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01.
arXiv (CS.AI) 2026-06-16

Beyond Predefined Schemas: TRACE-KG for Context-Enriched Knowledge Graph Generation

arXiv:2604.03496v2 Announce Type: replace Abstract: Knowledge graph generation typically relies either on predefined ontologies or on schema-free extraction. Ontology-driven pipelines enforce consistent typing but require costly schema design and maintenance, whereas schema-free methods often produce fragmented graphs with weak global organization, especially in long technical documents with dense, context-dependent information. We propose TRACE-KG (Text-dRiven schemA for Context-Enriched Knowledge Graphs), a framework that jointly constructs a context-enriched knowledge graph and an induced schema without assuming a predefined ontology. TRACE-KG captures conditional relations through structured qualifiers and organizes entities and relations using a data-driven schema that serves as a reusable semantic scaffold while preserving full traceability to the source evidence. Experiments show that TRACE-KG produces structurally coherent, traceable knowledge graphs and offers a practical alternative to both ontology-driven and schema-free construction pipelines.

03.
Nature Medicine 2026-06-16

<b>Engineered heart muscle passes early clinical milestone</b>

Engineered heart muscle allografts derived from induced pluripotent stem cells show promising early outcomes in patients with treatment-refractory advanced heart failure with reduced left ventricular ejection fraction, in support of further clinical investigation. Engineered heart muscle allografts derived from induced pluripotent stem cells show promising early outcomes in patients with treatment-refractory advanced heart failure with reduced left ventricular ejection fraction, in support of further clinical investigation.

04.
arXiv (CS.CL) 2026-06-11

GraphInfer-Bench: Benchmarking LLM's Inference Capability on Graphs

Graph analysis underlies many applications whose answers cannot be looked up in a single record or retrieved along a path: laundering rings, drug repurposing, user preference, and scientific theme are all inferred from a node together with its neighbourhood. We introduce GraphInfer-Bench, a benchmark for whether LLMs can perform this graph inference: producing an open-ended answer that no single node supports and no path retrieves. Existing graph-QA protocols cannot test this capability: algorithm simulation, node classification, single-node description, KG-QA, and GraphRAG all admit answers retrievable from one node or along a path. GraphInfer-Bench defines five tasks along Description (what a region is) and Comparison (how regions differ), each constructed so the ground truth lives in no single node. The release contains 42,000 samples across six real-world graphs, produced automatically and screened by a four-layer quality-control protocol. We evaluate four method families against the same tasks: graph-token alignment models, zero-shot frontier closed-source LLMs, Graph2Text supervised fine-tuning, and plain GNNs as a structural reference. No method family closes the gap. Graph-token alignment partially handles description tasks (relational, theme) but collapses on comparison tasks. Frontier LLMs lead on outlier detection and community partition among LLM-based methods but lag on masked-node prediction. Graph2Text SFT is the strongest LLM-based method on the description side yet falls behind frontier LLMs on comparison. Across every task, plain GNNs match or beat the strongest LLM-based row, with the largest margin on community detection. GraphInfer-Bench surfaces graph inference as an open capability gap rather than a property of any one architecture.

05.
arXiv (quant-ph) 2026-06-16

Discontinuous strong-to-weak symmetry breaking transition from thermal pure states

arXiv:2606.15062v1 Announce Type: new Abstract: We investigate the nonequilibrium dynamics of strong-to-weak spontaneous symmetry breaking in many-body quantum systems undergoing decoherence from thermal pure states. For generic initial pure states with volume-law entanglement entropy, we show that the system undergoes a discontinuous dynamical phase transition at a critical time. This transition is accompanied by a singularity in the entropy of the system, which saturates to its maximum value at the same critical time. Through numerical simulations of the dephasing Ising and hard-core boson models, we establish the universality of this transition across different symmetries. Our results reveal that the dynamical emergence of a decohered mixed state from a highly entangled state is not a gradual asymptotic relaxation, but rather a sharp phase transition driven by a sudden collapse of global coherence.

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

Planning with the Views via Scene Self-Exploration

Can VLMs predict how each camera move changes the view, and plan many such moves ahead? We call this capability view planning, requiring (1)understanding how a single action transforms the view, and (2)composing many such transformations across multi-turn plans to identify a target view. We probe both abilities in our proposed ViewSuite, a 3D point-cloud environment on real ScanNet scenes. Across 13 frontier VLMs, a critical planning gap emerges: they possess basic view-action knowledge but fail to compose it across multi-turn plans, with the gap widening as viewpoint distance grows. To close this gap, we propose an iterative framework that alternates self-exploration with view graph distillation. The key insight is that all exploration trajectories, regardless of their outcome, collectively form a view graph that compactly captures how viewpoints connect across a scene. Distilling this graph into diverse supervised tasks reshapes the policy distribution and overcomes the sparse rewards that stall pure RL. This improves Qwen2.5-VL-7B from 2.5% to 47.8% on interactive view planning, surpassing GPT-5.4 Pro (18.5%) and Gemini 3.1 Pro (21.4%). Self-exploration emerges as a promising path toward VLMs that can actively reason and plan in 3D space. Code and Data are at https://viewsuite.github.io.

07.
arXiv (CS.AI) 2026-06-15

The Shrinking Lifespan of LLMs in Science

arXiv:2604.07530v2 Announce Type: replace-cross Abstract: Scaling laws describe how language model capabilities grow with compute and data, but say nothing about how long a model matters once released. We introduce time-to-peak and lifespan as measures of model obsolescence and use them to characterize the scientific adoption trajectories of 62 LLMs across more than 108k citing papers (2019-2025), separating active adoption from background citation to recover per-model trajectories that citation counts cannot resolve. We find that a model's longevity is shaped more by when it was released than by its characteristics: release year predicts time-to-peak and lifespan more strongly than architecture, openness, or scale. LLM adoption follows an inverted-U curve (rising after release, peaking, and then declining), but this pattern is rapidly compressing. Each successive release year is associated with a 27% shorter time-to-peak and a 23% shorter lifespan ($p < 0.001$), robust to minimum-age thresholds and controls for model size. These adoption-side dynamics are invisible to scaling laws and suggest that specialization on any single model may be a depreciating investment, with costs falling on reproducibility and migration.

08.
medRxiv (Medicine) 2026-06-12

Association of circulating endothelial progenitor cell count and functional outcome in patients with acute ischemic stroke due to intracranial large vessel occlusion

Background: Circulating endothelial progenitor cells (cEPCs) contribute to vascular repair following an ischemic stroke. The aim of the study was to evaluate the association between cEPCs and functional outcomes in patients with acute ischemic stroke (AIS) due to large vessel occlusion (LVO) who received endovascular therapy (EVT). Methods: Prospective study of patients with LVO-AIS who received EVT. Blood samples were obtained within 24 +- 12 hours and on day 7+-1 from stroke onset. cEPCs were detected using flow cytometry (CD34+/VEGFR2+/CD133+). The primary endpoint was a favourable functional outcome (modified Rankin Scale 0-2) at three months of follow-up. Secondary endpoints include baseline to 24 hours/day 7 changes in the National Institutes of Health Stroke Scale (NIHSS) score and collateral circulation (CC) status. Bivariate and multivariable logistic regression analyses were performed. Results: Included were 90 patients (73.2+-12.7 years, 41.1% women) in 42 of whom (46.7%) cEPCs were detected at 24 hours. On day 7, cEPCs were detected in 27 (43.6%) of 62 patients for which this information was available. Atrial fibrillation, prior anticoagulant treatment and stroke onset-to-door time

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

DIRECT: When and Where Should You Allocate Test-Time Compute in Embodied Planners?

Vision-Language Models (VLMs) are increasingly deployed as high-level planners for embodied agents, with an emerging strategy of scaling test-time compute to improve capability. However, we observe that doing so increases latency, token usage, and FLOPs while yielding uneven, often diminishing gains in downstream success, limiting where embodied agents can be deployed. We argue that choosing when and where to spend test-time compute is central to bringing frontier performance to the real world. We introduce DIRECT, a routing framework that uses multimodal scene context to allocate compute per prompt, improving the success–cost Pareto frontier over fixed model selection. Across three dominant scaling axes, namely chain-of-thought depth, model size, and memory history, our experiments on VLABench and RoboMME show that test-time compute is not a uniform lever: different axes yield qualitatively distinct capability gains. We validate these insights on a physical Franka arm in a DROID setup spanning zero-shot manipulation and long-horizon chaining, where our router matches or exceeds a stronger model's success rate at up to 65% lower average latency. Ultimately, our results show that naively scaling test-time compute is wasteful, and that DIRECT can provide frontier-level embodied planning in robotic systems at a fraction of the cost. Project page can be found at jadee-dao.github.io/direct/.

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

A Comparative Study of Deep Learning Architectures for Multi-Horizon Behavioural Forecasting for Mobile Health

arXiv:2606.14604v1 Announce Type: cross Abstract: Wearable devices and smartphones generate rich behavioural time series that can support proactive health interventions, yet systematic comparisons of modern forecasting architectures for these data are lacking. In particular, it remains unclear how models generalise across populations, how different architectures respond to participant-level fine-tuning and how forecasting accuracy degrades across multi-day horizons. We benchmark six deep learning architectures, two zero-shot Foundation Models (FM) and statistical baselines on three public datasets encompassing over 800 participants, reporting per-feature metrics for step counts, screen time and sleep duration across 1-8 day horizons. We further conduct a per-feature personalisation study across all six architectures and assess FM transferability across dataset sizes and temporal granularities. Our key findings are: (i) no single architecture dominates, PatchTST leads among trained models while the three runners-up (TCN, MLP, Transformer) show no meaningful performance difference; (ii) the FM TimesFM matches or exceeds trained models zero-shot, especially in low-data regimes and (iii) participant-level fine-tuning reduces per-feature RMSE by 16-60\%, with sleep benefiting most and step counts least. These results provide practical guidance on architecture selection, FM applicability and personalisation strategies for mobile health forecasting. To the best of our knowledge, this is the first study to jointly evaluate modern deep learning, FMs and personalisation for multi-horizon behavioural forecasting from wearables.

11.
arXiv (quant-ph) 2026-06-12

The Pound-Drever-Hall Method for Superconducting-Qubit Readout

arXiv:2512.03138v3 Announce Type: replace Abstract: Scaling quantum computers to large sizes requires the implementation of many parallel qubit readouts. Here we present an ultrastable superconducting-qubit readout method using the multi-tone self-phase-referenced Pound-Drever-Hall (PDH) technique, originally developed for use with optical cavities. In this work, we benchmark PDH readout of a single transmon qubit, using room-temperature heterodyne detection of all tones to reconstruct the PDH signal. We demonstrate that PDH qubit readout is insensitive to microwave phase drift, displaying $0.73^\circ$ phase stability over 2 hours, and capable of single-shot readout in the presence of phase errors exceeding the phase shift induced by the qubit state. We show that the PDH sideband tones do not cause unwanted measurement-induced state transitions for a transmon qubit, leading to a potential signal enhancement of at least $14$~dB.

12.
arXiv (quant-ph) 2026-06-17

Full-state information-disturbance tradeoff for direction estimation with antiparallel spin-coherent pairs

arXiv:2606.18040v1 Announce Type: new Abstract: We determine the optimal information–disturbance tradeoff for estimating an unknown spatial direction encoded in two antiparallel spins. Rotational covariance reduces the optimization over all instruments to a finite-dimensional Choi problem: a positive seed operator obeys one trace constraint for each irreducible sector of the input representation, while both the directional score and the operation fidelity are linear functionals of this seed. For two antiparallel spin-$1/2$ particles, whose physical representation decomposes as $0\oplus1$, we derive the two-multiplier dual problem and characterize the optimal instrument from the kernel vectors of the dual slack operator. The optimal operation is a covariant filter with scalar–vector coherence and is generally not a convex interpolation between the identity channel and a measure-and-reprepare strategy. At maximum information we recover the Gisin–Popescu score, but the least disturbing output state is optimized independently, giving a smaller disturbance than both the parallel-spin benchmark and antiparallel measure-and-reprepare. We also formulate the parallel benchmark and, as a central extension of the method, treat antiparallel spin-coherent states of arbitrary spin $j$. In this case the signal coherently occupies all sectors $\ell=0,\ldots,2j$ of $j\otimes j$, the endpoint information is governed by nearest-neighbor sector coherences, and the endpoint disturbance is obtained from an explicit finite block-diagonal eigenvalue problem.

13.
arXiv (CS.AI) 2026-06-18

QSignAI: Quantum-Randomness-Seeded Identity Signatures at the Intersection of AI for Science and Science for AI

arXiv:2605.27729v2 Announce Type: cross Abstract: The 2024-2025 Nobel and Turing awards recognised AI and quantum science simultaneously. Yet no deployed system has brought these streams together for the public. This paper presents QSignAI, a production-deployed platform demonstrating a bidirectional AI-quantum relationship in a real-time event participation system. We address three questions: can quantum-randomness generation via a two-source extractor be embedded in an AI-driven social platform with acceptable latency; can an AI bot make quantum phenomena perceptually legible to general audiences; and does the combined system work in practice? A conversational bot routes each participant's first message through a quantum pipeline comprising a Toeplitz two-source extractor over independent single-qubit Hadamard measurements on SV1 and DM1 simulators, plus a 2-qubit Bell state, producing a unique quantum-randomness-seeded identity signature per participant. The first two questions are answered through system architecture and qualitative deployment evidence from live events; the third through successful production deployment. The current deployment uses cloud quantum simulators; physical QPU randomness is the near-term extension. Measurable benchmarks are identified as priority future work.

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

From Values to Tokens: An LLM-Driven Framework for Context-aware Time Series Forecasting via Symbolic Discretization

arXiv:2508.09191v2 Announce Type: replace-cross Abstract: Time series forecasting plays a vital role in supporting decision-making across a wide range of critical applications, including energy, healthcare, and finance. Despite recent advances, forecasting accuracy remains limited due to the challenge of integrating historical numerical sequences with contextual features, which often comprise unstructured textual data. To address this challenge, we propose TokenCast, a large language model (LLM) driven framework that leverages language-based symbolic representations as a unified intermediary for context-aware time series forecasting. Specifically, TokenCast employs a discrete tokenizer to transform continuous numerical sequences into temporal tokens, enabling structural alignment with language-based inputs. To effectively bridge the semantic gap between modalities, both temporal and contextual tokens are embedded into a shared representation space via a pre-trained LLM, further optimized with generative objectives. Building upon this unified semantic space, the aligned LLM is subsequently fine-tuned in a supervised manner to predict future temporal tokens, which are then decoded back into the original numerical space. Extensive experiments on real-world datasets demonstrate the effectiveness of our framework and highlight its potential as a generative framework for context-aware time series forecasting. The code is available at https://github.com/Xiaoyu-Tao/TokenCast.

15.
arXiv (CS.CL) 2026-06-12

PolyAlign: Conditional Human-Distribution Alignment

Post-training methods such as supervised fine-tuning (SFT) and preference optimization typically align language models toward a single global assistant behavior. While effective for improving average helpfulness, this can suppress the natural variation of human responses across languages, tasks, and dialogue settings. We study this problem as conditional human-distribution alignment: models should match the human response distribution appropriate to the current interaction context, rather than a universal response style. We introduce PolyAlign, a distribution-aware alignment framework that organizes bilingual interaction data into bucket-specific human reference distributions defined by language, interaction track, response family, and length. PolyAlign combines Bucket-Aware SFT, which balances optimization across heterogeneous buckets, with Human-Distribution Preference Optimization (HDPO), which regularizes preference learning using critic-estimated distance to bucket-specific human support. Across a bilingual evaluation suite covering English and Chinese single- and multi-turn settings, PolyAlign improves conditional naturalness and distributional faithfulness while preserving competitive task utility. The results suggest that post-training should move beyond global alignment objectives toward interaction-aware alignment with human response distributions.

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

Securing Multi-Agent GIS Systems: Risk Evaluation and Prompt Hardening Optimization

Agentic systems are increasingly integrated with geographic information systems (GIS), where multi-agent coordination enables complex conversational and spatial analysis but introduces security risks. This work presents a security-oriented framework for risk identification, evaluation, and mitigation in a multi-agent GIS system while maintaining adaptability to broader agentic architectures. We test the agentic system of a commercial geospatial partner while developing a modular state-machine-based orchestration framework that abstracts agent behavior into reusable components. We evaluate robustness using a red-teaming framework with an adaptive attacker LLM and a deterministic judge that produces binary outcomes with supporting rationales across multi-turn attacks. We further improve resilience with a prompt optimization framework that treats prompts as structured signatures and injects adversarial demonstrations, enabling systematic security improvements without degrading task performance.

17.
arXiv (CS.LG) 2026-06-18

A Guide to Estimating Conditional Average Treatment Effects in Competing Risks Settings

arXiv:2606.18281v1 Announce Type: cross Abstract: Conditional average treatment effects (CATEs) are central to treatment decision-making in personalized medicine. In competing risks settings, estimating CATEs from survival data allows for patient-specific assessments of treatment effectiveness for a specific event of interest while properly accounting for alternative event types. This distinction is essential in the presence of comorbidities, where competing causes of death may otherwise confound the therapeutic benefit. Focusing on right-censored survival times with binary treatment, we examine CATEs defined as covariate-conditional differences in the absolute risk for the event of interest at a fixed time. To this end, we study meta-learners which adapt machine learning algorithms for CATE estimation in competing risks scenarios. We systematically compare six meta-learners, combining Cox regression or random survival forests for risk modeling with elastic net regression or random forests for direct CATE modeling. To provide practical guidance on model selection, we evaluate their performance in multiple simulation settings, that differ in hazard complexity, treatment heterogeneity, treatment assignment, event type distribution and censoring. To facilitate applied use, we provide the R package, crsurvlearners, which implements all considered approaches.

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

Inference-Time Decision Calibration for Temporal Classification

arXiv:2606.16034v1 Announce Type: new Abstract: Temporal classification errors are often treated as representation failures, but they can also arise from how available evidence is converted into decisions. This paper proposes a representation–calibration decomposition for temporal classification. We keep a trained native classifier frozen and separate two inference-time interventions: a conservative residual multi-scale branch that adds auxiliary logits to the native prediction, and a post-hoc branch-aware calibrator that recombines native and residual evidence at decision time. This design distinguishes missing temporal evidence from underused decision-level evidence without retraining the backbone. Across FI-2010, PTB-XL, UCI-HAR, MHEALTH, and HARTH, we find that gains are strongly regime-dependent. Residual multi-scale evidence is most useful in noisy or representation-limited settings, especially short-horizon FI-2010 and weaker recurrent backbones, while branch-aware calibration helps when native and auxiliary logits contain complementary evidence not fully exploited by the raw decision rule. Near-saturated settings show limited gains from either intervention. These results suggest that temporal classification should be understood not only as representation learning, but also as the problem of trusting, combining, and calibrating evidence from multiple views.

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

A Multi-Agent AI System for Automated High School Transcript Processing: Collaborative Document Analysis at Scale

arXiv:2606.13916v1 Announce Type: new Abstract: Each year, college admissions offices face an overwhelming challenge: processing millions of high school transcripts, each with unique formats, grading systems, and layouts. This manual process creates operational bottlenecks that delay admissions decisions and consume valuable resources. We present a transformative solution through a multi-agent AI system where specialized agents collaborate to automatically process diverse transcript formats through intelligent coordination and communication. Our multi-agent architecture consists of three specialized agents-a Pattern Recognition Agent for format-specific parsing, a Semantic Analysis Agent for natural language understanding, and a Vision Intelligence Agent for multimodal document analysis-coordinated by an Orchestration Agent that manages agent communication and result reconciliation. Our key innovation lies in agent-based quality control using GPA extraction as a coordination signal, ensuring reliable agent collaboration and preventing critical information loss. When evaluated on 40 real world transcripts from high schools across 13 U.S. states, our agent system successfully processed every document, achieving 96.7% accuracy compared to expert manual review while maintaining practical processing speeds of 45 seconds per transcript. This work demonstrates how multi-agent coordination can solve complex document processing challenges, offering institutions a scalable, collaborative AI solution that preserves accuracy while dramatically reducing processing time.

20.
arXiv (CS.CV) 2026-06-18

Learned Radius Estimation for UDF-Based Point Cloud Reconstruction

Surface reconstruction from point clouds is important for consumer-grade 3D capture, including AR/VR and indoor scanning. Local-patch Unsigned Distance Field (UDF) methods are lightweight and generalizable, but their accuracy depends on the support radius, traditionally fixed or selected by a one-dimensional curvature heuristic that cannot capture heterogeneous local geometry. We propose a learned per-query radius selector that predicts a continuous support radius and plugs into a frozen LoSF-UDF backbone. The selector is trained using off-grid target radii obtained by parabolic interpolation of cached UDF error curves. Experiments show improved fine-scale reconstruction accuracy.

21.
arXiv (quant-ph) 2026-06-15

Efficient Simulation of Szegedy Quantum Walk Formulations and Algorithms

arXiv:2606.14226v1 Announce Type: new Abstract: Quantum walks provide a versatile framework for quantum algorithms across a wide range of applications. We develop efficient classical simulation methods for Szegedy quantum walks that avoid explicit construction of the full unitary evolution operator. Unlike previous approaches restricted to a particular walk formulation, our framework is built from fundamental update and reflection operators, enabling the simulation of a broader class of Szegedy walk formulations. We further extend these methods to phase-estimation-based algorithms coupled to the walk, including implementations suitable for large sparse graphs. The resulting methods achieve optimal $O(N^2)$ complexity for dense graphs with $N$ nodes. For sparse graphs, the computational cost scales linearly with the number of edges, which is $O(N)$ in many cases. We implement the framework in the Python package SQWLib and illustrate its capabilities through simulations of representative algorithms, including quantum simulated annealing and quantum search on graphs. These results provide a practical tool for studying Szegedy-walk-based algorithms numerically beyond purely analytical treatments.

22.
arXiv (math.PR) 2026-06-17

The Loss of Tension in an Infinite Membrane with Holes of Decaying Spatial Density

arXiv:2606.17792v1 Announce Type: new Abstract: What is the effect of randomly removing material from an infinite stretched membrane? Under what conditions can the membrane still sustain tension? This problem was introduced by Robert Connelly in connection with applications of rigidity theory in the natural sciences, and was later studied in M. V. Menshikov, K. A. Rybnikov, and S. E. Volkov, "The loss of tension in an infinite membrane with holes distributed according to a Poisson law" (2002); a discrete version was also considered in Robert Connelly, Konstantin Rybnikov, and Stanislav Volkov, "Percolation and the Loss of Tension in an Infinite Triangular Lattice" (2001). We study a mathematical framework based on a non-homogeneous Poisson point process whose intensity $\lambda$ tends to zero at infinity. The hole shapes are i.i.d.\ and independent of their locations. We show that if the intensity does not decay too quickly, then tension is still lost throughout the whole plane, as in the homogeneous model studied in 2002. Conversely, we give sufficient conditions under which complete loss of tension does not occur. Thus, both destruction and non-destruction regimes are possible even when the intensity tends to zero, indicating a phase transition in the model. The processes studied here are closely related to bootstrap percolation.

23.
arXiv (CS.CL) 2026-06-12

G-Long: Graph-Enhanced Memory Management for Efficient Long-Term Dialogue Agents

While Large Language Models (LLMs) have advanced open-domain dialogue systems, maintaining long-term consistency remains a challenge due to inherent limitations in long-context reasoning and the inefficiency of processing extensive raw text. Existing approaches typically rely on either unstructured memory storage, which is prone to information loss, or computationally expensive LLMs that incur high latency. To address these limitations, we propose G-Long, a graph-enhanced framework that utilizes a fine-tuned small Language Model (sLM) for structured triplet extraction and associative retrieval, significantly reducing operational costs. Furthermore, we introduce the novel attention-aware importance scoring mechanism that leverages the intrinsic cross-attention signals of a T5 summarizer to identify salient memories. Extensive experiments across diverse benchmarks demonstrate that G-Long achieves state-of-the-art performance in both response generation and memory retrieval, yielding performance gains of up to 9.8% in response quality on MSC and 40.8% in retrieval recall on LME, while significantly minimizing computational overhead.

24.
arXiv (math.PR) 2026-06-12

Averaging principles for nonautonomous multiscale McKean-Vlasov stochastic systems

arXiv:2606.12820v1 Announce Type: new Abstract: This paper investigates a class of nonautonomous multiscale McKean-Vlasov stochastic systems. By leveraging the nonautonomous Poisson equation, we rigorously establish both strong and weak averaging principles, accompanied by explicit convergence rates. Notably, the coefficients of the averaging equations derived in the general case retain dependence on the scaling parameter $\varepsilon$. However, under the additional assumptions that the fast-scale coefficients are either asymptotically convergent or time-periodic, we demonstrate that the slow component converges, in the strong or weak sense, to averaging equations with coefficients independent of $\varepsilon$.

25.
arXiv (CS.LG) 2026-06-11

Minimal surfaces, Knots, and Neural Networks

arXiv:2605.26234v2 Announce Type: replace-cross Abstract: A recent conjecture by Joel Fine posits a relationship between the coefficients of the HOMFLY polynomial of a knot $K$ in the 3-sphere $S^3$, and the signed count of minimal surfaces in hyperbolic 4-space $\mathrm{H}^4$ meeting the sphere at infinity at $K$, with prescribed genus and self-intersection number. In this paper, we develop a novel machine learning framework based on Physics-Informed Neural Networks (PINNs) to solve the minimal surface equation in hyperbolic space. We utilise this framework to test Fine's Conjecture by constructing near-minimal surfaces bounding various families of knots in $S^3$. Furthermore, we develop an algorithmic method to find self-intersections and compute their sign. For every knot analysed, the computationally discovered minimal surfaces and their self-intersection numbers perfectly align with the predictions of Fine's Conjecture, providing empirical evidence for it.