arXiv subjects

Kai Ren

Publications and source records attributed to Kai Ren.

At least 19 recordsLinked to original sources

arXiv2026

Enhancement of alpha-decay by positive hexadecapole deformation

Whether hexadecapole deformation ($\beta_4$) influences $\alpha$ decay remains controversial: machine-learning analyses suggest a strong link to cluster preformation, while empirical formulas find only marginal effects. We show that this discrepancy originates in the treatment of shell effects---without an explicit shell correction, residuals near magic numbers are absorbed into the deformation coefficients, obscuring the genuine $\beta_4$ dependence. Adding the inverse Casten factor $C_{pn}$, which encodes valence proton--neutron correlations relative to the nearest closed shells, and the parent-nucleus deformation $\beta_4^{(p)}$ to the Royer formula reduces the root-mean-square deviation from 0.309 to 0.184 for 192 even--even nuclei. The fitted negative $\beta_4^{(p)}$ coefficient shows that positive hexadecapole deformation systematically shortens half-lives, consistent with enhanced $\alpha$-cluster preformation at locally convex surface regions. For the $Z=94$ isotopic chain (Pu), where pronounced $\beta_4^{(p)}>0$ occurs, the original Royer formula overestimates half-lives by up to $\sim\!0.5$~dex, providing a clear, testable signature of this surface-preformation effect. The same correction also improves the UDL and yields predictions for 1060 even--even nuclei.

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arXiv2026

Extracting nuclear charge radii from binding energies: a single-parameter empirical formula with structural corrections

Nuclear binding energies and charge radii stem from the same underlying physics: saturation, isospin dependence, shell structure, and deformation. Binding-energy data therefore provide a natural constraint for charge-radius modeling. We propose a one-parameter charge-radius formula ($\mathrm{BECR}_\mathrm{1p}$) that combines binding-energy correlations with local structural corrections. On a curated set of 893 experimental charge radii, the macroscopic BECR term alone reproduces the leading charge-radius scale with a root-mean-square deviation (RMSD) of 0.0345 fm; adding shell, odd--even, finite-size, and deformation corrections further reduces the RMSD of BECR1p to 0.0138 fm. An anisotropic kernel ridge regression (AKRR) applied to the residuals further lowers the leave-one-out cross-validation RMSD to about 0.0081 fm. We use the formula to predict charge radii for 11205 nuclei across the nuclear chart.

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arXiv2026

Analytical penetration probability including the centrifugal potential: An improved Buck--Merchant--Perez model for alpha-decay half-lives

We derive a closed-form, non-perturbative WKB penetration formula for alpha-decay that explicitly incorporates the centrifugal potential within the Buck--Merchant--Perez (BMP) cluster model. The centrifugal term is shown to enhance the hindrance by effectively enlarging the barrier width: it pushes the outer turning point outward and, via the Bohr--Sommerfeld quantization condition, shifts the inner turning point inward. Building on this analytical result, we further develop an improved BMP model in which the nuclear potential depth is expressed as a unified four-parameter formula that simultaneously encodes shell corrections, odd-even pairing effects, and orbital-angular-momentum dependence. For 534 ground-state-to-ground-state alpha decays spanning Z = 60--118, the root-mean-square deviation of log base 10 T1/2 is reduced to 0.267, representing a 57% improvement over the original constant-depth BMP model (0.615), with robust performance for both favored (0.188) and unfavored (0.398) transitions. The framework is further applied to predict the half-lives of hitherto-unmeasured nuclei in the region Z = 117--120, providing quantitative benchmarks for future experimental investigations.

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arXiv2026

Probabilistic Recursively Feasible Motion Planning Under Uncertain Environments

Safe motion planning in uncertain, time-varying environments is challenging because the safe region can change unpredictably across planning steps, often causing a loss of recursive feasibility. In this work, we present a Probabilistic Recursively Feasible Model Predictive Control (PRF-MPC) framework that guarantees recursive feasibility with a specified probability. We introduce properties that an ideal predictor should satisfy to ensure distributional consistency, and use these properties to derive closed-form expressions for the means and covariances of trajectories predicted at future time steps. Building on this analysis, we construct safety constraints that ensure, with high probability, that the current safe set is contained within the safe sets at future time steps, thereby probabilistically guaranteeing recursive feasibility. Simulation results on a lane-change scenario demonstrate that the proposed method significantly improves recursive feasibility.

eess.SY↗

arXiv2026

Multi-Probe Zero Collision Hash (MPZCH): Mitigating Embedding Collisions and Enhancing Model Freshness in Large-Scale Recommenders

Embedding tables are critical components of large-scale recommendation systems, facilitating the efficient mapping of high-cardinality categorical features into dense vector representations. However, as the volume of unique IDs expands, traditional hash-based indexing methods suffer from collisions that degrade model performance and personalization quality. We present Multi-Probe Zero Collision Hash (MPZCH), a novel indexing mechanism based on linear probing that effectively mitigates embedding collisions. With reasonable table sizing, it often eliminates these collisions entirely while maintaining production-scale efficiency. MPZCH utilizes auxiliary tensors and high-performance CUDA kernels to implement configurable probing and active eviction policies. By retiring obsolete IDs and resetting reassigned slots, MPZCH prevents the stale embedding inheritance typical of hash-based methods, ensuring new features learn effectively from scratch. Despite its collision-mitigation overhead, the system maintains training QPS and inference latency comparable to existing methods. Rigorous online experiments demonstrate that MPZCH achieves zero collisions for user embeddings and significantly improves item embedding freshness and quality. The solution has been released within the open-source TorchRec library for the broader community.

cs.LG↗

arXiv2026

Dynamic Modeling, Parameter Identification and Numerical Analysis of Flexible Cables in Flexibly Connected Dual-AUV Systems

This research presents a dynamic modeling framework and parameter identification methods for describing the highly nonlinear behaviors of flexibly connected dual-AUV systems. The modeling framework is established based on the lumped mass method, integrating axial elasticity, bending stiffness, added mass and hydrodynamic forces, thereby accurately capturing the time-varying response of the forces and cable configurations. To address the difficulty of directly measuring material-related and hydrodynamic coefficients, this research proposes a parameter identification method that combines the physical model with experimental data. High-precision inversion of the equivalent Youngs modulus and hydrodynamic coefficients is performed through tension experiments under multiple configurations, effectively demonstrating that the identified model maintains predictive consistency in various operational conditions. Further numerical analysis indicates that the dynamic properties of flexible cable exhibit significant nonlinear characteristics, which are highly dependent on material property variations and AUV motion conditions. This nonlinear dynamic behavior results in two typical response states, slack and taut, which are jointly determined by boundary conditions and hydrodynamic effects, significantly affecting the cable configuration and endpoint loads. In this research, the dynamics of flexible cables under complex boundary conditions is revealed, providing a theoretical foundation for the design, optimization and further control research of similar systems.

cs.RO↗

arXiv2025

Unified Royer law revision for alpha-decay half-lives: shell corrections, pairing,and orbital-angular-momentum

The Royer law is a widely used empirical relation for calculating alpha-decay half-lives; however, it requires 12 parity-dependent parameters.It exhibits systematic deviations near the shell closure. We propose an improved Royer law by adding a shell-correction term, an odd-even pairing indicator, and an orbital-angular-momentum contribution. This unified framework reduces the number of free parameters to just four, leading to significant improvements in accuracy. The root-mean-square deviation across 550 experimental data points decreases from 0.520 to 0.279, corresponding to a 66.7% reduction in parameters and 46.3% improvement in accuracy. Using this refined formalism, we predict alpha-decay half-lives for superheavy nuclei with atomic numbers.

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arXiv2025

Identifying Time-varying Costs in Finite-horizon Linear Quadratic Gaussian Games

We address cost identification in a finite-horizon linear quadratic Gaussian game. We characterize the set of cost parameters that generate a given Nash equilibrium policy. We propose a backpropagation algorithm to identify the time-varying cost parameters. We derive a probabilistic error bound when the cost parameters are identified from finite trajectories. We test our method in numerical and driving simulations. Our algorithm identifies the cost parameters that can reproduce the Nash equilibrium policy and trajectory observations.

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arXiv2025

Massive Memorization with Hundreds of Trillions of Parameters for Sequential Transducer Generative Recommenders

Modern large-scale recommendation systems rely heavily on user interaction history sequences to enhance the model performance. The advent of large language models and sequential modeling techniques, particularly transformer-like architectures, has led to significant advancements recently (e.g., HSTU, SIM, and TWIN models). While scaling to ultra-long user histories (10k to 100k items) generally improves model performance, it also creates significant challenges on latency, queries per second (QPS) and GPU cost in industry-scale recommendation systems. Existing models do not adequately address these industrial scalability issues. In this paper, we propose a novel two-stage modeling framework, namely VIrtual Sequential Target Attention (VISTA), which decomposes traditional target attention from a candidate item to user history items into two distinct stages: (1) user history summarization into a few hundred tokens; followed by (2) candidate item attention to those tokens. These summarization token embeddings are then cached in storage system and then utilized as sequence features for downstream model training and inference. This novel design for scalability enables VISTA to scale to lifelong user histories (up to one million items) while keeping downstream training and inference costs fixed, which is essential in industry. Our approach achieves significant improvements in offline and online metrics and has been successfully deployed on an industry leading recommendation platform serving billions of users.

cs.IR↗

arXiv2025

Realizing Scaling Laws in Recommender Systems: A Foundation-Expert Paradigm for Hyperscale Model Deployment

Scaling laws have been established for recommender systems, yet efficiently deploying foundation model (FM) across multiple recommendation surfaces remains a major unsolved challenge. Existing methods for transfer learning face fundamental limitations in this setting: knowledge distillation suffers from transfer fidelity degradation in the large-data regime, and static user or item embeddings lack the expressiveness to capture contextualized user-item interactions. We propose the Foundation-Expert paradigm, where a central FM generates target-aware embeddings which are ingested by lightweight surface-specific expert models. Target-aware embeddings are representations that dynamically capture a user's interest in a specific item conditioned on their full interaction history. Unlike knowledge distillation, which transfers FM knowledge as soft labels, our approach provides these embeddings as input features to each expert model, enabling direct interaction with surface-specific representations. This paradigm achieves transfer ratios of 0.64--1.0 from FM to experts, substantially exceeding existing methods. Fully deployed at Meta serving tens of billions of daily requests since 2025, it delivers 0.050% statistically significant online topline metric improvement and 0.359% cumulative gains across multiple surfaces.

cs.IR↗

arXiv2025

Chance-Constrained Trajectory Planning with Multimodal Environmental Uncertainty

We tackle safe trajectory planning under Gaussian mixture model (GMM) uncertainty. Specifically, we use a GMM to model the multimodal behaviors of obstacles' uncertain states. Then, we develop a mixed-integer conic approximation to the chance-constrained trajectory planning problem with deterministic linear systems and polyhedral obstacles. When the GMM moments are estimated via finite samples, we develop a tight concentration bound to ensure the chance constraint with a desired confidence. Moreover, to limit the amount of constraint violation, we develop a Conditional Value-at-Risk (CVaR) approach corresponding to the chance constraints and derive a tractable approximation for known and estimated GMM moments. We verify our methods with state-of-the-art trajectory prediction algorithms and autonomous driving datasets.

cs.RO↗

arXiv2025

Chance-constrained Linear Quadratic Gaussian Games for Multi-robot Interaction under Uncertainty

We address safe multi-robot interaction under uncertainty. In particular, we formulate a chance-constrained linear quadratic Gaussian game with coupling constraints and system uncertainties. We find a tractable reformulation of the game and propose a dual ascent algorithm. We prove that the algorithm converges to a feedback generalized Nash equilibrium of the reformulated game, ensuring the satisfaction of the chance constraints. We test our method in driving simulations and real-world robot experiments. Our method ensures safety under uncertainty and generates less conservative trajectories than single-agent model predictive control.

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arXiv2024

MedSAM-U: Uncertainty-Guided Auto Multi-Prompt Adaptation for Reliable MedSAM

The Medical Segment Anything Model (MedSAM) has shown remarkable performance in medical image segmentation, drawing significant attention in the field. However, its sensitivity to varying prompt types and locations poses challenges. This paper addresses these challenges by focusing on the development of reliable prompts that enhance MedSAM's accuracy. We introduce MedSAM-U, an uncertainty-guided framework designed to automatically refine multi-prompt inputs for more reliable and precise medical image segmentation. Specifically, we first train a Multi-Prompt Adapter integrated with MedSAM, creating MPA-MedSAM, to adapt to diverse multi-prompt inputs. We then employ uncertainty-guided multi-prompt to effectively estimate the uncertainties associated with the prompts and their initial segmentation results. In particular, a novel uncertainty-guided prompts adaptation technique is then applied automatically to derive reliable prompts and their corresponding segmentation outcomes. We validate MedSAM-U using datasets from multiple modalities to train a universal image segmentation model. Compared to MedSAM, experimental results on five distinct modal datasets demonstrate that the proposed MedSAM-U achieves an average performance improvement of 1.7\% to 20.5\% across uncertainty-guided prompts.

cs.CV↗

arXiv2024

Recursively Feasible Chance-constrained Model Predictive Control under Gaussian Mixture Model Uncertainty

We present a chance-constrained model predictive control (MPC) framework under Gaussian mixture model (GMM) uncertainty. Specifically, we consider the uncertainty that arises from predicting future behaviors of moving obstacles, which may exhibit multiple modes (for example, turning left or right). To address the multi-modal uncertainty distribution, we propose three MPC formulations: nominal chance-constrained planning, robust chance-constrained planning, and contingency planning. We prove that closed-loop trajectories generated by the three planners are safe. The approaches differ in conservativeness and performance guarantee. In particular, the robust chance-constrained planner is recursively feasible under certain assumptions on the propagation of prediction uncertainty. On the other hand, the contingency planner generates a less conservative closed-loop trajectory than the nominal planner. We validate our planners using state-of-the-art trajectory prediction algorithms in autonomous driving simulators.

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arXiv2023

A New Causal Rule Learning Approach to Interpretable Estimation of Heterogeneous Treatment Effect

Interpretability plays a crucial role in the application of statistical learning to estimate heterogeneous treatment effects (HTE) in complex diseases. In this study, we leverage a rule-based workflow, namely causal rule learning (CRL), to estimate and improve our understanding of HTE for atrial septal defect, addressing an overlooked question in the previous literature: what if an individual simultaneously belongs to multiple groups with different average treatment effects? The CRL process consists of three steps: rule discovery, which generates a set of causal rules with corresponding subgroup average treatment effects; rule selection, which identifies a subset of these rules to deconstruct individual-level treatment effects as a linear combination of subgroup-level effects; and rule analysis, which presents a detailed procedure for further analyzing each selected rule from multiple perspectives to identify the most promising rules for validation. Extensive simulation studies and real-world data analysis demonstrate that CRL outperforms other methods in providing interpretable estimates of HTE, especially when dealing with complex ground truth and sufficient sample sizes.

cs.LG↗

arXiv2023

Uncertainty-informed Mutual Learning for Joint Medical Image Classification and Segmentation

Classification and segmentation are crucial in medical image analysis as they enable accurate diagnosis and disease monitoring. However, current methods often prioritize the mutual learning features and shared model parameters, while neglecting the reliability of features and performances. In this paper, we propose a novel Uncertainty-informed Mutual Learning (UML) framework for reliable and interpretable medical image analysis. Our UML introduces reliability to joint classification and segmentation tasks, leveraging mutual learning with uncertainty to improve performance. To achieve this, we first use evidential deep learning to provide image-level and pixel-wise confidences. Then, an Uncertainty Navigator Decoder is constructed for better using mutual features and generating segmentation results. Besides, an Uncertainty Instructor is proposed to screen reliable masks for classification. Overall, UML could produce confidence estimation in features and performance for each link (classification and segmentation). The experiments on the public datasets demonstrate that our UML outperforms existing methods in terms of both accuracy and robustness. Our UML has the potential to explore the development of more reliable and explainable medical image analysis models. We will release the codes for reproduction after acceptance.

cs.CV↗

arXiv2023

A novel integrated method of detection-grasping for specific object based on the box coordinate matching

To better care for the elderly and disabled, it is essential for service robots to have an effective fusion method of object detection and grasp estimation. However, limited research has been observed on the combination of object detection and grasp estimation. To overcome this technical difficulty, a novel integrated method of detection-grasping for specific object based on the box coordinate matching is proposed in this paper. Firstly, the SOLOv2 instance segmentation model is improved by adding channel attention module (CAM) and spatial attention module (SAM). Then, the atrous spatial pyramid pooling (ASPP) and CAM are added to the generative residual convolutional neural network (GR-CNN) model to optimize grasp estimation. Furthermore, a detection-grasping integrated algorithm based on box coordinate matching (DG-BCM) is proposed to obtain the fusion model of object detection and grasp estimation. For verification, experiments on object detection and grasp estimation are conducted separately to verify the superiority of improved models. Additionally, grasping tasks for several specific objects are implemented on a simulation platform, demonstrating the feasibility and effectiveness of DG-BCM algorithm proposed in this paper.

cs.RO↗

arXiv2023

SAM-U: Multi-box prompts triggered uncertainty estimation for reliable SAM in medical image

Recently, Segmenting Anything has taken an important step towards general artificial intelligence. At the same time, its reliability and fairness have also attracted great attention, especially in the field of health care. In this study, we propose multi-box prompts triggered uncertainty estimation for SAM cues to demonstrate the reliability of segmented lesions or tissues. We estimate the distribution of SAM predictions via Monte Carlo with prior distribution parameters, which employs different prompts as formulation of test-time augmentation. Our experimental results found that multi-box prompts augmentation improve the SAM performance, and endowed each pixel with uncertainty. This provides the first paradigm for a reliable SAM.

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