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01.
arXiv (math.PR) 2026-06-16

Geometry of critical discrete structures: long-range percolation on the hierarchical lattice and the discrete torus

arXiv:2509.09589v2 Announce Type: replace Abstract: Consider (a) balls $\Lambda_n$ of growing volumes in the $d$-dimensional hierarchical lattice, and (b) the $d$-dimensional discrete torus $\mathbb{T}_n^d$ on $n^d$ vertices. Place edges independently between each pair of vertices $x\neq y\in\Lambda_n$ or $\mathbb{T}_n^d$ with probability $1-\exp(-\beta J(x, y) )$ where $J(x, y) \asymp \| x-y \|^{-\alpha}$ for some $0

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

Steady-Forcing: Balancing Spatial Persistence and Motion Continuity in Long-Horizon Nature Video Diffusion

Autoregressive video diffusion models enable streaming generation but often degrade over long rollouts: static scene layouts drift, while mechanisms that improve spatial stability tend to suppress motion, causing natural flows such as water, fire, or smoke to stagnate. We study this stability-motion trade-off in fixed-camera long-horizon nature video generation, where the two failure modes can be more clearly separated than in moving-camera settings. We propose Steady-Forcing, a memory and training framework combining a persistent visual anchor (V-Sink), an exponential moving-average motion memory (EMA-Sink), block-relative temporal encoding, periodic cache purification, and distillation from a Wan2.1-14B teacher with motion-rewarded priors under task-focused configurations. Together, these components are designed to preserve background identity while sustaining visually plausible fluid dynamics over multi-minute autoregressive rollouts. Evaluations across seven baselines show that Steady-Forcing improves long horizon background consistency and imaging quality, while a blind user study indicates stronger perceived stability and motion continuity. The benchmark evaluation further suggest that generic VBench aggregate scores under-penalize fixed-camera artifacts as well as rewarding drift-induced optical flow as Dynamic Degree while not directly penalizing texture hardening or flow stagnation - motivating future task-specific benchmarks for static-camera nature-flow evaluation. Project page: https://minar09.github.io/steadyforcing/

04.
Nature Medicine 2026-06-11

Microglia at a key inflection point in Alzheimer’s disease

Authors: Unknown Author

We analyzed brains from octogenarians and cognitively resilient centenarians to understand why some individuals with substantial Alzheimer’s disease pathology develop dementia whereas others remain cognitively intact. Spatial transcriptomics revealed gene expression changes in discrete tissue domains surrounding amyloid plaques and tau pathology that distinguish early, clinically silent, disease from later stages associated with cognitive decline.

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

Hybrid NARX-LLM for Greenland Iceberg Discharge: Prompt-Driven Residual Correction

arXiv:2606.15288v1 Announce Type: cross Abstract: Greenland iceberg discharge exhibits complex nonlinear dynamics with limited observability, challenging traditional predictive models. We present a Hybrid NARX-LLM framework that combines a nonlinear autoregressive model with exogenous inputs (NARX) and a large language model (LLM) for residual correction. We further propose a Physics-Informed Prompt (PIP) method that transforms unstructured physical knowledge into structured prompts for zero-shot in-context reasoning. The primary objective is to explore the corrective potential of this framework for modeling Greenland iceberg discharge, rather than merely optimizing predictive accuracy. The NARX component captures intrinsic temporal dependencies, while the LLM, guided by PIP, encodes glacier dynamics and environmental drivers and perceives key trend patterns to correct systematic prediction errors. This integration allows the model to reason about unmodeled factors and produce interpretable residuals, enhancing overall predictive accuracy. Applied to Greenland iceberg discharge time series, our approach addresses extreme events that are difficult to predict due to rare variations and nonstationary trends, a limitation often overlooked by traditional methods. By fusing structured time-series modeling with knowledge-driven foundation AI, the framework offers a scalable and interpretable pathway to bridge data-limited climate forecasting with physics-informed LLM reasoning. The code is available.

06.
medRxiv (Medicine) 2026-06-23

Novel loci and multi-omics risk models for rheumatoid arthritis through a million-participant genome-wide association meta-analysis

Rheumatoid arthritis (RA) remains incompletely understood, limiting targeted prevention. In this work, genome-wide association study meta-analyses were performed for RA and seropositive RA, comprising approximately one million participants of European ancestry. Eight and six novel genomic risk loci were defined for RA and seropositive RA, and candidate causal genes were identified, highlighting relevant biological pathways, including established immune pathways and estrogen metabolism. Novel disease-specific polygenic risk scores (PRSs) were constructed, enhancing predictive performance over clinical risk factors (incremental C-statistics of 2.7 and 5.1 for RA and seropositive RA, respectively). In parallel, integrating metabolomic data into high-dimensional models enhanced risk stratification over models based on clinical risk factors and genomics, particularly for seropositive RA, where the hazard ratio of the highest decile increased from 4.869 to 5.697. These findings expand the understanding of genetic factors underlying RA and support the value of including PRSs in risk assessment, while suggesting metabolomic integration may further enhance risk stratification, particularly for seropositive RA.

07.
arXiv (quant-ph) 2026-06-24

Phase-space microscopes for quantum gases: Imaging conjugate variables and momentum-weighted densities

arXiv:2603.29568v2 Announce Type: replace-cross Abstract: Quantum gas microscopes offer unprecedented insights into quantum many-body states of cold atomic gases. Here we introduce concrete protocols for extending quantum gas microscopes to measure in phase space, by mapping momentum onto auxiliary degrees of freedom and using positive operator-valued measures. We distinguish between two distinct operational modes. In the Husimi-Q phase space microscope, position and momentum are jointly measured; in this mode the fundamental quantum noise is distributed between position and momentum. Conversely, the averaged-mode phase space microscope extracts the spatial dependence of averages of the momentum density (and its moments); these averages can be retrieved with arbitrary spatial resolution. We illustrate the utility of these techniques in diverse physical settings.

08.
arXiv (CS.LG) 2026-06-15

High-Frequency Pricing at Scale for E-Commerce

arXiv:2606.13741v1 Announce Type: new Abstract: This paper presents the design, development, and implementation of a specialized forecast-then-optimize algorithmic pricing tool for sales campaigns in fashion e-commerce. Sales events present unique challenges for pricing including volatile demand patterns, rapid pricing decisions, and the need to balance short-term revenue with long-term profitability. We describe our approach combining daily-resolution demand forecasting using gradient-boosted trees with a multi-objective optimization framework that maximizes both long-term profit and net merchandise value for more than 5 million articles. Our solution addresses key limitations of existing weekly-granularity systems by implementing a forecast-then-optimize architecture that reduces pricing decision time from hours to minutes. We validate our approach through 23 A/B tests across 12 markets during 2023-2024 sales campaigns at Zalando, one of Europe's leading online fashion retailers. Experimental results demonstrate that the new pricing system achieves approximately 6% higher profit while maintaining equivalent performance on sales and revenue compared to the previous manual-algorithmic hybrid approach. Based on these results, the algorithm was successfully deployed to production and now handles the majority of algorithmic pricing decisions for sales campaigns at the company.

09.
arXiv (CS.AI) 2026-06-16

AgenticRec: A Recommendation-Oriented Agentic Framework with Progressive Tool-Integrated Reasoning Optimization

arXiv:2603.21613v2 Announce Type: replace-cross Abstract: Recommender agents built on Large Language Models offer a promising paradigm for personalized recommendation. However, existing agents typically suffer from a misalignment between their tool-integrated reasoning trajectories and recommendation feedback, limiting their ability to distinguish fine-grained user preferences. To address these challenges, we propose AgenticRec, an agentic recommendation framework that formulates recommendation as a tool-integrated reasoning process over a recommendation-oriented tool suite. Built upon this framework, we further develop a dedicated two-stage training paradigm tailored for recommender agents. In the first stage, we introduce Recommendation-Oriented Trajectory Activation, optimize the agentic recommendation ability under implicit feedback. In the second stage, Progressive Preference Refinement further refines the agent through bidirectional preference reasoning over self-bootstrapped hard pairs, progressively sharpening preference boundaries. Theoretical analysis and extensive experiments demonstrate the effectiveness of AgenticRec. Our code is available at https://anonymous.4open.science/r/AgenticRec-FB16.

10.
bioRxiv (Bioinfo) 2026-06-15

SMLMFlow: Improving Structural Resolution in Single Molecule Localization Microscopy with Flow Matching

While Single Molecule Localization Microscopy (SMLM) aims to generate precise coordinates of molecular targets in cells, the resulting point clouds are inherently blurred by additive noise sources across the experimental, imaging, and processing workflow. This blurring often limits SMLM's ability to accurately quantify complex assembled structures required to address biological issues, despite reported localization precision down to a couple of nanometers. Here, we present SMLMFlow, a machine learning framework for improving structural resolution in SMLM datasets that combines a graph neural network and a hierarchical transformer with flow matching. We show that SMLMFlow improves structural resolution and downstream quantification across different structures, including filaments and protein nano-clusters, and generalizes to new unseen photophysics models.

12.
arXiv (CS.AI) 2026-06-24

Maestro Order: A Model-Agnostic Orchestration Harness

Authors:

arXiv:2606.23983v1 Announce Type: cross Abstract: A single forward pass of a capable model is a fast, fluent, and unreliable problem-solver: it is right often enough to be useful and wrong often enough to be dangerous; in language models, such confident errors are known as hallucinations. We present Maestro Order, a model-agnostic orchestration harness that turns unreliable solvers into reliable problem-solving systems by composing them according to four structural primitives (decompose, ensemble, verify, and recurse) and a budget-aware controller that decides where to spend compute. The harness treats any model as a black-box base solver behind a uniform interface, layers a verifier ensemble whose discrimination is measured online, and allocates verification and voting to the stages with the highest marginal reliability per unit cost. We give the architecture, the message and state schema, the controller algorithm, and the engineering that makes it deterministic, observable, and fault-tolerant. We then specify an evaluation methodology (reliability at fixed cost, coverage, calibration, and ablations) and report results from a faithful Monte Carlo simulation of the harness over a parameterized solver/verifier model. The simulation reproduces the predicted laws quantitatively: verification amplifies reliability geometrically (e.g. $0.55\to0.98$ with two gates, $\to0.999$ with four), voting helps only above chance and is limited by shared errors, and a budget-aware controller reaches a target reliability at a small fraction of the cost of voting alone by selecting the cheapest mechanism for each regime. We close with failure modes (verifier gaming, correlated errors, and decomposition error compounding) and concrete guidance: build robust checkers, diversify solvers, and let the controller put compute where the information is.

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

Evaluation Sovereignty in Metadata-Driven Classification: A Multi-Track Framework for Weakly Supervised Information Systems

arXiv:2606.13436v1 Announce Type: new Abstract: Evaluation in machine learning is typically treated as a neutral measurement process. However, in operational information systems, evaluation outcomes are often conditioned by the processes used to generate labels. This paper does not seek to improve classification performance. Instead, it examines the validity of performance measurement under differing label-authority regimes. This issue is particularly relevant in large-scale metadata-driven systems, where labels are often incomplete, inconsistent, or weakly supervised. We introduce evaluation sovereignty, defined as the degree to which performance metrics are independent of label authority and supervision regime, and propose a multi-track evaluation framework that systematically varies training and evaluation label sources. Using hierarchical multi-label classification on large-scale scientific metadata, we demonstrate that models exhibiting strong performance under operational ("silver") evaluation degrade substantially under independent ("gold") evaluation, particularly for fine-grained classification. For example, Micro-F1 decreases from approximately 0.54 to 0.03. Notably, ranking-based metrics remain above baseline, revealing a divergence between latent model signal and classification validity. These findings suggest that commonly reported performance metrics may reflect alignment with labeling processes rather than true predictive capability. We therefore reconceptualize evaluation validity as a system-level property shaped by label governance and provide a practical methodology for auditing intelligent systems operating under weak supervision.

14.
arXiv (CS.CV) 2026-06-16

Learning Topology-Aware Implicit Field for Unified Pulmonary Tree Modeling with Incomplete Topological Supervision

Pulmonary trees extracted from CT images frequently exhibit topological incompleteness, such as missing or disconnected branches, which substantially degrades downstream anatomical analysis and limits the applicability of existing pulmonary tree modeling pipelines. Current approaches typically rely on dense volumetric processing, explicit graph reasoning, or generic point cloud completion priors, leading to limited efficiency, weak structural awareness, and reduced robustness under realistic structural corruption. We propose TopoField, a topology-aware implicit modeling framework that treats topology repair as a first-class modeling problem and enables unified multi-task inference for pulmonary tree analysis. TopoField represents pulmonary anatomy using sparse surface and skeleton point clouds and learns a continuous implicit field that supports topology repair without relying on complete or explicit disconnection annotations, by training on synthetically introduced structural disruptions over already incomplete trees. Building upon the repaired implicit representation, anatomical labeling and lung segment reconstruction are jointly inferred through task-specific implicit functions within a single forward pass. Extensive experiments on the Lung3D+ dataset demonstrate that TopoField consistently improves topological completeness and achieves accurate anatomical labeling and lung segment reconstruction under challenging incomplete scenarios. We further validate TopoField on real incomplete outputs from an external segmentation model, demonstrating its applicability to realistic segmentation pipelines. Owing to its implicit formulation, TopoField attains high computational efficiency, completing all tasks in just over one second per case, highlighting its practicality for large-scale and time-sensitive clinical applications.

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

NaturalFlow: Reducing Disruptive Pauses for Natural Speech Flow in Simultaneous Speech-to-Speech Translation

Simultaneous speech-to-speech translation aims to enable near-real-time communication by minimizing latency, offering a compelling, real-time alternative to the high latency of consecutive translation. However, the excessive pursuit of low latency often results in fragmented chunk-wise speech. Consequently, listeners are subjected to an unnatural acoustic flow punctuated by frequent pauses, which could increase their cognitive load. To bridge this gap, we introduce a fluency-aware optimization framework designed to discover the sweet spot between the low-latency benefits of simultaneous translation and the natural flow of consecutive translation. Our framework minimizes inter-chunk silences by leveraging model-internal signals, including linguistic diversity and induced temporal variability in speech durations. Experiments on short- and long-form benchmarks show that our framework produces natural speech flow while maintaining competitive latency and translation quality.

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

FlowMPC: Improving Flow Matching policies with World Models

Authors:

arXiv:2606.16286v1 Announce Type: cross Abstract: Flow Matching (FM) is a powerful approach for behavior cloning in multimodal action spaces [Jiang et al., 2025], but because it is not trained to directly maximize expected return, there is still room to improve how FM policies act at test time. This work investigates whether a learned world model can improve FM policies by enabling Model Predictive Path Integral (MPPI) planning over candidate action sequences proposed by the policy. Building on TD-MPC2 [Hansen et al., 2024], I introduce FlowMPC, a framework that combines an imitation-learned FM policy with a learned world model for test-time planning in ManiSkill manipulation tasks [Tao et al., 2025]. Across PickCube and PickSingleYCB, adding the world model improved performance over the FM policy alone, with especially clear gains in end-of-episode success. These results suggest that world-model-based planning can effectively complement flow-based imitation policies without modifying the FM training objective.

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

EvidenceLens: A Claim-Evidence Matrix for Auditing Financial Question Answering

Large language models are increasingly used to answer questions over annual reports, earnings decks, and analyst notes, yet their outputs remain difficult to verify in high-stakes financial workflows. A fluent answer can blend directly grounded statements, weak synthesis, and unsupported claims across narrative text, tables, and charts. We present EvidenceLens, a visual analytics prototype that treats financial question answering as a claim-evidence alignment problem. The system decomposes an answer into atomic claims, summarizes support composition and confidence, support gaps, and coordinates claim-level inspection with source passages, table cells, and chart regions. Its core visual representation is a multimodal claim-evidence matrix that makes coverage, contradiction, and modality imbalance immediately visible. To support reproducibility, we also specify a JSON-based artifact schema, a lightweight multimodal alignment pipeline, and a deterministic review-priority ranking that maps backend signals into an auditable visual structure. Through representative report-auditing scenarios, we show how EvidenceLens helps analysts distinguish grounded claims from overconfident synthesis that conventional chat interfaces flatten.

18.
medRxiv (Medicine) 2026-06-22

Body composition subphenotypes, cardiometabolic risk and incident outcomes: validation in the population-based NAKO and UK Biobank imaging cohorts

Background Anthropometric measures do not adequately capture heterogeneity in body fat distribution and corresponding cardiometabolic risk, whereas magnetic resonance imaging (MRI) enables precise differentiation and quantification of adipose tissue compartments and ectopic fat. We aimed to validate previously derived MRI-based body composition subphenotypes and their cardiometabolic risk profiles in two independent European cohorts. Methods Using deep learning-based image analysis, we quantified bone marrow, visceral, subcutaneous, cardiac, renal sinus, hepatic, skeletal muscle, and pancreatic fat in the imaging substudies of two population-based cohorts: the German National Cohort (NAKO, N=29,314, age range 19-74 years) and the UK Biobank (N=36,109, age range 40-69 years). Body composition subphenotypes, previously identified by k-means clustering, were evaluated using a rigorous statistical cluster validation framework with method-based and results-based approaches. In NAKO, cross-sectional associations between subphenotypes and estimated cardiovascular disease risk scores were examined using linear regression. In UK Biobank, longitudinal associations between subphenotypes and incident cardiometabolic outcomes, ascertained through hospital record linkage, were analysed using Cox regression. Findings All five body composition subphenotypes were robustly validated across both cohorts, and showed distinct fat distribution patterns and cardiometabolic risk profiles: I "lean", II "average adiposity", III "bone and muscle adiposity", IV "hepato-abdominal adiposity", and V "general and pancreatic adiposity". Subphenotypes I-III showed progressive adipose tissue remodelling patterns likely reflecting ageing trajectories. The "hepato-abdominal adiposity" subphenotype showed highest risk of incident diabetes, whereas the "general and pancreatic adiposity" subphenotype showed highest overall cardiovascular disease burden and metabolic impairment. Interpretation MRI-derived body composition subphenotypes represent distinct fat distribution patterns that reflect ageing- and disease-related processes, which supports the potential of body composition phenotyping for improved cardiometabolic risk stratification and targeted prevention.

19.
arXiv (math.PR) 2026-06-11

Marked random graphs with given degree sequence: large deviations on the local topology

arXiv:2401.00351v2 Announce Type: replace Abstract: We investigate the behavior of the empirical neighborhood distribution of marked graphs in the framework of local weak convergence. Here we extend known results by considering uniform random graphs with given degree sequences and i.i.d. marks on half-edges and vertices. We establish a large deviation principle for such families of empirical measures. The proof builds on Bordenave and Caputo's seminal 2015 paper, and Delgosha and Anantharam's 2019 introduction of BC entropy, relying on combinatorial lemmas that allow one to construct suitable approximations of measures supported on marked trees. Possible applications of these results are in the study of interacting diffusions on top of random graphs.

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

Human genetic evidence is associated with drug approval across therapeutic areas: an observational analysis of 26,278 target-disease pairs with temporal validation and feature ablation

Genetic evidence is enriched among approved drug targets: in an observational analysis of 26,278 target-disease pairs from Open Targets and ChEMBL, targets with any genetic association had a 3.25-fold higher approval rate than those without (OR = 3.25, 95% CI 2.79-3.79, p = 1.91e-42). A target-level analysis accounting for non-independence of pairs sharing the same gene gave OR = 2.79 (bootstrap 95% CI 2.22-3.53); the oncology pair-level OR of 6.72 attenuates to 2.71 at the target level, illustrating how non-independence inflates area-specific estimates. The enrichment replicated in post-2015 approvals (OR = 3.51, p = 1.72e-8). Feature ablation across six evidence types revealed that literature mining alone accounts for most classifier performance (AUPRC = 0.099 versus 0.109 for all features), consistent with temporal leakage from post-approval publications. Excluding literature, remaining evidence types retain above-baseline signal (AUPRC = 0.084, 1.63x baseline). Sensitivity analyses bracket the pair-level OR between 3.25 and 4.93. Genetic evidence alone yields only a 1.0-percentage-point absolute AUPRC gain and the best model has poor calibration; the classifier has limited practical predictive value. We catalogue 1,433 genetically supported Phase 1/2 pairs as a hypothesis-generating resource. All findings are observational.

21.
arXiv (CS.LG) 2026-06-18

Generalised Eigenvalue Geometry of Semantic Adversarial Attacks

arXiv:2606.19212v1 Announce Type: cross Abstract: Recent empirical work shows that semantically equivalent paraphrases can fool financial sentiment classifiers: although a paraphrase remains close to the original under a strong reference embedding, it may shift the target model's representation enough to change the predicted class. Existing robustness theory either assumes a single-model threat model or focuses mainly on empirical attack algorithms. We develop a continuous local model of semantic paraphrase perturbations that captures this two-model structure. We show that the worst-case local displacement of the target representation, subject to a proxy-model budget, is governed by the largest generalised eigenvalue of a matrix pencil $(A,B)$ constructed from the Jacobians of the two embedding maps. The resulting attackability index $\lambda^*(x)$ is intrinsic to the local paraphrase geometry and the chosen embedders, yields a closed-form prediction-flip condition for affine readouts, and supports conservative population and finite-sample attackability certificates. For uniform control over classes of affine readouts, we derive a distribution-free VC bound for binary attackability indicators and a scale-sensitive margin bound based on an attackability-adjusted margin that subtracts a local geometric penalty from the standard classifier margin. We also connect the continuous theory to discrete paraphrase search, identify an asymmetry between successful and unsuccessful finite searches, and give a covering condition under which the discrete and continuous settings agree. Finally, we propose an empirical verification framework using soft-token relaxations and generated paraphrase sets to assess the local eigenvalue geometry, prediction-flip condition, and finite-search approximation on a deployed financial-text classifier.

22.
arXiv (CS.LG) 2026-06-24

Adversarial dynamical systems characterize when data-driven learning succeeds or fails

arXiv:2407.06312v2 Announce Type: replace-cross Abstract: Many systems resist analytical modeling, making data-driven inference of dynamics important. Yet data-driven methods can fail to converge or generalize, leaving open a central question: When can system behavior be learned reliably from data, and when is such learning impossible? We answer this question using adversarial dynamical systems to identify the boundary between accessible and inaccessible regimes. In Koopman operator learning, a leading framework for representing nonlinear dynamics through linear spectral objects, we design optimal data-driven spectral algorithms with convergence and certification guarantees under conditions arising broadly in physical systems. This yields a convergence theory for Koopman-operator approximations and resolves a longstanding open problem in Koopman spectral analysis. Conversely, by constructing adversarial systems, we prove matching impossibility results: without these conditions, no single-sequence limiting procedure can guarantee learning, regardless of data quality. These results sharply characterize when data-driven spectral learning can succeed and when it must fail. We validate the framework on oscillators, chaotic fluid flows and Arctic sea ice concentration forecasting. In the latter, we uncover hidden modes of Arctic sea ice decline, deliver long-range forecasts with geographic error bounds, and outperform state-of-the-art dynamical and deep learning models at substantially lower computational cost, enabling real-time deployment on standard CPUs.

23.
arXiv (CS.CL) 2026-06-15

Protean Compiler: An Agile Framework to Drive Fine-grain Phase Ordering

The phase ordering problem has been a long-standing challenge since the late 1970s, yet it remains an open problem due to having a vast optimization space and an unbounded nature, making it an open-ended problem without a finite solution, one can limit the scope by reducing the number and the length of optimizations. Traditionally, such locally optimized decisions are made by hand-coded algorithms tuned for a small number of benchmarks, often requiring significant effort to be retuned when the benchmark suite changes. In the past 20 years, Machine Learning has been employed to construct performance models to improve the selection and ordering of compiler optimizations, however, the approaches are not baked into the compiler seamlessly and never materialized to be leveraged at a fine-grained scope of code segments. This paper presents Protean Compiler: An agile framework to enable LLVM with built-in phase-ordering capabilities at a fine-grained scope. The framework also comprises a complete library of more than 140 handcrafted static feature collection methods at varying scopes, and the experimental results showcase speedup gains of up to 4.1% on average and up to 15.7% on select Cbench applications wrt LLVM's O3 by just incurring a few extra seconds of build time on Cbench. Additionally, Protean compiler allows for an easy integration with third-party ML frameworks and other Large Language Models, and two applications of this two-step optimization show a gain of 10.1\% and 8.5\% speedup w.r.t. -O3 on CBench's Susan and Jpeg applications. Protean compiler is seamlessly integrated into LLVM and can be used as a new, enhanced, full-fledged compiler. We plan to release the project to the open-source community in the near future.

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

The quantum harmonic oscillator and the real Hilbert space

arXiv:2606.12060v1 Announce Type: new Abstract: The harmonic oscillator is considered within generalized frameworks using complex and quaternionic numbers. The classical oscillator is considered in terms of a complex position function, and quantum oscillators are examined in terms of complex wave functions, and in terms of quaternionic wave functions as well. Both of the quantum solutions are obtained within the real Hilbert space formalism. The results reveal the complex and quaternionic descriptions as suitable frameworks for non-stationary processes, including damped oscillations, forced oscillations, and additionally self-interacting processes that cannot be appropriately described otherwise.

25.
arXiv (CS.AI) 2026-06-17

Adaptive Domain Models: Bayesian Evolution, Warm Rotation, and Principled Training for Geometric and Neuromorphic AI

arXiv:2603.18104v5 Announce Type: replace Abstract: Prevailing AI training assumes reverse-mode automatic differentiation over IEEE-754 arithmetic. The memory overhead of training relative to inference, optimizer complexity, and structural degradation of geometric properties through training are consequences of this arithmetic substrate. This paper develops an alternative training architecture grounded in three prior results: the Dimensional Type System and Deterministic Memory Management framework (Haynes 2026), which establishes stack-eligible gradient allocation and exact quire accumulation as design-time verifiable properties; the Program Hypergraph (Haynes 2026), which establishes grade preservation through geometric algebra computations as a type-level invariant; and the b-posit bounded-regime design (Jonnalagadda et al. 2025), which makes posit arithmetic tractable across hardware targets conventionally considered inference-only. Their composition enables depth-independent training memory bounded to approximately twice the inference footprint, grade-preserving weight updates, and exact gradient accumulation, applicable uniformly to loss-function-optimized and spike-timing-dependent neuromorphic models. We introduce *Bayesian distillation*, a mechanism by which the latent prior structure of a general-purpose model is extracted through the ADM training regime, resolving the data-scarcity bootstrapping problem for domain-specific training. For deployment, we introduce *warm rotation*, an operational pattern in which an updated model transitions into an active inference pathway without service interruption, with correctness formalized through PHG certificates and signed version records. The result is a class of domain-specific AI systems that are smaller and more precise than general-purpose models, continuously adaptive, verifiably correct with respect to the physical structure of their domains, and initializable from existing models.