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

TA-RAG: Tone-Aware Retrieval-Augmented Generation for Peer-Support Health Communication

Retrieval-augmented generation (RAG) successfully grounds large language model (LLM) outputs in trusted documents, but factual grounding alone is insufficient for sensitive peer-support health communication. In domains such as HIV peer support, responses must also be accessible, stigma-free, empathetic, and tailored to the recipient. This paper presents TA-RAG, a lightweight, prompt-based tone-aware RAG framework that embeds explicit tone control into a RAG pipeline without requiring model fine-tuning. We operationalise tone across four core components: stigma-free rewriting, readability adjustment, recipient adaptation, and empathy rephrasing. We evaluate TA-RAG through component-level tests using questions derived from HIV Online Learning Australia (HOLA), UNAIDS terminology guidance, readability metrics, peer-support standards from National Association of People with HIV Australia (NAPWHA), and a public empathy dataset. Results show that the TA-RAG's components improve their targeted communication quality while preserving key content. These findings emphasise that prompt-based tone control is a potential direction for making RAG outputs suitable for sensitive peer-support health communication.

03.
arXiv (math.PR) 2026-06-16

A non-asymptotic bound on the TV distance between a Wishart matrix and an appropriately scaled GOE matrix

arXiv:2606.16018v1 Announce Type: new Abstract: In this note, we prove a non-asymptotic version of a theorem by Bubeck, Ding, Eldan, and Rácz, showing that a Wishart matrix is close in total variation to an affine transformation of a GOE matrix. The proof mirrors the proof given by Bubeck et al., with some changes made to make it non-asymptotic.

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

A Multi-level Analysis of Factors Associated with Student Performance: A Machine Learning Approach to the SAEB Microdata

arXiv:2510.22266v3 Announce Type: replace-cross Abstract: Identifying the factors that influence student performance in basic education is a central challenge for formulating effective public policies in Brazil. This study introduces a multi-level machine learning approach to classify the proficiency of 9th-grade and high school students using microdata from the System of Assessment of Basic Education (SAEB). Our model uniquely integrates four data sources: student socioeconomic characteristics, teacher professional profiles, school indicators, and principal management profiles. A comparative analysis of four ensemble algorithms confirmed the superiority of a Random Forest model, which achieved 90.2% accuracy and an Area Under the Curve (AUC) of 96.7%. To move beyond prediction, we applied Explainable AI (XAI) using SHAP, which revealed that the school's average socioeconomic level is the most dominant predictor, demonstrating that systemic factors have a greater impact than individual characteristics in isolation. The primary conclusion is that academic performance is a systemic phenomenon deeply tied to the school's ecosystem. This study provides a data-driven, interpretable tool to inform policies aimed at promoting educational equity by addressing disparities between schools.

05.
arXiv (CS.LG) 2026-06-19

Mask-Morph Graph U-Net: A Generalisable Mesh-Based Surrogate for Crashworthiness Field Prediction under Large Geometric Variation

arXiv:2605.15231v2 Announce Type: replace Abstract: Nonlinear finite element crash simulations are accurate but computationally expensive, limiting their use in iterative design optimisation. Machine-learning surrogate models based on graph neural networks (GNNs) offer a faster alternative. Message-passing GNNs are widely used for mesh simulation, and their shared node and edge update functions are relatively generalisable across varying graph structures. By contrast, non-shareable edge-specific aggregation layers can capture nonlinear relationships more accurately but usually require fixed graph connectivity, which limits generalisability. This paper presents Mask-Morph Graph U-Net (MMGUNet), a practical approach to addressing the limitation of hierarchical Graph U-Net architectures that use edge-specific downsampling and upsampling layers. Fixed coarse graph connectivity is required for edge-specific layers. To retain this while improving spatial correspondence, the proposed method morphs the coarsened graph hierarchy to each input mesh using feature-aligned barycentric parameterisation before constructing cross-graph edges. It further applies node masking during supervised pretraining, followed by parameter-efficient fine-tuning in which high-parameter edge-specific layers are frozen. The proposed approach is evaluated in in-distribution, out-of-distribution, and cross-component transfer settings using mean Euclidean distance and maximum intrusion percentage error. Results show that coarse-graph morphing improves test accuracy relative to a fixed-coarse-graph baseline, while masked supervised pretraining reduces the train-test discrepancy and improves data efficiency during transfer. The proposed model also achieves lower prediction error compared with external baselines. These results demonstrate a practical route toward reusable, data-efficient mesh-based surrogate modelling for crashworthiness design exploration.

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

Protein Design with Agent Rosetta: A Case Study for Specialized Scientific Agents

arXiv:2603.15952v2 Announce Type: replace Abstract: Large language models (LLMs) are capable of emulating reasoning and using tools, creating opportunities for autonomous agents that execute complex scientific tasks. Protein design provides a natural testbed: although machine learning (ML) methods achieve strong results, these are largely restricted to canonical amino acids and narrow objectives, leaving unfilled need for a generalist tool for broad design pipelines. We introduce Agent Rosetta, an LLM agent paired with a structured environment for operating Rosetta, the leading physics-based heteropolymer design software, capable of modeling non-canonical building blocks and geometries. Agent Rosetta iteratively refines designs to achieve user-defined objectives, combining LLM reasoning with Rosetta's generality. We evaluate Agent Rosetta on design with canonical amino acids, matching specialized models and expert baselines, and with non-canonical residues – where ML approaches fail – achieving comparable performance. Critically, prompt engineering alone often fails to generate Rosetta actions, demonstrating that environment design is essential for integrating LLM agents with specialized software. Our results show that properly designed environments enable LLM agents to make scientific software accessible while matching specialized tools and human experts.

07.
arXiv (CS.LG) 2026-06-17

Randomized Midpoint Method for Log-Concave Sampling under Constraints

arXiv:2405.15379v3 Announce Type: replace-cross Abstract: In this paper, we study the problem of sampling from log-concave distributions supported on convex and compact sets, with a particular focus on the randomized midpoint discretization of both overdamped and kinetic Langevin diffusions in constrained domains. We revisit the proximal framework for handling constraints through projection operators and develop a more general formulation that encompasses Euclidean, Bregman, and Gauge projections. The resulting smooth approximation allows a unified and tractable analysis of Langevin algorithms and their variants under constraints. Within this framework, we establish convergence guarantees in Wasserstein-$q$ $(q\geqslant 1)$ distances between the smooth surrogate and the target distribution. We further derive complementary lower bounds, showing that the results are near-optimal in order. Building upon this tight approximation analysis, we obtain new convergence guarantees for the randomized midpoint Langevin algorithms and refined bounds for both vanilla and kinetic Langevin Monte Carlo methods under constraints, thereby advancing the theoretical understanding of constrained diffusion-based sampling.

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

Discovering Subgroups with Exceptional Survival Characteristics

arXiv:2602.22179v2 Announce Type: replace Abstract: In many applications, it is important to identify subpopulations that survive longer or shorter than the rest of the population. In medicine, for example, it allows determining which patients benefit from treatment, and in predictive maintenance, which components are more likely to fail. Existing methods for discovering subgroups with exceptional survival characteristics rely on restrictive assumptions about the survival model (e.g. proportional hazards), require pre-discretized features, and, as they compare average statistics, tend to overlook individual heterogeneity. In this paper, we propose Sysurv, a non-parametric, fully differentiable method that discovers human-readable rules selecting subgroups with exceptional survival characteristics. Empirical evaluation on a wide range of datasets and settings, including a case study on cancer data, shows that Sysurv reveals insightful and actionable survival subgroups, outperforming the state of the art.

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

Adaptive Model-Predictive Control of a Soft Continuum Robot Using a Physics-Informed Neural Network Based on Cosserat Rod Theory

arXiv:2508.12681v3 Announce Type: replace-cross Abstract: Dynamic control of soft continuum robots (SCRs) holds great potential for expanding their applications, but remains a challenging problem due to the high computational demands of accurate dynamic models. While data-driven approaches like Koopman-operator-based methods have been proposed, they typically lack adaptability and cannot reconstruct the full robot shape, limiting their applicability. This work introduces a real-time-capable nonlinear model-predictive control (MPC) framework for SCRs based on a domain-decoupled physics-informed neural network (DD-PINN) with adaptable bending stiffness. The DD-PINN serves as a surrogate for the dynamic Cosserat rod model with a speed-up factor of up to 44,000. It is also used within an unscented Kalman filter for estimating the model states and bending compliance from end-effector position measurements. We implement a nonlinear evolutionary MPC running at 70 Hz on the GPU. In simulation, it demonstrates accurate tracking of dynamic trajectories and setpoint control with end-effector position errors below 3 mm (2.3\% of the actuator's length). In real-world experiments, the controller achieves similar accuracy and accelerations up to 3.55 m/s2.

12.
arXiv (CS.CV) 2026-06-16

CPS4: Class Prompt driven Semi-Supervised Spine Segmentation with Class-specific Consistency Constraint

Vision Language Model (VLM) has great potential to enhance the quality of pseudo labels in semi-supervised spine segmentation by leveraging textual class prompts to generate segmentation map, but no one has studied it yet. Although promising, it lacks explicit constraints to ensure consistency between spine class prompts and spine unit region, resulting in unsatisfactory performance in multi-class segmentation map generation. In this paper, we propose CPS4, the first text-guided semi-supervised spine segmentation network using class prompts to enhance the quality of spine pseudo labels. Specifically, CPS4 is implemented through two training stages. (i) Class-specific consistency constrained VLM pretraining stage: we propose token- and pixel-level attention loss to optimize the consistency between class prompts and spine units, forcing the textual class prompt to be closely coupled with the target spine unit in the semantic space. (ii) Class Prompt driven semi-supervised spine segmentation stage: using the pretrained vision-text encoder, we derive each class-specific binary segmentation map for the unlabeled spine image and integrate them into an unified multi-class segmentation map, improving the quality of the spine pseudo label generated by the semi-supervised spine segmentation network. Experimental results show that our CPS4 achieves superior spine segmentation performance with Dice of 80.44%, only using 5% labeled data on the public spine segmentation dataset, surpassing popular semi-supervised learning and VLM methods. Our code will be available.

13.
arXiv (math.PR) 2026-06-16

Purely unrectifiable sets, fractal percolation and graphs of functions

arXiv:2606.15745v1 Announce Type: cross Abstract: This paper contains a survey of some of the results of the author related to unrectifiablity and is an extended version of the author's talk given at the Second Winter School Geometric Measure Theory Rectifiability vs. Pure Unrectifiability in Hanghzou, China. These results include irregular/purely unrectifiable $1$-sets on the graphs of continuous functions like the Takagi, the Weierstrass-Cellerier and the typical (in the sense of Baire) continuous function. It is also discussed that there exists $ {\alpha}_{0}\alpha_0$. The background of the $1$-unrectifiability is discussed in more detail.

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

Oops, Wait: Discourse Tokens Matter in Reasoning Model

Recent studies suggest that even data-efficient training with ($\simeq$1K) reasoning trajectories can induce non-trivial reasoning capabilities in large language models through post-training. Such training corpora often contain iconic tokens such as "wait", "so", and "alternatively", which frequently appear in reasoning trajectories and may play a role in this process. This paper focuses on characterizing observable token-level patterns in post-training and a case study of how data-efficient supervised fine-tuning (SFT) differs from, and falls short of, large-scale post-training. To this end, we first identify tokens that correlate with correct answers along reasoning trajectories across models and training setups. We then focus on the distribution and (functional) roles of the "wait" token to primarily study the model trained in a data-efficient manner compared with the counterpart. Our study finds that discourse tokens are associated with correctness and a reasoning accuracy jump, even in data-efficient SFT. This suggests data-efficient SFT can partially reproduce discourse-token patterns to mimic meaningful reasoning behavior, but the patterns are less aligned with high-confidence answer transitions than those from large-scale post-training.

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

LooseControlVideo: Directorial Video Control using Spatial Blocking

Precise 3D spatial orchestration in text-to-video generation remains a significant challenge, particularly for multi-object scenes where semantic layout and temporal dynamics are often entangled. While existing depth-conditioned models achieve good structural fidelity, they necessitate dense, frame-accurate guidance that is labor-intensive to author for dynamic events involving deformable objects. We present LooseControlVideo, a framework that enables intuitive and expressive control by using sparse, oriented 3D boxes as a "blocking" proxy. This allows users to author high-level layout and trajectory while leveraging a video generative model to generate realistic occlusions, dynamics and interactions. We achieve this by fine-tuning a Wan 2.2 backbone on a video dataset annotated with DNOCS, a novel encoding for 3D size, orientation and depth-ordered occlusions. Furthermore, our method allows for localized refinement, such as adjusting a jump trajectory or adding an interaction, with minimal disruption to the global scene context. Extensive evaluations on the nuScenes, HO-3D, and BEHAVE benchmarks demonstrate that LooseControlVideo significantly outperforms existing 2D-box and flow-based baselines. Our findings indicate a 1.2x to 3x improvement in Trajectory Error; 2x improvement in Rigid Motion Consistency; and a 1.5x to 2x increase in Occlusion Accuracy over current state-of-the-art layout-conditioned models, demonstrating that oriented 3D primitives provide good geometric prior for complex, multi-agent video authoring.

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

UtVAA: Ultra-tiny Vision Transformer with Affix Attention for Mobile Image Classification

Vision Transformers (ViTs) have demonstrated strong representation capability in image classification. However, their quadratic self-attention complexity and large parameter counts limit deployment on resource-constrained mobile and edge devices. This paper introduces UtVAA, an ultra-tiny Vision Transformer architecture designed for efficient visual recognition under strict computational budgets. It incorporates a novel Affix Attention block that combines depthwise-pointwise local feature extraction, linear self-attention, coordinate attention for spatial dependency modelling, and a lightweight ternary fusion strategy to integrate local and global representations. In addition, Dilated Bottleneck blocks expand the receptive field using dilated depthwise separable convolutions while maintaining low FLOPs and stable optimisation through residual connections. UtVAA is implemented in scalable Tiny, Medium, and Large variants, with the smallest model containing 204.67K parameters and 53.95M FLOPs. Experimental results on CIFAR-10, CIFAR-100, PlantVillage-Tomato and SLIF-Tomato datasets show that UtVAA achieves competitive accuracy within a sub-million-parameter regime. Overall, the results demonstrate that transformer-based vision models can be redesigned into ultra-tiny architectures without significant loss in discriminative performance, making UtVAA suitable for mobile and edge deployment. Code is available at https://github.com/romiyal/UtVAA

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

Long-Context Modeling via GSS-Transformer Hybrid Architecture with Learnable Mixing

Modeling long-range dependencies remains a central challenge in natural language processing. Transformer architectures achieve strong performance via self-attention but scale quadratically ($O(N^2)$) with sequence length, while State Space Models (SSMs) scale linearly ($O(N)$) but suffer from a selective recall bottleneck, struggling to retrieve precise information from compressed states. This creates a fundamental tradeoff between efficiency and perplexity. To tackle these challenges, we propose the Parallel Hybrid Architecture (PHA), which runs Gated State Spaces (GSS), Grouped Query Attention (GQA), and Feed-Forward Networks (FFNs) as independent parallel branches fused by a learnable mixing mechanism. Instead of forcing SSMs to approximate attention or serializing the two paradigms, PHA allows each branch to specialize: GSS captures global context, while attention performs selective retrieval, with FFN providing complementary processing. On WikiText-103, PHA achieves 16.51 PPL at 125M parameters, outperforming Hedgehog (16.70) and H3-125M (23.70). Scaling to 180M parameters yields 16.42 PPL, which gives comparable results with the pure attention baseline while delivering 24\% higher throughput and up to 40\% lower memory usage at long contexts. On OpenWebText, our 125M model achieves 19.72 PPL, outperforming standard Transformers (20.60) and GSS hybrid baselines (19.80). These results demonstrate that separating sequence modeling paradigms into parallel specialists enables Transformer-level perplexity with substantially improved efficiency for long-context language modeling.

18.
medRxiv (Medicine) 2026-06-16

Adverse Childhood Experiences and Growth Outcomes in Childhood: A Longitudinal EHR-Based Study

Question Are adverse childhood experiences (ACEs) associated with altered growth trajectories in childhood? Findings In this cohort study of 412,549 children and adolescents, ACEs were associated with lower height throughout childhood, earlier pubertal timing, and shorter final stature. Height differences emerged approximately 2 years before ACE documentation and were greatest among those with earlier documentation. Meaning These findings suggest that early adversity affects physical growth in children and may serve as a measurable indicator of the biological consequences of early-life stress, especially in those with documentation of ACEs prior to the onset of typical pubertal growth. Importance Adverse childhood experiences (ACEs) are among the strongest risk factors for long-term mental and physical health complications, yet their impact on physical growth in childhood remains incompletely understood. Objective To determine the association of ACEs on childhood growth trajectories and growth dynamics. Design, Setting and Participants Retrospective cohort study using longitudinal electronic health record data. Data was collected from participants between February 1999 and August 2025. A large academic medical center biobank linked to deidentified electronic health records in the southeastern United States. A total of 412,549 individuals with at least 2 recorded height measurements between the ages of 2 and 20 were included in the primary analysis. Growth curve analyses were performed in a subset of 199,844 individuals with at least 3 height measurements spanning at least 2 years. Genetic analyses were performed in a subset of 10,114 individuals of primarily European ancestry. Exposure(s) Documented exposure to adverse childhood experiences before age 18 years identified through a natural language processing algorithm. Main Outcome(s) and Measure(s) Height-for-age z-scores across childhood, final attained height, and growth curve parameters estimated using SuperImposition by Translation and Rotation (SITAR) modeling. Results Among 412,549 participants, 18,502 (4.5%) had clinically documented ACEs during childhood. ACE documentation was associated with lower height-for-age z-scores throughout childhood and adolescence. Final attained height was significantly lower among ACE-documented individuals, with mean differences of -3.0 cm among males (174.0 cm vs 177.0 cm, p < 0.001) and -1.3 cm among females (161.8 cm vs 163.1 cm, p < 0.001). Height differences emerged approximately 2 years before clinical ACE documentation. Earlier age at first ACE documentation was associated with progressively shorter final attained height, with each year decrease in age at ACE documentation associated with a decrease in final height of -0.20 cm in females and -0.35 cm in males. Those with first ACE documented prior to pubertal age also showed the most pronounced growth dynamic differences, with males demonstrating a mean reduction in size of 5.25 cm (95% CI, -6.79 cm to -3.70 cm) and 1.26-year earlier pubertal timing (95% CI, -1.50 to -1.03 years), and females demonstrating a reduction in growth curve size of 3.62 cm (95% CI, -4.83 to -2.41 cm) and 1.14-year earlier pubertal timing (95% CI, -1.29 to -0.99 years). Conclusions and Relevance In this large clinical cohort, clinically documented ACEs were associated with time-dependent reductions in stature, earlier pubertal timing, and short final attained height. These findings suggest that early childhood adversity may have lasting effects on physical development and highlight growth trajectories as a potential marker of the biological consequences of early-life stress.

19.
arXiv (CS.LG) 2026-06-16

Closing the Approximation Gap in Simulation-free Latent SDEs

arXiv:2606.16138v1 Announce Type: cross Abstract: Recovering dynamical systems from noisy observations is a recurring challenge across scientific domains, including neuroscience and physics. Latent stochastic differential equations (SDEs) address this by modeling the system as an unobserved state that evolves according to a learnable SDE and generates the observations. Variational inference (VI) provides a tractable objective for fitting latent SDEs. Traditional VI algorithms evaluate this objective by numerical simulation over a time discretization, trading fidelity for computational cost. A recent class of algorithms, simulation-free VI, sidesteps this tradeoff by parameterizing the posterior through its instantaneous marginals rather than its drift. In this work, we show that the efficiency of existing simulation-free VI algorithms comes at a price: their parameterizations restrict the approximate posterior to a subset of the SDEs available to simulation-based methods, degrading posterior inference and parameter learning. We propose Helmholtz-SDE, a simulation-free VI algorithm that closes this gap by optimizing over path laws compatible with a prescribed collection of marginals. Helmholtz-SDE recovers dynamics more faithfully than prior simulation-free methods, with the largest gains under high posterior uncertainty. It further matches the performance of simulation-based VI at a fraction of the runtime.

20.
arXiv (quant-ph) 2026-06-11

Global vs. Local Discrimination of Locally Implementable Multipartite Unitaries

arXiv:2509.10430v2 Announce Type: replace Abstract: We study single-shot distinguishability of locally implementable multipartite unitaries under Local Operations and Classical Communication (LOCC) and global operations. As unitary discrimination depends on both the choice of probing states and the measurements on the evolved states, we classify LOCC and global distinguishability into two categories: adaptive strategies, where probing states are chosen based on measurement outcomes from other subsystems, and restricted strategies, where probing states remain fixed. Our findings uncover three surprising features in the bipartite setting and establish new structural limits for unitary discrimination: (i) Certain pairs of unitaries are globally distinguishable with restricted strategies but indistinguishable under LOCC, even with adaptive strategies. (ii) There exist sets of four unitaries that are distinguishable via LOCC, yet remain globally indistinguishable with restricted strategies. (iii) Some sets of unitaries are globally indistinguishable under adaptive strategies, when probed with separable states, but become distinguishable via LOCC.

21.
arXiv (CS.LG) 2026-06-16

SDVDiag: Multimodal Causal Discovery for Online Diagnosis in Software-defined Vehicles

arXiv:2606.15559v1 Announce Type: cross Abstract: The transition toward software-defined vehicles concentrates an increasing share of vehicle functionality into distributed software services, where failures propagate through service dependencies and the surface symptom is often several causal hops away from the underlying defect. Existing approaches to causal root-cause analysis in such systems address this only partially: they typically reason over a single observability modality and operate in an offline, operator-driven mode that does not match the demands of continuous vehicle operation. This paper presents SDVDiag, a multimodal causal-discovery pipeline that fuses log-based and metric-based service representations into a shared embedding space before graph construction, coupled with an anomaly-driven trigger that converts the diagnostic platform from a manually operated batch tool into a continuously running online system. Evaluation on an Autonomous Valet Parking testbed shows that the multimodal pipeline produces sparser causal graphs than a metrics-only baseline (134 vs. 182 edges on average) and consistently outperforms it in edge-weighted reward against an expert knowledge graph at every stage of human-feedback refinement, showing a 2.4-fold improvement over the baseline after 60 feedback queries. An end-to-end fault-injection scenario further demonstrates that the integrated trigger correctly recovers a true root cause located two causal hops upstream of the observable symptom.

22.
arXiv (CS.AI) 2026-06-11

Noise-Guided Transport for Imitation Learning

arXiv:2509.26294v2 Announce Type: replace-cross Abstract: We consider imitation learning in the low-data regime, where only a limited number of expert demonstrations are available. In this setting, methods that rely on large-scale pretraining or high-capacity architectures can be difficult to apply, and efficiency with respect to demonstration data becomes critical. We introduce Noise-Guided Transport (NGT), a lightweight off-policy method that casts imitation as an optimal transport problem solved via adversarial training. NGT requires no pretraining or specialized architectures, incorporates uncertainty estimation by design, and is easy to implement and tune. Despite its simplicity, NGT achieves strong performance on challenging continuous control tasks, including high-dimensional Humanoid tasks, under ultra-low data regimes with as few as 20 transitions.

23.
arXiv (CS.LG) 2026-06-18

Strategic Feature Selection

arXiv:2606.18867v1 Announce Type: new Abstract: When algorithmic predictors inform resource allocation in high-stakes domains such as healthcare, these predictors must account for strategic manipulation of input features. The typical solution is to redesign the predictor itself to explicitly account for strategic interactions. In practice, however, decision makers are often constrained to adjusting coarser levers within existing prediction pipelines. For example, healthcare organizations often select which features to exclude based on perceived manipulability, while using standard regularization procedures to shrink the coefficients of retained features. In this work, we initiate a formal study of strategic classification through feature selection and its interaction with ridge regularization. Our main finding is that excluding individual features based on their manipulability alone is generally suboptimal. We provide a fine-grained characterization of the performance of a feature subset under optimal regularization, yielding new insights for policy design. Motivated by this characterization, we develop a practical algorithm for jointly choosing the feature set and the level of ridge regularization. Through a real-world case study on a healthcare payments benchmark, we illustrate how our algorithm can guide the design of coarse policy levers in practice. Our results provide a principled, practical framework for mitigating the effects of strategic behavior in algorithmic decision-making systems.

24.
arXiv (math.PR) 2026-06-19

Model-independent upper bounds for the prices of Bermudan options with convex payoffs

arXiv:2503.13328v3 Announce Type: replace-cross Abstract: Suppose $\mu$ and $\nu$ are probability measures on $\mathbb{R}$ satisfying $\mu \leq_{cx} \nu$. Let $a$ and $b$ be convex functions on $\mathbb{R}$ with $a \geq b \geq 0$. We are interested in finding $$\sup_{\mathbf{M}} \sup_{\tau} \mathbb{E}^{\mathbf{M}} \left[ a(X) I_{ \{ \tau = 1 \} } + b(Y) I_{ \{ \tau = 2 \} } \right] $$ where the first supremum is taken over consistent models $\mathbf{M}$ (i.e., filtered probability spaces $(\Omega, \mathbf{F}, \mathbb{F}, \mathbb{P})$ such that $Z=(z,Z_1,Z_2)=(\int_{\mathbb{R}} x \mu(dx) = \int_{\mathbb{R}} y \nu(dy), X, Y)$ is a $(\mathbb{F},\mathbb{P})$ martingale, where $X$ has law $\mu$ and $Y$ has law $\nu$ under $\mathbb{P}$) and $\tau$ in the second supremum is a $(\mathbb{F},\mathbb{P})$-stopping time taking values in $\{1,2\}$. Our contributions are first to characterise and simplify the dual problem, and second to completely solve the problem under some structural assumptions on the measures $\mu$ and $\nu$ (namely that $\mu$ and $\nu$ are absolutely continuous probability measures that satisfy the Dispersion Assumption). A key finding is that the canonical set-up in which the filtration is that generated by $Z$ is not rich enough to define an optimal model and additional randomisation is required. This holds even though the marginal laws $\mu$ and $\nu$ are atom-free. The problem has an interpretation of finding the robust, or model-free, no-arbitrage bound on the price of a Bermudan option with two possible exercise dates, given the prices of co-maturing European options.

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

LLM-Aided Joint Secrecy Precoding and Trajectory for RSMA-Based Heterogeneous UAV Networks

arXiv:2507.17188v3 Announce Type: replace-cross Abstract: This paper investigates secure communications in rate-splitting multiple access (RSMA) enabled heterogeneous UAV networks, where multiple UAVs collaboratively serve ground terminals in the presence of eavesdroppers. By jointly considering secrecy rate maximization and propulsion energy consumption minimization, we formulate a multi-objective optimization problem involving UAV trajectory design, service association, power allocation, and secrecy precoding under mobility, collision-avoidance, service-capacity, and communication constraints. The formulated problem is highly non-convex due to the coupling among UAV trajectories, RSMA transmission variables, and secrecy constraints.To address the resulting non-convex and highly coupled optimization problem, we propose a hierarchical optimization framework. The inner layer uses a semidefinite relaxation (SDR)-based S2DC algorithm combining penalty functions and difference-of-convex (D.C.) programming to solve the secrecy precoding problem with fixed UAV positions. The outer layer introduces a Large Language Model (LLM)-guided heuristic multi-agent reinforcement learning approach (LLM-HeMARL) for trajectory optimization. LLM-HeMARL efficiently incorporates LLM-generated expert heuristic policy, enabling UAVs to learn energy-aware, security-driven trajectories without the inference overhead of real-time LLM calls. The simulation results show that our method outperforms existing baselines in secrecy rate and energy efficiency, with consistent robustness across varying UAV swarm sizes and random seeds.