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

Probabilities

arXiv:2601.18853v4 Announce Type: replace-cross Abstract: Probabilities is the English translation of the book Probabilités Tome 1 and Tome 2. The mathematic content is authored by Prof. Jean-Yves Ouvrard. The English version has been done by his eldest son Dr. Xavier Ouvrard. This probability theory book covers not only an introduction to this field, but also advanced concepts based on measure theory. The first part introduces the fundamentals of probability theory across 7 chapters, targeting bachelor level, including event algebras, random variables, independence, conditional probabilities, moments of discrete and continuous random variables, generating functions, and limit theorems. The second part contains 10 chapters and corresponds to master level. Following a brief introduction to measure theory, this part develops more advanced topics: probability measures and their complements, distributions and moments of random variables, modes of convergence, laws of large numbers, conditional expectation, Fourier transforms and characteristic functions, Gaussian random variables, convergence of measures, convergence in distribution, discrete-time stochastic processes, martingales, and Markov chains. The reader's work is greatly facilitated by the inclusion, in every chapter, of numerous exercises, all accompanied by detailed solutions that often provide substantial extensions to the theoretical material.

02.
arXiv (CS.AI) 2026-06-17

Comprehensive pKa Data Augmentation from Limited Real Data through an Engineered Models-Quantum Framework

arXiv:2606.17077v1 Announce Type: cross Abstract: Proton dissociation constants (pKa) are critical for functional molecule discovery and molecular modeling. Building on iBonD, the largest experimental pKa database established, we and other researchers have developed several methods including machine-learning-based empirical prediction and high-accuracy energy calculations. Despite this foundation, the rapid augmentation of high-quality pKa data remains fundamentally constrained. As part of this work, we performed large-scale regression-based pKa prediction on unlabeled molecular datasets using a collection of extensively optimized machine-learning models. The results indicate that, since the feature distributions of unlabeled molecular datasets, the pKa data distribution approximates normality, with extreme scarcity of tail-region samples. Although such augmentation is highly valuable for improving overall data availability and predictive modeling, it remains insufficient for efficiently discovering molecules with broad-spectrum pKa properties. To address this, we explore the targeted generation of molecules with sparse pKa properties from the vast chemical space. Given that traditional continuous latent space VAE-RNN methods for molecular generation suffer from insufficient stability and fail to demonstrate clear advantages in complementing sparse data, we design and implement a quantum-assisted sparse-pKa molecular generation. Feasibility is validated on a simulated quantum annealer, and superior extreme-value sampling is further achieved on physical coherent Ising machines (CIMs). (to be continued)

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

Semantic DLM+: Improving Diffusion Language Models through Bias-variance Trade-off in Transition Kernel Design

arXiv:2606.15327v1 Announce Type: new Abstract: Diffusion Language Models (DLMs) have demonstrated strong scaling capacity as alternatives to autoregressive language models. However, their performance is highly sensitive to the choice of transition kernels, and poorly designed kernels can lead to issues like training instability, slow convergence, and biased sampling. In this paper, we study this sensitivity through a principled analysis of generalization error and identify three critical factors: asymptotic bias (difficulty in approximating the posterior distribution), exposure bias (error propagation during sampling), and optimization variance induced by kernel dispersion. We further compare different transition kernels: masking diffusion yields sparse and easier posterior-approximation targets, while uniform diffusion provides stronger sampling-side repair but induces harder approximation. Motivated by this trade-off, we revisit a previously overlooked variant, semantic DLM (SemDLM), where the transition kernel corrupts tokens to neighborhoods that are semantically similar. Our theory suggests that SemDLM can serve as a plausible middle ground by reducing the posterior approximation difficulty of uniform diffusion while retaining repair ability. However, we find that SemDLM suffers from a semantic basin problem, where sampling repeatedly stays within a semantic region and produces low-diversity text. To address this, we propose SemDLM+, which adds a global transition and a semantic-frequency penalty during sampling. Experiments on LM1B and OpenWebText show that SemDLM+ improves training dynamics and achieves competitive language modeling and generation quality with satisfactory diversity.

04.
arXiv (CS.CL) 2026-06-16

Can Agents Read the Room? Benchmarking Visual Social Intelligence in Multimodal Simulation

Social interaction depends on both language and visible social signals, such as facial expressions, posture, gaze, and emotional shifts. Yet existing social-agent benchmarks are largely text-based and rarely test whether multimodal agents can use visual cues to guide interaction. We introduce \textsc{\benchmarkname{}}, a benchmark evaluating visual social intelligence in multimodal social simulation. It contains 240 scenarios, 585 role instances, and 2,340 role-task instances, combining aligned textual-visual evidence, structured role profiles, and four role-level tasks: expression task, characteristic task, interaction regulation task, and interaction outcome task. Evaluating seven recent MLLMs under verbalized-vision and direct-vision reveals a clear gap between local role enactment and interaction management: role-specific expression and conflict handling are near saturation, whereas interaction regulation and visually grounded outcome achievement remain substantially more difficult. The code is released at https://github.com/JunsWan/AgentViSS, and the dataset is available at https://huggingface.co/datasets/JunsWan/AgentViSS.

05.
arXiv (CS.LG) 2026-06-17

Reconfigurable Computing Challenge: Transformer for Jet Tagging on Versal AI Engines

arXiv:2606.17500v1 Announce Type: new Abstract: Transformer-based models achieve strong performance for jet tagging at the CERN LHC, but deploying them in low-latency, resource-constrained trigger systems is challenging. We present an initial implementation of a quantized, integer-only transformer for jet tagging on the AMD Versal AI Engine (AIE), mapping dense and multi-head attention (MHA) layers to AIE tiles. The main contribution is a reusable software framework that represents transformer layers as composable AIE building blocks and automatically generates the corresponding Vitis graph code from a high-level Python model description. This framework provides a foundation for future research and is released as open-source software at https://github.com/KastnerRG/particle_transformer_aie.

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

CreativeBench: Benchmarking and Enhancing Machine Creativity via Self-Evolving Challenges

The saturation of high-quality pre-training data has shifted research focus toward evolutionary systems capable of continuously generating novel artifacts, leading to the success of AlphaEvolve. However, the progress of such systems is hindered by the lack of rigorous, quantitative evaluation. To tackle this challenge, we introduce CreativeBench, a benchmark for evaluating machine creativity in code generation, grounded in a classical cognitive framework. Comprising two subsets – CreativeBench-Combo and CreativeBench-Explore – the benchmark targets combinatorial and exploratory creativity through an automated pipeline utilizing reverse engineering and self-play. By leveraging executable code, CreativeBench objectively distinguishes creativity from hallucination via a unified metric defined as the product of quality and novelty. Our analysis of state-of-the-art models reveals distinct behaviors: (1) scaling significantly improves combinatorial creativity but yields diminishing returns for exploration; (2) larger models exhibit ``convergence-by-scaling,'' becoming more correct but less divergent; and (3) reasoning capabilities primarily benefit constrained exploration rather than combination. Finally, we propose EvoRePE, a plug-and-play inference-time steering strategy that internalizes evolutionary search patterns to consistently enhance machine creativity.

07.
arXiv (CS.AI) 2026-06-16

HoloRec: Holistic Encoding and Interleaved Reasoning for Generative Recommendation

arXiv:2606.15331v1 Announce Type: cross Abstract: Generative recommendation models that formulate the task as sequence generation overcome the objective fragmentation problem of traditional cascade architectures, yet existing approaches still suffer from flat semantic representations lacking hierarchical structure for multi-step reasoning and an externally constructed chain-of-thought (CoT) that requires expensive annotations and remains disconnected from the generation objective. We propose HoloRec, an endogenous chain-of-thought recommendation mechanism that unifies representation, reasoning, and generation by constructing a hierarchical semantic encoding matrix via multi-granularity nested residual quantization optimized by a holistic reconstruction loss. HoloRec supports two inference modes: a non-thinking mode that uses lightweight multi-granularity supervised alignment for fast prediction, and a thinking mode that employs an interleaved reasoning scheme to generate CoT steps on the fly, directly embedding reasoning into the generation process without external data. Experiments on multiple public recommendation datasets demonstrate that HoloRec consistently outperforms baselines, with especially significant gains in sparse scenarios, and the thinking mode achieves better accuracy than the non-thinking mode with only modest inference overhead.

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

Modeling Doppler Shifts in Radial-Velocity Data with Deep Learning toward Earth-mass Exoplanet Detection

arXiv:2606.18464v1 Announce Type: cross Abstract: Detecting the tiny Doppler shifts induced by Earth-mass planets in stellar radial-velocity measurements remains extremely challenging due to stellar activity. Many deep-learning methods performing well on simulated data remain difficult to apply reliably on real stellar spectra. The aim of this work is to develop a deep-learning framework that generalizes to real, unseen spectra and improves the detectability of Earth-mass planets in radial-velocity data. We train artificial neural networks on HARPS-N solar spectra with injected planetary signals, using physics-motivated spectral representations based on flux and line-formation temperature, together with their velocity gradients. Two training strategies are explored: hold-out testing and cross-validation. Model robustness is enhanced through genetic-algorithm-based hyperparameter optimization, and predictive uncertainty is quantified using Monte Carlo dropout. Our most precise neural network model reliably retrieves, under the cross-validation strategy, the amplitudes, phases, and orbital periods of planetary signals with amplitudes greater than or equal to 25 cm/s and periods between 10 and 550 days. In addition, in all cases tested here, the successfully recovered signals correspond to the most significant peaks in the periodograms of the Doppler-shift predictions. Temperature-based spectral-shell representations consistently outperform flux-based shells. We also release doppleriann, a Python package implementing the proposed framework. Our results demonstrate that combining physically motivated spectral representations with deep learning provides a promising pathway toward the detection of Earth-mass planets in radial-velocity data from real observations, supported by a modeling framework that is both physically grounded and statistically rigorous, incorporating uncertainty quantification and optimized training strategies.

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

FreeBridge: Variational Schrödinger Bridges for Cellular Transition Dynamics

arXiv:2606.11286v1 Announce Type: cross Abstract: High-content imaging assays quantify cellular responses to chemical and genetic perturbations, yet continuous trajectories of individual cells are unobservable because cells are chemically fixed at acquisition. Perturbation modeling therefore reduces to inferring stochastic transport between control and treated populations observed only as separate marginals. While recent generative models achieve strong end-point alignment, boundary consistency does not determine intermediate evolution: multiple stochastic processes may connect identical marginals while traversing regions unsupported by observed single-cell morphologies. We introduce FreeBridge, a Schrödinger Bridge formulation for single-cell transition modeling under endpoint-only supervision. FreeBridge defines atomic states as instance-segmented single-cell representations, establishing a fixed cellular manifold, and learns stochastic transport constrained within this geometry via empirical latent support regularization. Across BBBC021, RxRx1, and JUMP, FreeBridge maintains competitive or improved endpoint fidelity and mechanism-of-action retention under a unified evaluation protocol; on BBBC021, it further reduces intermediate support violations. These findings highlight the importance of geometric grounding for biologically interpretable perturbation dynamics. Project page: https://y-research-sbu.github.io/FreeBridge/.

10.
arXiv (CS.AI) 2026-06-16

Few-shot Class-variable Incremental Audio Classification via Prototype Adaptation and Pseudo Class-variable Training

arXiv:2606.08898v2 Announce Type: replace-cross Abstract: In the task of few-shot class-incremental audio classification, the number of classes is assumed to always increase without considering the possibility of decrease. However, the number of classes generally increases or decreases in practice. In this paper, we investigate a problem of Few-shot Class-variable Incremental Audio Classification (FCIAC), in which the number of classes increases or decreases. We propose a FCIAC method using prototype adaptation and pseudo class-variable training. The model in our method consists of an encoder and a classifier. The classifier is initialized by a class-variable prototype adaptation network, whose structure dynamically changes with the change of classes. In addition, we design a pseudo class-variable training strategy to enhance the model's adaptability to changing classes. Experiments on three public datasets show that our method exceeds previous methods in average accuracy. The code is at: https://github.com/cgq2971-afk/FCIAC.

11.
arXiv (CS.CV) 2026-06-12

High-Fidelity Two-Step Image Generation via Teacher-Aligned End-to-End Distillation

Few-step diffusion distillation has become increasingly mature for 4-8-step generation, yet pushing further to 2 steps remains challenging. In this work, we introduce Z-Image Turbo++, a high-quality 2-step image generation model distilled from the 8-step Z-Image Turbo teacher. Our method addresses the central bottlenecks of increased task difficulty and limited model capacity in 2-step generation through three simple but effective design choices tailored to this regime. First, we propose Distribution-Aligned Adversarial Learning, which uses teacher-generated images rather than external real images as real samples for GAN training, providing a more attainable and informative adversarial target. Second, we adopt Step-Decoupled Parameterization, assigning independent model parameters to the two denoising steps to better match their distinct capacity demands. Third, we perform End-to-End Training with Iterative Regularization, allowing the first step to receive gradients from final image quality while preserving a meaningful intermediate generation through an explicit step-1 loss. Together, these designs substantially narrow the quality gap between 2-step and 8-step generation in both qualitative and quantitative evaluations, highlighting the potential of carefully tailored distillation strategies for improving the quality-efficiency trade-off in few-step generation.

12.
arXiv (quant-ph) 2026-06-16

Entanglement-Rank Duality in Quadratic Phase Quantum States

arXiv:2605.05167v2 Announce Type: replace Abstract: Absolutely maximally entangled (AME) states are fundamental resources in quantum information theory, yet their construction and certification remain a nontrivial problem. Within the family of quadratic phase quantum states, defined by symmetric matrices $P$ over finite fields $\mathbb{F}_{p^m}$, we show that the Rank-Purity Duality $\operatorname{Tr}(\rho_S^2) = |\mathbb{F}|^{-\operatorname{rk}_{\mathbb{F}}(P_{S,\bar{S}})}$ follows from additive character orthogonality and holds over all $\mathbb{F}_{p^m}$, yielding a polynomial-time AME certification criterion. For square-free dimensions $d = p_1\cdots p_r$, the Chinese Remainder Theorem induces a prime-field factorisation. This implies additivity of Rényi-2 entropy and yields sharp obstruction criteria that rule out cases such as $\operatorname{AME}(4,6)$ and constrain the open case $\operatorname{AME}(8,6)$. As a proof of concept, we construct an explicit $\operatorname{AME}(17,10001)$ state, certified across all $65{,}535$ bipartitions, demonstrating that the framework scales to large systems and previously inaccessible local dimensions.

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

From Imitation to Alignment: Human-Preference Flow Policies for Long-Horizon Sidewalk Navigation

arXiv:2606.12603v1 Announce Type: cross Abstract: Autonomous long-horizon sidewalk navigation is essential for micro-mobility applications such as robotic food delivery and assistive electronic wheelchairs. Unlike autonomous driving on the road, long-horizon sidewalk navigation requires precise maneuvering through unpredictable sidewalk terrains and pedestrians, with a lightweight perception stack as minimal as a single monocular RGB camera. While imitation learning (IL) from demonstrations offers a practical solution, the resulting autopilot policy often suffers from compounding errors, a lack of social compliance on sidewalks, and deficiencies in counterfactual reasoning to handle complex situations. To address these challenges, we introduce FlowPilot, a mapless navigation policy that achieves robust and efficient long-horizon navigation performance using only a monocular RGB camera. We first propose to use anchored flow matching as an action representation for policy pre-training on large-scale robot fleet data and to capture the diverse, complex, multimodal distribution of sidewalk navigation behaviors. To bridge the gap between imitation and alignment, we further design a human-in-the-loop preference learning scheme to tune the policy on a small amount of human intervention data. It strengthens the model's counterfactual reasoning and social compliance on sidewalks. We evaluate FlowPilot through extensive simulation and real-world experiments in diverse sidewalk environments. FlowPilot achieves 42% success rate and 66% route completion in simulation, while FlowPilot-HP further improves real-world robustness and social compliance, reducing IR by 40.0% and NIR by 52.1% relative to the base model.

14.
arXiv (CS.AI) 2026-06-19

VERITAS: Verifier-Guided Proof Search for Zero-Shot Formal Theorem Proving

arXiv:2606.19399v1 Announce Type: cross Abstract: LLM-based formal provers often collapse rich verifier signals (syntax errors, type mismatches, partial goal progress) into a binary pass/fail bit. We present VERITAS, a zero-shot framework that routes every verifier signal back into proof search through a two-phase protocol: Best-of-N sampling first, then a critic-guided MCTS pass that ingests Phase 1 failures as explicit negative examples. The protocol preserves every theorem solved by its own Phase 1 sweep, so Phase 2's additional solves are attributable to feedback-driven exploration. VERITAS reaches 40.6% on miniF2F (vs. an independently run Best-of-5 at 36.9%, Portfolio 26.2%) and 7.3% on VERITAS-CombiBench, a 55-theorem combinatorics benchmark we release on which Best-of-5 (1.8%) falls below Portfolio (3.6%), exposing that unguided sampling hurts when correct lemma names must be recovered iteratively from verifier feedback. Artifacts are available on GitHub.

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

Peak-Based Nuclide Identification in HPGe $\gamma$-Spectrometry with Machine Learning and SHAP

arXiv:2606.14874v1 Announce Type: cross Abstract: High-purity germanium gamma spectra often require time-consuming analyses from subject matter experts. Photopeaks within these spectra are carefully fitted and numerical methods are employed to assist with nuclide identification (NID) and quantification. Amending the list of nuclides identified by analysis software can be nontrivial. When many samples need to be analyzed, it is therefore challenging to make timely and correct decisions. Supervised machine-learning-based NID can serve as an expert-informed, automated tool to improve the initial set of radionuclides suggested to an analyst and more effectively drive subsequent quantification. To that end, we implemented machine learning models that map photopeaks carefully fitted by analysts to NID results for experimental spectra containing various isotopic combinations drawn from a set of 65 isotopes. The best model achieved an F1 score of 0.97, markedly surpassing the F1 score of 0.84 achieved by traditional software when compared using a nuclide library comprising the same 65 isotopes assessed by the models. Finally, we illustrated the most important input features for model predictions using Shapley Additive Explanations. These explanations revealed that the models use physically relevant photopeaks when making predictions for the isotopes in our nuclide library.

16.
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.

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

Low-resource Language Discrimination Towards Chinese Dialects with Transfer learning and Data Augmentation

Chinese dialects discrimination is a challenging natural language processing task due to scarce annotation resource. In this article, we develop a novel Chinese dialects discrimination framework with transfer learning and data augmentation (CDDTLDA) in order to overcome the shortage of resources. To be more specific, we first use a relatively larger Chinese dialects corpus to train a source-side automatic speech recognition (ASR) model. Then, we adopt a simple but effective data augmentation method (i.e., speed, pitch, and noise disturbance) to augment the target-side low-resource Chinese dialects, and fine-tune another target ASR model based on the previous source-side ASR model. Meanwhile, the potential common semantic features between source-side and target-side ASR models can be captured by using self-attention mechanism. Finally, we extract the hidden semantic representation in the target ASR model to conduct Chinese dialects discrimination. Our extensive experimental results demonstrate that our model significantly outperforms state-of-the-art methods on two benchmark Chinese dialects corpora.

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

Circuit Synchronization Precedes Generalization: Causal Evidence from Fourier Structure in Grokking Transformers

arXiv:2606.12966v1 Announce Type: new Abstract: Grokking – where a transformer on modular arithmetic suddenly transitions from near-chance to near-perfect validation accuracy – is attributed to a Fourier circuit, but its timing, causal structure, and controllability remain poorly understood. We introduce the Frequency Synchronization Degree (FSD), a normalised, permutation-tested metric for Fourier circuit synchronisation requiring no prior circuit knowledge. Across nine modular addition configurations (primes p in {53, 71, 97, 113, 131}, three seeds), FSD synchronises 500-3,000 steps before grokking (mean lead +1,722 steps; all nine positive, sign-test p~0.004), and precedes a restricted-logit loss baseline (Nanda et al.'s excluded loss) in all nine cases, making it the earliest available predictor. We provide direct causal evidence that the inter-phase gap is a regularisation phenomenon: forking training at the FSD-ceiling step and varying weight decay lambda produces strictly monotone earlier grokking, with Delta_t proportional to 1/lambda. This law replicates across three primes (p in {53,97,131}; R^2=1.00 and R^2=0.99 for two clean cases), captured as Delta_t ~ C/lambda, consistent with (1/lambda)*log(||W_mem||/tau). Architecture ablations show an attention-only model groks with a strong FSD precursor; an MLP-only model never groks; a single-layer model's FSD lags, confirming the precursor is a multi-block circuit property.

19.
arXiv (CS.CL) 2026-06-11

Can AI Agents Synthesize Scientific Conclusions?

Scientific AI agents increasingly retrieve evidence, reason across sources, and synthesize conclusions used in consequential decisions. Yet, their ability to do so in high-stakes domains such as health remains unclear. We introduce SciConBench, a large-scale live benchmark of 9.11K questions and expert-written conclusions from systematic reviews to evaluate open-domain scientific conclusion synthesis. The benchmark draws on an expert-validated automated evaluation pipeline that decomposes conclusions into atomic facts and measures correctness and comprehensiveness via factual precision and recall. To mitigate data leakage, we further introduce SciConHarness, a clean-room evaluation harness that equips agents with controlled web interaction to ensure valid measurement. Evaluating 8 frontier models and deep research agents, we find that factual quality remains low: under clean-room settings, the best agent achieves only a factual F1 of 0.337. Our clean-room setting consistently reduces performance relative to unconstrained evaluation, suggesting that leakage inflates estimates of models' true synthesis capabilities. Finally, we audit consumer-facing agents (e.g., Google AI Overview, OpenEvidence) and find they frequently generate incomplete and sometimes contradictory conclusions, even when the ground-truth answer is available. Overall, our results show that reliable synthesis of scientific conclusions remains an open challenge, and that clean-room evaluation is essential for assessing open-domain AI agents.

20.
arXiv (CS.AI) 2026-06-11

Internet of Everything in the 6G Era: Paradigms, Enablers, Potentials and Future Directions

arXiv:2604.25018v2 Announce Type: replace-cross Abstract: The Internet of Everything (IoE) represents an evolution of the Internet of Things (IoT) by integrating people, data, processes, and things into a unified intelligent ecosystem. IoE aims to enhance automation, decision-making, and service efficiency across multiple application domains such as smart cities, healthcare, industry, and next-generation wireless networks. This paper provides a structured overview of the IoE concept, its core components, architectural foundations, enabling technologies, and major research challenges. Finally, open research directions toward 6G-enabled intelligent IoE systems are discussed, with emphasis on scalability, security, privacy, and energy efficiency.

21.
arXiv (CS.AI) 2026-06-17

KFTD: Koopman-Fourier Time-Differentiable Network for Continuous Ocean Spatiotemporal Forecasting

arXiv:2606.17070v1 Announce Type: cross Abstract: Accurate oceanic forecasting is critical for climate monitoring and disaster early warning. However, ocean spatiotemporal forecasting encounters the double challenges of modeling complex dynamical systems and ensuring computational efficiency. We present Koopman Fourier Time-Differentiable (KFTD) Network, a time continuous twostage paradigm that decouples interpolation from prediction to achieve efficient and scalable spatiotemporal modeling. We map complex nonlinear dynamics into the Koopman linear space and exploit Fourier analysis to enable continuous time interpolation at arbitrary sub-steps. A lightweight residual network consumes the high fidelity intermediate states to yield the final forecast. Unlike diffusion models, KFTD eliminates multi step noise sampling and directly evolves the system in continuous time, yielding a 4 computational speedup. We further introduce a DPP Loss that supports arbitrary PDE constraints in an endtoend manner, breaking the physical consistency bottleneck of pure data-driven approaches. Empirical results on four ocean datasets confirm that our continuous time framework reduces MSE by an average of 5.6% (up to 12.7% for SST) and improves efficiency over MCVD by 76.25%.

22.
arXiv (CS.AI) 2026-06-17

Treatment Response Optimized Clinical Decision Support AI System via Digital Twin Simulation

arXiv:2606.17405v1 Announce Type: new Abstract: Clinical decision support AI systems (CDSASs) must adapt to evolving patient conditions in real-time while adhering to strict safety constraints. We present an online adaptive framework that integrates Treatment Effect (TE) estimation to quantify clinical benefits, a patient Digital Twin (DT) to simulate treatment trajectories, and Reinforcement Learning (RL) for sequential decision-making. The AI system is initially trained on historical medical records and operates in a continuous learning loop. To ensure safety, a rule-based module monitors vital signs and blocks contraindicated treatments. Cases with strong internal model disagreement are flagged for clinician review, simulated in our experiments via a pre-trained outcome model. We validate our framework using both a synthetic clinical simulator and a real-world ovarian cancer dataset from The Cancer Genome Atlas (TCGA). In both simulated and clinical settings, our method demonstrated superior effectiveness and stability in recommending treatments compared to standard computational baselines. Furthermore, the AI system maintains low latency and requires expert consultation for only a minority of cases in our experimental validation, demonstrating its potential as a safe, clinician-supervised tool for personalized medicine that continuously improves through practical use.

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

Is Stochastic Gradient Descent Effective? A PDE Perspective on Machine Learning processes

arXiv:2501.08425v3 Announce Type: replace Abstract: In this paper we analyze the behaviour of the stochastic gradient descent (SGD), a widely used method in supervised learning for optimizing neural network weights via a minimization of non-convex loss functions. Since the pioneering work of E, Li and Tai (2017), the underlying structure of such processes can be understood via parabolic PDEs of Fokker-Planck type, which are at the core of our analysis. Even if Fokker-Planck equations have a long history and a extensive literature, almost nothing is known when the potential is non-convex or when the diffusion matrix is degenerate, and this is the main difficulty that we face in our analysis. We identify two different regimes: in the initial phase of SGD, the loss function drives the weights to concentrate around the nearest local minimum. We refer to this phase as the drift regime and we provide quantitative estimates on this concentration phenomenon. Next, we introduce the diffusion regime, where stochastic fluctuations help the learning process to escape suboptimal local minima. We analyze the Mean Exit Time (MET) and prove upper and lower bounds of the MET. Finally, we address the asymptotic convergence of SGD, for a non-convex cost function and a degenerate diffusion matrix, that do not allow to use the standard approaches, and require new techniques. For this purpose, we exploit two different methods: duality and entropy methods. We provide new results about the dynamics and effectiveness of SGD, offering a deep connection between stochastic optimization and PDE theory, and some answers and insights to basic questions in the Machine Learning processes: How long does SGD take to escape from a bad minimum? Do neural network parameters converge using SGD? How do parameters evolve in the first stage of training with SGD?

24.
arXiv (CS.LG) 2026-06-19

Variational Consensus Monte Carlo for Bayesian Mixture

arXiv:2606.19643v1 Announce Type: cross Abstract: Motivated by the privacy, sensitivity and sharing limitations of health data, we present a comprehensive pipeline for inference of Bayesian mixture models within a federated learning setting, i.e. when data cannot be fully shared or pooled across compute nodes. We adopt a Consensus Monte Carlo (CMC) approach, in which an MCMC algorithm is run independently within each data silo to estimate local posterior distributions, which are then aggregated to approximate the posterior over the full data. The variational CMC approach of Rabinovich, Angelino and Jordan (2015) [1] frames the aggregation step as a variational inference problem, but their application to mixtures assumes the number of clusters and key mixture parameters to be known. Our main methodological contributions are: (i) an extension of variational CMC to over-fitted Bayesian mixture models that infer the number of clusters and all model parameters, without requiring conjugacy; (ii) novel cluster-matching algorithms suitable for cross-silo settings in which not every cluster appears in each local dataset; (iii) a number of inference strategies for the aggregation step, matched to different federated learning constraints; and (iv) guidelines for choosing among these in practice. A comprehensive simulation study validates the framework and allows us to compare to state-of-the-art federated learning alternatives. Notably, we show that when the composition of local datasets reflects the underlying clustering structure in the data, our approach can recover small clusters with greater accuracy than standard MCMC applied to the pooled data. We illustrate the framework on large-scale electronic health record data, identifying multi-morbidity patterns in a British geriatric population.

25.
arXiv (quant-ph) 2026-06-16

Complete Relational Description of Spin in a Quantum Background

arXiv:2606.15873v1 Announce Type: new Abstract: The standard description of the state of a spin in quantum mechanics presupposes externally fixed directions – a classical background. Can a spin be fully described instead in relation to other quantum mechanical systems? Poulin suggested twenty years ago group averaging over rotations the joint state of a fundamental spin and a reference spin with large angular momentum which, however, yields a classical bit in a probabilistic mixture. We revisit this idea and show that when the quantum reference system is augmented to two large spins, the standard quantum mechanical description of a spin is recovered in the limit of large quantum numbers for the reference system.