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01.
arXiv (CS.CL) 2026-06-15

Can Post-Training Turn LLMs into Good Medical Coders? An Empirical Study of Generative ICD Coding

Automated International Classification of Diseases (ICD) coding is a core medical-coding task for billing, epidemiology, and clinical decision support. Generative large language models (LLMs) are often reported as weak medical coders, but this finding mainly comes from inference-time settings such as prompting, retrieval, reranking, or tool use, leaving the role of task-specific post-training underexplored. We present a controlled empirical study of post-training for generative ICD coding, comparing discriminative baselines with LLM coders across prompting, supervised fine-tuning, and reinforcement learning under a common protocol and metric set. To our knowledge, this is the first study to evaluate RL-based post-training for generative LLM coders in ICD coding. We further introduce PHI, a diagnostic curriculum that extends GRPO to refine missed-code cases. Our results show that prompting-only evaluation substantially underestimates the potential of LLMs for ICD coding. SFT provides the main capability jump, GRPO further improves code-set prediction beyond SFT, and PHI provides targeted gains on macro-level performance. These findings suggest that the main bottleneck is not the generative formulation alone, but how the model is adapted and optimized for full-taxonomy recall. We release our code, data splits, and checkpoints at https://github.com/AlexandreWANG915/LLM4ICD.

02.
arXiv (quant-ph) 2026-06-16

Improved Cryogenic Photodiode Optical Biasing for Low-Noise and Low-Jitter Superconducting Nanowire Single-Photon Detectors

arXiv:2606.07140v2 Announce Type: replace Abstract: We experimentally demonstrate an improved optical biasing scheme for superconducting nanowire single-photon detectors (SNSPDs), which employs a cryogenic InGaAs-InP photodiode (PD) as a local bias source. It is found that, under illumination from a stable external light source, this PD generates a stable photocurrent in a cryogenic environment (~2.3 K), with fluctuations in the photocurrent primarily attributed to fluctuations in the incident optical power. Furthermore, by screening and effectively blocking stray photons leaking from the PD, which give rise to background dark counts, we have achieved an SNSPD exhibiting an ultra-low intrinsic dark count rate of 1e-4 cps. Utilizing this improved optical biasing technique, our SNSPD achieved performance comparable to that obtained under conventional electrical biasing: a system detection efficiency of 80.7%, a background dark count rate of 32.6 cps, and a minimum timing jitter of 57.5 ps. These results indicate that cryogenic-PD-based optical biasing serves as a viable, low-noise, and low-jitter alternative to traditional electrical biasing. Moreover, this work offers useful design guidance for the future development of PD-based low-noise bias sources and for the construction of all-photonic SNSPD systems tailored for high-precision quantum photonics applications.

03.
arXiv (quant-ph) 2026-06-11

Quantum Correlation Hierarchy and Teleportation in Dephased Hydrogen Hyperfine System

arXiv:2606.11731v1 Announce Type: new Abstract: We study the dynamics of quantum correlations in the hydrogen hyperfine spin system subject to Markovian phase noise. Treating the electron and proton spin degrees of freedom as an open two-qubit system governed by an isotropic hyperfine Hamiltonian and local dephasing, we obtain the exact time-dependent density matrix and derive analytical expressions for the full X-state family. We compute concurrence($C$), trace-distance measurement-induced nonlocality (Trace MIN–$\mathcal{N}_1$), and average steering coherence (ASC) in closed form and establish their strict ordering $ C(t)\leq \mathcal{N}_1(t)\leq \mathrm{ASC}(t) $ at all times. Entanglement is identified as the most fragile resource, undergoing sudden death at a finite time. Trace MIN exhibits dephasing-immune freezing for states with nonzero population imbalance, while ASC is the most robust quantity, persisting longest in every scenario studied.We additionally demonstrate that the dephased thermal hyperfine state serves as a resource for quantum teleportation, deriving a closed-form expression for the average fidelity and establishing that the teleportation advantage window coincides exactly with the entanglement survival interval, $\mathcal{F}_A > 2/3 \Longleftrightarrow \mathcal{C} > 0$, for the full X-state family with maximally mixed marginals. We identify four distinct dynamical regimes and map all three correlation measures onto directly measurable Pauli spin correlators, enabling experimental reconstruction of the full hierarchy without full state tomography.

04.
arXiv (math.PR) 2026-06-17

Time-dependent averages of a critical long-range stochastic heat equation

arXiv:2411.09058v2 Announce Type: replace Abstract: We study the time-dependent spatial averages of a critical stochastic partial differential equation, namely the stochastic heat equation in dimension $d\geq 3$ with noise white in time and colored in space with covariance kernel $\|\cdot\|^{-2}$. The solution to this SPDE is a singular measure and was constructed by Mueller and Tribe in [MT04]. We show that the time-dependent spatial averages of this SPDE over a ball of radius $R$ at time $t$ have different limits under different space-time scales. In particular, when $t\ll R^2$, the central limit theorem holds; when $t=R^2$, the spatial average is a non-Gaussian random variable; when $t\gg R^2$, the spatial average becomes extinct.

05.
arXiv (quant-ph) 2026-06-11

A quantum implementation of high-order power method for estimating geometric entanglement of pure states

arXiv:2405.19134v3 Announce Type: replace Abstract: Entanglement is one of the fundamental properties of a quantum state and is a crucial differentiator between classical and quantum computation. There are many ways to define entanglement and its measure, depending on the problem or application under consideration. Each of these measures may be computed or approximated by multiple methods. However, hardly any of these methods can be run on near-term quantum hardware. This work presents a quantum adaptation of the iterative high-order power method for estimating the geometric measure of entanglement of multi-qubit pure states using rank-1 tensor approximation. This method is executable on early fault-tolerant (hybrid) quantum hardware and does not depend on quantum memory. We simulate this algorithm and mitigate the effects of noise on the results of the computation using a theoretical model based on a known mitigation approach, which assumes a global depolarising noise channel.

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

Broadcast Product: Redefining Shape-aligned Element-wise Multiplication and Beyond

arXiv:2409.17502v2 Announce Type: replace Abstract: Broadcast operations are widely used in scientific computing libraries, yet their mathematical formulation is often implicit and inconsistently represented in machine learning literature. This problem frequently leads to invalid equations when element-wise products are written despite mismatched tensor shapes. In this paper, we formalize such operations by introducing the broadcast product $\boxdot$, which explicitly extends the Hadamard product through shape-aligned element duplication. We provide a rigorous definition of the broadcast product, analyze its algebraic properties, and show how it can be expressed using standard linear algebra. Building on this framework, we formulate least-squares problems and sketch a proof-of-concept broadcast decomposition. As a preliminary illustration, we show that the formalism enables a new family of decompositions with distinct structural properties from conventional tensor decompositions. This work establishes a mathematical foundation for broadcast-aware tensor operations, connecting practical implementations with rigorous tensor analysis.

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

Apparent Psychological Profiles of Large Language Models are Largely a Measurement Artifact

Psychological instruments designed for humans are increasingly used to assign large language models (LLMs) stable psychological profiles that affect their usability, safety assessment, and use as proxies for human participants in research. Using a formal psychometric framework, we show that these profiles are largely a measurement artifact. Administering a battery of personality and risk-preference instruments spanning self-reports and behavioral tasks to 56 instruction-tuned LLMs alongside large human reference samples, we report four findings. First, differences between models are driven not by the traits an instrument targets but by a directional response bias, a tendency to respond toward one end of the scale, or one labeled option, regardless of item content; a variance decomposition attributes 81-90% of between-model variation to this bias, against 9-16% in humans. Second, the bias declines with model capability but is not eliminated by it. Third, because bias rather than trait drives responding, an instrument's apparent reliability is almost entirely predicted by its response orthogonality, a term we coin for the proportion of items for which trait and bias point in opposite directions. Fourth, the profile a model appears to have shifts with the items used and can be manufactured through item selection. These results demonstrate that the apparent psychological profiles of LLMs are artifacts of the instrument used to measure them, not properties of the models themselves. As instruments borrowed from human psychology are rarely fully orthogonal and may inherently lack validity for LLMs, we call for dedicated assessments centered on response orthogonality.

08.
arXiv (CS.AI) 2026-06-19

Reinforcement-aware Knowledge Distillation for LLM Reasoning

arXiv:2602.22495v3 Announce Type: replace-cross Abstract: Reinforcement learning (RL) post-training has recently driven major gains in long chain-of-thought reasoning large language models (LLMs), but the high inference cost of such models motivates distillation into smaller students. Most existing knowledge distillation (KD) methods are designed for supervised fine-tuning (SFT), relying on fixed teacher traces or teacher-student Kullback-Leibler (KL) divergence-based regularization. When combined with RL, these approaches often suffer from distribution mismatch and objective interference: teacher supervision may not align with the student's evolving rollout distribution, and the KL regularizer can compete with reward maximization and require careful loss balancing. To address these issues, we propose RL-aware distillation (RLAD), which performs selective imitation during RL – guiding the student toward the teacher only when it improves the current policy update. Our core component, Trust Region Ratio Distillation (TRRD), replaces the teacher-student KL regularizer with a PPO/GRPO-style likelihood-ratio objective anchored to a teacher–old-policy mixture, yielding advantage-aware, trust-region-bounded distillation on student rollouts and naturally balancing exploration, exploitation, and imitation. Across diverse logic reasoning and math benchmarks, RLAD consistently outperforms offline distillation, standard GRPO, and KL-based on-policy teacher-student knowledge distillation.

09.
arXiv (CS.LG) 2026-06-15

Shuttling Compiler for Trapped-Ion Quantum Computers Based on Large Language Models

arXiv:2512.18021v3 Announce Type: replace-cross Abstract: We present the first shuttling compiler based on large language models (LLMs) for trapped-ion quantum computers, where qubits are shuttled between segments for gate execution and qubit storage. We fine-tune pre-trained LLMs on examples from linear and branched one-dimensional shuttling architectures. Thus, we obtain a layout-independent compilation strategy that learns the required shuttling operations directly from data. Using benchmark circuits with up to 16 qubits, such fine-tuned LLMs can now generate valid schedules for shuttling architectures. Notably, we also obtain a valid schedule for a previously unseen four-way junction layout. This demonstrates that trained LLMs can generalize to layouts not encountered during training. For various architectures, LLM-based schedules improve upon state-of-the-art baseline compiler results, reducing the shuttling effort by up to 15%.

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

Q-Learning with Fine-Grained Gap-Dependent Regret

arXiv:2510.06647v2 Announce Type: replace-cross Abstract: We study fine-grained gap-dependent regret bounds for model-free reinforcement learning in episodic tabular Markov Decision Processes. Existing model-free algorithms achieve minimax worst-case regret, but their gap-dependent bounds remain coarse and fail to fully capture the structure of suboptimality gaps. We address this limitation by establishing fine-grained gap-dependent regret bounds for both UCB-based and non-UCB-based algorithms. In the UCB-based setting, we develop a novel analytical framework that explicitly separates the analysis of optimal and suboptimal state-action pairs, yielding the first fine-grained regret upper bound for UCB-Hoeffding (Jin et al., 2018). To highlight the generality of this framework, we introduce ULCB-Hoeffding, a new UCB-based algorithm inspired by AMB (Xu et al.,2021) but with a simplified structure, which enjoys fine-grained regret guarantees and empirically outperforms AMB. In the non-UCB-based setting, we revisit the only known algorithm AMB, and identify two key issues in its algorithm design and analysis: improper truncation in the $Q$-updates and violation of the martingale difference condition in its concentration argument. We propose a refined version of AMB that addresses these issues, establishing the first rigorous fine-grained gap-dependent regret for a non-UCB-based method, with experiments demonstrating improved performance over AMB.

11.
arXiv (math.PR) 2026-06-16

The Ornstein$-$Uhlenbeck process on $\mathscr P_2$ with a volatility operator

arXiv:2606.14917v1 Announce Type: new Abstract: We analyze a diffusion ${(\mu_t)}_{t\geq 0}$ on the $2$-Wasserstein space $\mathscr P_2$ over $\mathbb R^d$ for which \begin{equation*} |\mu_t|_2^2-|\mu_0|_2^2-2ct+2\int_0 ^t|\mu_s|_2^2\,d s,\qquad t\geq 0, \end{equation*} is a martingale, where the constant $c\in(0,\infty)$ equals the trace of a volatility operator on a Hilbert space and $|\mu_t|_2:=(\int_{\mathbb R^d}x^T x\mu_t(d x ))^{1/2}$. The invariant measure of ${(\mu_t)}_{t\geq 0}$ is a Gaussian on $\mathscr P_2$, as introduced by P. Ren and F.-Y. Wang. Moreover, the Dirichlet form and its generator are given explicitly on a dense subspace of $L^2$.

12.
arXiv (math.PR) 2026-06-15

Scaling limits of multitype Bienaymé trees

arXiv:2507.23241v2 Announce Type: replace Abstract: We consider critical multitype Bienaymé trees that are either irreducible or possess a critical irreducible component with attached subcritical components. These trees are studied under two distinct conditioning frameworks: first, conditioning on the value of a linear combination of the numbers of vertices of given types; and second, conditioning on the precise number of vertices belonging to a selected subset of types. We prove that, under a finite exponential moment condition, the scaling limit as the tree size tends to infinity is given by the Brownian Continuum Random Tree. Additionally, we establish strong nonasymptotic tail bounds for the height of such trees. Our main tools include a flattening operation applied to multitype trees and sharp estimates regarding the structure of monotype trees with a given sequence of degrees.

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

The Stable Recovery Manifold: Geometric Principles Governing Recoverability in Continual Learning

arXiv:2606.13637v1 Announce Type: new Abstract: Catastrophic forgetting is often viewed as the destruction of previously learned knowledge during sequential learning. Building on the Accessibility Collapse framework, we investigate the geometric structure of recoverability in continual learning. Using Split CIFAR-100 and a sequentially trained ResNet-18, we analyze recoverability, representational drift, and recovery complexity across ten tasks. We introduce Recovery Subspace Dimensionality (k_t), a measure of the minimum number of singular directions required to preserve 90 percent of full probe performance. Contrary to our Recoverability Diffusion hypothesis, recovery dimensionality remains stable throughout training (mean k_t = 8.0) despite substantial representational drift. Principal-angle drift strongly predicts recoverability (r = -0.862), and a simple geometric model explains 82.2 percent of recoverability variance. These findings support the Stable Recovery Manifold hypothesis, suggesting that forgotten knowledge remains compactly decodable despite representational reorganization. The results indicate that catastrophic forgetting is primarily an accessibility and manifold-alignment problem rather than information destruction.

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

The Art of Mixology: Mixup-based Obfuscation for Privacy-Preserving Split Learning in Large Language Models

Split learning provides a practical paradigm for resource-constrained users to train Large Language Models (LLMs) by offloading computation-intensive layers to a server while keeping raw data local. However, existing privacy-preserving split learning methods still face a difficult trade-off among utility, privacy, efficiency, and stability. Specifically, these methods often suffer from substantial utility degradation, remain vulnerable to advanced data reconstruction attacks, incur prohibitive computational and communication overhead, or exhibit unstable performance across different tasks. In this paper, we propose MIXGUARD, a novel mixup-based privacy-preserving split learning framework for LLMs. MIXGUARD introduces token-level obfuscation, representation-level obfuscation, and adaptive gradient perturbation mechanisms, which operate jointly to preserve useful learning signals while preventing privacy leakage to the server. Technically, MIXGUARD first constructs a lightweight calibration model on a public dataset to refine the approximated target representation, and then applies this model during privacy-preserving fine-tuning on private data. We conduct extensive experiments on four classification tasks and four text generation tasks across multiple LLM families, model sizes, architectures, and fine-tuning strategies. The results show that MIXGUARD preserves model utility comparable to non-split training baselines, consistently achieves stronger privacy protection than existing split learning defense methods against state-of-the-art data reconstruction attacks, and remains robust under adaptive attack settings.

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

SP$^3$: Spherical Priors for Plug-and-Play Restoration

In this paper, we introduce SP$^3$, a novel Plug-and-Play algorithm that accelerates maximum a posteriori image restoration by replacing denoisers with Spherical Encoders (SE) as generative priors. SP$^3$ approximates the intractable proximal prior step by utilizing the SE tightly structured latent space as a robust projection onto the natural image manifold. Alternating this projection with a closed-form data-consistency step, via Half-Quadratic Splitting, achieves stable convergence without requiring gradient computation during inference. This unique formulation unlocks "anytime" restoration capabilities, producing sharp, plausible images from the first iteration. Evaluations across a variety of image restoration tasks demonstrate that SP$^3$ achieves perceptual quality comparable to state-of-the-art zero-shot diffusion and flow methods while being $3$-$630\times$ faster.

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

Enhancing Decision-Making with Large Language Models through Multi-Agent Fictitious Play

Large language model (LLM)-based multi-agent systems (MAS) have demonstrated great potential in solving tasks with execution complexity, by distributing subtasks across cooperative agents. However, this divide-and-conquer paradigm falls short on decision-making tasks that are also prevalent in the real world. These tasks require simultaneous reasoning from the stances of all involved stakeholders whose decisions are mutually dependent and thus cannot be solved in isolation. We characterize this challenge as stance entanglement, a form of decision complexity distinct from execution complexity. To address it, we propose Multi-Agent Fictitious Play (MAFP), a novel MAS paradigm that represents stakeholder stances as agents and formulates decision-making as an equilibrium-seeking process. Built on the game-theoretic principle of fictitious play, MAFP iteratively updates each agent's decision by best responding to the empirical mixture of other agents' past decisions. This enables agents to expose and address one another's weaknesses, progressively improving decision quality and robustness. We evaluate MAFP on challenging decision-making tasks that test the capability of deciding strategies for competitive scenarios prior to acting. MAFP outperforms both single-round and multi-round baselines on two complementary metrics, tournament strength and robustness, demonstrating its effectiveness in addressing stance entanglement.

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

Graph Reinforcement Learning for Calibration-Aware Quantum Circuit Routing

arXiv:2606.12816v1 Announce Type: cross Abstract: Quantum circuit routing is a key step in compiling programs for noisy intermediate-scale quantum processors. Routes that appear efficient by standard overhead metrics can still lose fidelity when they pass through poorly calibrated couplers. We study a calibration-aware graph reinforcement-learning router that uses same-day IBM Heron r2 calibration data to choose hardware-edge SWAPs. We train the policy with proximal policy optimization and evaluate it with exact simulated fidelity across nine Munich Quantum Toolkit (MQT) Bench circuits and three calibration snapshots. Across these evaluations, pooled mean exact fidelity is $0.727$, compared with $0.440$ for SABRE-best20 and $0.481$ for target-aware SABRE. Fidelity gains come with higher routed two-qubit counts and are concentrated in the 5q and 8q circuit families; under the fixed tree action graph, all 10q families favor SABRE-best20. Overall, our results show that calibration-aware learned routing can improve fidelity beyond gate-count-driven compilation.

18.
medRxiv (Medicine) 2026-06-17

High burden of subclinical TB in Africa revealed from a postmortem cohort.

Tuberculosis (TB) is increasingly recognised as a spectrum of infection and disease, yet the prevalence of viable, asymptomatic Mycobacterium tuberculosis (M.tb) infection remains uncertain. Subclinical Tuberculosis (scTB), defined as microbiologically confirmed M.tb infection in the absence of recognised symptoms, is under detected by symptom, sputum and imaging-based approaches. We conducted postmortem examinations of 94 adults who died from non-infectious causes, none of whom were clinically suspected of TB or reported TB related symptoms prior to death. Lung and extrapulmonary tissues were cultured for M.tb. Viable M.tb was confirmed in six individuals, corresponding to a prevalence of 6.4% (95% CI: 2.4 to 13.4%). These findings provide direct tissue-based evidence that viable, asymptomatic M.tb infection can persist beyond the reach of conventional clinical detection. Our data suggest that a biologically active reservoir of infection may exist undetected within high-burden settings, with implications for surveillance strategies aimed at TB elimination.

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

Learning Dynamics Reveal a Hierarchy of Weight-Induced Layerwise Gram Metrics

arXiv:2606.09744v3 Announce Type: replace Abstract: We study feed-forward ReLU networks with fixed readout and quadratic loss. The aim is to rewrite gradient descent not primarily as a dynamics in weight space, but as a collective dynamics closed in terms of fields defined on the training-set space. For a single hidden layer, the weight variables can be eliminated from the activation dynamics, yielding a closed equation for the residuals governed by a collective kernel that factorizes into an input-geometric matrix and a dynamical co-activation matrix. For deeper networks, the residual dynamics retains a clean layer-wise kernel structure. However, from depth three onward, closure requires a hierarchy of weight-induced Gram operators that mediate information transport across layers. Moreover, the conjugate-field dynamics is governed by operators satisfying a backward pullback recursion, of which the weight-induced Gram operators are the first nontrivial instances.

20.
PLOS Computational Biology 2026-06-22

<i>HoloBio</i>: A holographic microscopy tool for quantitative biological analysis

Authors:

by Waira Mona, Maria J. Gil-Herrera, Emanuel Mazo, Daniel Córdoba, Sofia Obando-Vasquez, Maria J. Lopera, Rene Restrepo, Carlos Trujillo, Ana Doblas, Raul Castaneda Holographic imaging in microscopy enables label-free quantitative information of biological specimens and has found applications across a wide range of biomedical studies, from cell morphology to particle dynamics; yet its widespread adoption is often limited by the lack of accessible and standardized analysis software. We present HoloBio, an open-source, Python-based graphical user interface developed to address this issue. This software offers two primary operational modes: a Real-Time mode that enables live processing of holograms at video frame rates, and an Offline mode designed for post-processing previously recorded holograms. HoloBio is compatible with holograms recorded using both lens-based and lensless systems, supporting off-axis architectures in telecentric and non-telecentric configurations, as well as slightly off-axis and in-line optical setups. The software incorporates tools for cell tracking, phase profiling, thickness estimation, and morphological analysis, including cell counting and object area quantification. HoloBio is designed to be accessible for users without coding expertise, offering a reproducible, high-throughput environment tailored for researchers in biology, biophotonics, and biomedical imaging.

21.
arXiv (CS.LG) 2026-06-12

A Stationary (and Therefore Compatible) Representation is All You Need

arXiv:2606.12488v1 Announce Type: new Abstract: Learning compatible representations aims to learn feature representations that can be used interchangeably over time whenever a model undergoes updates. In this paper, we demonstrate that stationary representations learned by d-Simplex fixed classifiers imply compatibility as in its formal definition. This result establishes a foundation for future works and can be directly exploited in practical learning scenarios. We address the challenge of learning compatibility using $d$-Simplex fixed classifiers when the model is sequentially fine-tuned. Learning according to a d-Simplex fixed classifier with the cross-entropy loss aligns feature distributions at the first-order statistics. Consequently, it may not fully capture higher-order dependencies in the representation between model updates. To address this issue, we demonstrate that training the model using a $d$-Simplex fixed classifier through a convex combination of the cross-entropy loss and a contrastive loss not only captures higher-order dependencies, but is also equivalent to learning with the cross-entropy under the compatibility constraints. We confirm our findings with extensive experiments also considering a new scenario where a pre-trained model is sequentially fine-tuned and occasionally replaced with an improved model. We show that stationary representations enable uninterrupted retrieval services (without reprocessing gallery images) while improving performance during model updates and replacements, achieving state-of-the-art. Code at https://github.com/miccunifi/iamcl2r.

22.
arXiv (math.PR) 2026-06-11

Feynman–Kac formula for the heat equation with a one-center point interaction in $d=3$

arXiv:2606.11677v1 Announce Type: new Abstract: We study Schrödinger operators with a one-center point interaction, formally defined by \begin{align*} -\Delta_\alpha=-\Delta+\alpha\,\delta_0(\cdot), \end{align*} for $\alpha\in\mathbb{R}$, and the associated heat equation \begin{align} \partial_t u=\tfrac{1}{2}\Delta_{\alpha} u,\quad u(0,x)=u_0(x)\in C_c^{\infty}(\mathbb{R}^3\setminus\{0\}).\label{eq:HEapp} \end{align} Here $\Delta$ denotes the Laplacian (self-adjoint on $L^2(\mathbb{R}^3)$) and $\delta_x$ the Dirac measure at $x$. The operator $-\Delta_\alpha$ can be realized either as a self-adjoint extension of $-\Delta|_{C_0^{\infty}(\mathbb{R}^3\setminus\{0\})}$ in $L^2(\mathbb{R}^3)$, or as the norm-resolvent limit of $-\Delta+\lambda_\varepsilon V(\cdot/\varepsilon)$ for suitable $\lambda_\varepsilon$ and $V:\mathbb{R}^3\to\mathbb{R}$. In this paper we construct, for each $t>0$ and $x\in\mathbb{R}^3\setminus\{0\}$, a probability law on path space and a normalizing function $G_t^\alpha(x)$ giving the following probabilistic representation of the solution to the associated equation: \begin{align*} u(t,x)=G_t^\alpha(x)\,\mathbb{E}\bigl[u_0\bigl(W^{t,x}(t)\bigr)\bigr], \end{align*} where $\{W^{t,x}(s):0\le s\le t\}$ is a continuous process depending on $(t,x,\alpha)$. The result provides a Feynman–Kac type formula for the heat equation with a one-point interaction in three dimensions.

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

Ride, Track, and Recover: Pilot Randomized Trial of a Wearable Digital Self-Management Intervention During a Veteran Endurance-Cycling Program

arXiv:2606.13529v1 Announce Type: cross Abstract: Post-traumatic stress disorder (PTSD) in veterans is characterized by persistent hyperarousal and comorbid anxiety and depressive symptoms that are difficult to monitor and manage outside clinical settings. Thirteen veterans participating in a Project Hero cycling event in Texas were randomized by computer-generated sequence in a naturalistic setting to two arms: (1) digital intervention plus physical activity, or (2) physical activity only, plus a third at-home monitoring control cohort consisting of 7 veterans selected from the broader Project Hero veteran community. Continuous smartwatch sensing combined heart rate and accelerometer features to detect hyperarousal events, which were confirmed in real time by participants. Weekly self-report measures of anxiety, depression, and PTSD severity were collected. Generalized additive mixed models characterized nonlinear trajectories over time. Baseline-normalized hyperarousal trajectories differed significantly across conditions, with the digital intervention group (n=7) showing structured stabilization compared to late-study escalation in the physical-only group (n=3). Both cycling groups exhibited acute symptom improvements during the endurance event; however, the digital intervention group demonstrated a higher overall maintenance of gains. The at-home control group (n=4) showed gradual symptom declines. Perceived precision of ML detections varied substantially across individuals and was positively associated with symptom severity, with higher-severity participants confirming a greater proportion of detected events. These results suggest that coupling wearable detection with digital self-management tools may support stabilization of hyperarousal and symptom improvement while emphasizing the importance of personalization and human-centered design in wearable mental health systems.

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

CausalT5k: Diagnosing Refusal and Failure Modes in Trustworthy Causal Reasoning Across Causal Rungs

arXiv:2602.08939v2 Announce Type: replace Abstract: Large language models increasingly produce fluent causal explanations, yet they often fail in ways aggregate accuracy cannot diagnose: confusing association with intervention, abandoning correct judgments under pressure, over-refusing valid claims, or answering when evidence is underdetermined. We introduce CTK, a diagnostic benchmark of 5,147 cases and growing, across 10 domains and all three levels of Pearl's Ladder of Causation. Unlike benchmarks that only score correctness, CTK reveals why a model failed by annotating causal rung, trap type, pressure sensitivity, refusal quality, and Utility-Safety tradeoffs. Its Sheep/Wolf taxonomy separates valid causal designs from inferential traps; paired neutral/pressure variants measure sycophantic drift through Bad Flip Rate; and Wise Refusal fields test whether a model identifies the missing information needed before endorsing a claim. CTK exposes failure modes hidden by aggregate accuracy: the Skepticism Trap, Rung Collapse under scaling, pressure-induced drift, Detection-Correction gaps, and counterfactual error modes. Rather than prescribing a correction method, it provides the diagnostic substrate for studying causal-reasoning failure profiles.