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01.
arXiv (CS.LG) 2026-06-17

Evaluating Intersectional Fairness across Clinical Machine Learning Use Cases using Fairlogue and the All of Us Research Program

arXiv:2604.16450v2 Announce Type: replace-cross Abstract: Intersectional biases in healthcare data can produce compound disparities in clinical machine learning models, yet most fairness evaluations assess demographic attributes independently. FairLogue, a toolkit for intersectional fairness auditing, was applied across multiple clinical prediction tasks to evaluate disparities across combined demographic groups. Using the All of Us dataset, two published models were selected for replication and evaluation: (A) prediction of selective serotonin reuptake inhibitor associated bleeding events and (B) two-year stroke risk in patients with atrial fibrillation. Observational fairness metrics were computed across race, gender, and intersectional subgroups, followed by counterfactual analysis to evaluate whether disparities were attributable to group membership. Intersectional evaluation revealed larger disparities than single-axis analyses; however, counterfactual diagnostics indicated that most observed disparities were comparable to those expected under randomized group membership. These results highlight the importance of intersectional fairness auditing and demonstrate how FairLogue provides deeper insight into bias in clinical machine learning systems.

02.
arXiv (quant-ph) 2026-06-16

Non-perturbative CPMG scaling and qutrit-driven breakdown under compiled superconducting-qubit control: a single-qubit study

作者:

arXiv:2603.29525v3 Announce Type: replace Abstract: Decoherence in superconducting qubits arises from both multilevel dynamics and structured environmental noise, yet perturbative models cannot capture all resulting signatures. Here, EmuPlat couples instruction-set-architecture-level waveform generation to the hierarchical equations of motion HEOM under $1/f$ non-Markovian pure dephasing. In the resulting non-perturbative regime – where filter-function predictions become quantitatively uninformative – CPMG scaling of a three-level superconducting transmon yields one calibration result, two physical findings, and one structural null. Y-CPMG exhibits axis-dependent scaling-law breakdown – non-monotonic decoherence, partial coherence revival, and pronounced X–Y population asymmetry ($0.204$ vs ${

03.
arXiv (CS.CV) 2026-06-11

RankVR: Low-Rank Structure Perception and Value Recalibration for Robust Composed Image Retrieval

Composed Image Retrieval (CIR) constitutes a pivotal paradigm requiring models to perform joint reasoning on reference images and modification texts. However, the prevalence of Noisy Triplet Correspondence (NTC) in large-scale datasets severely constrains model performance. Existing denoising methods either target binary mismatches or rely on scalar-based point-wise estimation, neglecting rich global structural correlations among sample populations and dynamic value variations during training, thereby yielding suboptimal results. This paper identifies two critical unresolved challenges: Global Structural Inconsistency of Semantic Correlations and Hard Sample Discrimination Uncertainty. To address these, we propose RankVR, a framework designed to construct a robust CIR model via global structure consistency and dynamic value perception. Specifically, we introduce the Global Structure Consistency Perception (GSCP) module, which utilizes the Effective Rank of the Correlation Matrix to decouple clean samples from structural noise. By measuring rank difference, GSCP identifies samples disrupting macroscopic semantic symmetry. Furthermore, we develop the Adaptive Semantic Value Calibration (ASVC) module to distinguish high-value hard clean samples. By integrating training potential and reliability, it dynamically quantifies the semantic value of each triplet, ensuring effective utilization of hard samples while suppressing noise characterized by logical conflicts. Extensive experiments on the FashionIQ and CIRR benchmark datasets demonstrate that RankVR significantly outperforms existing state-of-the-art methods, validating its superior robustness in noisy environments.

04.
arXiv (CS.CV) 2026-06-17

SierpinskiCam: Camera-Controlled Video Retaking with Sierpinski Triangle Pattern Cues

Generating novel renderings of a scene along user-defined camera trajectories from a single monocular video, dubbed video retaking, is a compelling but difficult problem in content creation and visual effects. Existing geometry-guided approaches reconstruct a 4D representation from the source video and render it along the target trajectory to condition video diffusion models. However, this guidance degrades as the target camera departs from the source trajectory, leaving newly revealed regions sparse or entirely missing. We propose SierpinskiCam, which addresses this limitation by augmenting geometry-based guidance with Sierpinski dome texture cues that contains rich trackable features even under large viewpoint changes. We further introduce a reference video conditioning mechanism that appends source-video tokens to the target-token sequence and separates the two streams with negative RoPE indices, enabling appearance grounding without architectural modification or per-video adaptation. Extensive experiments show that SierpinskiCam achieves significant gains in camera controllability, geometric consistency, and video quality across diverse and challenging retaking scenarios. Project page: https://hyelinnam.github.io/SierpinskiCam/.

05.
arXiv (CS.LG) 2026-06-18

On the Stability of Nonlinear Dynamics in GD and SGD: Beyond Quadratic Potentials

arXiv:2602.14789v2 Announce Type: replace Abstract: The dynamical stability of the iterates during training plays a key role in determining the minima obtained by optimization algorithms. For example, stable solutions of gradient descent (GD) correspond to flat minima, which have been associated with favorable features. While prior work often relies on linearization to determine stability, it remains unclear whether linearized dynamics faithfully capture the full nonlinear behavior. Recent work has shown that GD may stably oscillate near a linearly unstable minimum and still converge once the step size decays, indicating that linear analysis can be misleading. In this work, we explicitly study the effect of nonlinear terms. Specifically, we derive an exact criterion for stable oscillations of GD near minima in the multivariate setting. Our condition depends on high-order derivatives, generalizing existing results. Extending the analysis to stochastic gradient descent (SGD), we show that nonlinear dynamics can diverge in expectation even if a single batch is unstable. This implies that stability can be dictated by a single batch that oscillates unstably, rather than an average effect, as linear analysis suggests. Finally, we prove that if all batches are linearly stable, the nonlinear dynamics of SGD are stable in expectation.

06.
arXiv (quant-ph) 2026-06-19

Complexity of detecting large coefficients in the Pauli basis

arXiv:2606.19545v1 Announce Type: new Abstract: We study the problem of deciding, given a mechanism to prepare a quantum state $\rho$ and a value $\varepsilon > 0$, whether there is some non-identity Pauli matrix $P$ such that $|Tr(P \rho)| \geq \varepsilon$. We consider that the state $\rho$ is described as the result of tracing out some of the qubits of a pure state prepared by a circuit $C$, and we assume the promise that either there is a Pauli matrix satisfying the stated condition or, instead, that for all non-identity Pauli matrices $P$ it is the case that $|Tr(P\rho)|\leq \varepsilon/2$. The problem is in $QCMA$, and we prove that if it belongs to $BQP$ then $NP \subseteq BQP$. The result is obtained through a reduction from the minimum-weight code problem, and it holds even when $\rho$ is assumed to be a pure state (i.e. when no qubits are discarded) and $\varepsilon$ is constant. This resolves an open question regarding the existence of efficient tomographic procedures to find the largest coefficients of a quantum state in the Pauli basis: namely, they do not exist under the standard hypothesis $NP \nsubseteq BQP$.

07.
arXiv (quant-ph) 2026-06-16

Efficient Magic State Factory Via Transversal Non-Clifford Gate

arXiv:2606.16199v1 Announce Type: new Abstract: Magic-state preparation is a central component of fault-tolerant quantum computing. Recent theoretical and experimental successes in code-switch-based magic-state preparation have underscored the promise of these methods for quantum error correction. Similarly, magic-state cultivation has likewise been demonstrated in both numerical and experimental settings. However, a thorough comparison between magic-state cultivation and code-switch-based magic-state factories is still missing. In this work, we carry out end-to-end simulations of magic-state preparation using code switching and compare its resource requirements and performance against magic-state cultivation. As part of this analysis, we develop a lattice-surgery protocol for transfer between the doubled color code and the rotated surface code. We extend the complete code-switching protocol to the $d=5$ doubled color code and perform the corresponding end-to-end simulations. Finally, we propose two fault-tolerant magic-state preparation protocols that combine phase-kickback checks with a transversal non-Clifford gate.

08.
arXiv (quant-ph) 2026-06-19

Faking entanglement with imperceptible measurement deviations

arXiv:2606.20396v1 Announce Type: new Abstract: Quantum entanglement is a central resource underpinning emerging quantum technologies, enabling capabilities beyond those of classical systems. Accurate verification of entanglement is therefore crucial. However, experimental schemes usually rely on the assumption that quantum measurements can be realized exactly. As the complexity of a quantum system grows, this assumption typically becomes increasingly unrealistic, therefore leading to a widening mismatch between theoretical models and experimental implementations. Here we demonstrate that arbitrarily small measurement errors, when adversarially encoded in the measurement apparatus, can lead to the false certification of high-dimensional entanglement in systems that are, in fact, separable. This is achieved by introducing explicit hacking attacks to measurement devices in well-established entanglement verification tests. We further experimentally demonstrate this effect using classical photonic states encoded in the spatial degree of freedom, spanning up to 61 dimensions with measurement fidelity errors as low as 0.23%. Our results uncover a fundamental vulnerability in current methods for high-dimensional entanglement detection, highlighting the susceptibility of complex quantum devices to small adversarial perturbations. The findings underscore the need for developing secure verification of quantum information that is robust to bounded discrepancies between theory and experiment.

09.
medRxiv (Medicine) 2026-06-16

Validating an Early Pregnancy HbA1c as the Screening Test for Gestational Diabetes Mellitus: Findings from PRISMA Pakistan Cohort

Background: Early identification of gestational diabetes mellitus (GDM) is critical to improving maternal and neonatal outcomes, particularly in resource-constrained settings where universal oral glucose tolerance testing (OGTT) is burdensome. We assessed whether early-pregnancy HbA1c alone or combined with common risk factors can predict GDM and reduce the burden of OGTT requirements in a peri-urban cohort in Karachi, Pakistan. Methods: We conducted a secondary analysis of the Pregnancy Risk Infant Surveillance and Measurement Alliance (PRISMA) Pakistan cohort. Women enrolled before 20 weeks' gestation with available early-pregnancy HbA1c and a 2-hour 75g OGTT at 24 to 28 weeks were included. We externally validated GDM prediction models originally developed in the STRiDE-India cohort. Model performance was evaluated using receiver operating characteristic (ROC) curves and area under the curve (AUC). We assessed four models: HbA1c alone (Model 1a); age, BMI, and family history of diabetes mellitus (FH DM) (Model 1b); HbA1c combined with age, BMI, and FH DM (Model 2); and an extended model, i.e., Model 2 combined with socioeconomic status, gestational age, parity, systolic and diastolic blood pressure (Model 3). A dual-threshold approach was applied to assess rule-in and rule-out performance. Results: Among 2,489 women, GDM incidence was 7.5% (n=186). Models with a broader set of predictors demonstrated higher AUC values, with Model 2 achieving an AUC of 0.61 (95% CI: 0.57, 0.66). Including additional factors (Model 3) did not further improve predictive ability (AUC: 0.62; 95% CI: 0.58, 0.66). In addition, at predefined thresholds, Model 2 achieved sensitivity of 73.7% (rule-out) and specificity of 83.5% (rule-in), with the potential to reduce OGTT requirements (58.5%). Conclusions: Early-pregnancy risk stratification using HbA1c combined with simple clinical predictors offers a pragmatic approach to streamline GDM screening among high-risk pregnant women. A dual-threshold strategy using Model 2 could reduce reliance on universal OGTT while prioritizing high-risk women for confirmatory testing.

10.
arXiv (CS.AI) 2026-06-12

(Human) Attention Is (Still) All You Need: Human oversight makes AI-assisted social science reliable

arXiv:2606.12848v1 Announce Type: new Abstract: Large language models (LLMs) are increasingly used for tasks once reserved for trained researchers, including hypothesis generation, specification choice, and drafting conclusions. We argue that the reliability of AI-assisted research depends not only on model capability, but also on how cognitive labour is structured between humans and machines. We study this problem through Human-in-the-Loop Economic Research (HLER), a decision architecture based on pre-commitment, decision sequencing, accountability, and attention allocation. In a pre-specified 2*4 factorial experiment with 280 complete research runs across four datasets, an unconstrained multi-agent baseline produced critical failures in 72% of runs. Using the same underlying model, the same agent decomposition, and identical prompts for the shared reasoning agents, HLER reduced the failure rate to 16% by imposing three architectural commitments: LLMs reason but do not execute data work, data and estimation are handled deterministically, and three human decision gates bind the workflow. Fisher's exact test rejects equality of failure rates at p

11.
arXiv (CS.CV) 2026-06-15

QualiaNet: An Experience-Before-Inference Network

作者:

Human 3D vision involves two distinct stages: an Experience Module, where stereo depth is extracted relative to fixation, and an Inference Module, where this experience is interpreted to estimate 3D scene properties. Paradoxically, although stereo vision does not provide us with absolute distance information, it nonetheless affects our inferences about distance. We propose the Inference Module exploits a natural scene statistic: near scenes produce vivid disparity gradients, while far scenes appear comparatively flat. QualiaNet implements this two-stage architecture computationally: disparity maps simulating human stereo experience are passed to a CNN trained to estimate distance. The network can recover distance from disparity gradients alone, validating this approach.

12.
PLOS Computational Biology 2026-06-09

Evolution of phenocopying in a dynamical model of developmental trajectories

by Yuuki Matsushita, Archishman Raju Developmental trajectories are known to be canalized, or robust to both environmental and genetic perturbations. However, even when these trajectories are decanalized by an environmental perturbation outside the range of conditions to which they are robust, they often produce phenotypes similar to known mutants, called phenocopies. This correspondence between the effects of environmental and genetic perturbations has received little theoretical attention. Here, we study an abstract regulatory model that is evolved to follow a specific trajectory. We then study the effects of small and large perturbations to the trajectory, both by changing parameters and by perturbing the state at specific times. We find that the phenomenon of phenocopying emerges in evolved trajectories and is not present in a null model of randomly sampled trajectories. Our results suggest that, in this class of dynamic models, evolution can allow high-dimensional phenotypic landscapes to simultaneously exhibit robustness and phenocopying.

13.
arXiv (CS.CL) 2026-06-12

From Isolation to Entanglement: When Do Interpretability Methods Identify and Disentangle Known Concepts?

A goal of interpretability is to recover disentangled representations of latent concepts (features) from the activations of neural networks. The quality of features is typically evaluated in isolation, and under implicit independence assumptions that may not hold in practice. Thus, it is unclear to what extent common featurization methods such as sparse autoencoders (SAEs) and probes disentangle one concept from another. We propose a multi-concept evaluation setting using concepts including sentiment, domain, voice, and tense. We evaluate how well featurizers produce disentangled representations of each concept, observing that features are typically sensitive to only one concept, but also that concepts are distributed across many features. Then, we steer these features, measuring whether each concept is independently manipulable, and whether features interact. Even in idealized settings, steering a feature often affects many concepts, despite a near absence of interaction effects. These results suggest that correlational metrics are insufficient to establish steering selectivity, and that demonstrating that two features operate in separate spaces is insufficient to claim that they will be selective for one concept. These results underscore the importance of multi-concept evaluations in interpretability research.

14.
arXiv (math.PR) 2026-06-16

Effective Resistances and Commute Times in Sparse Random Geometric Graphs

arXiv:2606.14895v1 Announce Type: new Abstract: The commute time between two nodes in a network - the expected number of steps for a random walk to travel from one node to the other and then return - is a metric of broad importance arising in community detection, network routing, dimensionality reduction, and diffusion modeling. For random geometric graphs (RGGs), in which nodes are placed at random in a spatial domain and connected pairwise wherever their Euclidean distance is below a threshold radius, the relationship between commute times and the embedding geometry remains poorly understood outside very dense settings (where the role of the geometry disappears and commute times degenerate to a sum of inverse degrees). We develop and numerically validate a model for approximating commute times in sparse RGGs on a torus by combining theoretically motivated geometric contributions with an inverse degree sum. The geometric terms include a universal logarithmic contribution from the Laplacian, a quadratic correction encoding the compact topology of the torus, and a quartic angular term reflecting the square anisotropy of the domain. We fit this model to samples of node pairs across a range of graph sizes and mean degrees, demonstrating good predictive performance and that the geometric terms contribute significantly to model fit. We then study the continuous perturbation of the model from a regular square lattice to a fully random geometric graph, further validating the functional model form through this transition and showing how commute times in sparse RGGs retain meaningful geometric information about the embedding space.

15.
arXiv (CS.CL) 2026-06-16

Connecting Speech to Words through Images

How can we learn the mapping between written words and their spoken counterparts in the absence of explicit textual supervision? We present a visually grounded method for building a vocabulary of spoken words using only images and their spoken descriptions. First, image captioning systems are used to build a vocabulary of written words representing salient visual concepts in the images. For each word, we then find utterances whose image captions contain that word. Then we use an unsupervised word discovery technique to align these utterances to locate instances of the target word. The result is spoken word segments that are linked to written words – all accomplished without any text supervision. In spoken word retrieval and keyword spotting experiments, the proposed approach outperforms a strong neural baseline while being more interpretable. These results demonstrate the feasibility of the approach in English and motivate future work on low-resource languages without transcripts.

16.
arXiv (CS.CV) 2026-06-19

Training-Free Metrics for Synthetic Object Detection Data: A Proxy for Detector Performance

With the recent advent of image generative models, synthetic data are increasingly being used to supplement limited real datasets for training computer vision models. However, not all synthetic datasets improve performance equally, and their effectiveness can only be assessed by training a downstream model, which is computationally expensive and time-consuming. This problem is pronounced in the task of object detection, where the required annotations are much more dense due to bounding boxes. In this paper, we propose a pre-computable metric family, dubbed Conditional-Composition Domain Match (CCDM), which serves as a proxy for the relative utility of candidate synthetic training sets for downstream detection. Experiments on the VisDrone-DET dataset show that the CCDM metric families achieve a Spearman correlation of 1.0 with the downstream performance of YOLOv8, clearly outperforming existing metrics for synthetic image evaluation.

17.
arXiv (quant-ph) 2026-06-19

Extracting the physical content of Liouvillian eigenmodes: Semiclassical quantization

arXiv:2606.20271v1 Announce Type: new Abstract: Unlike in closed quantum systems where individual energy eigenstates are understood as physical excitations, open quantum systems have distinct right and left eigenstates of the Liouvillian that decay with time and are difficult to interpret. Here we introduce a physically motivated quasiprobability measure combining the two types of eigenstates that interprets a Liouville eigenmode as a set of coherences. This coherence measure is intimately connected to the return probability and allows one to visualize the modes as quasiprobability distributions in a "doubled" phase space. Using this measure we show that, remarkably, an oscillator retains its quantized "orbits" in phase space for a large class of linear and nonlinear damping, thus providing a formulation of semiclassical quantization for open systems. The orbits have measurable dynamical signatures and are broadened in the presence of a thermal bath, similar to energy levels. For quadratic systems, our results yield an extension of the concept of invariant tori, which play a central role in Hamiltonian systems.

18.
arXiv (CS.CL) 2026-06-16

Tying the Loop – Tied Expert Layers in Mixture-of-Experts Language Models

作者:

Mixture-of-Experts (MoE) architectures efficiently scale Large Language Models (LLMs) by activating only a small fraction of their experts per token, yet the full parameter count - dominated by the expert parameters - must be held in training and inference memory. To address this, we introduce Expert Tying, an architectural modification that shares expert parameters across consecutive transformer layers while preserving independent, layer-wise routing and attention. We evaluate this approach across common, state-of-the-art architectures, including OLMoE, Qwen3, and DeepSeek-style MoEs. Our pretraining experiments demonstrate that tying experts can reduce memory footprint by almost 2x at virtually no degradation in perplexity or downstream quality. By exploiting the parameter redundancy inherent in MoE pathways, our method provides a highly favorable compute-to-memory trade-off, advancing efficient training and scaling of next-generation LLMs.

19.
arXiv (math.PR) 2026-06-17

Decay of correlations and zeros for the hard-core model

arXiv:2603.17858v2 Announce Type: replace Abstract: In a recent paper the last author proved that absence of complex zeros of the partition function of the hard-core model near a parameter $\lambda>0$ implies a form of correlation decay called strong spacial mixing. In this paper we investigate the reverse implication. We introduce a strengthening of strong spatial mixing that we call very strong spatial mixing (VSSM). Our main result is that if VSSM holds at a parameter $\lambda>0$ for a family of graphs, this implies that the partition function has no zeros near that parameter for each graph in the family. We also demonstrate that a closely related variant of very strong spatial mixing does not imply zero-freeness. As a consequence of our main result, we moreover obtain that VSSM implies spectral independence. Our proof relies on transforming the problem to the analysis of an induced non-autonomous dynamical system given by Möbius transformations.

20.
arXiv (CS.AI) 2026-06-17

Like a Hammer, It Can Build, It Can Break: Large Language Model Uses, Perceptions, and Adoption in Cybersecurity Operations on Reddit

arXiv:2604.09998v2 Announce Type: replace-cross Abstract: Large language models (LLMs) have recently emerged as promising tools for augmenting Security Operations Center (SOC) workflows, with vendors increasingly marketing autonomous AI solutions for SOCs. However, there remains a limited empirical understanding of how such tools are used, perceived, and adopted by real-world security practitioners. To address this gap, we conduct a mixed-methods analysis of discussions in cybersecurity-focused forums to learn how a diverse group of practitioners use and perceive modern LLM tools for security operations. More specifically, we analyzed 892 posts between December 2022 and September 2025 from three cybersecurity-focused forums on Reddit, and, using a combination of qualitative coding and statistical analysis, examined how security practitioners discuss LLM tools across three dimensions: (1) their stated tools and use cases, (2) the perceived pros and cons of each tool across a set of critical factors, and (3) their adoption of such tools and the expected impacts on the cybersecurity industry and individual analysts. Overall, our findings reveal nuanced patterns in LLM tools adoption, highlighting independent use of LLMs for low-risk, productivity-oriented tasks, alongside active interest around enterprise-grade, security-focused LLM platforms. Although practitioners report meaningful gains in efficiency and effectiveness in LLM-assisted workflows, persistent issues with reliability, verification overheads, and security risks sharply constrain the autonomy granted to LLM tools. Based on these results, we also provide recommendations for developing and adopting LLM tools to ensure the security of organizations and the safety of cybersecurity practitioners.

21.
arXiv (CS.AI) 2026-06-19

Stabilizing the Q-Gradient Field for Policy Smoothness in Actor-Critic Methods

arXiv:2601.22970v2 Announce Type: replace-cross Abstract: Policies learned via continuous actor-critic methods often exhibit erratic, high-frequency oscillations, making them unsuitable for physical deployment. Current approaches attempt to enforce smoothness by directly regularizing the policy's output. We argue that this approach treats the symptom rather than the cause. In this work, we theoretically establish that policy non-smoothness is fundamentally governed by the differential geometry of the critic. By applying implicit differentiation to the actor-critic objective, we prove that the sensitivity of the optimal policy is bounded by the ratio of the Q-function's mixed-partial derivative (noise sensitivity) to its action-space curvature (signal distinctness). To empirically validate this theoretical insight, we introduce PAVE (Policy-Aware Value-field Equalization), a critic-centric regularization framework that treats the critic as a scalar field and stabilizes its induced action-gradient field. PAVE rectifies the learning signal by minimizing the Q-gradient volatility while preserving local curvature. Experimental results demonstrate that PAVE achieves smoothness comparable to policy-side smoothness regularization methods, while maintaining competitive task performance, without modifying the actor.

22.
arXiv (CS.CL) 2026-06-12

LLMs Can Better Capture Human Judgments–With the Right Prompts

Are large language models (LLMs) bad at capturing human judgment? Two commonly stated limitations are that LLMs fail to capture full distributions of responses, and that their judgments are unstable across wording variations. We demonstrate simple prompting strategies that mitigate these limitations. Across two datasets–a U.S.-representative set of 144 moral scenarios and 38 moral beliefs from the International Social Survey Programme's Family and Changing Gender Roles module covering 32 countries–we show how simple elicitation techniques help improve AI-human alignment. First, prompting models to report standard deviations and response proportions recovers the full range of human responses better than common strategies. Second, ensuring scenarios are clear to human participants–as reflected in human confusion ratings–boosts model alignment, and LLMs can track human confusion ratings. At the same time, we find that LLMs' estimates of their own error are poorly calibrated, though they can predict human variability relatively well. These results suggest that asking better questions to LLMs can yield better answers.

23.
arXiv (math.PR) 2026-06-16

A Tail-Respecting Splitting Numerical Scheme for Lévy-Driven SDEs With Superlinear Drifts

arXiv:2504.07255v3 Announce Type: replace Abstract: We present an explicit numerical approximation scheme, denoted by $\{X^n\}$, for the effective simulation of solutions $X$ to a multivariate stochastic differential equation (SDE) with a superlinearly growing $\kappa$-dissipative drift, where $\kappa>1$, driven by a multiplicative heavy-tailed Lévy process that has a finite $p$-th moment, with $p>0$. We show that the strong $L^{p_X}$-convergence $\sup_{t\in[0,T]}\mathbf E \|X^n_t-X_t\|^{p_X}=\mathcal O (h_n^{\gamma})$ holds for any $p_X\in (0,p+\kappa-1)$, which is exactly the range where the $p_X$-moment of the solution is known to be finite. Additionally, for any $p_X\in (0,p)$ we establish strong uniform convergence: $\mathbf E\sup_{t\in[0,T]} \|X^n_t-X_t\|^{p_X}=\mathcal{O} ( h_n^{\delta} )$. In both cases we determine the convergence rates $\gamma$ and $\delta$. In the special case of SDEs driven solely by a Brownian motion, our numerical scheme preserves super-exponential moments of the solution. The scheme $\{X^n\}$ is realized as a combination of a well-known Euler method with a Lie-Trotter type splitting technique.

24.
arXiv (CS.LG) 2026-06-16

HRIR-Former: Grid-Free Time-Domain Reconstruction of Head-Related Impulse Responses with a Spatially Encoded Transformer

arXiv:2603.27998v2 Announce Type: replace-cross Abstract: Individualized head-related impulse responses (HRIRs) enable binaural rendering, but dense per-listener measurements are costly. We address HRIR spatial up-sampling from sparse per-listener measurements: given a few measured HRIRs for a listener, predict HRIRs at unmeasured target directions. Prior learning methods often work in the frequency domain, rely on minimum-phase assumptions or separate timing models, and use a fixed direction grid, which can degrade temporal fidelity and spatial continuity. We propose HRIR-Former, a time-domain, grid-free binaural Transformer for reconstructing HRIRs at arbitrary directions from sparse inputs. It uses sinusoidal spatial features, a Conv1D refinement module, and auxiliary interaural time difference (ITD) and interaural level difference (ILD) heads. On SONICOM, it improves normalized mean squared error (NMSE), cosine distance, and ITD/ILD errors over prior methods; ablations validate modules and show minimum-phase preprocessing is unnecessary.

25.
arXiv (CS.LG) 2026-06-16

Smoothness Errors in Dynamics Models and How to Avoid Them

arXiv:2602.05352v3 Announce Type: replace Abstract: Modern neural networks have shown promise for solving partial differential equations over surfaces, often by discretizing the surface as a mesh and learning with a mesh-aware graph neural network. However, graph neural networks suffer from oversmoothing, where a node's features become increasingly similar to those of its neighbors. Unitary graph convolutions, which are mathematically constrained to preserve smoothness, have been proposed to address this issue. Despite this, in many physical systems, such as diffusion processes, smoothness naturally increases and unitarity may be overconstraining. In this paper, we systematically study the smoothing effects of different GNNs for dynamics modeling and prove that unitary convolutions hurt performance for such tasks. We propose relaxed unitary convolutions that balance smoothness preservation with the natural smoothing required for physical systems. We also generalize unitary and relaxed unitary convolutions from graphs to meshes. In experiments on PDEs such as the heat and wave equations over complex meshes and on weather forecasting, we find that our method outperforms several strong baselines, including mesh-aware transformers and equivariant neural networks.