arXiv subjects

Lei Song

Publications and source records attributed to Lei Song.

At least 19 recordsLinked to original sources

arXiv2026

Syzygies of Polarized Abelian Surfaces: A Reider-Type Criterion

Let $(X,L)$ be a polarized complex abelian surface with $L^2=2d$. We establish a Reider-type criterion for Property $N_p$. If $d\geq7$, then $L$ satisfies Property $N_0$ if and only if there is no elliptic curve $E\subseteq X$ with $L\cdot E\leq2$, with one explicitly described exception. If $p\geq1$ and $d\geq(p+2)^2+1$, then $L$ satisfies Property $N_p$ if and only if there is no elliptic curve $E\subseteq X$ with $L\cdot E\leq p+2$. The numerical bounds on $d$ are optimal for $p=0,1$. These results improve upon earlier work of Küronya--Lozovanu, Ito, and Rojas. We also construct a polarized abelian surface whose basepoint-freeness threshold is irrational.

math.AG↗

arXiv2026

Rethinking Reward Models for Multi-Domain Test-Time Scaling

The reliability of large language models (LLMs) during test-time scaling is often assessed with \emph{external verifiers} or \emph{reward models} that distinguish correct reasoning from flawed logic. Prior work has studied both outcome reward models (ORMs), which assess only the final answer, and process reward models (PRMs), which score intermediate reasoning steps. Although PRMs are often viewed as advantageous due to their finer-grained supervision, much of the supporting evidence comes from math-adjacent settings, and their relative benefits across broader domains remain unclear. We present the first unified evaluation of four reward model variants, discriminative ORM and PRM (dORM, dPRM) and generative ORM and PRM (gORM, gPRM), across 14 diverse domains. Contrary to conventional wisdom, we find that (i) dORM performs on par with dPRM, (ii) gPRM is not competitive, and (iii) overall, gORM is the most robust, yielding significant and consistent gains across every tested domain. We attribute the worse performance of gPRM to the stepwise scoring process, which inherits label noise from LLM-based automatic labeling, leading to difficulties in evaluating long reasoning trajectories, including those involving self-correcting reasoning. Both our theoretical analysis and empirical observations indicate that stepwise aggregation compounds errors as reasoning length increases. These findings challenge the common assumption that fine-grained supervision is always better and support generative outcome verification for multi-domain deployment. Our \href{https://github.com/db-Lee/Multi-RM}{\underline{code}} is publicly available to facilitate future research in multi-domain settings.

cs.AI↗

arXiv2026

The integral closedness of lattice simplices with large lattice length

We prove that every $n$-dimensional lattice simplex $P$ whose lattice length $L(P)\ge n-1$ is integrally closed. As an application, we obtain a simple criterion for the projective normality of ample line bundles on $\mathbb{Q}$-factorial toric Fano varieties with Picard number one. We further obtain a refinement of this result in terms of the invariant $Γ_{P}$.

math.AG↗

arXiv2026

On Covering Simplices by Dilations in Dimensions 3 and 4

We propose a conjecture regarding the integrally closedness of lattice polytopes with large lattice lengths. We demonstrate that a lattice simplex in dimension 3 (resp. 4) with lattice length of at least 2 (resp. 3 and no edge has lattice length 5) can be covered by dilated simplices of the form $sQ$, where integer $s\ge 2$ (resp. 3) and $Q$ is a lattice simplex. The covering property implies these simplices are integrally closed. As an application, we obtain a simple criterion for the projective normality of ample line bundles on 3-(resp. 4-) dimensional $\mathbb{Q}$-factorial toric Fano varieties with Picard number one. Along the way, we discover certain unexpected phenomenon.

math.AG↗

arXiv2026

PBSD: Privileged Bayesian Self-Distillation for Long-Horizon Credit Assignment

Long-horizon agentic tasks pose a fundamental credit assignment challenge for outcome-base reinforcement learning: trajectory-level rewards verify final correctness but provide limited guidance on which intermediate reasoning steps or tool interactions contribute to the outcome. The difficulty is especially pronounced in multi-turn search agents, where successful trajectories may contain misleading actions and failed trajectories may contain valuable evidence-gathering steps. We propose PBSD (Privileged Bayesian Self-Distillation), a Bayes-calibrated self-distillation method for fine-grained credit assignment under sparse final rewards. PBSD measures trajectory quality through the posterior-to-prior probability ratio of the verified answer and applies Bayes' rule to convert this hard-to-estimate answer-side ratio into a tractable likelihood ratio between a standard student model and a privileged answer-conditioned teacher model. Autoregressive decomposition of this Bayesian evidence score yields turn-level signals that identify whether each intermediate turn supports or undermines the verified outcome. Consequently, PBSD provides a principled and elegant reweighting scheme that transforms sparse outcome supervision into Bayes-calibrated turn-level credit signals, while remaining fully compatible with standard policy optimization. Experiments demonstrate that PBSD consistently enhances performance across both in-domain and out-of-domain settings, and effectively transfers knowledge from short-context training to long-context inference, suggesting that its fine-grained credit assignment mechanism facilitates more effective policy learning and yields improved generalization.

cs.LG↗

arXiv2026

SurgAM: Surgical Affordance Map Prediction with Multimodal Feature Fusion for Robot Autonomy

Surgical automation is being increasingly studied, yet bridging visual scene understanding with autonomous action planning remains a fundamental challenge. While much research effort has been made on scene perception (e.g., tool recognition and scene segmentation), understanding and predicting actionable possibilities for surgical automation is still underexplored. In this paper, we introduce surgical affordance prediction, which identifies actionable regions for fundamental surgical actions from visual data. Specifically, a novel adaptive feature fusion framework is proposed that leverages the complementary strengths of a self-supervised vision transformer encoder for its superior semantic understanding and a large-scale generative model encoder for its spatially-aware capability. Furthermore, we introduce a hierarchical prompt learning mechanism to adapt to varying procedural contexts. Finally, a scene-guided attention decoder is proposed to focus on critical surgical areas while suppressing background distractions. To validate the effectiveness, we established a new dataset, derived from publicly available surgical datasets with affordance annotations for three basic surgical actions: aspiration, clipping, and retraction. Extensive experiments demonstrate that our approach achieves state-of-the-art performance. Moreover, we validate our framework's applicability for downstream automation on a realistic lung and prostate phantom, and results show that the predicted affordance maps successfully enable autonomous surgical actions.

cs.RO↗

arXiv2026

On Property $N_p$ of line bundles on smooth projective toric varieties

We establish a criterion for Property $N_p$ for line bundles on a class of smooth projective toric varieties. More precisely, we prove that if a smooth projective toric variety $X$ of dimension $n\ge2$ satisfies the uniform unimodularity condition and the Thomsen stratification intersection-number condition, then any line bundle $L$ on $X$ with $L\cdot C\ge n-1+p$ for every $T$-invariant curve $C$ satisfies Property $N_p$. We also show that these two conditions hold for several families of toric varieties and are preserved under finite products.

math.AG↗

arXiv2026

Experience-Evolving Multi-Turn Tool-Use Agent with Hybrid Episodic-Procedural Memory

As intents unfold and environments change, multi-turn agents face continuously shifting decision contexts. Although reusing past experience is intuitively appealing, existing approaches remain limited: full trajectories are often too context-specific to transfer, while tool-level reuse ignores the surrounding context and environment. In this paper, we introduce a hybrid episodic-procedural memory strategy (H-EPM) that enables experience-induced self-evolution of multi-turn tool-use policies by adaptively reusing partially overlapping successful experiences during both inference and training. Inspired by human episodic-procedural integration, we construct a tool graph from accumulated trajectories, where recurring tool-to-tool dependencies capture procedural routines and each edge is augmented with compact episodic summaries of relevant context. At inference time, the agent dynamically balances episodic recall for contextual reasoning with procedural execution for routine steps. Beyond inference, H-EPM introduces a memory-guided reinforcement learning paradigm that directly addresses a core challenge in multi-turn agent reinforcement learning, namely ineffective exploration over long trajectories. By biasing exploration toward historically successful tool transitions, H-EPM learns a stronger policy that generalizes at inference time without relying on domain-specific experience collection. Experiments show that H-EPM consistently delivers substantial inference-time gains over strong baselines across multi-turn tool-use benchmarks, reaching improvements of up to fifty percent. It also improves reinforcement learning policy performance, achieving gains of up to forty percent on out-of-distribution tasks.

cs.LG↗

arXiv2026

The Quality-Utility Paradox: Why High-Reward Data Impairs Small Model Mathematical Reasoning

Knowledge distillation from powerful reasoning models is widely used to improve Small Language Models (SLMs) on mathematical reasoning, often assuming that traces with higher reward model scores provide more useful supervision. We identify a counterintuitive \textbf{Quality-Utility Paradox} in mathematical reasoning distillation. Data refined or synthesized by a stronger Oracle obtains higher perceived quality according to reward models, yet consistently underperforms traces generated by the SLM itself and selected through rejection sampling across Qwen2.5, LLaMA-3, and DeepSeek families. Our analysis shows that Oracle refinement couples logical repair with distributional drift away from the SLM's native reasoning distribution. This drift increases the learner's adaptation cost and can outweigh the benefit of improved reasoning logic. To test this mechanism, we introduce \textbf{Style-Aligned Refinement}, which preserves the native trajectory of the SLM while retaining logical repair from the Oracle. This intervention lowers adaptation cost and restores downstream utility. These findings suggest that effective mathematical reasoning distillation should jointly optimize perceived solution quality and learner-data compatibility, rather than relying solely on reward-model scores. The datasets and code are available at https://github.com/Dracoqhl/Quality-Utility-Paradox.

cs.AI↗

arXiv2026

MedFeat: Model-Aware and Explainability-Driven Feature Engineering with LLMs for Clinical Tabular Prediction

In clinical tabular prediction, classical machine learning models with feature engineering often outperform neural methods. LLMs are increasingly used to automate this process, acting as domain experts that propose diverse feature transformations to boost downstream performance. However, existing LLM-based methods decouple feature generation from the downstream model: the LLM receives no signal about which features currently drive predictions or where the model's representational capacity falls short, so proposals are neither targeted to promising regions of the feature space nor tailored to the learner's inductive bias. This shortcoming is amplified in healthcare data, which simultaneously exhibits class imbalance, heterogeneous feature spaces, and strict interpretability requirements. In this paper, we propose MedFeat, the first feature engineering framework inspired by the workflow of machine learning practitioners, leveraging model-awareness and feature importance signals to iteratively guide feature discovery for clinical tabular learning. We evaluate MedFeat on a broad range of challenging real-world clinical tasks and show that it statistically significantly outperforms state-of-the-art baselines, with an average improvement of more than 10% over the baseline across models with distinct inductive biases.

cs.LG↗

arXiv2026

Finite-inertia effects in Langevin dynamics of a lopsided elastic dumbbell using exponential-time differencing schemes

Inertia effects in the Langevin dynamics of a lopsided elastic dumbbell are investigated using exponential-time-differencing (ETD) integrators for the corresponding stiff stochastic equations at small mass limit. Starting from the bead-level underdamped Langevin model, we formulate the dynamics in modal coordinates, highlighting two distinct friction scales: an additive friction $ζ_{\rm trans}=ζ_1+ζ_2$ controlling translation ($ζ_i, i=1,2$ are the friction factor on bead $i$), and an effective internal friction $1/ζ_{\rm eff}=1/ζ_1+1/ζ_2$ controlling configurational relaxation, with relaxation time $τ_R=ζ_{\rm eff}/H$ for a Hookean spring of stiffness $H$. We benchmark ETD against Euler--Maruyama and overdamped Brownian dynamics using equilibrium statistics, time-domain autocorrelations, and frequency-domain power spectra of the end-to-end vector. When time is rescaled by $τ_R$, configurational and orientational relaxation curves collapse across asymmetry ratios, showing that the dominant long-time structural dynamics remains close to the overdamped description. Inertial signatures are instead confined to short-time transients, high-frequency modifications of the configurational spectrum, and a transient coupling between translational and internal modes. This study provides a practical and accurate route for lopsided dumbbells across overdamped and weakly underdamped regimes, and clarify how mass and friction asymmetry affect the translational and internal dynamics.

cond-mat.soft↗

arXiv2026

Sample-efficient LLM Optimization with Reset Replay

Recent advancements in LLM post-training, particularly through reinforcement learning and preference optimization, are key to boosting their reasoning capabilities. However, these methods often suffer from low sample efficiency and a susceptibility to primacy bias, a phenomenon where overfitting to initial experiences diminishes network plasticity and damages the learning process. To address these challenges, we introduce LLM optimization with Reset Replay (LoRR), a general and powerful plugin for enhancing sample efficiency in preference-based optimization. Its core mechanism enables high-replay training to maximize the utility of each data batch. To mitigate overfitting, LoRR orchestrates a periodic reset strategy that reuses the initial data and policy to maintain network plasticity, and further adopts a hybrid optimization objective to better exploit training data. Extensive experiments show that LoRR significantly boosts the performance of various preference optimization methods on both mathematical and general reasoning benchmarks. Notably, an iterative DPO framework augmented with LoRR achieves comparable performance on challenging math tasks, rivaling many complex or computationally expensive baselines. Our findings highlight that LoRR offers a practical and sample-efficient paradigm from limited offline data, unlocking greater performance with minimal changes to existing post-training workflows.

cs.LG↗

arXiv2026

Time-RA: Towards Time Series Reasoning for Anomaly Diagnosis with LLM Feedback

Time series anomaly detection (TSAD) has traditionally focused on binary classification and often lacks the fine-grained categorization and explanatory reasoning required for transparent decision-making. To address these limitations, we propose Time-series Reasoning for Anomaly (Time-RA), a novel task that reformulates TSAD from a discriminative into a generative, reasoning-intensive paradigm. To facilitate this, we introduce RATs40K, the first real-world large-scale multimodal benchmark with ~40,000 samples across 10 domains, integrating raw time series, textual context, and visual plots with structured reasoning annotations. Extensive benchmarking shows that while supervised fine-tuning and visual representations boost diagnostic accuracy and reasoning consistency, performance varies across complex scenarios. Notably, fine-tuned models demonstrate strong "plug-and-play" transferability, outperforming traditional baselines on unseen real-world datasets. Our work establishes a foundation for interpretable, multimodal time series analysis. All code (https://github.com/yyysjz1997/Time-RA) and the RATs40K dataset (https://huggingface.co/datasets/Time-RA/RATs40K) are fully open-sourced to facilitate future research.

cs.LG↗

arXiv2026

Analytic Drift Resister for Non-Exemplar Continual Graph Learning

Non-Exemplar Continual Graph Learning (NECGL) seeks to eliminate the privacy risks intrinsic to rehearsal-based paradigms by retaining solely class-level prototype representations rather than raw graph examples for mitigating catastrophic forgetting. However, this design choice inevitably precipitates feature drift. As a nascent alternative, Analytic Continual Learning (ACL) capitalizes on the intrinsic generalization properties of frozen pre-trained models to bolster continual learning performance. Nonetheless, a key drawback resides in the pronounced attenuation of model plasticity. To surmount these challenges, we propose Analytic Drift Resister (ADR), a novel and theoretically grounded NECGL framework. ADR exploits iterative backpropagation to break free from the frozen pre-trained constraint, adapting to evolving task graph distributions and fortifying model plasticity. Since parameter updates trigger feature drift, we further propose Hierarchical Analytic Merging (HAM), performing layer-wise merging of linear transformations in Graph Neural Networks (GNNs) via ridge regression, thereby ensuring absolute resistance to feature drift. On this basis, Analytic Classifier Reconstruction (ACR) enables theoretically zero-forgetting class-incremental learning. Empirical evaluation on four node classification benchmarks demonstrates that ADR maintains strong competitiveness against existing state-of-the-art methods.

cs.LG↗

arXiv2026

In-Context Compositional Q-Learning for Offline Reinforcement Learning

Accurate estimation of the Q-function is a central challenge in offline reinforcement learning. However, existing approaches often rely on a shared global Q-function, which is inadequate for capturing the compositional structure of tasks that consist of diverse subtasks. We propose In-context Compositional Q-Learning (ICQL), an offline RL framework that formulates Q-learning as a contextual inference problem and uses linear Transformers to adaptively infer local Q-functions from retrieved transitions without explicit subtask labels. Theoretically, we show that, under two assumptions -- linear approximability of the local Q-function and accurate inference of weights from retrieved context -- ICQL achieves a bounded approximation error for the Q-function and enables near-optimal policy extraction. Empirically, ICQL substantially improves performance in offline settings, achieving gains of up to 16.4% on kitchen tasks and up to 8.8% and 6.3% on MuJoCo and Adroit tasks, respectively. These results highlight the underexplored potential of in-context learning for robust and compositional value estimation and establish ICQL as a principled and effective framework for offline RL.

cs.LG↗

arXiv2026

3DMedAgent: Unified Perception-to-Understanding for 3D Medical Analysis

3D CT analysis spans a continuum from low-level perception to high-level clinical understanding. Existing 3D-oriented analysis methods adopt either isolated task-specific modeling or task-agnostic end-to-end paradigms to produce one-hop outputs, impeding the systematic accumulation of perceptual evidence for downstream reasoning. In parallel, recent multimodal large language models (MLLMs) exhibit improved visual perception and can integrate visual and textual information effectively, yet their predominantly 2D-oriented designs fundamentally limit their ability to perceive and analyze volumetric medical data. To bridge this gap, we propose 3DMedAgent, a unified agent that enables 2D MLLMs to perform general 3D CT analysis without 3D-specific fine-tuning. 3DMedAgent coordinates heterogeneous visual and textual tools through a flexible MLLM agent, progressively decomposing complex 3D analysis into tractable subtasks that transition from global to regional views, from 3D volumes to informative 2D slices, and from visual evidence to structured textual representations. Central to this design, 3DMedAgent maintains a long-term structured memory that aggregates intermediate tool outputs and supports query-adaptive, evidence-driven multi-step reasoning. We further introduce the DeepChestVQA benchmark for evaluating unified perception-to-understanding capabilities in 3D thoracic imaging. Experiments across over 40 tasks demonstrate that 3DMedAgent consistently outperforms general, medical, and 3D-specific MLLMs, highlighting a scalable path toward general-purpose 3D clinical assistants.Code and data are available at \href{https://github.com/jinlab-imvr/3DMedAgent}{https://github.com/jinlab-imvr/3DMedAgent}.

cs.CV↗

arXiv2026

Diffusion Stabilizer Policy for Automated Surgical Robot Manipulations

Intelligent surgical robots have the potential to revolutionize clinical practice by enabling more precise and automated surgical procedures. However, the automation of such robot for surgical tasks remains under-explored compared to recent advancements in solving household manipulation tasks. These successes have been largely driven by (1) advanced models, such as transformers and diffusion models, and (2) large-scale data utilization. Aiming to extend these successes to the domain of surgical robotics, we propose a diffusion-based policy learning framework, called Diffusion Stabilizer Policy (DSP), which enables training with imperfect or even failed trajectories. Our approach consists of two stages: first, we train the diffusion stabilizer policy using only clean data. Then, the policy is continuously updated using a mixture of clean and perturbed data, with filtering based on the prediction error on actions. Comprehensive experiments conducted in various surgical environments demonstrate the superior performance of our method in perturbation-free settings and its robustness when handling perturbed demonstrations.

cs.RO↗

arXiv2026

SSP: Safety-guaranteed Surgical Policy via Joint Optimization of Behavioral and Spatial Constraints

The paradigm of robot-assisted surgery is shifting toward data-driven autonomy, where policies learned via Reinforcement Learning (RL) or Imitation Learning (IL) enable the execution of complex tasks. However, these ``black-box" policies often lack formal safety guarantees, a critical requirement for clinical deployment. In this paper, we propose the Safety-guaranteed Surgical Policy (SSP) framework to bridge the gap between data-driven generality and formal safety. We utilize Neural Ordinary Differential Equations (Neural ODEs) to learn an uncertainty-aware dynamics model from demonstration data. This learned model underpins a robust Control Barrier Function (CBF) safety controller, which minimally alters the actions of a surgical policy to ensure strict safety under uncertainty. Our controller enforces two constraint categories: behavioral constraints (restricting the task space of the agent) and spatial constraints (defining surgical no-go zones). We instantiate the SSP framework with surgical policies derived from RL, IL and Control Lyapunov Functions (CLF). Validation on in both the SurRoL simulation and da Vinci Research Kit (dVRK) demonstrates that our method achieves a near-zero constraint violation rate while maintaining high task success rates compared to unconstrained baselines.

cs.RO↗