Papers

Bayesian inference for latent point process intensities often relies on per-dataset sampling or optimization, making repeated inference computationally expensive. We propose a neural-network-based amortized variational framework that learns a reusable inference rule mapping a variable number of replicated point patterns to a distribution over their shared latent intensity. Trained from event times using the point process likelihood, the model learns an amortized inference rule without ground-truth intensity supervision. At test time, it performs inference of the latent distribution in a forward pass. On synthetic data, additional realizations improve intensity recovery and yield narrower credible intervals with broadly stable coverage. Our method is tested on bicycle-sharing data and achieves the highest mean held-out log likelihood among the evaluated methods while requiring substantially less inference time than the Log-Gaussian Cox Process baseline.

We prove an upper bound for the error term in the higher rank hyperbolic lattice counting problem for ${\hbox{SL}(n, \mathbb{Z})}$. Blomer and Lutsko achieved recently a significant improvement of previous known results by Duke–Rudnick–Sarnak and Gorodnik–Nevo–Yehoshua. We deduce an improved upper bound for the error which holds for almost all pairs $z,w \in {\hbox{SL}(n, \mathbb{R})}$. We also derive a $\Omega$-result for the error term, in the spirit of Rudnick–Phillips.

Accurate modelling of soft tactile sensors remains difficult because finite element methods (FEM) are computa- tionally expensive, while real-time simulators often lack fidelity for hyperelastic deformation. Large physical datasets are also impractical to collect because repeated testing can damage fragile sensors. We present a data-efficient framework that combines limited real-world validation, high-fidelity FEM, and graph neural networks (GNNs) for accurate real-time prediction of two-dimensional tactile deformation in a planar soft tactile structure. The key idea is to decouple validation from training: 82 camera-tracked contact configurations are used only to tune and validate an ANSYS FEM model, which then generates 768 synthetic contact scenarios for GNN training. We evaluate both forward prediction from marker deformation to contact localisation and inverse inference from contact configuration to marker deformation. The validated FEM achieves sub-0.5 mm error in more than 90% of validation cases, while the learned GNN surrogate reaches a mean absolute error of 0.32 mm with millisecond-scale inference, compared with minute-scale FEM simulation. Models trained entirely on synthetic FEM data retain sub-millimetre accuracy on real measurements from the 2D tactile structure, demonstrating strong sim-to-real transfer within the tested planar setting. We further integrate the learned model into a real-time visualisation pipeline, enabling rapid deformation prediction for virtual prototyping and simulator-based design exploration without extensive physical testing.

Vision-language models (VLMs) like CLIP have shown great success in image tasks, however, applying CLIP to open-vocabulary video recognition poses challenges. Due to the limited text information, directly fine-tuning CLIP on video recognition datasets may lead to overfitting and hinder its generalizability. A prevalent method is to enrich text information by generating prompts using Large Language Models (LLMs). However, limited efforts have been made to explore how to generate higher-quality prompts that can contribute to classify unseen categories, and how to further enhance vision-text alignment based on these prompts. In this paper, we propose P2CLIP (Prompt-guided CLIP), which aims to bridge this gap by exploring the impact of prompts across three aspects: category, video, and frame. At the category level, we argue that LLM-generated prompts under simple instructions may suffer from semantic overgeneralization, which can blur the category boundaries and hinder the performance of the model. To address this issue, we design Generic-Discriminative Prompt using LLMs to obtain discriminative category embeddings with rich semantic information. At the video and frame levels, we first use VLM and LLM to generate frame and video descriptions for enhancing vision-text alignment. Then we propose a Knowledge-Guided Temporal Aggregation mechanism, which leverages the expert knowledge derived from LLMs to guide the temporal modeling of videos and encourage a better construction of the joint visual-textual feature space. Extensive experiments across various benchmarks, including zero-shot and few-shot settings, demonstrate the effectiveness of our method.

In this work, we study restricted Laistrygonian algebras over a field of positive characteristic $p$. We compute their Drinfeld double $\mathtt{D_p(q,a)}$ and give explicit presentations by generators and relations. We prove that $\mathtt{D_p(q,a)}$ is a pointed Hopf algebra. For $\mathtt{D_p(1,a)}$, we describe an abelian exact sequence of Hopf algebras and identify one of its quotients as a restricted enveloping Lie algebra. This exact sequence enables us to classify the finite-dimensional simple $\mathtt{D_p(1,a)}$-modules. We also introduce an infinite-dimensional Hopf algebra covering the restricted Drinfeld double and study its relation with the corresponding finite-dimensional case. Using this covering together with a Frobenius map, we construct a $3\times 3$ commutative diagram whose rows and columns are exact sequences of Hopf algebras. In particular, our approach provides a unified treatment of the Drinfeld doubles associated with restricted Laistrygonian algebras in arbitrary positive characteristic.

There is growing interest in applying Parameter-Efficient Fine-Tuning (PEFT) to Continual Learning, as it enables faster training, mitigates catastrophic forgetting, and facilitates better adaptation to new tasks. Prior approaches have explored a range of strategies, including extending new LoRA branches for each incoming task, training under orthogonal loss objectives across all task-specific LoRA modules, and employing gating mechanisms to integrate new and existing LoRA modules. However, these methods incur memory costs that grow linearly with the number of tasks, limiting their scalability. More recent approaches investigate training a single LoRA by leveraging asymmetries in its parameterization; however, they often suffer from insufficient representational alignment across the LoRA parameter space. To address these limitations, we propose Stiefel Optimization and Aligned Rotation (SOAR), a two-stage framework for continual LoRA learning. First, we constrain the A matrix to lie on the Stiefel manifold, thereby reducing coordinate misalignment to the space of orthogonal rotation matrices. Second, we introduce an Orthogonal Procrustes alignment procedure for the B matrix to estimate the optimal rotation, coupled with a per-rank retention merging strategy that quantifies directional agreement between representations of new and previously learned tasks. We conduct extensive experiments across multiple models and benchmarks, demonstrating that SOAR achieves strong continual learning performance without incurring additional memory overhead.

Within the framework of non-extensive statistical mechanics, $q$-Gaussian distributions arise as maximum-entropy solutions of Tsallis entropy under suitable escort moment constraints. Although widely used in physics, biology, geology, finance, and related fields, standard $q$-Gaussians are intrinsically symmetric and cannot capture asymmetric fluctuations often observed in empirical data. We ask whether asymmetry can arise from the Tsallis maximum-entropy principle without externally skewing or joining distributions. We show that this is achieved by retaining the Tsallis entropy and imposing a global escort mean together with distinct downside and upside escort semi-variances. The key step is to reformulate the problem of maximum Tsallis entropy in terms of the escort density. The nonlinear escort constraints then become affine, while maximizing Tsallis entropy becomes equivalent to maximizing a strictly concave functional over a convex feasible set. Consequently, any admissible stationary solution is the unique global maximizer of the corresponding variational problem. The finite-sample approximation properties of the proposed asymmetric $q$-Gaussian are studied through Monte Carlo experiments using synthetic data generated from Azzalini skew-Student distributions. Compared with the classical symmetric $q$-Gaussian, the asymmetric specification systematically provides a closer approximation to synthetic asymmetric heavy-tailed distributions. Finally, we fit the model to return series from major equity indices, a commodity, and cryptocurrencies, and compare its in-sample goodness of fit with that of a symmetric $q$-Gaussian. The results show that the asymmetric model offers a closer in-sample description of unconditional return distributions, most clearly in the tails.

Intermediate-orbit ($\sim 1$ AU) brown dwarfs with absolute mass measurements are essential for understanding the evolution of substellar objects. Although such systems remain rare, their number is now being enlarged thanks to astrometry. Here, we present the absolute mass measurements for HD 203771B, a massive brown dwarf orbiting a K dwarf ($M_\ast=0.79\pm0.08\ M_\odot$) with a period of 1140 days on an eccentric ($e\approx0.5$) and inclined ($i\approx 130^{\circ}$) orbit. Through joint analysis of (1) radial velocities and Gaia two-body solution, as well as (2) radial velocities, Hipparcos Intermediate Astrometric Data and two-epoch Gaia astrometry, we obtain true companion masses of $74.20^{+3.46}_{-3.64} M_{\mathrm{J}}$ and $69.03^{+4.99}_{-4.95} M_{\mathrm{J}}$, respectively, agreeing with each other within $1\sigma$. Taking a sample of 159 brown dwarfs with absolute mass measurements from different detection techniques, we investigate their eccentricity distributions across different semi-major axis ranges by fitting a Beta distribution. We find that the peak of eccentricity distribution tends to gradually shift toward lower values from wide orbits ($a>20$ AU) to intermediate ($1<a<20$ AU) and inner ($0.1<a<1$ AU) regions. Such trend is plausibly due to disk friction during orbital evolution. Together with obliquity studies showing that brown dwarfs are mostly aligned, our result suggests that brown dwarfs may migrate inward through quiescent coplanar disk-driven processes.

An LLM agent using tools can fail silently. It stops before the task is done, raises no error, and answers fluently. Two kinds of monitor address this, one deciding whether a run failed and the other naming the step where failure became unavoidable. Much of the reported performance on both tasks comes from regularities that need no model. Failing runs are longer, and the step labelled decisive is usually the last. A rule that always names the last step is correct $67\%$ to $96\%$ of the time here, without reading the run at all. That ceiling reflects how the labels were written, not how agents break. On failures whose decisive step replay can confirm, it falls to near chance. Reporting gain over that rule therefore changes what a score means. Under that correction, methods tested here gain nothing on give-up failures, while several published systems keep a clear advantage on other splits. For detection, the agent's internal states beat transcript length and text similarity on the agent benchmark, and hold up where the text baseline does not. Precision stays low when failures are rare, so such a monitor should rank runs for review, not replace it.

Information-theoretic and geometric compression have been widely studied as possible explanations for generalization. Yet their temporal dynamics in recurrent networks remain largely unexplored. Using discretized LSTMs, whose finite embedding space enables direct estimates of information quantities, we observe pronounced compression across the final timesteps of many datasets. We explain this effect through three competing mechanisms: (i) class separability permits stronger compression at the final timestep; (ii) shared recurrent dynamics propagate this pressure across timesteps with similar activation states, making its extent depend on temporal stationarity; and (iii) limited representational capacity opposes prolonged compression because it restricts information available for subsequent computation. We systematically test these mechanisms through controlled synthetic interventions and real-world sequence tasks. Our results identify class separability, temporal stationarity, and network capacity as key determinants of temporal compression, and suggest that compression acts as a regularizer-potentially beneficial when excess capacity is available, but harmful to generalization when it consumes memory needed for the task.

In this work, we present a comprehensive theoretical study for the topological and anomalous transport properties of type-II SDSMs under three scenarios, i.e., static symmetry-breaking perturbations, periodic Floquet driving by two-frequency orthogonally polarized light (TFOPL), and their cooperative effects in the hybrid scenario. We first show that a static mass $m_z$ opens a bulk gap and drives the system into a Chern insulator with Chern number $C^{\rm per}=\pm 2\,{\rm sgn}(m_z)$. In comparison, TFOPL alone only shifts the positions of Dirac points and cannot open a full gap. Nevertheless, it produces a Berry curvature odd in the $x$-direction, yielding a finite Berry curvature dipole (BCD) along $x$ proportional to the sine of the initial phase, while the $y$-component vanishes. The hybrid scenario, by contrast, exhibits a remarkably rich phenomenology. Specifically, its gap-closure criterion becomes cubic and thus admits up to three real roots when the effective parameter along the $x$-direction is negative, thereby producing multiple light-tunable gap-closing points and a series of topological phase transitions. In particular, the BCD exhibits a double-peak structure with strong enhancement near gap-closing manifolds and synchronized sign reversal of the full vector under external tuning. We further analyze the anomalous Hall conductivity (AHC), anomalous Nernst conductivity (ANC), and anomalous thermal Hall conductivity (ATHC). The AHC and ATHC exhibit quantized plateaus that serve as signatures of Chern-insulator phases, while the ANC, being a Fermi-surface probe, provides complementary local information and can identify light-induced gaps even when global topological invariants remain unchanged. Taken together, these results offer useful insights into the topological properties of 2D type-II SDSMs and related systems.

In this paper we show there does not exist any arrangement of degree $7$ consisting of $k\geq 1$ conics and $d\geq 1$ lines admitting certain naturally chosen ${\rm ADE}$-singularities.

In this note we show that all interval exchange transformations of three intervals (3-IETs) are spectrally disjoint from all mixing and disjoint from lightly mixing systems. Until now, it was known that almost every 3-IET is rigid, which implies this property. However, not all 3-IETs are rigid, hence our result is a strict improvement of current knowledge. We then use this result, among many others, to prove that although some 3-IETs are mildly mixing, they are always disjoint in the sense of Furstenberg from lightly mixing systems.

Wireless propagation modeling is foundational to the evaluation and design of modern communication systems. To achieve accurate wireless propagation prediction, recent learning-based approaches leverage scene geometry and materials, demonstrating promising generalization across transceiver locations and unseen scenes. However, these approaches remain largely confined to a fixed configuration of array size, receiver orientation, and transmit beam. In this work, we introduce RFWeave, a learned wireless propagation model designed to generalize across scenes, transceiver locations, and transceiver configurations. To accommodate varying array structures, RFWeave incorporates variable-length transceiver tokens that represent antenna elements individually. Furthermore, to capture the geometry between transmit and receive antenna elements, RFWeave aggregates their pairwise spatial relations into propagation tokens. A configuration-conditioned decoder predicts the spatial spectrum and received power. RFWeave is trained on a large-scale simulated dataset spanning 10,000 indoor scenes and more than 5 million channel records under diverse transceiver configurations. Extensive evaluations show that RFWeave achieves state-of-the-art performance across all evaluated generalization settings, improving spatial spectrum structural similarity (SSIM) by up to 15.7% and reducing received power mean absolute error (MAE) by up to 35.4% over the strongest baselines on unseen scenes. Additional experiments on measured DICHASUS data and in beam management further demonstrate RFWeave's broader applicability to real-world channels and downstream wireless tasks.

Decision APIs that return a probability for each option are routinely used as if those probabilities were properties of the options themselves. That reading is valid only if the model satisfies independence of irrelevant alternatives (IIA): adding an option that is neither the right answer nor its strongest rival should leave the odds between those two unchanged. We test this in a pre-registered study of jev-1.13.0, a hosted decision model, using 299,463 calls on intent classification (BANKING77, CLINC150) and topic classification (AG News). Every added option moves the log-odds between the gold label and the strongest wrong label: the root-mean-square systematic shift is 0.20-0.52 nats, 1.2 to 3 times the run-to-run variation, even when the added option takes at most 0.1% of the probability mass. The shifts are directional. An option similar to the wrong answer draws probability from it (+0.10 nats toward the gold label). A paraphrase of the wrong answer produces an intermediate pattern: the gold label's probability is almost conserved, but the paraphrase receives only about a third of the wrong answer's share rather than the half that strict substitution implies. The distortion grows steadily with the logarithm of the number of options, reaching about 1 nat at 255 options, and off-domain padding pushes the odds against the gold label. In contrast, questions packed into one call do not interact (bias < 0.001). Scoring each option with an independent yes/no question removes the option-set dependence but picks the right answer 8.7 points less often. Jev sits between two local baselines, an option-independent scorer and a prompt readout. Its probabilities are best read as relative to the option list they were computed over.

Flow matching models are typically trained to transport a Gaussian source to the data distribution, with source and target samples paired independently. We replace the source with a fitted Gaussian mixture and couple each data point to a mixture component through an entropic optimal transport problem. We show that the resulting transport reduces to the standard Gaussian-source problem up to a guidance-like correction, which enables the reuse of a pretrained velocity field. This correction is a closed-form function of the fitted mixture plus a term that we learn with a small correction network. We test our model on published checkpoints for CIFAR-10 and CelebA-HQ. It improves FID at every step count, and on CelebA-HQ it reaches the quality of the baseline with about half the steps. The closed-form term alone, with no training, already delivers most of this improvement; the small correction network accounts for the rest.

Counting is a simple task on which transformers can nevertheless fail at long sequence lengths. We study the cost of counting in a single attention layer, up to a maximum length $L$, focusing on how softmax attention and layer normalization shape the representation from which the count is recovered. We mainly focus on regression read-out but also consider classification read-out. For regression, we show unnormalized linear attention counts exactly at parameter norms independent of $L$. For softmax attention, regression cannot count exactly with finite parameters; it recovers the count after rounding, but only when the vector parameter norms grow with $L$. We measure this cost by $B_{\min}$, the smallest bound that can be placed on every trainable vector to ensure exact counting after rounding, and derive tight rates. At fixed model dimension, $B_{\min}$ grows as $L$ without normalization, as $L^{3/2}$ under bare post-normalization, and as $L^{3/4}$ with learned post-normalization. The last rate is unexpected: post-normalization discards the magnitude that carries the count and might be expected to make counting harder, yet with a learnable gain it counts at a smaller norm than softmax without normalization. Bare pre-normalization is different: it bounds the attention scores, so beyond a finite length no parameter norm suffices. A classification read-out keeps every norm bounded under every placement, but a dense head stores one output vector per count and costs more in storage. Experiments on the post-normalized model reproduce this split between the two read-outs. Together, our theoretical and empirical findings characterize how self-attention, layer-normalization placement, and read-out choice shape the representation geometry and parameter cost of counting in the minimal single-head architecture studied here.

We introduce IND-Eval, a public benchmark that organizes industrial time series across domains into source-specific forecasting tasks. Relative to established benchmarks such as GIFT-Eval, it emphasizes finer sampling resolutions and a greater prevalence of multivariate forecasting. Evaluating Chronos-2, TiRex-2, and TimesFM-3, we find that TimesFM-3 achieves the lowest source-balanced aggregate nMASE and nCRPS and leads seven of nine sources under each metric; source-specific exceptions reinforce the need for domain-representative evaluation for model selection. These findings also motivate improving domain alignment during pretraining, where real industrial data are often too scarce to close domain-specific gaps directly; we therefore investigate whether a domain's statistical structure can guide simulator design. In a case study on two offshore well-monitoring regimes, we improve a general simulator's coverage using an oscillator-augmented simulation pipeline. This lowers forecasting error in the target domain but reduces performance on the subset of GIFT-Eval with natively univariate targets. A 50/50 mixture of the general and augmented simulation recipes achieves the lowest error among the three training recipes for all four event-metric pairs in the case study while recovering most of the lost GIFT-Eval performance. Together, these results illustrate how domain-representative evaluation can guide model selection and the composition of simulated data while revealing a trade-off between specialization and generality.

Industrial software applications often require engineers to tune the software deployment platform. Configuration tuning identifies valuable configurations that minimize costs while ensuring the application performance. However, finding these configurations is difficult. The number of tunable configuration parameters in industrial applications is large, and engineers cannot assess different configurations in production because users may experience performance degradation. This work targets Kubernetes: A system for automating the deployment, scaling, and management of containerized applications. This paper proposes a domain-knowledge-driven solution for finding configurations of industrial applications in a practical time. The solution relies on a catalog of constraints encountered by domain experts in similar applications. Depending on the problem under analysis, engineers can customize the optimization problem by selecting the relevant constraints from the catalog for the application at hand. We rely on two alternative solvers to find an optimal configuration: The first is based on heuristics, while the second reuses existing optimization-based solutions. We implemented our solution within an industrial tool from a software company specializing in performance engineering and optimization. We compare our solution to a baseline, considering a set of predefined configuration values provided by engineers. Our results confirm the effectiveness of our solution: Compared to the baseline, the heuristic-based and optimization-based solutions provide significant average savings of 11591 USD/mo and 15874 USD/mo per Kubernetes, respectively, accounting for 24.03% and 32.90% of the costs, in practical time (0.71 seconds per extraction for the heuristic-based and 45.54 seconds per extraction for the optimization-based solution).

We study the propagation of a neutral vector test field non-minimally coupled to the Einstein tensor on a Reissner–Nordström black hole. The interaction vanishes on a vacuum background, so electric charge is required to activate the curvature-induced response. The parity potentials have one symmetry: reversing the sign of the coupling exchanges the electric and magnetic susceptibilities. Because of this symmetry, the two polarizations respond identically at first order in the coupling. The dominant propagation-level effect is therefore a common shift of the effective photon sphere and of the shadow radius, not a birefringent splitting. The variation of shadow size can mimic the charge variation of a black hole. When the coupling is weak, polarization splitting appears only in the second-order term, distinguishing this interaction from corrections involving only charge. We follow this ordering through full-frequency absorption and scattering, the semiclassical glory, and ray-traced double shadows. The absorption parity asymmetry and the shadow rim splitting probe the difference between the effective potentials. The polarization-summed backward scattering isolates the helicity-reversing response, which is zero without the coupling. At the positive-coupling boundary the splitting grows but stays finite. Beyond it the even-parity potential has a pole outside the horizon. In the high-multipole limit, the two boundaries of the stability window both correspond to the thresholds of bound-state instability, but their physical properties differ: the negatively coupled boundary forms a regular potential well, while the positively coupled boundary marks the breaking of regularity. A Frobenius analysis shows a forced logarithmic branch at that pole. Without an additional physical connection condition, the continuation across the pole is not unique.

The sums of the absolute values of higher-order cumulants are classical contrast functions for independent component analysis (ICA) and lead naturally to robust approximate diagonalization of higher-order cumulant tensors using $\ell_1$-based diagonalization over the orthogonal or unitary group. We propose Jacobi-SubG, a Jacobi-type framework that selects index pairs using Riemannian subdifferential information and performs plane rotations with a refinement step that preserves nonzero diagonal contractions. For the general tensor model, we prove global convergence of the entire iterate sequence from any initialization with nonzero diagonal contractions, provided that the subproblem solvers satisfy a uniform sufficient-ascent estimate. For real and complex third- and fourth-order cumulant tensors, which are widely used in ICA, we develop specialized subproblem solvers satisfying these conditions. The resulting algorithms thus enjoy global convergence under the simple initialization condition that all diagonal contractions are nonzero. Numerical experiments on ICA and tensor diagonalization show that the proposed Jacobi-SubG variants achieve better source recovery and higher final objective values in several settings, particularly at the higher tested noise levels.

Let $\Phi(G)$ denote the number of perfect matchings of a graph $G$. Goedgebeur et al. posted two questions about the perfect matchings of planar 3-connected graphs: does there exist an infinite family of matchable planar 3-connected graphs of girth 5 with a constant number of perfect matchings? Whether there exist infinitely many planar 3-connected graphs with minimum degree 5 which have a constant number of perfect matchings. We present answers to those questions. First, we construct, for every even $n\ge196$, a simple planar 3-connected graph of order $n$ and girth five with exactly $c$ perfect matchings, where $c$ is a fixed positive integer. Second, for a simple planar 3-connected graph $G$ with a perfect matching and minimum degree at least five, we show that $\Phi(G)\ge2^{\lceil(|V(G)|+20)/22\rceil}$. This implies that, for each positive integer $t$, only finitely many such graphs, up to isomorphism, have at most $t$ perfect matchings.

Muons have fascinated physicists since their discovery in cosmic rays almost a century ago. Their large mass and relatively long lifetime allow relativistic muons to traverse large amounts of matter, a property that has been exploited to probe otherwise inaccessible structures, from volcanoes and archaeological monuments to shielded nuclear materials. Here, we experimentally demonstrate for the first time that muon scattering tomography can be extended to biological soft tissue. We image an anthropomorphic thorax phantom using a 2 GeV/c muon beam at the CERN Proton Synchrotron and reconstruct its three-dimensional scattering density from the measured deflections of individual muons. Despite the weak scattering produced by tissue-equivalent materials, the reconstructed density agrees with the expectation from simulation at the percent level. Our results extend muon imaging into a previously unexplored regime and open the possibility of using muons as a complementary probe for medical imaging.

Machine translation (MT) is increasingly utilized in multilingual crisis communication, yet conventional evaluation does not directly assess whether translated emergency messages preserve their actionability. We introduce SIREN (Situation-aware Index for Response and Emergency ActioNability), a human evaluation framework assessing whether translation choices compromise protective action, directive force, and urgency of the source text. We evaluate SIREN in two complementary settings. At the error level, we apply it to HOPE-annotated Italian–English translations produced by ChatGPT-4o and Google Translate: 31.63% and 48.73% of errors, respectively, compromise actionability, predominantly by affecting the protective action. At the message level, we evaluate English–French translations produced by TranslateGemma-4B and Google Translate, with actionability preserved in 85.34% and 92.67% of translations, respectively. TranslateGemma-4B failures predominantly weaken directive force, whereas Google Translate failures more often compromise protective actions and receive Major impact ratings. These findings show that translation systems can differ not only in how often actionability is lost, but also in the nature and functional impact of these failures. Alongside SIREN, we contribute an English–French crisis-translation resource with human actionability annotations and post-edited reference translations, supporting further research on function-oriented evaluation for crisis communication. Our experimental data is available at https://github.com/mcstaiano/SIREN.

Recovering divergence-free velocity fields from sparse and corrupted observations requires reconciling physical consistency, expressive representations, and robustness to missing data. We introduce DFK-Former, a set-to-field transformer that reconstructs divergence-free velocity fields from sparse, noisy, and irregularly sampled 3D observations. The model is inherently invariant to the number and ordering of input samples and predicts the parameters of a divergence-free kernel representation, producing continuous, mesh-free velocity fields that satisfy incompressibility exactly by construction rather than approximately through soft constraints or projection operators. Unlike existing divergence-free kernel approaches, which estimate kernel coefficients via a separate optimization for each field, DFK-Former predicts these coefficients directly in a single forward pass. This eliminates costly iterative fitting while providing a learned prior that enables accurate reconstruction even when observations are insufficient to uniquely determine the field. To enhance representational power, we introduce adaptive and anisotropic divergence-free kernels that preserve exact incompressibility guarantees while capturing more complex flow structures. Extensive experiments across varying levels of sparsity, noise, and occlusion, including transfer to real Direct Numerical Simulation (DNS) turbulence data, demonstrate substantial gains in both accuracy and efficiency. DFK-Former reduces endpoint error by up to 4.6x compared to per-field divergence-free-kernel optimization, while reconstructing each field in 7.5 ms instead of 9.8 s, yielding a speedup of more than three orders of magnitude. These results establish direct, feed-forward prediction of divergence-free kernel parameters as a practical and effective paradigm for physically consistent velocity-field reconstruction from sparse observations.

Learning a response law for continuous decisions from observational time series is central to many real-world decision systems, yet temporal non-stationarity poses a fundamental challenge: as outcomes drift over time, naively pooled models can conflate action effects with shifting baselines and even reverse action rankings. Even when the one-step response is identifiable, unrestricted cross-time generalization remains fundamentally ill-posed. We therefore seek the part of the response that remains stable for decisions even when outcome levels do not. We propose deployable causal action geometry: the action-response shape that remains after anchoring away action-independent level shifts on a selected link scale and profiling out positive amplitude variation. Building on this target, we develop a two-stage orthogonal estimator that first obtains cross-fitted pilot estimates of anchored responses and then performs honest profiled selection over link, representation, and shape classes. The resulting estimator admits oracle guarantees for the restricted target and, under approximate persistence, produces decision rules that remain near optimal in future periods. Experiments on synthetic data and Dominick's support the proposed target and its transfer behavior. In a randomized Taobao A/B test, the deployed system improves GMV and purchase counts by \(1.16\%\) and \(1.70\%\).

The deep hole problem is a fundamental problem in coding theory, and it has many important applications in code constructions and cryptography. The deep hole problem of Reed-Solomon codes has gained a lot of attention. As a generalization of Reed-Solomon codes under Hamming metric, we study the covering radius and deep holes of Hyperderivative Reed-Solomon (HRS) codes under the Niederreiter-Rosenbloom-Tsfasman (NRT) metric. We determine the NRT covering radius of HRS code and characterize its NRT deep holes via Maximum Distance Separable (MDS) extensions and polynomial remainder conditions. We further relate the enumeration of NRT deep holes to the characteristic polynomial of an associated hyperplane arrangement. We also provide three classes of explicit NRT deep-hole constructions, propose a Cheng-Murray type conjecture for HRS codes under the NRT metric and obtain a conditional low-layer description. Using these characterizations, we derive exact enumeration formulas in several special cases.

Ultrasound image quality depends on both the probe geometry and the transmit and receive processing, but engineers usually design the two separately. Physics-based simulators (Field II, k-Wave, MUST/SIMUS) compute the radio-frequency channel data but give no gradients, so design studies must use grid or black-box searches that become slow as the number of parameters increases. We present a fully differentiable end-to-end pipeline for plane-wave ultrasound imaging, with synthetic speckle phantoms, an analytical frequency-domain RF simulator, delay-and-sum beamforming and an extensible image-quality objective. The element pitch, the transmit and receive apodization and the global speed of sound are differentiable parameters of one computation graph, so one reverse-mode pass gives their exact joint gradients. Studies of each parameter rank the design parameters: the optimized pitch decreases the grating lobes, and the speed-of-sound autofocus gives clear contrast and resolution gains. Over 15 test phantoms, the optimized pitch increases the cyst gCNR from 0.55 to 0.66 (about 20%), and the speed-of-sound correction adds a further 0.05. The lateral point-spread function agrees with Field II within about 10%, and on 49 real CUBDL plane-wave acquisitions from five institutions, the framework finds the global speed of sound with a mean absolute difference of 16.6 m/s from the published corrections and phantom speed of sound.

Cross-task generalization remains difficult for world action models (WAMs), even when their predicted futures depict plausible manipulation. This gap can be attributed directly: we make this gap directly testable by decoupling a WAM into a world model and an inverse-dynamics model (IDM), then holding the IDM fixed while replacing the source of future images. We introduce Align Once, Evaluate Everywhere (AoE), a camera-space inverse-dynamics model pretrained on large-scale robot data, which provides this recovery interface for different future sources across tasks and environments. Through it, we find that actions recovered from recorded futures of unseen tasks execute almost as well as replayed demonstrations, whereas futures predicted by world models collapse across benchmarks. The failures are not generic: they concentrate on the gripper and interaction geometry while generation capacity is spent on task-irrelevant background. This diagnosis suggests that supervision should target exactly these regions. We therefore introduce the vision-to-action (VITA) loss, which passes generated futures through the frozen AoE and penalizes discrepancies in the recovered actions, redirecting generation toward action-relevant detail. Across two world models and three manipulation benchmarks, this simple change raises the execution success of generated futures from near zero to 47.0%. The same loss also transfers to WAMs and yields consistent gains in native control.

This paper studies the topological entropy of real-analytic Liouville integrable Hamiltonian systems. We prove that the Hamiltonian flow on a compact connected regular energy hypersurface has zero topological entropy whenever a complete family of commuting real-analytic first integrals is generically independent in a connected neighborhood of that hypersurface. The proof uses finite normal expansions along minimal analytic carriers and an ergodic version of Ziglin's leading-term argument to obtain independent invariant normal polynomials, whose Poisson geometry makes all tangent Lyapunov exponents of the carriers vanish. In particular, we prove that a real-analytic Liouville integrable geodesic flow on a closed real-analytic Riemannian manifold has zero topological entropy, giving a positive answer to the conjecture proposed by Paternain in 1992.