. Differentiation with respect to the bubble scale then yields a finite matrix whose exact sign analysis establishes the required indefiniteness in the stated dimension ranges. After continuation to real $n$, this matrix changes from negative definite to indefinite at $n_N=2N+a_*+c_*N^{-1}+O(N^{-2})$ as $N\to\infty$, with $a_*\approx16.201871$ and $c_*\approx13.512880$, explaining the eventual bound $n\ge2N+17$.

First-generation quantum repeaters are essential in distributing entanglement over long distances since they could mitigate losses in optical fiber. Repeaters split the total distance into shorter, easier to generate links. Then, entanglement swapping establishes long range entanglement by performing local measurements at the repeaters and heralding their results. In this work, we develop an analytical model that estimates the impact of decoherence during heralding for a given protocol. Furthermore, we identify a competition between two phenomena: as repeater count increases, so does entanglement generation, but the additive impact of memory decoherence on final entanglement rate increases too. Therefore, we find that an optimal number of repeaters exists. These findings could lead the design of future quantum networks, both in the inter-repeater distance and swapping timings.

Model merging aims to build a multi-task model cheaply by combining the weights of individual task-specific models. To perform well across multiple tasks, most existing merging methods use an additional dataset to find the coefficients for the best linear combination of task-specific weight updates. However, we identify an implicit regularization in this standard practice: searching over coefficients restricts the candidate models to a subspace spanned by task-specific weight updates. In this work, we investigate whether this regularization is actually useful. Surprisingly, empirical results show that optimizing merged-model weights without this regularization significantly boosts the performance of common merging methods across multiple architectures, domains, and even in an extremely data-limited scenario where only one instance is available per class. Moreover, directly optimizing the pretrained model weights even outperforms some existing merging methods. Analysis shows that better multi-task weights exist outside the subspace and can be found using multiple methods. We study different strategies for using the additional dataset, discussing their practical use and implications for model merging. Overall, this work calls for revisiting the existing model-merging pipeline, motivating a broader exploration of the weight space and a reconsideration of the implicit regularization induced by task arithmetic.

Splitting the exponential and exponential-like functions can significantly reduce the overall computational cost of exponential integrators, providing a strong motivation for their rigorous analysis. In this paper, we analyze splitting errors for two noncommuting unbounded operators and derive new representations that include the popular Lie–Trotter and Strang cases. Moreover, within the abstract framework of strongly continuous semigroups, we prove the convergence of a split version of the exponential Euler method and a second-order exponential Runge–Kutta method for semilinear problems. Numerical experiments on a nonlinear dispersive equation and a diffusion–reaction equation demonstrate the theoretical findings, stability properties, and efficiency of the proposed split exponential integrators compared to the state of the art.

Uniform color spaces and color-difference formulae rest on visual data obtained almost entirely with surface samples and conventional displays, whose primaries confine the measurements to a limited chromaticity range. The highly saturated region of color space is therefore the least measured part of human color perception, at the moment when quantum-dot, microLED, and laser displays have begun to operate inside it. Closing this gap requires stimuli more saturated than any fixed-primary device can produce, together with the stability and uniformity demanded by visual experiments. We present an acousto-optic colorimeter built for this purpose. A four-channel acousto-optic tunable filter selects narrow spectral components from a supercontinuum laser over the calibrated range of 443–660~nm, with measured linewidths of 1.37–3.20~nm; the wavelength and radiance of every component are set electronically, so the primary set itself becomes an experimental variable. A compact diffuser–light-pipe homogenizer combines the selected components into a uniform observation field, and spectral feedback stabilizes their intensities. The calibrated primary set covered 95% of the area enclosed by the CIE 1964 $10^{\circ}$ spectral locus in the $x,y$ chromaticity plane. The calculated maximum luminance reached 1406~cd\,m$^{-2}$, with 328~cd\,m$^{-2}$ available at the gray Robertson chromaticity. Across an 18-mm observation field the mean spatial $\Delta E_{00}$ difference was 0.913, and five Robertson color centers reproduced under continuous feedback gave mean target errors of 0.34–1.26~$\Delta E_{00}$ over 10-min intervals. The instrument thus delivers calibrated, uniform, and stable highly saturated stimuli, and is intended to extend the empirical basis of color-difference measurement into the region where data are still absent.

Multimodal large language models have become the dominant paradigm for visual understanding, but incur substantial costs by encoding inputs into dense, fixed-size patch tokens. However, visual information is unevenly distributed: some regions require fine-grained detail, while others admit compact representations. Downsampling sacrifices this detail, while existing token pruning and adaptive approaches remain limited in content-adaptive granularity, task generalization, and integration with modern MLLMs and serving infrastructure. Overcoming these limitations calls for foundation models that learn, end to end, where-and at what granularity-to allocate visual representations, a native capability we term elastic visual representation weaving. We introduce VisionWeave, establishing this capability in frontier-level MLLMs through large-scale training. It combines two components: a gated spatial pooler constructs coarse-grained representations alongside native fine-grained representations within a shared MRoPE coordinate, while a granularity router learns their content-adaptive allocation. Through self-distillation alone, we validate this capability on Qwen3.5-4B and scale to Qwen3.8-27B with over 30K A100 GPU-hours. Based on Qwen3.8-27B, VisionWeave adaptively adjusts token savings to visual content, saving 43.0% tokens on average while retaining 98.9% native performance across eight benchmarks, versus only 88% performance preserved for token pruning baselines with a fixed 50% savings target. Extensive evaluations confirm robust efficiency-quality trade-offs across diverse tasks, resolutions and video frames. When deployed on SGLang serving engine, our method achieves a 2.3x throughput gain while reducing mean TTFT by 54.4% and mean TPOT by 60.6%. Together, we believe these results position elastic visual weaving as a promising capability for next-generation multimodal models.

We study divisibility of finite-dimensional quantum dynamics in the Heisenberg picture when the dynamical maps need not be invertible. Heisenberg divisible dynamics determines unique reduced propagators on the accessible operator systems, and Heisenberg CP-divisibility is shown to be equivalent to an operator-norm monotonicity. Although each reduced propagator admits a unital completely positive extension, independently chosen extensions need not satisfy a composition law. Generalized inverses restore this law algebraically, but do not, in general, preserve complete positivity. We characterize the resulting obstruction and give a sufficient construction based on unital completely positive projections onto the accessible operator systems. It is shown that for qubit dynamics Heisenberg CP-divisibility always guarantees a completely positive generalized-inverse propagator. Finally, we analyze time-local generators at singular times and identify the associated gauge freedom on dynamically inaccessible directions.

We give a unified analytic account of a finite bid–ask spread in a two-field reaction–diffusion order book. The model retains separate bid and ask densities in operational time, with diffusion, cancellation, reaction and external order creation. On the symmetric equal-coefficient branch, the imbalance field determines the reaction price, while the total standing density carries the spread geometry. A market-making source is introduced by withholding order placement over a finite interval around the reaction boundary, representing round-trip replenishment displaced from the quote. Under a separated, quasistationary and weak-overlap approximation, transport penetrates inward from the placement edges over the cancellation length, giving the quoted spread as the sub-threshold core of the placement-source-free interval. Market orders remove standing density at the observed quote, whereas replenishment is delivered outside it and must diffuse back across the penetration depth. We derive the resulting delayed and attenuated quote-level response in operational time. On that branch, finite spread and price impact arise from distinct response sectors, while their calendar-time appearance requires a separate observation clock.

Multimodal assistants answer questions from long-term memories that contain images. After retrieval, each retrieved image reaches the answering model either as pixels, at about a thousand visual tokens per image, or as a stored text proxy that often misses the detail the question asks about. We find that the benefit of pixels usually comes from one or two retrieved memories, and that it can be predicted before the answering model runs, without reading any full-resolution image. In PixelTriage, a plug-in placed after retrieval, a small model that does not generate text reads the dialogue, a short note and a thumbnail of each retrieved memory and predicts how much its pixels would add. It is trained on synthetic memory episodes labeled by a frozen 27B model that answers each question with and without each memory's pixels. With a 7B answering model, PixelTriage lies on the accuracy–cost frontier of M$^3$Exam, DMV and MemEye and uses 11–23% of the visual tokens without a significant loss of accuracy. On DMV it answers 2.9 times faster than opening all images. It outperforms retrieval order and uniform down-sizing at equal budgets and transfers to other memory systems and to a 397B answering model.

The stylic monoid $\mathrm{Styl}_n$, introduced by Abram and Reutenauer, is the quotient of the plactic monoid by the relations $x^2=x$, and its elements are represented by $N$-tableaux. Volkov showed that the Catalan monoid $\mathrm{Cat}_n$ of order-preserving, order-decreasing self-maps of $\{0,1,\ldots,n\}$ is a quotient of $\mathrm{Styl}_n$. However, the quotient map is defined on generators, and it is not apparent how to see, from an $N$-tableau, the map in $\mathrm{Cat}_n$ it corresponds to. In this paper we give a simple visual way to read off this map, and some of its main properties, from the $N$-tableau. The new ingredient is that we do not insist on drawing an $N$-tableau as a classical Young tableau: we allow the entries of each row to be shifted relative to the row below, as long as each entry stays above a smaller one. We call this a positioning, and prove that the column word read from any positioning is plactically equivalent to the usual column word; so every positioning can be used to compute the quotient map. We work with the tight positioning, in which each entry is pushed as far right as possible, and define the full core of an $N$-tableau: the part of each column that climbs by consecutive values from the bottom row. We call an $N$-tableau full if it equals its full core. We prove that passing to the full core does not change the image in $\mathrm{Cat}_n$, that full $N$-tableaux are in bijection with $\mathrm{Cat}_n$, and we show how to read the corresponding map directly off a full $N$-tableau.

Monocular metric depth estimation and 3D visual grounding represent the two complementary cornerstones of monocular 3D spatial understanding (M3Sun), from which the fundamental 3D spatial information required by M3Sun can be acquired. However, these complementary tasks are generally conducted by separate frameworks, which pose challenges of inflexible and unaligned spatial information access for embodied intelligence systems. In this paper, we propose a unified agent for monocular 3D spatial understanding (M3SunAgent) that leverages a large language model (LLM) as a task planner for spatial visual programming, which flexibly generate structured programs and coordinate tools. For instance-level metric depth estimation task, M3SunAgent invokes an object detector tool to locate the target, estimates depth at selected points with a depth estimation tool, and aggregates these predictions into an instance-level depth estimate. We also construct the M3Sun Instance (M3SI) dataset, a benchmark with 2,910 samples for evaluation. For monocular 3D visual grounding task, M3SunAgent uses a vision-language model (VLM) tool to locate the target and output basic spatial attributes, then combines back-projection tool with a dimension-lifting tool to predict its 3D bounding box. Experimental results demonstrate the superior performance of M3SunAgent. Specifically, in evaluations of instance-level monocular metric depth estimation, M3SunAgent achieves the best performance among all compared models, 52.61% of predicted instances are distributed below depth error 0.25 ($\delta < 0.25$). In evaluations of monocular 3D visual grounding, M3SunAgent demonstrates overall competitive performance than vision and VLM models, reaching a 3D mean intersection over union (mIoU) of 41.73% and exceeding the state-of-the-art MonoVLM model by 3.62%.

Higher-order models (e.g., hypergraph neural networks) often outperform lower-order baselines on hypergraph learning benchmarks, and their advantages are commonly attributed to their ability to exploit higher-order information. However, better performance alone does not establish this explanation. We therefore ask: Do higher-order models win for higher-order reasons? To investigate this question, we introduce a controlled performance-attribution framework that perturbs higher-order information while preserving the lower-order, i.e., pairwise, information. Across 25 commonly used hypergraph learning benchmarks spanning three tasks, we frequently observe an intriguing pattern: higher-order models originally outperform lower-order baselines, yet retain most of their advantage after perturbation. This suggests that much of the observed advantage remains achievable without the higher-order information. We then investigate potential lower-order explanations for these remaining gaps. We find that simple additions to a lower-order baseline, e.g., richer pairwise weighting, more steps of pairwise feature propagation, and normalization, reduce the remaining performance gaps, supporting lower-order explanations for part of the observed advantage. Our analysis calls for the hypergraph learning community to rethink performance attribution by distinguishing performance gains from their explanations, adopt stronger lower-order baselines, and use suitable benchmarks that better test the value of higher-order information.

High-temperature creep in metals remains challenging due to the complex interplay of deformation and failure mechanisms across multiple length scales. The trade-off between inter- and trans-granular cracking governs the transition of creep rupture behaviour in metallic materials. However, the micromechanical basis of the transition and its linkage to the macroscopic brittle to ductile transition in creep rupture behaviour remain unresolved. Here, the stress-dependent competition between grain-boundary cavitation and slip-induced intragranular cracking is revealed via a unified crystal plasticity fracture framework. The framework incorporates crystal plasticity, grain-boundary cavitation, and crystallographic crack propagation within an explicit polycrystalline microstructure. The microscale computation reveals the transition from trans-granular-dominated cracking at high stress levels to mixed inter- and trans-granular cracking at intermediate stresses and inter-granular-dominated cracking at lower stresses, accompanied by distinct damage localization modes and the evolution of crack paths from grain boundary to grain-interior propagation. The results further quantify the linkage between microscopic fracture mechanisms and macroscopic creep rupture behaviour, including changes in rupture ductility and creep life. Under high-stress conditions, deformation-driven trans-granular damage localization promotes ductile rupture through extensive strain accumulation, whereas under lower-stress conditions, time-dependent grain-boundary damage accumulation leads to quasi-brittle rupture through localized inter-granular fracture.

As agents continuously improve by generating and revising Skills, the process that discovers and refines those Skills becomes a learnable object in its own right. Task-Skills directly act on task execution, whereas Meta-Skills govern how agents discover and improve future Skills; their value therefore emerges through the subsequent search processes they induce. Existing approaches improve Meta-Skills from observed raw Skill-search trajectories and branch outcomes. However, branch performance entangles the effects of the initial discovery state and the Meta-Skill revision that generated the search process, making it difficult to characterize what a particular revision actually changed, and pushing updates toward revisions that benefit from favorable states rather than those that improve the process. We introduce HMED (Hindsight Meta-Experience Distillation), a mechanism for constructing Meta-Experience for self-improving agents. HMED revisits the completed event from which a revision originates and re-executes the incumbent and revised Meta-Skills from the same restored discovery state, so that the changes associated with the revision can be observed under a shared condition. Each comparison is distilled into a Meta-Experience, a structured record that can be reused by future updates, so that even revisions that are not ultimately retained still contribute a learning signal. Across three interactive agent benchmarks and both open-source and closed-source models, HMED consistently improves Skill discovery performance over strong baselines, shifting Meta-Skill learning beyond branch outcomes toward the consequences of changing the improvement process.

In this paper, we study one-dimensional semilinear stochastic wave equations driven by multiplicative space-time $G$-white noise under sublinear expectation. We establish the existence and uniqueness of global mild solutions. By developing the quadratic variation structure of space-time $G$-white noise and establishing a Burkholder-Davis-Gundy inequality for the associated stochastic integrals, we derive higher-order moment estimates and prove the quasi-sure Hölder continuity of the solutions. We further show that the mild solution satisfies the corresponding weak formulation.