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02.
arXiv (math.PR) 2026-06-15

The 1/4-phenomenon of placement probabilities of tilings in the Aztec diamond

作者:
Marcus Sch\"onfelder↗

arXiv:2512.08377v2 Announce Type: replace-cross Abstract: We consider domino tilings of the Aztec diamond. Using the Domino Shuffling algorithm introduced by Elkies, Kuperberg, Larsen, and Propp in arXiv:math/9201305, we are able to generate domino tilings uniformly at random. In this paper, we investigate the probability of finding a domino at a specific position in such a random tiling. We prove that this placement probability is always equal to $1/4$ plus a rational function, whose shape depends on the location of the domino, multiplied by a position-independent factor that involves only the size of the diamond. This result leads to significantly more compact explicit counting formulas compared to previous findings. As a direct application, we derive explicit counting formulas for the domino tilings of Aztec diamonds with $2\times 2$-square holes at arbitrary positions.

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03.
arXiv (CS.LG) 2026-06-16

Analytic Torsion and Spectral Gap Capture Persistent-Laplacian Performance

作者:
Jernej Grlj↗Aaron D. Lauda↗

arXiv:2606.16990v1 Announce Type: new Abstract: While persistent Laplacians (PL) offer a richer geometric representation of data than persistent homology, utilizing their full eigenspectrum for learning tasks is often hampered by high dimensionality and the ``varying length'' problem across different filtration scales. We propose a compact spectral representation that distills the persistent Laplacian into three mathematically grounded invariants: Betti numbers, the spectral gap, and analytic torsion. Across benchmark datasets including MNIST, QM-3D, and SKEMPI WT, we demonstrate that this reduced feature space captures the essential predictive signal of the full spectrum, and in some cases outperforms it, while significantly reducing computational overhead and preventing the noise introduced by higher-frequency eigenvalues. Our results suggest that these invariants provide a principled, fixed-length interface between spectral geometry and topological learning.

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04.
arXiv (CS.CV) 2026-06-15

Pano3D: Unified 3D Reconstruction and Panoptic Segmentation

作者:
Victor Barberteguy↗Ahmet Iscen↗Mathilde Caron↗Alireza Fathi↗G\"ul Varol↗Cordelia Schmid↗

Recent advances in 3D feedforward reconstruction neural networks have achieved remarkable success in dense reconstruction from images without any camera parameters. Yet, equipping these models with robust semantic understanding remains an open problem. Here we introduce an approach that performs 3D reconstruction and 3D panoptic segmentation in a unified framework. We build on existing 3D reconstruction models and augment them with a set-based mask decoder. The approach is jointly trained with a geometric and semantic loss, which are shown to be mutually beneficial. More precisely, the features are initialized from the geometric information and then finetuned to capture jointly geometry and semantics. We demonstrate the generality of our approach by successfully applying our framework both to online and all-to-all attention reconstruction backbones. Our method achieves state-of-the-art performance in 3D panoptic segmentation across ScanNet, ScanNet200, and ScanNet++ datasets. Ablation studies show that such joint training of a unified model equips 3D feedforward reconstruction neural networks with panoptic segmentation and yields mutually beneficial improvements.

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05.
arXiv (CS.CV) 2026-06-16

Kairos: A Native World Model Stack for Physical AI

作者:
Kairos Team↗Fei Wang↗Shan You↗Qiming Zhang↗Tao Huang↗Zuoyi Fu↗Zhisheng Zheng↗Yunlong Xi↗Feng Lv↗Xiaoming Wu↗Zeyu Liu↗Cong Wan↗…

World models are transitioning from passive visual generators to foundational, operational infrastructure for Physical AI: they must natively acquire world knowledge from heterogeneous experience, maintain persistent states over long horizons, and execute efficiently within real deployment constraints. We introduce Kairos, a native world model stack designed around these requirements. (1) Kairos learns the world by pioneering a Native Pre-training Paradigm governed by a Cross-Embodiment Data Curriculum, which organizes open-world videos, human behavioral data, and robot interactions into a progressive developmental pathway. (2) Kairos maintains the world by unified world understanding, generation, and prediction within a Native Unified Architecture equipped with Hybrid Linear Temporal Attention, where sliding-window attention captures local dynamics, dilated sliding windows capture mid-range dependencies, and gated linear attention maintains persistent global memory. We establish formal theoretical bounds demonstrating that this temporal factorization strictly limits error accumulation, mathematically guaranteeing state propagation across extended horizons. (3) Kairos runs the world by incorporating a Deployment-Aware System Co-Design to support low-latency rollout generation on server and consumer-grade hardware for real-world observation-action-feedback loops. Experiments on embodied world-model, long-horizon, and action-policy benchmarks show that Kairos achieves top level performance while offering a strong efficiency-capability trade-off. Together, these results position Kairos as a cohesive operational foundation for future self-evolving physical intelligence.

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

Questioning the Coverage-Length Metric in Conformal Prediction: When Shorter Intervals Are Not Better

作者:
Yizhou Min↗Yizhou Lu↗Lanqi Li↗Zhen Zhang↗Jiaye Teng↗

arXiv:2601.21455v2 Announce Type: replace-cross Abstract: Conformal prediction(CP) has become a cornerstone of distribution-free uncertainty quantification, conventionally evaluated by its coverage and interval length. This work critically examines the sufficiency of these standard metrics. We demonstrate that the interval length might be deceptively improved through a counter-intuitive approach termed Prejudicial Trick(PT), while the coverage remains valid. Specifically, for any given test sample, PT probabilistically returns an interval, which is either null or constructed using an adjusted confidence level, thereby preserving marginal coverage. While PT potentially yields a deceptively lower interval length, it introduces practical vulnerabilities: the same input can yield completely different prediction intervals across repeated runs of the algorithm. We formally derive the conditions under which PT achieves these misleading improvements and provide extensive empirical evidence across various regression and classification tasks. Furthermore, we introduce a new metric interval stability which helps detect whether a new CP method implicitly improves the length based on such PT-like techniques. Code is available at https://github.com/benben-cd/PT-Conformal-Prediction.

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07.
arXiv (CS.CV) 2026-06-19

VisDom: Sparse Novel View Synthesis with Visible Domain Constraint

作者:
Mariia Gladkova↗Tarun Yenamandra↗Edmond Boyer↗Robert Maier↗Tony Tung↗Daniel Cremers↗

Sparse novel view synthesis (NVS) remains challenging due to the ambiguity of recovering 3D geometry from few input views. While NeRF- and Gaussian Splatting (GS)-based methods perform well with dense supervision, they often overfit in sparse settings, producing floating artifacts and inconsistent geometry. Silhouette consistency is commonly used as a regularizer, but it remains insufficient, as silhouette-consistent regions can extend beyond the true object geometry. We introduce VisDom, a learning-free geometric constraint that augments classical carving-based visual hull reconstruction by enforcing a minimum multi-view visibility requirement. Specifically, we define a visible domain as the subset of 3D space observed by at least $K$ views and use it as an additional filtering criterion on top of standard silhouette-based reconstruction. This provides a stronger spatial prior in sparse-view settings. We integrate VisDom into both implicit (NeRF) and explicit (GS) pipelines by restricting volumetric sampling and guiding Gaussian placement during optimization. Experiments on three challenging datasets show consistent improvements in sparse-view NVS, enabling high-quality object-centric reconstruction from as few as four input images. Our method is domain-agnostic, requires only silhouettes, and introduces no learned parameters, making it a simple complement to existing approaches. Applying VisDom on top of GaussianObject further improves performance on Omni3D and MipNeRF360, while matching or surpassing it at 22 $\times$ lower training cost.

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08.
arXiv (CS.CV) 2026-06-18

A Prototypical Signature Approach for Writer-Independent Offline Signature Verification

作者:
Kecia G. de Moura↗Robert Sabourin↗Rafael M. O. Cruz↗

Offline handwritten signature verification aims to distinguish genuine from forged signatures using static images. Since real forgeries are rarely available, negative samples are usually randomly drawn from genuine signatures of other users to create training data. However, this random selection often lacks diversity, increases redundancy, and escalates computational cost, leading to inefficient training. We propose a data-driven strategy to generate diverse, informative negative samples using prototypical signatures, which are compact, non-identifiable summaries of genuine signature features. Based on the experiments results, we conclude that (i) prototypical signatures yield more informative negative samples, improving the detection of skilled forgeries; (ii) the proposed approach is backbone-agnostic, showing robustness across architectures; and (iii) when combined with a primal-form linear SVM, it serves as an alternative to RBF-based models while significantly improving scalability and computational efficiency. Implementation of the method is available at https://github.com/kdmoura/proto_hsv.

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09.
arXiv (CS.CV) 2026-06-11

ActionMap: Robot Policy Learning via Voxel Action Heatmap

作者:
Pei Yang↗Hai Ci↗Yanzhe Chen↗Qi Lv↗Han Cai↗Mike Zheng Shou↗

Vision-language-action (VLA) models have advanced rapidly across backbones, training recipes, and data scale, yet the action decoder, which converts the backbone's hidden state into a continuous control signal, has barely changed and remains a single-point predictor across the majority of current VLAs. Whether implemented via autoregressive token bins, L1 regression, or flow-matching denoising, the resulting decoder treats the action space as unstructured, leaving the geometric proximity of neighboring actions unexploited during training. To advance this, we introduce ActionMap, a voxel heatmap action head that drops into an existing VLA in place of its native action decoder. For each new action, the head predicts a voxel heatmap over the action space, where each voxel directly stores the probability of the corresponding action. Across LIBERO simulation and real-world Franka manipulation, our heatmap head surpasses two architecturally distinct backbones at matched training steps (e.g., +8.2% over OpenVLA-OFT's L1 regression head on the LIBERO four-suite average), converges at comparable or faster rates on both backbones, and remains markedly more data-efficient at low training data. The cross-backbone consistency indicates that action representation is a real lever for VLA performance, distinct from further backbone or recipe scaling. Project Page: https://showlab.github.io/ActionMap/.

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10.
bioRxiv (Bioinfo) 2026-06-16

THEOBROMA: an aggregated open database of 1.13 million natural products with per-compound license auditing, three-tier classification, and stereochemistry-aware deduplication

作者:
Klamt↗Jaczkowski↗Franke↗Nejdl↗

Natural products remain one of the most productive sources of pharmacologically active compounds for drug discovery, yet the current open aggregator landscape attributes licenses at database rather than compound granularity, with consequences that have become tangible as the field grows. A recent relicensing event in one constituent source (the September 2024 transition of the Natural Products Atlas to CC BY-NC 4.0) demonstrates how database-level licensing propagates across an aggregate and motivates the per-compound audit framework presented here. The same peer cohort separately leaves classification provenance and stereoisomer-family relations coarser than either layer warrants. THEOBROMA, accessible at url{https://theobroma.l3s.uni-hannover.de}, integrates 1{,}133{,}004 natural products from 29 open sources under a per-compound license audit that resolves each compound's license tier across all attesting sources under a most-restrictive-wins rule, identifying 900{,}170 compounds (79.4%) under open-use licenses and exposing the per-source attestation chain and resolved tier through a dedicated audit endpoint and a query-time license filter. A three-tier classification stratifies 89.3% coverage into 35.1% curated, 43.9% high-confidence inferred, and 10.3% exploratory tiers, with 486{,}215 stereoisomer families preserved by full 27-character InChIKey deduplication and exposed via a dedicated texttt{/api/stereoisomers/} endpoint and a radial-family display. Per-compound license provenance is the primary differentiator. Classification stratification and stereoisomer-family exposure add finer-grained access to two related axes, supporting license-compatible virtual screening and isomer-specific bioactivity analysis at corpus scale. As an evolving open resource, THEOBROMA pairs continuous pipeline maintenance with interactive geographic, taxonomic, and chemical-space exploration.

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

From Static Inference to Dynamic Interaction: A Survey of Streaming Large Language Models

作者:
Junlong Tong↗Zilong Wang↗YuJie Ren↗Peiran Yin↗Hao Wu↗Wei Zhang↗Xiaoyu Shen↗

Standard Large Language Models (LLMs) are predominantly designed for static inference with pre-defined inputs, which limits their applicability in dynamic, real-time scenarios. To address this gap, the streaming LLM paradigm has emerged. However, existing definitions of streaming LLMs remain fragmented, conflating streaming generation, streaming inputs, and interactive streaming architectures, while a systematic taxonomy is still lacking. This paper provides a comprehensive overview and analysis of streaming LLMs. First, we establish a unified definition of streaming LLMs based on data flow and dynamic interaction to clarify existing ambiguities. Building on this definition, we propose a systematic taxonomy of current streaming LLMs and conduct an in-depth discussion on their underlying methodologies. Furthermore, we explore the applications of streaming LLMs in real-world scenarios and outline promising research directions to support ongoing advances in streaming intelligence. We maintain a continuously updated repository of relevant papers at https://github.com/EIT-NLP/Awesome-Streaming-LLMs.

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

TEDD: Robust Detection of Unstable Temporal Features

作者:
Ricardo Ribeiro Pereira↗Bruno Casal Lara\~na↗N\'adia Soares↗Miguel Ara\'ujo↗

arXiv:2606.12643v1 Announce Type: new Abstract: When working with real-world temporal data, it is common to encounter features whose distribution is changing over time. The naive employment of Machine Learning models on this unstable data might lead to rapidly degrading performance, especially if the new distribution is much different from what was previously seen during training. In order to cope with this problem, it is critical to automatically identify features that are changing over time. With these features detected, data scientists and other practitioners will be able to mitigate the issue (for instance, by applying data transformations), deploying more robust models that retain high performance for longer periods of time. In this paper, we describe which temporal changes a feature should not suffer from, and propose TEDD, a technique to a) identify when a dataset might lead to an unstable Machine Learning model and b) automatically detect which features cause such lack of robustness. In order to achieve it, we leverage a regression model to highlight which features contribute to a good prediction of an instance's timestamp. We compare our approach to other methods in real and synthetic data, testing their detection capability on all simple change patterns. We show that our method: detects all types of basic changes, both for numerical and categorical features; can detect multivariate drifts; returns a comparable value measuring the amount of change of each feature; requires no parameter tuning; and is scalable both on number of features and instances of the dataset.

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13.
arXiv (CS.CL) 2026-06-17

Speaking in Self-Assessing Tongues: On the Verbalized Confidence of LLMs in Machine Translation

作者:
Ali Marashian↗Alexis Palmer↗Katharina von der Wense↗

The rapid rise in popularity of large language models (LLMs) for translation calls for a thorough study of the reliability of their confidence in their own outputs. Unlike many generation tasks, translation errors and confidence levels can be useful at different levels of granularity (tokens, words, or spans). Unsupervised approaches based on internal signals like predicted probabilities can be misleading because they reflect certainty among alternatives rather than correctness. In addition, they require access to such internal signals. Here, we devise five verbalized methods of extracting an LLM's per-token confidence without those shortcomings and compare their reliability with that of the model's internal signals of certainty. We evaluate reliability using two forms of alignment: fine-grained error detection and calibration. For both, internal and verbalized methods perform similarly, although results vary by model. Interestingly, we find little to no correlation between internal and verbalized methods.

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14.
arXiv (CS.CV) 2026-06-17

DriveJudge: Rethinking Autonomous Driving Evaluation with Vision-Language Models

作者:
Xinglong Sun↗Kevin Xie↗Jenny Schmalfuss↗Despoina Paschalidou↗Xiuming Zhang↗Sanja Fidler↗Kashyap Chitta↗Jose M. Alvarez↗

Autonomous driving has shifted towards end-to-end policy learning, where reliable, interpretable policy evaluation is a fundamental challenge as driving quality is highly context-dependent. Commonly used rule-based driving metrics like EPDMS are interpretable but lack context-awareness, while recent VLMbased evaluations are context-aware but limited by ambiguous VLM outputs and weak physical grounding. To evaluate driving in a manner that is both interpretable and context-aware, we introduce DriveJudge. DriveJudge is a driving evaluation agent that combines rule-grounded evaluation with Vision-Language Model (VLM) reasoning and selectively invokes physically-grounded deterministic rule functions after interpreting the environmental context. To train and evaluate DriveJudge, we curate a large-scale dataset of 33,577 challenging driving samples with human annotations on whether the driving behavior is reasonable in the given scenario. With this dataset, we address the underexplored problem of driving metric evaluation, and introduce two human-aligned benchmark tasks: Driving Quality Classification and Trajectory Preference Selection. DriveJudge outperforms EPDMS for driving quality classification by 21.23 AUC, and the recent VLM-based DriveCritic for trajectory preference selection by 6.5%, setting a new standard for interpretable and precise driving evaluation.

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15.
arXiv (CS.AI) 2026-06-19

Secure Coding Drift in LLM-Assisted Post-Quantum Cryptography Development: A Gamified Fix

作者:
R. D. N. Shakya↗C. P. Wijesiriwardana↗S. M. Vidanagamachchi↗Nalin A. G. Arachchilage↗

arXiv:2606.19474v1 Announce Type: cross Abstract: The transition to Post Quantum Cryptography (PQC) introduces considerable implementation complexity, requiring strict adherence to constant-time execution, side channel resistance, and precise parametrisation. Simultaneously, large language models (LLMs) are heavily embedded in software development workflows, including cryptographic engineering. While LLMs improve productivity, evidence shows that they frequently generate insecure or suboptimal code, particularly in security critical domains. This paper introduces Secure Coding Drift in PQC, a novel socio technical vulnerability model capturing the gradual degradation of secure coding practices due to sustained reliance on LLM-generated code. Unlike prior work that focuses on static vulnerabilities, we conceptualise security risk as a longitudinal behavioural phenomenon rising from human AI interaction. To mitigate this, we propose a gamified, LLM augmented secure coding framework that embeds adversarial evaluation, behavioural feedback, and security scoring into development workflows. Our approach reframes LLMs from passive assistants into active security co-pilots, contributing toward safer PQC implementation in AI mediated environments.

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16.
arXiv (quant-ph) 2026-06-17

Asymptotically Optimal Circuit Depth for Diagonal Unitary Synthesis and Compilation on Two-Dimensional Grids

作者:
Chengzhuo Xu↗Xiao Chen↗Zhihao Liu↗Zhigang Li↗

arXiv:2606.17589v1 Announce Type: new Abstract: Diagonal unitaries are a fundamental but resource-intensive class of quantum operations, arising as the phase separators of QAOA and the time-evolution blocks of Hamiltonian simulation. Under all-to-all connectivity their optimal depth is established, but on nearest-neighbor hardware general-purpose compilers fall back on heuristic search, which yields no analyzable cost bound and becomes intractable at the very sizes where depth is the bottleneck. We address synthesis and compilation jointly. On the synthesis side, we develop a Gray-Path Framework (GPF) that realizes any $n$-qubit diagonal unitary in asymptotically optimal $R_z$ and CNOT depth $O(2^n/n)$ without ancillas. Our main result is that compiling GPF onto a two-dimensional nearest-neighbor grid preserves this optimality: routing adds depth $\Theta(2^n/n)$ and gate count $\Theta(2^n)$. Because GPF fixes its entire interaction structure in advance, routing reduces to scheduling a known sequence, with no heuristic search. We give the construction both with and without ancillas: the ancilla-free, cost-optimized layout is a two-row grid, and a $2k$-row layout introduces a space–time tradeoff that cuts depth by $1/k$ while remaining asymptotically optimal for the enlarged register; both are deterministic and analyzed in closed form. The same complexity is also attained on a linear nearest-neighbor chain, so the preservation is topology-independent, holding on any architecture that contains such a chain. All routing bounds are closed-form, giving the concrete resource estimates that heuristic compilers cannot provide at scale.

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17.
arXiv (CS.CV) 2026-06-12

V-JEPA 2.1: Unlocking Dense Features in Video Self-Supervised Learning

作者:
Lorenzo Mur-Labadia↗Matthew Muckley↗Amir Bar↗Mido Assran↗Koustuv Sinha↗Mike Rabbat↗Yann LeCun↗Nicolas Ballas↗Adrien Bardes↗

We present V-JEPA 2.1, a family of self-supervised models that learn dense, high-quality visual representations for both images and videos while retaining strong global scene understanding. The approach combines four key components. First, a dense predictive loss uses a masking-based objective in which both visible and masked tokens contribute to the training signal, encouraging explicit spatial and temporal grounding. Second, deep self-supervision applies the self-supervised objective hierarchically across multiple intermediate encoder layers to improve representation quality. Third, multi-modal tokenizers enable unified training across images and videos. Finally, the model benefits from effective scaling in both model capacity and training data. Together, these design choices produce representations that are spatially structured, semantically coherent, and temporally consistent. Empirically, V-JEPA 2.1 achieves state-of-the-art performance on several challenging benchmarks, including 7.71 mAP on Ego4D for short-term object-interaction anticipation and 40.8 Recall@5 on EPIC-KITCHENS for high-level action anticipation, as well as a 20-point improvement in real-robot grasping success rate over V-JEPA-2 AC. The model also demonstrates strong performance in robotic navigation (5.687 ATE on TartanDrive), depth estimation (0.307 RMSE on NYUv2 with a linear probe), and global recognition (77.7 on Something-Something-V2). These results show that V-JEPA 2.1 significantly advances the state of the art in dense visual understanding and world modeling.

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

Metastability for the Curie-Weiss-Potts model with unbounded random interactions

作者:
Johan L. A. Dubbeldam↗Vicente Lenz Burnier↗Elena Pulvirenti↗Martin Slowik↗

arXiv:2505.11260v2 Announce Type: replace Abstract: We analyse the metastable behaviour of the disordered Curie–Weiss–Potts (DCWP) model subject to a Glauber dynamics. The model is a randomly disordered version of the mean-field $q$-spin Potts model (CWP), where the interaction coefficients between spins are general independent random variables. These random variables are chosen to have fixed mean (for simplicity taken to be $1$) and well defined cumulant generating function, with a fixed distribution not depending on the number of particles. The system evolves as a discrete-time Markov chain with single spin flip Metropolis dynamics at finite inverse temperature $\beta$. We provide a comparison of the metastable behaviour of the CWP and DCWP models, when $N \to \infty$. First, we establish the metastability of the CWP model and, using this result, prove metastability for the DCWP model (with high probability). We then determine the ratio between the metastable transition time for the DCWP model and the corresponding time for the CWP model. Specifically, we derive the asymptotic tail behavior and moments of this ratio. Our proof combines the potential-theoretic approach to metastability with concentration of measure techniques, the latter adapted to our specific context.

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

Multi-Granular Attention-Driven Reinforcement Learning Framework for Web Intelligent Enhancement Systems

作者:
Navin Chhibber↗Deepak Singh↗Anokh Kishore↗Nikita Chawla↗K. Anguraj↗

arXiv:2606.19690v1 Announce Type: new Abstract: From the past few years, web intelligent enhancement systems increasingly rely on heterogeneous and dynamic web data to deliver personalized, context-aware services. However, traditional machine learning, deep learning, and reinforcement learning models often struggle with semantic understanding, adaptability, and scalability in continuously evolving web environments. In this research, a Multi-Granular Attention-based Reinforcement Web Intelligent Enhancement System (MGAR-WIES) is proposed to address the challenges by integrating semantic graph modeling, attention mechanisms, and adaptive reinforcement learning. Initially, heterogeneous web data comprising structured, semi-structured and unstructured sources are collected and preprocessed for generating unified feature representations. These representations are transformed into a dynamic semantic graph, where entities and their relationships are modeled by using graph embeddings enhanced by attention mechanisms for capturing both local relevance and global contextual dependencies. Subsequently, an adaptive multi-agent reinforcement learning strategy leverages the attention-aware semantic states to optimize personalized web actions like content recommendation, navigation optimization, and service adaptation. Finally, the continuous online feedback is further integrated to update graph representations and learning policies in real time by ensuring sustained adaptability and performance. The proposed MGAR-WIES acheived better results in terms of accuracy (80%) when compared with existing approaches.

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20.
arXiv (quant-ph) 2026-06-15

Spin mixing induced dynamics of spinor solitons in $F=1$ Bose Einstein condensates

作者:
T. Panagos↗A. Romero-Ros↗G. C. Katsimiga↗P. Schmelcher↗P. G. Kevrekidis↗

arXiv:2606.14231v1 Announce Type: cross Abstract: We explore soliton interactions in a homogeneous spinor $F=1$ Bose Einstein Condensate (BEC) in the presence of a magnetic field, focusing on dark bright dark and bright dark bright configurations. We investigate how these interactions depend on the phase differences among bright solitons and their influence during the dynamics. Our findings align with prior non spinor results, i.e., repulsion among in phase bright solitons and attraction among out of phase pairs in self repulsive atomic BECs. The potential bright soliton attraction, added to the short range repulsion of dark dark soliton interactions, can lead to bound states. However, we find that these bound states break in the presence of spinor interactions due to the particle exchange dynamics between the hyperfine states of the components. Additonally, we develop an effective classical model to describe the soliton dynamics, using a Lagrangian approach. The accuracy of the model is tested by comparing it against numerical simulations. Our results suggest that the proposed model captures the essential features of soliton behavior in the presence of spin interactions, and provides congruent soliton trajectories and interspecies particle exchange dynamics in most of the cases.

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21.
arXiv (quant-ph) 2026-06-11

Linear Combination of Hamiltonian Simulation with Commutator Scaling

作者:
Junaid Aftab↗Dong An↗Konstantina Trivisa↗

arXiv:2606.11475v1 Announce Type: new Abstract: The Linear Combination of Hamiltonian Simulation (LCHS) framework simulates dissipative linear dynamics by representing time evolution as an integral over unitary operators, which is discretized by quadrature and implemented via Hamiltonian simulation. While existing analyses achieve near-optimal scaling in time and precision using norm-based quantities of the dissipative generator, we show that implementing the Hamiltonian simulation steps with Multi-Product Formulas (MPFs) yields commutator-sensitive error and complexity bounds. We demonstrate that the quadrature rule affects not only discretization error but also commutator structure and query complexity. This dependence is quantified through post-quadrature analysis for abstract MPF error profiles and for general time-independent and local Hamiltonians using known commutator-sensitive MPF error estimates. We compare uniform trapezoidal and free-scale sinh–sinh quadrature, showing improved quadrature-cardinality scaling for the latter, and illustrate the framework with applications to fractional diffusion, advection–diffusion, and open quantum systems.

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22.
arXiv (math.PR) 2026-06-18

Delayed blow-up by transport noise for the 3D Navier-Stokes equation with Navier-slip boundary conditions

作者:
Meng Zhao↗

arXiv:2606.19060v1 Announce Type: cross Abstract: We study the vorticity formulation of the 3D Navier-Stokes equation driven by transport noise in a periodic channel with Navier-slip boundary conditions. We consider both non-degenerate transport noise and degenerate tangential transport noise. For any prescribed $T>0$ and $\epsilon>0$, we prove that, by choosing the noise intensity sufficiently large and concentrating the noise on sufficiently high modes, the solution exists up to $T$ with probability at least $1-\epsilon$. A main contribution of this work is to identify and analyze the interaction between enhanced dissipation induced by transport noise and physical boundary effects. The no-flux condition breaks the isotropy of the noise and changes the scaling limit of the Itô-Stratonovich corrector. In the non-degenerate case, a boundary feedback term appears in the limiting effective operator; in the degenerate case, the limiting operator is a nonlocal anisotropic tangential dissipation. The proof is based on a combination of a boundary correction operator, a Meyers-type estimate, a scaling-limit analysis of the Itô-Stratonovich corrector, and resolvent estimates for the deterministic limiting equations.

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23.
arXiv (CS.CL) 2026-06-17

Do Large Language Models Always Tell The Same Stories?

作者:
Thennal DK↗Hans Ole Hatzel↗

Recent advances in large language models (LLMs) have enabled the generation of high-quality prose, yet the question of whether these models are capable of generating diverse outputs remains contested. In this work, we investigate the diversity of LLM-generated stories through the framework of narrative similarity. Using a contrastive framework and a dataset of human-written stories and prompts from r/WritingPrompts, we collect narrative similarity judgments across 10 representative LLMs, utilizing both human evaluations and three different automatic annotation methods. Our findings reveal a consistent trend: LLM-generated narratives are consistently more similar to each other than human-written stories are. We demonstrate that frontier models in particular converge on a ``mean'' generic narrative that approximates individual human stories but lacks the collective diversity of human authors. Finally, we show that common mitigation strategies, including negative prompting and temperature scaling, fail to meaningfully address this homogeneity.

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24.
arXiv (quant-ph) 2026-06-11

Tight Bounds for Quantum Phase Estimation and Related Problems

作者:
Nikhil S. Mande↗Ronald de Wolf↗

arXiv:2305.04908v3 Announce Type: replace Abstract: Phase estimation, due to Kitaev [arXiv'95], is one of the most fundamental subroutines in quantum computing. In the basic scenario, one is given black-box access to a unitary $U$, and an eigenstate $\lvert \psi \rangle$ of $U$ with unknown eigenvalue $e^{i\theta}$, and the task is to estimate the eigenphase $\theta$ within $\pm\delta$, with high probability. The cost of an algorithm for us is the number of applications of $U$ and $U^{-1}$. We tightly characterize the cost of several variants of phase estimation where we are no longer given an eigenstate, but are required to estimate the maximum eigenphase of $U$, aided by advice in the form of states (or a unitary preparing those states) which are promised to have at least a certain overlap $\gamma$ with the top eigenspace. We give algorithms and nearly matching lower bounds for all ranges of parameters. We show that a small number of copies of the advice state (or of an advice-preparing unitary) are not significantly better than having no advice at all. We also show that having lots of advice (applications of the advice-preparing unitary) does not significantly reduce cost, and neither does knowledge of the eigenbasis of $U$. We immediately obtain a lower bound on the complexity of the Unitary recurrence time problem, resolving an open question of She and Yuen~[ITCS'23]. Lastly, we study how efficiently one can reduce the error probability in the basic phase-estimation scenario. We show that a phase-estimation algorithm with precision $\delta$ and error probability $\epsilon$ has cost $\Omega\left(\frac{1}{\delta}\log\frac{1}{\epsilon}\right)$, matching an easy upper bound. This contrasts with some other scenarios in quantum computing (e.g., search) where error-probability reduction costs only a factor $O(\sqrt{\log(1/\epsilon)})$. Our lower bound uses a variant of the polynomial method with trigonometric polynomials.

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

Transformers Learn the Mestre-Nagao Heuristic

作者:
Pranav Venkata Konda↗

arXiv:2606.15036v1 Announce Type: new Abstract: We train a two-layer transformer encoder to classify rational elliptic curves $E/\mathbb{Q}$ of conductor $\leq 10000$ as either rank 0 or rank 1 from the first 128 normalized Frobenius traces. We achieve >99% accuracy on both classes, and accuracy is essentially unchanged on test curves with no isogeny or quadratic-twist relative in the training set. We then apply techniques from mechanistic interpretability such as attention analysis, linear probing, activation patching, logit attribution, and neuron-level circuit analysis to reverse-engineer the algorithm the (centroid in function space) model learned. We find that a sparse circuit of 20 out of 512 layer-1 MLP neurons is sufficient for rank prediction under a linear probe with an AUROC of 0.992 at plateau, implementing a push-pull detector architecture of rank-0 and rank-1 detectors with a one-sided readout. However, we notice that the model has sub-optimal readout problems indicating a mismatch in rank-order between the readout pathway and the discriminative circuit. Critically, the learned input weights of the top discriminating neuron match the Mestre-Nagao sum heuristic weights $\log(p)/(p\cdot \log{B})$ with a Spearman coefficient $r = 0.997$ and Pearson coefficient $r = 0.952$: the model has learnt a result from analytic number theory from the Frobenius trace data alone. We additionally find that all 50 independently trained models concentrate CLS attention on prime positions at 2-50$\times$ the rate of composite positions. The CLS embedding encodes $\log{L(E,1)}$ with $R^2 = 0.962\pm 0.011$ across the 50 models (after controlling for the conductor). Activation patching analysis reveals that attention weights are dissociated from causal information flow. Additionally, the 50 solutions from training are near-identical in function space (with pairwise agreement $>$98.8%) despite large weight space barriers.

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