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01.
arXiv (math.PR) 2026-06-17

On Injectivity of Phase Retrieval

Authors:
Zhangsong Li↗

arXiv:2606.17922v1 Announce Type: cross Abstract: In this short note, we prove that if $A \in \mathbb C^{N \times M}$ with $N=4M-5$ has i.i.d.\ standard complex Gaussian entries, then the probability that the phase retrieval map generated by $A$ is not injective is positive. This proves Part (1) of a conjecture of Cynthia Vinzant, which was later restated by Afonso S. Bandeira in [BDL+26]. The main result of this paper was obtained using generative AI, in particular the Rethlas system.

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02.
arXiv (CS.LG) 2026-06-11

Few-Shot Resampling for Scalable Statistically-Sound Data Mining

Authors:
Leonardo Pellegrina↗Fabio Vandin↗

arXiv:2606.11235v1 Announce Type: new Abstract: A key step in knowledge discovery is the evaluation of data mining results. In several applications, including pattern mining, graph analysis, and others, this step includes the evaluation of the statistical significance of the results, to avoid spurious discoveries due only to noise or random fluctuations in the data. While specialized procedures have been developed for some specific applications, resampling-based approaches are widely used, in particular for complex analyses where analytical results cannot be derived. However, current resampling-based approaches require the generation and analysis of thousands of resampled datasets, and are therefore impractical for large datasets or computationally intensive analyses. In this paper, we introduce FewRS, a simple and effective resampling-based approach to assess the statistical significance of data mining results with rigorous guarantees on the probability of false discoveries. Our approach can be used in every situation where resampling-based approaches are applied. FewRS builds on our derivation of a novel bound to the supremum deviation of test statistics representing the quality of data mining results. We prove that FewRS needs to generate and analyze an extremely small number of resampled datasets, leading to a highly scalable approach with wide applicability. We test our approach on common tasks such as pattern mining and network analysis. In all cases, our approach results in a reduction of up to two orders of magnitude in running time compared to the state of the art, while preserving high statistical power, enabling the statistical validation of data mining results on large-scale real-world datasets.

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03.
arXiv (quant-ph) 2026-06-17

On the entanglement induced by the deformation of phase-space

Authors:
Shilpa Nandi↗Shatarupa Maity↗Pinaki Patra↗

arXiv:2606.17587v1 Announce Type: new Abstract: Most quantum gravity theories propose that the fundamental concept of space-time is mostly compatible with quantum theory in noncommutative (NC) space. In the present paper, we revisit the notion of entanglement induced by NC deformations of phase space. The positive partial transpose (PPT) criterion for separability of bipartite Gaussian states is extended to a general class of Bopp's shift. In particular, we have considered both the position-position and momentum-momentum noncommutativity, with deformation parameters $\theta$ and $\eta$, respectively. It turns out that $\theta$ and $\eta$ induce the entanglement. We have directly applied the formalism for an anisotropic two-dimensional harmonic oscillator. Peres-Horodecki separability condition leads to a constraint equation for the parameter values of the oscillator in NC space. It turns out that the bipartite Gaussian state is almost always entangled in deformed space. To implement the theoretical idea, we provide an outline for a gedankenexperiment to identify the signature of phase-space noncommutativity, i.e., quantum gravity. In particular, the gedankenexperiment is devised to test the separability of supposedly separable Gaussian states in the usual commutative space, through the covariance matrix, which is constructed via measured output photocurrents after interaction of input Gaussian states and reference states. If the experiment shows that the supposedly separable states are actually entangled, then the entanglement is created through the intermediate background noncommutative space, which is a signature of the quantum nature of gravity.

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

HRDX: A Large-Scale Vector HD-Map Dataset

Authors:
Sahith Reddy Chada↗Isht Dwivedi↗Nirav Savaliya↗

Reliable autonomous driving requires vectorized HD maps that are geometrically accurate, semantically rich, and scalable to long-horizon driving. However, existing public HD map datasets are limited in scale, provide sparse semantic attributes, and lack modalities such as aerial imagery that could enable new research directions. We present HRDX, a large-scale dataset for vector HD-map construction, spanning about 40 hours (1,400 km) of minimally overlapping drives, which is several times larger than prior public HD map datasets. Data is captured using six synchronized surround cameras, a 128-beam LiDAR, and centimeter-level RTK GNSS/IMU, and is further complemented by precisely aligned aerial orthoimagery. Annotations cover 10 vector map classes, complemented with over 20 semantic and topological attributes. To evaluate this richer ontology, we introduce the Composite Score (CS) to jointly assess geometric fidelity and attribute correctness. Benchmark experiments show that HRDX's scale improves online vector-map construction, and that aligned aerial imagery provides a useful structural prior: using aerial imagery at training and/or inference improves geometric map quality, while aerial-augmented teachers can transfer part of this benefit to camera-only students without increasing inference-time sensor requirements. HRDX is intended to support reproducible research on large-scale HD-map learning, multimodal BEV fusion, and training-time privileged information. HRDX dataset and benchmarks are available at https://github.com/honda-research-institute/HRDX

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05.
arXiv (quant-ph) 2026-06-11

Gate-tunable spin-valley transport via carrier velocity in monolayer WSe$_2$

Authors:
Otman Bouladiane↗Hocine Bahlouli↗Clarence Cortes↗David Laroze↗Ahmed Jellal↗

arXiv:2606.12353v1 Announce Type: cross Abstract: We theoretically investigate spin- and valley-resolved quantum transport in monolayer tungsten diselenide (WSe$_2$) described by an effective massive Dirac Hamiltonian. Particular attention is devoted to a finite barrier region characterized by simultaneously modulated Fermi velocity and scalar potential. The barrier velocity $v_2$ is related to the external velocity $v_1$ through a velocity ratio $\xi=v_2/v_1$, motivated by an optical analogy with the Snell-Descartes law. The exact refraction condition depends on the full spin- and valley-resolved dispersion, and the simple ratio $\xi=v_2/v_1$ is recovered only in the massless, symmetric limit. The interplay of intrinsic spin-orbit coupling in the conduction and valence bands, quantified by $\lambda_c$ and $\lambda_v$, with spin- and valley-dependent Zeeman fields, $M_s$ and $M_v$, gives rise to substantial changes in the quasiparticle dispersion, leading to pronounced modifications of the transport characteristics. By solving the Dirac equation and enforcing current-conserving matching conditions at the interfaces, we compute the spin- and valley-dependent transmission probability and conductance. Our results demonstrate that the barrier velocity, scalar potential, incidence angle, incident energy, and barrier width serve as effective control parameters for transport, giving rise to strong anisotropy and resonant tunneling features. Furthermore, we show that both the magnitude and orientation of spin- and valley-polarized currents can be continuously tuned via velocity and potential modulation. These findings establish combined velocity and potential engineering as a powerful theoretical framework for controlling spin-valley physics in two-dimensional transition-metal dichalcogenides.

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06.
arXiv (math.PR) 2026-06-18

Finite free perpetuities

Authors:
Julia Le Bihan↗Bartosz Ko{\l}odziejek↗

arXiv:2606.19115v1 Announce Type: new Abstract: We introduce and study finite free perpetuities, defined as monic polynomial solutions of degree $n$ to the affine fixed-point equation \[ p(z) = \mathbb{E}\!\left[ A^{n}\,p\!\left(\frac{z-B}{A}\right)\mathbf{1}_{\{A\neq0\}} \right] + \mathbb{E}\!\left[ (z-B)^n\mathbf{1}_{\{A=0\}} \right], \] where $A$ and $B$ are complex-valued random variables with finite moments up to order $n$. Equivalently, if $p(z)=\mathbb{E}[(z-X)^n]$, then $p$ encodes a truncated moment version of the classical perpetuity equation $X\stackrel{d}{=}AX+B$ with $X$ and $(A,B)$ independent. This places finite free perpetuities between classical perpetuities and free-probabilistic fixed-point laws. We prove existence and uniqueness under weak conditions, and we identify a broad class of admissible pairs $(A,B)$ for which the resulting polynomial has only real, nonnegative zeros. Our approach uses finite free additive and multiplicative convolutions together with a probabilistic representation via the $U$-transform. As a motivating example, we exhibit an explicit family of finite free perpetuities expressed in terms of Jacobi polynomials and show that their empirical root distributions converge to a free-beta-prime law. More generally, for admissible sequences of parameters, we prove weak convergence of the empirical root distributions of finite free perpetuities to the law of a free perpetuity characterized by the corresponding free fixed-point equation. This yields a finite-degree polynomial model approximating free perpetuities and clarifies the connection between classical affine recursions, finite free convolutions, and free probability.

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07.
arXiv (CS.AI) 2026-06-11

SPEA2$^+$: Improved Density Estimation in SPEA2 with Provable Runtime Guarantees

Authors:
Duc-Cuong Dang↗Andre Opris↗Dirk Sudholt↗

arXiv:2606.12382v1 Announce Type: cross Abstract: The Strength Pareto Evolutionary Algorithm 2 (SPEA2) is a popular and prominent evolutionary algorithm for solving multi-objective optimisation problems. Despite its popularity, theoretical analyses of SPEA2 have only appeared recently. Moreover, these analyses focus exclusively on how SPEA2 handles non-dominated solutions and disregard the algorithmic components responsible for handling dominated solutions. We conduct a first runtime analysis of SPEA2 for which these components are analysed. We prove that, unlike other prominent algorithms, including NSGA-II, NSGA-III and SMS-EMOA under the same setting of constant population size and duplicate elimination, SPEA2 is unable to cover the Pareto front of the OneTrapZeroTrap benchmark efficiently. Our results indicate that using k-th nearest-neighbour distance in the fitness assignment provides an insufficient signal to maintain diversity among dominated individuals. To address this issue, we propose an improved variant, SPEA2$^+$, that considers all pairwise distances. The new algorithm achieves the same performance guarantees as the other prominent algorithms on OneTrapZeroTrap, while matching the performance of the original SPEA2 on simpler problems. Experimental results complement our theoretical findings.

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08.
arXiv (CS.AI) 2026-06-11

Quantized Stochastic Primal-Dual Methods for Distributed Optimization under Relaxed Global Geometry

Authors:
Susmit Sarkar↗Abhinav Raghuvanshi↗Kushal Chakrabarti↗Mayank Baranwal↗

arXiv:2606.11339v1 Announce Type: cross Abstract: We study distributed optimization with stochastic gradients and finite-bit communication modeled by random (unbiased) quantization. We propose q-PDGD, a quantized stochastic primal-dual method, and analyze it under relaxed global geometry. Under restricted secant inequality (RSI), a constant step-size yields linear contraction to an explicit neighborhood determined by gradient noise, quantization distortion, and network connectivity, while a diminishing step-size achieves O(1/k) convergence without shared-minimizer assumptions. Under Polyak-Lojasiewicz (PL) inequality, we obtain linear-to-neighborhood convergence in the same stochastic quantized setting. Our results match the best-known centralized stochastic rates in oracle complexity, and are supported by experiments demonstrating the predicted tradeoffs between quantization level, step-size choice, and graph structure.

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09.
arXiv (CS.AI) 2026-06-15

Korzhinskii-Net: Physics-Informed Neural Network for Sub-Surface Mineral Prospectivity Modelling

Authors:
Boris Kriuk↗

arXiv:2606.13695v1 Announce Type: cross Abstract: Mineral prospectivity modelling (MPM) underpins exploration economics, yet most operational pipelines reduce to data-driven classifiers trained on shallow surface proxies. Such models are blind to the subsurface physics that actually localises ore: heat advection, fluid flow, and lithology-dependent precipitation. We present Korzhinskii-Net, a 2-D radial physics-informed neural network (PINN) that couples Darcy flow, advective-diffusive heat transport, and a softplus-saturated reaction rate into a single differentiable forward model, weakly supervised by surface and remote-sensing proxies. The network is named after Dmitri S. Korzhinskii (1899-1985), whose theory of infiltration metasomatism provides the physical scaffold. We evaluate Korzhinskii-Net on five ore provinces spanning four commodity classes – Norilsk (Ni-Cu-PGE), Pechenga (Ni-Cu sulphide), Udokan (sandstone-hosted Cu), Sukhoi Log (orogenic Au), and Mirny (kimberlitic diamond) – under a fair, leakage-controlled 5-fold cross-validation protocol with hard ring-shaped negatives. Korzhinskii-Net attains a mean PR-AUC of 0.885 versus 0.281 for the strongest classical baseline (gradient boosting), and a mean fractional rank of 0.019 versus 0.413. The improvement is consistent across all five provinces and four commodity systems, suggesting that physics-informed differentiable simulators, even when constrained only by global open-data proxies, can recover localisation patterns that pure feature-based learners systematically miss. We release the full pipeline and evaluation harness as open source.

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10.
arXiv (CS.AI) 2026-06-15

Applicability Condition Extraction for Therapeutic Drug-Disease Relations

Authors:
Guanting Luo↗Noriki Nishida↗Yuji Matsumoto↗Yuki Arase↗

arXiv:2606.14031v1 Announce Type: new Abstract: Identifying conditions that a certain drug takes therapeutic effect on a target disease is crucial for clinical decision-making support. However, most existing biomedical information extraction methods have focused on identifying only relations between drugs and diseases, while largely overlooking the context-specific conditions where such relations can apply. To address this problem, we introduce the task of applicability condition extraction for therapeutic drug–disease relations from biomedical research literature. We create the first dataset that has manually annotated triples of drugs, diseases, and applicability conditions on biomedical paper abstracts with 1,119 drug-disease pairs. Using this dataset, we systematically evaluate the performance of a range of existing methods. In addition, we propose a new method that enhances LoRA to consider relations between drugs and diseases. Our method consistently outperforms strong baselines across different evaluation settings. The source code and dataset of this paper can be obtained from: https://github.com/guantingluo98/Drug-ACE

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11.
arXiv (CS.LG) 2026-06-16

Filtered Conformal Ellipsoids for Graph-Native Time Series

Authors:
Yannick Limmer↗

arXiv:2606.17014v1 Announce Type: new Abstract: Joint prediction sets for multivariate time series should control a single event while adapting to cross-coordinate dependence. We study filtered conformal ellipsoids: a frozen state-space filter emits a one-step predictive mean and covariance, and split-conformal calibration is applied to the resulting Mahalanobis scores. The filter is used to choose the ellipsoid shape; conformal calibration chooses the scalar radius, so the construction benefits from a learned predictive covariance without relying on Gaussian tail probabilities for coverage. The main difficulty is that filtered scores are dependent and learned recurrent filters need not contract in their raw hidden state; we therefore analyse contraction in an observable predictive-law quotient that identifies hidden states producing the same future sequence of emitted Gaussian laws. Under a stable Bayes Gaussian-projection filter, covariance bounds, and a finite-horizon observability Fisher condition, small excess Gaussian negative log-likelihood implies contraction of the learned emitted laws. Combined with a threshold-autocovariance envelope this yields a Chebyshev-type approximate coverage bound for filtered split-conformal prediction under dependence; a sharper Bernstein-type bound requires an additional geometric-mixing concentration assumption. Under Gaussian oracle realisability we also obtain a near-oracle log-volume comparison within the class of conditionally valid Gaussian ellipsoid rules. We instantiate the framework with a GCN-GRU filter with diagonal-plus-low-rank covariance. On moderate-size graph-native traffic benchmarks (METRLA-$20$ and PEMSBAY-$50$), the learned filter gives sharper at-target ellipsoids than static-covariance and non-filter baselines; at full-graph scale and on non-graph-native datasets, factor and copula baselines can be stronger.

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12.
arXiv (CS.LG) 2026-06-19

Effective Dimension Governs Generalization in Quantum Kernel Vision Models

Authors:
Jian Xu↗Delu Zeng↗John Paisley↗Qibin Zhao↗

arXiv:2606.20183v1 Announce Type: new Abstract: Recent quantum vision models-quantum vision transformers and quantum convolutional networks-report two striking but unexplained empirical phenomena: (i) ansatze with more, or more uniformly distributed, entanglement generalize better, and (ii) injecting quantum noise can improve test accuracy rather than degrade it. These observations are currently treated as curiosities, discovered by grid search and explained, if at all, by hand. We show that both are manifestations of a single, measurable quantity: the effective dimension $d_eff$ of the (noise-shaped) quantum feature kernel. Working primarily with quantum-kernel vision models-a quantum feature map read out by a kernel classifier-we give a spectral account in which entanglement structure and quantum noise are two knobs that move $d_eff$; in an overfitting regime, contracting $d_eff$ acts as ridge-like regularization. We analyze the mechanism: an exact decomposition of the depolarized kernel $K_p=(1-p)^2K+\tfrac{p(2-p)}{D}\mathbf{1}\mathbf{1}^\top$ with $d_eff(K_p)\to1$, a contraction result (and its boundary) for amplitude damping, a kernel-machine capacity bound, and a capacity/alignment risk decomposition; the monotone contraction operative in our entangled experiments is verified empirically, not proven in general. Along the one-parameter depolarizing family the collapse is instead exact by construction; we use it only to confirm the kernel decomposition to machine precision and at up to $12$ qubits, not as evidence for $d_eff$. Amplitude damping contracts $d_eff$ and lifts test accuracy by up to $+13\%$ along an inverted-U sweet spot; the effect's sign flips between the over- and under-fitting regimes; noise injection matches an explicit spectral-filtering frontier. Our results organize two reported anecdotes into a single measurable principle for designing quantum-vision models.

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13.
arXiv (quant-ph) 2026-06-11

Measurement incompatibility and quantum steering via linear programming

Authors:
Lucas E. A. Porto↗S\'ebastien Designolle↗Sebastian Pokutta↗Marco T\'ulio Quintino↗

arXiv:2506.03045v3 Announce Type: replace Abstract: The problem of deciding whether a set of quantum measurements is jointly measurable is known to be equivalent to determining whether a quantum assemblage is unsteerable. This problem can be formulated as a semidefinite program (SDP). However, the number of variables and constraints in such a formulation grows exponentially with the number of measurements, rendering it intractable for large measurement sets. In this work, we circumvent this problem by transforming the SDP into a hierarchy of linear programs that compute upper and lower bounds on the incompatibility robustness with a complexity that grows polynomially in the number of measurements. The hierarchy is guaranteed to converge and it can be applied to arbitrary measurements – including non-projective POVMs (Positive Operator-Valued Measures) – in arbitrary dimensions. While convergence becomes impractical in high dimensions, in the case of qubits our method reliably provides accurate upper and lower bounds for the incompatibility robustness of sets with several hundred measurements in a short time using a standard laptop. We also apply our methods to qutrits, obtaining non-trivial upper and lower bounds in scenarios that are otherwise intractable using the standard SDP approach, although such bounds are significantly looser than the ones obtained in the qubit case. Finally, we show how our methods can be used to construct local hidden state models for states (i.e., to prove that a state cannot lead to steering under any possible local measurements), or conversely, to certify that a given state exhibits steering; for two-qubit quantum states, our approach is comparable to, and in some cases outperforms, the current best methods.

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14.
arXiv (CS.AI) 2026-06-18

Rescaling MLM-Head for Neural Sparse Retrieval

Authors:
Youngjoon Jang↗Seongtae Hong↗Jonah Turner↗Heuiseok Lim↗

arXiv:2606.18811v1 Announce Type: cross Abstract: Learned sparse retrieval (LSR) models such as SPLADE have traditionally used BERT-style masked language models as backbone encoders. A natural expectation is that replacing BERT with stronger pretrained encoders should improve retrieval effectiveness. However, we find that under standard SPLADE training recipes, backbones with large MLM-head L2 norms can suffer performance degradation and even training collapse under standard SPLADE training recipes. We identify this failure as a scale mismatch in the MLM head: SPLADE directly uses MLM-head outputs to construct sparse lexical representations, and query-document relevance is computed by an unnormalized dot product over these representations. As a result, an inflated MLM-head scale can amplify sparse activations, distort matching scores, and destabilize contrastive training under common training settings. To address this issue, we introduce a simple initialization-time correction that rescales the MLM-head projection by a constant factor before SPLADE training. This zero-cost adjustment improves training stability without modifying the model architecture or training objective. Across both in-domain and out-of-domain retrieval benchmarks, this simple correction substantially improves large-norm backbones such as ModernBERT and Ettin, turning unstable training runs into competitive sparse retrievers. In several settings, the corrected models further match or surpass the classic BERT-SPLADE baseline. These findings suggest that the bottleneck in adapting pretrained encoders to LSR is not encoder capacity alone, but the calibration of the MLM-head scale used to construct sparse lexical representations.

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15.
arXiv (CS.AI) 2026-06-18

A Taxonomy of Mental Health and Technology Needs for Alzheimer's and Dementia Caregivers

Authors:
Keran Wang↗Drishti Goel↗Jiayue Melissa Shi↗Violeta J. Rodriguez↗Daniel S. Brown↗Dong Whi Yoo↗Ravi Karkar↗Koustuv Saha↗

arXiv:2606.19247v1 Announce Type: cross Abstract: Family members caring for individuals with Alzheimer's disease and related dementias (AD/ADRD) provide the foundation of long-term care worldwide. In 2023, more than 11 million U.S. family and friends contributed 18 billion hours of unpaid care, often at the cost of their own physical and mental health. These informal caregivers – also referred as the "invisible second patients" – experience elevated rates of mental health problems. Yet research commonly reduces their complex psychosocial experiences to a single construct of caregiver burden, obscuring which specific needs are unmet or effectively supported. At the same time, digital and AI-enabled technologies are rapidly expanding, from smartphone apps and videoconferencing to sensor platforms and AI chatbots. However, the absence of shared frameworks across medicine, psychology, and technology research limits cumulative progress. This study introduces a Caregiver Mental Health and Technology Taxonomy that systematically links AD/ADRD caregiver needs with corresponding classes of technology-based interventions. Drawing from an interdisciplinary literature review and two qualitative studies with caregivers, the taxonomy identifies mismatches between caregiver priorities and existing technological support, highlights under-served domains such as relational strain and compassion fatigue, and proposes design directions for adaptive, responsive systems. The framework offers a shared vocabulary to guide clinicians, researchers, and technology designers in developing more person-centered and clinically grounded innovation in dementia care.

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

R2RDreamer: 3D-aware Data Augmentation for Spatially-generalized 2D Manipulation Policies

Authors:
Xiuwei Xu↗Haowen Sun↗Angyuan Ma↗Yiwei Zhang↗Zhenyu Wu↗Xiaofeng Wang↗Bingyao Yu↗Zheng Zhu↗Jie Zhou↗Jiwen Lu↗

Spatial generalization is critical for imitation-learned manipulation policies, but achieving it typically requires scaling demonstrations across diverse object poses, robot configurations, and camera viewpoints. Data augmentation from a few source demonstrations offers a practical alternative to costly real-world collection. Simulation-based augmentation can create controllable variation, but requires complex environment and object setup and may introduce a sim-to-real gap. Recent real-to-real methods avoid these issues by jointly editing 3D observations and action trajectories from real demonstrations, yet they still rely on strong 3D scene parsing and geometry completion, and often produce observations tailored to 3D pointcloud policies rather than RGB-based 2D policies. We propose R2RDreamer, a real-to-real demonstration augmentation framework that preserves the geometric consistency of 3D action-observation editing while moving visual completion to 2D video space. Specifically, R2RDreamer first performs lightweight 3D augmentation by editing incomplete object pointclouds and end-effector trajectories in a shared 3D frame; it then projects the edited scene into masked image-space control videos with occlusion-aware reasoning and uses a dense-control image-to-video model to complete temporally coherent RGB observations. Experiments on spatially shifted manipulation tasks with both 2D diffusion-style policies and vision-language-action policies show that R2RDreamer improves spatial generalization from limited source demonstrations, with analyses validating the contributions of 3D editing, occlusion-aware projection, and video completion.

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17.
arXiv (CS.CL) 2026-06-16

MyPCBench: A Benchmark for Personally Intelligent Computer-Use Agents

Authors:
Lawrence Keunho Jang↗Andrew Keunwoo Jang↗Jing Yu Koh↗Ruslan Salakhutdinov↗

Current benchmarks for computer-use agents evaluate models in impersonal environments. This leaves a gap between evaluation and deployment where personal assistants are expected to work across a user's whole digital life, including their context, historical data, and logged-in accounts. This gap is widest on web tasks, where live web evaluations cannot exercise sites that require logging in or personal information, the kind of site a real personal assistant has to drive. We introduce MyPCBench, which tests computer-use agents as personal assistants on a Linux desktop populated with 17 simulated real-world web applications and a full desktop stack, all seeded for one canonical persona, Michael Scott from The Office. We define 184 tasks in this environment, each inspired by a real request drawn from the OpenClaw community, and benchmark six closed and open-weight models with a uniform computer+bash tool surface. We find that the best model, Claude Opus 4.6, fully solves 55.4\% of the tasks, the only model above 50\%. Model failures cluster on tasks that span many applications and on long trajectories, where personalization stresses an assistant the most. We release the environment, task set, and agent harness at https://mypcbench.com.

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18.
arXiv (quant-ph) 2026-06-12

Non-invertible symmetries out of equilibrium: Eigenstate order and Floquet physics

Authors:
Yabo Li↗Aditi Mitra↗

arXiv:2508.14213v2 Announce Type: replace-cross Abstract: Through the study of the Rep($D_8$) non-invertible symmetry, we show how non-invertible symmetries manifest in dynamics. Results are presented for dynamics generated by Hamiltonians as well as Floquet unitaries. For both examples, the role of the non-invertible symmetry is studied through the appearance of non-invertible symmetry protected edge modes. In addition, the role of the non-invertible symmetry for the Hamiltonian is studied through eigenstate order. In particular, by considering the effect of symmetry preserving disorder, the non-invertible symmetry is shown to give rise to degeneracies in the spectra of the Hamiltonian that can only be completely lifted at orders of perturbation that scale with system size. The eigenstates of disordered Hamiltonians, whose ground state correspond to non-trivial symmetry protected topological (SPT) states, are shown to have either trivial or non-trivial SPT order that are detected as non-zero expectation value of string order-parameters. In contrast, non-trivial SPT order is absent in the eigenstates of trivial SPT Hamiltonians with disorder. The interface between two different SPT phases host edge modes whose dynamics is studied numerically and analytically. The edge mode is shown to oscillate at frequencies related to different effective chain lengths that are weighted by the temperature, becoming an exact zero mode in the limit of zero temperature. A Floquet model with the non-invertible symmetry is constructed whose edge mode is shown to exhibit period-doubled dynamics at low effective-temperatures. The zero and period-doubled edge modes differ from those in conventional SPTs by being symmetric under the invertible symmetry, while being charged under the non-invertible symmetry.

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

Ricci-Filtration: Boosting Retrieval-Augmented Generation Reranker to Query-Answer Tasks by Discrete Ricci Flow

Authors:
Tian Qin↗Wei-Min Huang↗

arXiv:2606.15482v1 Announce Type: cross Abstract: Ricci flow is a curvature-guided diffusion process that deforms space by shrinking regions of high positive curvature and expanding those with negative curvature. Similarly, discrete Ricci flow on weighted graphs modifies edge weights by shrinking edges with positive Ricci curvature and stretching those with negative Ricci curvature, effectively increasing the separation between clusters. Inspired by these two cornerstone works, we propose a geometry-based RAG reranker enhancement procedure called Ricci-Filtration. By modeling the input query and initial retrieved chunks as a network, where the input query and chunks serve as nodes and embedding-based pairwise relations define an initial graph, Ricci-Filtration leverages discrete curvature and Ricci flow to evaluate the structural importance of each chunk with respect to the user query. The system first filters the initial chunks based on their geometric curvature relative to the query; then, a reranker processes the remaining chunks to enhance generative performance. We theoretically prove that normalized discrete Ricci flow can detect community structures by identifying distinct asymptotic behaviors in edge weights. This supports the removal of ``noisy'' document chunks characterized by large weights and negative Ricci curvature relative to the query node. Extensive experiments confirm that Ricci-Filtration outperforms several baseline reranking methods in accuracy, precision, recall, and F1 scores. Furthermore, ablation studies demonstrate that the Ricci-Filtration generally outperforms the baseline under various settings, highlighting the framework's robustness across different architectures.

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20.
arXiv (CS.LG) 2026-06-16

Asymptotically Optimal Sequential Testing with Markovian Data

Authors:
Alhad Sethi↗Kavali Sofia Sagar↗Shubhada Agrawal↗Debabrota Basu↗P. N. Karthik↗

arXiv:2602.17587v3 Announce Type: replace-cross Abstract: We study one-sided and $\alpha$-correct sequential hypothesis testing for data generated by an ergodic, finite-state Markov chain. The null hypothesis is that the unknown transition matrix belongs to a prescribed set $P$ of stochastic matrices, and the alternative corresponds to a disjoint set $Q$. We establish a non-asymptotic instance-dependent lower bound on the expected stopping time of any valid sequential test under the alternative, which is asymptotically tight. Our novel analysis improves the existing lower bounds, which are either asymptotic or provably sub-optimal in this setting. Our lower bound incorporates both the stationary distribution and the transition structure induced by the unknown Markov chain. We further propose an optimal test whose expected stopping time matches this lower bound asymptotically as $\alpha \to 0$. We illustrate the usefulness of our framework through applications to sequential detection of model misspecification in Markov Chain Monte Carlo and to testing structural properties, such as the linearity of transition dynamics, in Markov decision processes. Our findings yield a sharp and general characterization of optimal sequential testing procedures under Markovian dependence.

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

Your Mouse and Eyes Secretly Leak Your Preference: LLM Alignment using Implicit Feedback from Users

Authors:
Haw-Shiuan Chang↗Jeffrey Gomez↗Mehul Patwari↗Aryan Sajith↗Hamed Zamani↗

To align a Large Language Model (LLM), most existing methods collect explicit human feedback and train a reward model to predict the human preference based on the response text. These existing methods have two key limitations. First, the users rarely provide explicit feedback for LLM responses, which makes the high-quality preference annotation expensive to collect. Second, the methods do not leverage implicit human feedback, which has proven vital to the economic moats of Internet giants. To quantify the value of implicit feedback, we build a new dataset called IFLLM, which collects 1336 multi-turn questions from the 59 Mechanical Turk workers, their mouse trajectories, and eye gazing points to the LLMs' responses from their webcams. IFLLM shows that the users have very diverse types of gazing behavior and mouse trajectories. Our reward model based on the implicit user feedback boosts the accuracy of the text-based reward model from 55% to 64% and nearly triples the relative response quality improvements after applying the DPO to eight LLMs, demonstrating the value of implicit feedback in the wild. Our data collection website, dataset, and codes can be found at https://github.com/themehulpatwari/llm-implicit-feedback/.

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22.
medRxiv (Medicine) 2026-06-17

Cardio Heart Connect: Protocol for a Randomized Trial of a Commercially Available mHealth Fitness Intervention for Cardiac Rehabilitation After Transcatheter Aortic Valve Replacement

Authors:
Rosen↗Butala↗N. M↗Kramer↗D. B↗Helmkamp↗L. J↗Gama↗Goldberg↗Marzec↗Peterson↗P. N↗…

Background: Despite ample evidence of the benefits of cardiac rehabilitation (CR), few transcatheter aortic valve replacement (TAVR) patients participate. Commercially available mobile health offers an opportunity to deliver activity-promotion content to populations that are challenged to participate in CR. This study aims to test the efficacy of clinically controlled, commercially available fitness programming for improving physical activity and cardiovascular health outcomes designed to be initiated while patients are on waitlists for traditional CR. Methods: The Cardio Heart Connect study is a hybrid type I effectiveness-implementation trial aiming to enroll N=200 patients who have been placed on a cardiac rehab waitlist following a TAVR procedure from the University of Colorado Hospital Heart and Vascular Center. Participants will be randomized 1:1 to the Cardio Heart Connect intervention with commercially available fitness or attention control, designed to control for technology access. At baseline, post-intervention (8 weeks), and follow-up (12 months), we will assess the primary outcome of participants? daily steps as measured by smartwatch accelerometer and secondary outcomes of interest including functional capacity (Duke Activity Status Index; VO2max), quality of life (Kansas City Cardiomyopathy Questionnaire), and cardiovascular health status (Life Essential 8). In addition, we will use mixed methodologies to evaluate the implementation of intervention using the Reach, Effectiveness, Adoption, Implementation, and Maintenance (RE-AIM) Framework. Conclusions: Commercially available fitness programs have the potential to provide more accessible opportunities for patients recovering from TAVR to engage in physical activity and may be preferred due to their customizability, convenience, and ease of scheduling. Overall, this study will provide insight into the use of commercial mHealth to promote activity following TAVR.

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23.
arXiv (CS.LG) 2026-06-16

TextResNet: Decoupling and Routing Optimization Signals in Compound AI Systems via Deep Residual Tuning

Authors:
Suizhi Huang↗Mei Li↗Han Yu↗Xiaoxiao Li↗

arXiv:2602.08306v2 Announce Type: replace Abstract: Textual Gradient-style optimizers (TextGrad) enable gradient-like feedback propagation through compound AI systems. However, they do not work well for deep chains. The root cause of this limitation stems from the Semantic Entanglement problem in these extended workflows. In standard textual backpropagation, feedback signals mix local critiques with upstream contexts, leading to Attribution Ambiguity. To address this challenge, we propose TextResNet, a framework that reformulates the optimization process to achieve precise signal routing via four key innovations. Firstly, in the forward pass, it enforces Additive Semantic Deltas to preserve an Identity Highway for gradient flow. Secondly, in the backward pass, it introduces Semantic Gradient Decomposition via a Semantic Projector to disentangle feedback into causally independent subspaces. Thirdly, it implements Causal Routing, which routes projected signals to their specific components. Finally, it performs Density-Aware Optimization Scheduling to leverage the disentangled signals to dynamically allocate resources to key system bottlenecks. Our results show that TextResNet not only achieves superior performance compared to TextGrad, but also exhibits remarkable stability for agentic tasks in compound AI systems where baselines collapse. Code is available at https://github.com/JeanDiable/TextResNet.

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

Learning Fine-Grained Correspondence with Cross-Perspective Perception for Open-Vocabulary 6D Object Pose Estimation

Authors:
Yu Qin↗Shimeng Fan↗Fan Yang↗Zixuan Xue↗Zijie Mai↗Wenrui Chen↗Kailun Yang↗Zhiyong Li↗

Open-vocabulary 6D object pose estimation empowers robots to manipulate arbitrary unseen objects guided solely by natural language. However, a critical limitation of existing approaches is their reliance on unconstrained global matching strategies. In open-world scenarios, trying to match anchor features against the entire query image space introduces excessive ambiguity, as target features are easily confused with background distractors. To resolve this, we propose Fine-grained Correspondence Pose Estimation (FiCoP), a framework that transitions from noise-prone global matching to spatially-constrained patch-level correspondence. To systematically eliminate background interference, FiCoP first employs an object-centric disentanglement step to isolate the target from macro-level environmental noise. Building upon this localized region, our core methodological innovations are twofold. Firstly, a Cross-Perspective Global Perception (CPGP) module is proposed to fuse dual-view features, establishing structural consensus through explicit context reasoning and text-guided semantic injection. Secondly, we design a Patch Correlation Predictor (PCP) that leverages a patch-to-patch correlation matrix as a structural prior. This generates a precise block-wise association map, acting as a spatial filter to enforce fine-grained, noise-resilient matching. Experiments on the REAL275 and Toyota-Light datasets demonstrate that FiCoP improves Average Recall by 8.0% and 6.1%, respectively, compared to the state-of-the-art method, highlighting its capability to deliver robust and generalized perception for robotic agents operating in complex, unconstrained open-world environments. The source code will be made publicly available at https://github.com/zjjqinyu/FiCoP.

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

Diffusion Models for Adaptive Sequential Data Generation

Authors:
Haoyang Cao↗Minshuo Chen↗Yinbin Han↗Renyuan Xu↗

arXiv:2606.06007v2 Announce Type: replace Abstract: Generating realistic synthetic sequential data is critical in real-world applications across operations research, finance, healthcare, energy systems, and scientific computing, where time-indexed observations are used for prediction, simulation, risk assessment, and data-driven decision-making. While diffusion models have achieved remarkable success in generating static data, their direct extensions to sequential settings often fail to capture temporal dependence and information structure. Designing diffusion models that can simulate sequential data in an adapted manner, and hence without anticipation of future information, therefore remains an open challenge. In this work, we propose a sequential forward-backward diffusion framework for adapted time series generation. Our approach progressively injects and removes noise along the sequence, conditioning on the previously generated history to ensure adaptiveness. A novel score-matching objective is introduced for efficient parallel training. We derive rigorous statistical guarantees under a generic framework, then establish score approximation, score estimation, and distribution estimation results with ReLU networks serving as a concrete instance. Empirically, we validate our method on synthetic data, including ARMA models and Gaussian processes, and demonstrate its effectiveness in constructing mean-variance optimal portfolios.

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