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02.
medRxiv (Medicine) 2026-06-15

Routine use of oral iron for people with heart failure and iron deficiency in primary care; retrospective cohort study

Aims: Iron deficiency is common among people with heart failure and associated with morbidity and mortality. While intravenous iron improves clinical outcomes, oral iron continues to be prescribed in routine practice despite limited evidence of benefit. Methods: We completed a retrospective primary care cohort study (2016 to 2021) to investigate the proportion of people with an incident diagnosis of heart failure who had iron deficiency identified (defined as ferritin

03.
medRxiv (Medicine) 2026-06-16

Cardiac positronium lifetime in human PET: a reproducible right-left ventricular contrast that is not explained by blood oxygenation

Background. Ortho-positronium (o-Ps) lifetime, now measurable in vivo on long-axial-field-of-view (LAFOV) PET/CT, has been proposed as a biomarker of tissue oxygenation and hypoxia. Because o-Ps lifetime is dominated by tissue free-volume structure while the oxygen- specific contribution is small, whether an in-vivo lifetime contrast reflects oxygenation rather than anatomy is an open, identifiability-limited question. Aim. To test the oxygenation hypothesis directly using the heart's natural arterial/venous oxygenation contrast, with a built-in anatomical control. Methods. We re-analysed a public [82Rb]Cl human cardiac LAFOV PET/CT dataset (5.30 x 10^8 evaluated three-photon events). Per-compartment o-Ps lifetimes were extracted with a background-plus-two-component exponentially-modified-Gaussian (EMG) model. The list-mode to image mapping and right/left ventricle (RV/LV) identity were established lifetime-free (the mapping reproduces the provider's reconstructed image at block-correlation 0.998 and wins a joint multi-organ alignment panel). We applied a confound battery: registration stress test, blood-core vs wall, lung-air and wall-myocardium partial-volume, tissue density; and a structure/position-matched control (pulmonary artery, deoxygenated, vs aorta, oxygenated). An isotope-matched 82Rb uniform-quartz reference bounded the instrument's positional behaviour. All results were produced by two independent analysis pipelines. Results. RV o-Ps lifetime exceeded LV by delta tau = +0.304 ns (RV 1.700 +/- 0.172, LV 1.396 +/- 0.130 ns; about 1.4 sigma), in the oxygen-expected direction; the contrast was stable across +/-16 mm registration perturbation (sign preserved in 100% of 342 shifts) and resided in the blood core, not the wall. However, the matched-vessel control was null: pulmonary artery minus aorta = -0.011 +/- 0.344 ns. Lung-air and wall-myocardium partial-volume were disfavoured, and the effect fell within the isotope-matched 82Rb instrumental positional envelope (about 0.1-0.35 ns over 40 mm in uniform material). Conclusion. On this single subject, the cardiac o-Ps lifetime contrast does not provide a clean readout of blood oxygenation: an oxygenation effect of the observed (about 0.3 ns) magnitude is ruled out by the matched control, while a small physiological effect cannot be excluded. We provide a reusable confound-control battery for evaluating future in-vivo o-Ps oxygenation claims. Multi-subject replication with anatomy decoupled from oxygenation is required.

05.
arXiv (CS.LG) 2026-06-12

Contrastive Geometric Learning Unlocks Unified Structure- and Ligand-Based Drug Design

arXiv:2601.09693v3 Announce Type: replace Abstract: Structure-based and ligand-based computational drug design have traditionally relied on disjoint data sources and modeling assumptions, limiting their joint use at scale. In this work, we introduce Contrastive Geometric Learning for Unified Computational Drug Design (ConGLUDe), a single contrastive geometric model that unifies structure- and ligand-based training. ConGLUDe couples a geometric protein encoder that produces whole-protein representations and implicit embeddings of predicted binding sites with a fast ligand encoder, removing the need for predefined pockets. By aligning ligands with both global protein representations and multiple candidate binding sites through contrastive learning, ConGLUDe supports ligand-conditioned pocket prediction in addition to virtual screening and target fishing, while being trained jointly on protein-ligand complexes and large-scale bioactivity data. Across diverse benchmarks, ConGLUDe achieves competitive zero-shot virtual screening performance, substantially outperforms existing methods on a challenging target fishing task, and demonstrates state-of-the-art ligand-conditioned pocket selection. These results highlight the advantages of unified structure-ligand training and position ConGLUDe as a step toward general-purpose foundation models for drug discovery.

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

LP-Based Algorithms for Scheduling in a Quantum Switch

作者:

arXiv:2603.27812v2 Announce Type: replace-cross Abstract: We consider scheduling in a quantum switch with stochastic entanglement generation, finite quantum memories, and decoherence. The objective is to design a scheduling algorithm with polynomial-time computational complexity that stabilizes a nontrivial fraction of the capacity region. Scheduling in such a switch corresponds to finding a matching in a graph subject to additional constraints. We propose an LP-based policy, which finds a point in the matching polytope, which is further implemented using a randomized decomposition into matchings. The main challenge is that service over an edge is feasible only when entanglement is simultaneously available at both endpoint memories, so the effective service rates depend on the steady-state availability induced by the scheduling rule. To address this, we introduce a single-node reference Markov chain and derive lower bounds on achievable service rates in terms of the steady-state nonemptiness probabilities. We then use a Lyapunov drift argument to show that, whenever the request arrival rates lie within the resulting throughput region, the proposed algorithm stabilizes the request queues. We further analyze how the achievable throughput depends on entanglement generation rates, decoherence probabilities, and buffer sizes, and show that the throughput lower bound converges exponentially fast to its infinite-buffer limit as the memory size increases. Numerical results illustrate that the guaranteed throughput fraction is substantial for parameter regimes relevant to near-term quantum networking systems.

07.
arXiv (quant-ph) 2026-06-15

Resolving the Edge of a Quantum Pyramid

arXiv:2606.14698v1 Announce Type: new Abstract: Standing on the shoulders of giants, we resolve the quantum pyramids conjecture, confirming the globally information-optimal measurement for an ensemble of equiangular equiprobable pure states, as conjectured by Englert and \v{R}eháček (arXiv:0905.0510). We do so by proving the remaining entropy inequalities of Holevo and Utkin (arXiv:2506.06700), which certify optimality for obtuse and flat pyramids. For obtuse pyramids, our key contribution is a rigorous proof that local minimizers of the corresponding entropy inequality cannot have three distinct coordinate values. We show that eliminating this family can be reduced to a neat algebraic reciprocal inequality relating branches of the Lambert $W$ function, which may be of independent interest. For flat pyramids, we prove a tight $\ell^p$ inequality for zero-sum vectors that was recently conjectured, proved analytically in dimension $d=3$, and computationally verified for $d\leq 200$ by Holevo and Utkin (arXiv:2603.24017). We prove this bound for all $d\geq 2$ via a technique in symmetric inequalities known as the equal variables method.

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

EARS: Explanatory Abstention for Reliable Sub-Agent Modeling in Large-scale Multi-Agent Systems

In large-scale enterprise settings, centralized multi-agent systems (MAS) are increasingly adopted, in which a coordinator delegates user requests to lightweight, domain-specialized sub-agents. While this architecture improves modularity, scalability, and cost efficiency, its reliability depends not only on accurate routing but also on sub-agents' ability to calibrate their responses to capability constraints. In particular, sub-agents built on smaller fine-tuned models often struggle with such calibration, leading them to over-answer ambiguous, underspecified, misrouted, or unsupported requests and produce hallucinated outputs instead of actionable feedback. To address this challenge, we present EARS (Explanatory Abstention for Reliable Sub-Agent Modeling), a production-oriented framework that reframes sub-agent abstention as an inter-agent communication protocol: a sub-agent does not merely abstain, but exposes an actionable failure state to the coordinator. EARS curates human-agent interaction data using an ensemble of calibrated LLM-as-a-Judge models, producing structured abstention labels and rationales under a taxonomy of sub-agent failure modes. These data are used to fine-tune sub-agents to detect failure conditions and return rationales for coordinator-level clarification, rerouting, or fallback. We evaluate EARS in a large-scale production e-commerce assistant supporting enterprise business intelligence workflows. EARS improves the overall response pass rate from 68.5% to 78.9%, demonstrating that sub-agent-side explanatory abstention improves MAS reliability.

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

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

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

10.
arXiv (CS.AI) 2026-06-17

CMIP-Forge: An Agentic System that Retrieves, Computes, and Self-Reviews Climate Science

arXiv:2606.17076v1 Announce Type: cross Abstract: The Coupled Model Intercomparison Project Phase 6 (CMIP6) has generated thousands of peer-reviewed publications documenting model configurations, evaluation procedures, emergent constraints, and projection uncertainties. As the community transitions toward CMIP7, efficiently extracting and operationalizing this unstructured knowledge alongside live data analysis represents a critical bottleneck. Here we present CMIP-Forge, a hybrid retrieval-augmented generation (RAG) and autonomous analysis system that bridges the gap between scientific literature and Earth System Grid Federation (ESGF) data archives. The system pairs a curated corpus of 6,581 CMIP6-related open-access publications (101,828 indexed chunks) with an agentic pipeline in which a tool-augmented worker plans and executes Python workflows over live climate data, while a panel of independent reviewer models audits its methodology end to end. CMIP-Forge introduces a multi-layered Defense-in-Depth architecture that enforces physical and methodological invariants through executable mechanisms: Abstract Syntax Tree (AST) static analysis, audited scientific primitives, and an autonomous adversarial peer-review protocol. We demonstrate the system's capabilities through end-to-end autonomous research pipelines spanning atmospheric teleconnections, ocean dynamics, regional extremes, and global warming projections. An agentic analysis system grounded in peer-reviewed literature, constrained by automated code guardrails, and audited by an independent adversarial review loop can complete complex climate-research workflows autonomously. The same experiments expose concrete failure modes of the review loop (sycophantic regression, REVISE verdicts that are never resolved, and the submission of stub code for review), each diagnosable from the immutable telemetry and provenance record released with the article.

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

Schrödinger's Navigator: Imagining an Ensemble of Futures for Zero-Shot Object Navigation

Zero-shot object navigation (ZSON) requires robots to find target objects in unseen environments without task-specific fine-tuning or pre-built maps, a key capability for general-purpose service robots. Yet methods that perform well in simulation often degrade in cluttered real-world scenes with severe occlusion and latent hazards, where large unseen regions make single-scene inference brittle and unsafe. We propose Schrödinger's Navigator, a belief-aware framework that reasons at inference time over multiple trajectory-conditioned imagined 3D futures. Given candidate paths, a trajectory-conditioned 3D world model predicts hypothetical observations and maintains a superposition of plausible scene realizations rather than committing to one map. An adaptive occluder-aware sampler directs imagination to uncertainty-critical regions, while a Future-Aware Value Map (FAVM) aggregates imagined futures for robust, proactive action selection. Experiments in simulation and on a physical Go2 quadruped show that Schrödinger's Navigator outperforms strong ZSON baselines, improving hidden-target discovery and risk-aware waypoint selection in occlusion-heavy navigation scenarios. These results highlight imagined 3D futures as a scalable and generalizable strategy for zero-shot navigation in uncertain real-world environments.

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

Proper and improper mixed states serve as different prior beliefs for quantum state retrodiction

arXiv:2502.10030v2 Announce Type: replace Abstract: A mixed quantum state can be taken as capturing an unspecified form of ignorance; or as describing the lack of knowledge about the true pure state of the system ("proper mixture"); or as arising from entanglement with another system that has been disregarded ("improper mixture"). These different views yield identical density matrices and therefore identical predictions for future measurements. But when used as prior beliefs for inferring the past state from later observations ("retrodiction"), they lead to different updated beliefs. This is a purely quantum feature of Bayesian agency. Based on this observation, we establish a framework for retrodicting on any quantum belief and we prove a necessary and sufficient condition for the equivalence of beliefs. We also illustrate how these differences have operational consequences in quantum state recovery.

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

A Tutorial on World Models and Physical AI

作者:

arXiv:2606.12783v1 Announce Type: new Abstract: World modeling is emerging as a central principle for building intelligent systems capable of prediction, reasoning, and decision making. A central distinction can be drawn between explicit world models, which learn structured dynamics for rollout-based reasoning and planning, and implicit world models, which encode predictive structure within scalable learned representations. These complementary paradigms provide a foundation for physical AI in domains such as robotics and autonomous driving, enabling intelligence beyond reactive control under real-world constraints. Recent foundation models further suggest a pathway toward unified systems integrating perception, prediction, and action. Despite rapid progress, major challenges remain in hierarchical reasoning, long-horizon planning, and autonomous goal formation, which are critical for advancing toward artificial general intelligence. This tutorial presents a coherent framework in which diverse world modeling approaches are unified through shared predictive structure and differentiated by how such structure is represented and exploited.

14.
medRxiv (Medicine) 2026-06-11

Malaria Risk among Internally Mobile Individuals and Heterogeneous Mobility Patterns in Two Hypoendemic Communities: Implications for Malaria Elimination in the Peruvian Amazon.

Background: Human mobility is increasingly recognized as a key factor influencing malaria transmission dynamics, particularly in low-transmission settings approaching elimination. This study aimed to assess mobility patterns and their association with malaria risk in two hypoendemic communities in the Peruvian Amazon. Method: A longitudinal study was conducted in the communities of Libertad and Urcomirano (Mazan River basin). Monthly population screenings were combined with weekly active and passive case detection. A total of 678 individuals were enrolled. Mobility patterns were assessed through structured questionnaires, and social network analysis was used to characterize travel connections. Log-binomial regression analysis was applied to identify risk factors associated with malaria infection. Result: Internally, mobile individuals in Libertad showed a higher malaria incidence (>32.47 cases per 1,000 person-months) than those in Urcomirano (

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

D2H-AD: A Hybrid Model Utilizing Hyperdimensional Computing for Advanced Anomaly Detection

arXiv:2606.13754v1 Announce Type: new Abstract: Anomaly detection is a fundamental component of intelligent systems with applications in healthcare, cybersecurity, smart grids, and IoT environments. Although conventional machine learning and deep learning methods have demonstrated effectiveness in identifying anomalies, they often rely on large labeled datasets, incur high computational costs, and face scalability challenges in edge and high-dimensional settings. This paper presents D2H-AD, a novel anomaly detection framework based on Hyperdimensional Computing (HDC), a brain-inspired paradigm that represents information using high-dimensional distributed vectors. Unlike existing HDC-based methods, D2H-AD integrates distance-based similarity and density-aware encoding within a unified framework, improving anomaly representation and detection performance. Ablation studies show that hyperdimensional encoding alone yields up to 5.4% higher ROC-AUC than applying the same density-distance scoring directly in the original feature space. Furthermore, D2H-AD consistently outperforms five established baselines, namely HDAD, ODHD, One-Class SVM, Isolation Forest, and Autoencoders, across all evaluated datasets. The framework is lightweight, interpretable, and computationally efficient, making it suitable for resource-constrained and real-time applications. We validate D2H-AD on five benchmark datasets and demonstrate superior F1-score and ROC-AUC performance, together with robustness to class imbalance, noise, and data complexity. In addition to improved accuracy, D2H-AD offers scalability, a small memory footprint, and low-latency operation enabled by binary computations and a compact design. These properties make it particularly attractive for TinyML and edge AI deployments. The proposed framework highlights the potential of HDC for accurate, interpretable, and energy-efficient anomaly detection in dynamic environments.

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

Object Tokens as a Bridge Between Segmentation and Visual Question Answering in Robotic Surgery

Visual Question Answering (VQA) in robotic surgery, referred to as surgical VQA, requires high-level understanding of complex surgical scenes and the integration of visual perception with language reasoning, with the potential to support surgical training and intraoperative decision-making. Recent Vision-Language Models (VLMs) have shown promising performance through parameter-efficient fine-tuning; however, most existing approaches rely on coarse visual grounding, typically limited to bounding boxes, which fails to capture the fine-grained spatial structure of surgical objects. In this work, we propose a unified framework that jointly performs pixel-level segmentation and visual question answering within a single framework. Our approach integrates a VLM with a Segment Anything Model (SAM)-based decoder and represents scene elements as object tokens generated by the VLM. These object tokens guide answer prediction and are further projected to the SAM-based decoder to produce segmentation masks. By optimizing the object token embeddings through both segmentation and question answering objectives, the model learns spatially grounded representations that enhance visual reasoning while providing explicit pixel-level grounding. We evaluate the proposed method on the private RAMIE (Robot-Assisted Minimally Invasive Esophagectomy) dataset and the public EndoVis18 dataset, where it consistently outperforms baseline methods for surgical VQA. These results demonstrate that incorporating context-aware object tokens into vision-language models improves fine-grained surgical scene understanding.

18.
arXiv (CS.AI) 2026-06-12

Boosting Direct Preference Optimization with Penalization

作者:

arXiv:2606.12505v1 Announce Type: cross Abstract: Offline preference optimization has become a practical substitute for reinforcement learning from human feedback, but pairwise objectives such as Direct Preference Optimization (DPO) and its variants use only the chosen and rejected responses stored in a static dataset. This leaves a useful signal unused: the response that the reference model itself would generate for the same prompt. We propose Direct Preference Optimization with Penalization (DPOP), a simple extension of DPO that augments the base preference loss with a gated penalty on reference-greedy responses. DPOP activates this penalty only when the current policy still assigns a lower likelihood to the preferred response than to the rejected response. On AlpacaEval 2.0, DPOP improves length-controlled win rate over DPO, SimPO, and AlphaDPO on both Llama-3-8b-it and Gemma-2-9b-it, achieving relative gains of 5.3\% and 4.4\% over baselines on the two models, respectively. Ablations further show that a SimNPO-style length-normalized penalty is stronger than NPO and token-level unlikelihood in this setting.

19.
arXiv (CS.AI) 2026-06-18

Quality Perceptions and Intended Engagement in Response to AI-Generated and AI-Assisted News

arXiv:2409.03500v4 Announce Type: replace-cross Abstract: The increasing use of artificial intelligence (AI) in news production raises important questions about how audiences perceive and respond to AI-generated journalism. This preregistered survey experiment (N = 599, German-speaking Switzerland) examines (i) perceptions of article quality (measured as credibility, readability, and expertise) across news excerpts that were human-written, AI-assisted, or fully AI-generated, and (ii) self-reported intentions to engage following disclosure of AI involvement. Participants rated two short news excerpts before learning how they had been produced. Articles across all conditions were evaluated similarly in perceived quality. After disclosure, participants in the AI-assisted and AI-generated conditions reported a higher willingness to continue reading their assigned articles compared to the control group, but future willingness to read AI-generated news did not differ across conditions. Overall, the findings suggest that readers assess AI-generated and human-written news comparably in quality, while disclosure of AI use can momentarily increase curiosity or interest without yet changing longer-term reading intentions.

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

Depth-Width tradeoffs in Algorithmic Reasoning of Graph Tasks with Transformers

Transformers have revolutionized the field of machine learning. In particular, they can be used to solve complex algorithmic problems, including graph-based tasks. In such algorithmic tasks a key question is what is the minimal size of a transformer that can implement the task. Recent work has begun to explore this problem for graph-based tasks, showing that for sub-linear embedding dimension (i.e., model width) logarithmic depth suffices. However, an open question, which we address here, is what happens if width is allowed to grow linearly, while depth is kept fixed. Here we analyze this setting, and provide the surprising result that with linear width, constant depth suffices for solving a host of graph-based problems. This suggests that a moderate increase in width can allow much shallower models, which are advantageous in terms of inference and train time. For other problems, we show that quadratic width is required. Our results demonstrate the complex and intriguing landscape of transformer implementations of graph-based algorithms. We empirically investigate these trade-offs between the relative powers of depth and width and find tasks where wider models have the same accuracy as deep models, while having much faster train and inference time due to parallelizable hardware.

21.
Science (Express) 2026-06-02

Another red alert for American science | Science

作者: 未知作者

Although research has bipartisan support in the US Congress, and trust in science is above 75% across the country, the Trump administration seems as determined as ever to mortally wound the nation’s scientific enterprise. After the scientific community persuaded Congress to restore most of the president’s draconian cuts to research funding last year, the White House Office of Management and Budget (OMB), under Russell Vought, has found new ways to circumvent the will of Congress and starve American science. At the beginning of this year, OMB dragged its feet in releasing instructions to federal agencies for how to distribute the funding appropriated by Congress, leading to lags in dispersal. Now, OMB has proposed revising the rules that govern how federal dollars are spent. The changes would inevitably lead to unlegislated reductions in funding and damage US leadership in science, both in academia and industry.

22.
arXiv (CS.CL) 2026-06-16

Do Safety Monitors Stay Reliable After an Update? Benchmarking and Predicting Activation-Monitor Staleness

作者:

Activation monitors-lightweight probes trained on a language model's internal representations-are an increasingly common layer in deployment safety stacks. Deployed models however are rarely static: they are quantized, fine-tuned, adapted with LoRA, or served with merged adapters while the monitor remains frozen. We present the first systematic test of whether this implicit contract holds: whether activation monitors trained on a base model remain reliable after these routine model updates. Across multiple safety-relevant monitors, model depths, update families, and open-weight models, we find a sharp split: quantization-style updates largely preserve frozen probe performance, while fine-tuning-style updates frequently make probes stale. Fragility is highly monitor-dependent, with privacy/PII probes most affected and refusal-compliance probes comparatively stable, showing that retraining a behavior need not stale its corresponding monitor. QLoRA is especially damaging despite NF4 quantization alone being relatively benign, suggesting that quantization becomes riskier when combined with adaptation. We further show that degradation is predictable from pre-deployment features, enabling revalidation budgets to be triaged toward the monitors most likely to fail. These results suggest that fine-tuning should trigger activation-monitor revalidation by default, while prediction can help prioritize which monitors to check first.

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

Combining Retrieval-Augmented Text Generation with LLMs for Reading Content Recommendations

arXiv:2606.14817v1 Announce Type: cross Abstract: This work presents the design, implementation, and evaluation of a system for generating personalized reading content using Large Language Models (LLMs) combined with Retrieval-Augmented Generation (RAG). The proposed architecture consists of four modules: Input, RAG, Generation, and Judging and enables users to specify both a question and a target reading content complexity. RAG is employed to retrieve relevant information from the Internet, enriching and grounding the content produced by three modern LLMs: Meta LLaMA 4 Scout, LLaMA 3.1 8B Instant, and Google Gemma2 9B. Reading materials are generated using three prompting strategies (Chain-of-Thought, zero-shot, and few-shot), and the LLM-as-a-Judge module automatically evaluates answer quality and alignment with the desired readability level. Experimental results show that RAG consistently improves system performance across all models and prompting techniques, increasing relevance and particularly groundedness by up to 26-35 percentage points. Overall, the findings demonstrate that the RAG-augmented architecture effectively produces reading content tailored to user queries and desired textual complexity.

24.
arXiv (CS.LG) 2026-06-17

Edge Flow: A Tractable and Predictive Continuous-Time Model for Gradient Descent at the Edge of Stability

arXiv:2606.18080v1 Announce Type: new Abstract: Gradient descent in deep learning may operate at the edge of stability (EoS), a regime in which the largest eigenvalue of the loss Hessian hovers near the stability threshold $2/\eta$, where $\eta$ is the learning rate. Classical analysis tools such as gradient flow and the descent lemma do not apply here, motivating the search for a continuous-time model valid at EoS. We propose Edge Flow, a system of three coupled ordinary differential equations that provides a tractable, faithful, and predictive model of gradient descent dynamics at EoS. Edge Flow decomposes the dynamics into a center, an oscillation direction, and an oscillation magnitude. The center follows a modified gradient flow on a symmetrized loss; the direction tracks a top eigenvector of the Hessian via Rayleigh quotient dynamics; and the magnitude grows or decays exponentially depending on whether the sharpness exceeds or falls below the threshold $2/\eta$. Crucially, sharpness stabilization emerges from the coupled dynamics via a self-stabilization feedback loop. Discretizing Edge Flow only requires two gradient evaluations and one Hessian–vector product at each iteration. We demonstrate empirically that Edge Flow tracks the dynamics of gradient descent at least as faithfully as previously proposed continuous-time EoS models, while in addition resolving the oscillation of the sharpness at the onset of EoS, and that it provides a principled framework for understanding and mitigating instabilities in this regime.

25.
medRxiv (Medicine) 2026-06-18

Plasma proteomics reveals clinical and mechanistic heterogeneity among individuals who develop coronary artery disease

BACKGROUND: Individuals who develop coronary artery disease (CAD) are clinically and mechanistically heterogeneous, and understanding this variation is crucial for precise risk stratification and tailored interventions. However, the molecular mechanisms that connect these two kinds of heterogeneity remain unclear, limiting progress toward biologically grounded risk stratification and targeted interventions. Here, we investigated the heterogeneity of individuals who develop CAD by leveraging plasma proteomic signatures, placed individuals along continuous metabolic gradients and revealed the molecular programs underlying these patterns, thereby linking mechanistic variation to clinical heterogeneity. METHODS AND RESULTS: From 42,803 UK Biobank participants, including 3,713 individuals who developed CAD within 10 years (incident CAD), we first identified a 320-protein panel from 2,923 baseline proteins that improved prediction of incident CAD beyond clinical risk scores. Using reverse graph embedding, we reduced the proteomic data to two dimensions and mapped each incident case onto the resulting two-dimensional latent proteomic space. These proteomic dimensions show significant associations with cardiometabolic and kidney-related clinical markers. The patterns were replicated in the EPIC-Norfolk study. Phenome-wide Cox regression analyses further linked these proteomic dimensions to 10-year incidence rates for various diseases, including type 2 diabetes, obesity, and chronic kidney disease (CKD). Furthermore, adding the proteomic dimensions to clinical variable-based Cox regression model improved prediction of 10-year incidence of CKD and other diseases, demonstrating the value of proteomic dimensions beyond conventional clinical risk factors. Moreover, individuals with prevalent CAD (diagnosed before proteomic sampling) exhibited high, metabolically adverse dimension values, indicating that these axes capture cumulative metabolic burden. Pathway enrichment analyses implicated altered extracellular matrix organization and immune programs among the proteins contributing to the proteomic dimensions. CONCLUSIONS: Our findings demonstrate that plasma proteomic signatures can dissect the heterogeneity of individuals who develop CAD in continuous phenotypic gradients, improve prediction of CAD and comorbidities, and map underlying biological mechanisms.