arXiv subjects

Wenyuan Li

Publications and source records attributed to Wenyuan Li.

At least 37 records · Page 2Linked to original sources

arXiv2025

Mean Field Analysis of Mutual Insurance Market

A mutual insurance company (MIC) is a type of consumer cooperative owned by its policyholders. By purchasing insurance from an MIC, policyholders effectively become member-owners of the company and are entitled to a share of the surplus, which is determined by their own collective claims and premium contributions. This sharing mechanism creates an interactive environment in which individual insurance strategies are influenced by the actions of others. Given that mutual insurers account for nearly one-third of the global insurance market, the analysis of members' behavior under such a sharing mechanism is of both practical and theoretical importance. This article presents a first dynamic study of members' behavior in the prevalent mutual insurance market under the large-population limit. With members' wealth processes depending on the law of the insurance strategies, we model the surplus-sharing mechanism using an extended mean field game (MFG) framework and address the fundamental question of how strategic interactions in this setting influence individual decisions. Mathematically, we establish the global-in-time existence and uniqueness of the mean field forward-backward stochastic differential equation (MF-FBSDE) characterizing the Nash equilibrium strategy, employing techniques to accommodate realistic insurance constraints. Computationally, we develop a modified deep BSDE algorithm capable of solving the extended MFG problem with an additional fixed-point structure on the control. Utilizing this scheme, we examine how structural features of the MIC's design, such as the composition of risk classes and surplus-sharing proportions, reshape members' decisions and wealth through collective interactions, underscoring the central role of these mechanisms in MICs.

q-fin.RM↗

arXiv2025

EmbodiedBrain: Expanding Performance Boundaries of Task Planning for Embodied Intelligence

The realization of Artificial General Intelligence (AGI) necessitates Embodied AI agents capable of robust spatial perception, effective task planning, and adaptive execution in physical environments. However, current large language models (LLMs) and multimodal LLMs (MLLMs) for embodied tasks suffer from key limitations, including a significant gap between model design and agent requirements, an unavoidable trade-off between real-time latency and performance, and the use of unauthentic, offline evaluation metrics. To address these challenges, we propose EmbodiedBrain, a novel vision-language foundation model available in both 7B and 32B parameter sizes. Our framework features an agent-aligned data structure and employs a powerful training methodology that integrates large-scale Supervised Fine-Tuning (SFT) with Step-Augumented Group Relative Policy Optimization (Step-GRPO), which boosts long-horizon task success by integrating preceding steps as Guided Precursors. Furthermore, we incorporate a comprehensive reward system, including a Generative Reward Model (GRM) accelerated at the infrastructure level, to improve training efficiency. For enable thorough validation, we establish a three-part evaluation system encompassing General, Planning, and End-to-End Simulation Benchmarks, highlighted by the proposal and open-sourcing of a novel, challenging simulation environment. Experimental results demonstrate that EmbodiedBrain achieves superior performance across all metrics, establishing a new state-of-the-art for embodied foundation models. Towards paving the way for the next generation of generalist embodied agents, we open-source all of our data, model weight, and evaluating methods, which are available at https://zterobot.github.io/EmbodiedBrain.github.io.

cs.CV↗

arXiv2025

Hyperbolic Dataset Distillation

To address the computational and storage challenges posed by large-scale datasets in deep learning, dataset distillation has been proposed to synthesize a compact dataset that replaces the original while maintaining comparable model performance. Unlike optimization-based approaches that require costly bi-level optimization, distribution matching (DM) methods improve efficiency by aligning the distributions of synthetic and original data, thereby eliminating nested optimization. DM achieves high computational efficiency and has emerged as a promising solution. However, existing DM methods, constrained to Euclidean space, treat data as independent and identically distributed points, overlooking complex geometric and hierarchical relationships. To overcome this limitation, we propose a novel hyperbolic dataset distillation method, termed HDD. Hyperbolic space, characterized by negative curvature and exponential volume growth with distance, naturally models hierarchical and tree-like structures. HDD embeds features extracted by a shallow network into the Lorentz hyperbolic space, where the discrepancy between synthetic and original data is measured by the hyperbolic (geodesic) distance between their centroids. By optimizing this distance, the hierarchical structure is explicitly integrated into the distillation process, guiding synthetic samples to gravitate towards the root-centric regions of the original data distribution while preserving their underlying geometric characteristics. Furthermore, we find that pruning in hyperbolic space requires only 20% of the distilled core set to retain model performance, while significantly improving training stability. To the best of our knowledge, this is the first work to incorporate the hyperbolic space into the dataset distillation process. The code is available at https://github.com/Guang000/HDD.

cs.LG↗

arXiv2025

$C^0$-rigidity of Legendrians and coisotropics via sheaf quantization

We prove that in the standard cosphere bundle, for any contact homeomorphism in the closure of the compactly supported contactomorphism group, when the image of a coisotropic submanifold (not necessarily properly embedded) is smooth, it is still coisotropic. Moreover, when contactomorphisms in the sequence are in the identity component and the image of a Legendrian is smooth, the Maslov data is preserved, and the category of sheaves with singular support on the Legendrian and the microstalk corepresentative are also preserved (and thus so is the wrapped Floer cochains of the linking disks). The main ingredients are the result of Guillermou--Viterbo, a new sheaf quantization result for $C^0$-small contactomorphisms (not necessarily in the identity component) different from Guillermou--Kashiwara--Schapira, and continuity of the interleaving distance of sheaves with respect to the Hofer--Shelukhin distance and the $C^0$-distance. The appendix contains different arguments for local $C^0$-limits and certain Hausdorff limits of Legendrians without appealing to the interleaving distance.

math.SG↗

arXiv2025

Decompositions of augmentation varieties via weaves and rulings

The braid variety of a positive braid and the augmentation variety of a Legendrian link both admit decompositions coming from weaves and rulings, respectively. We prove that these decompositions agree under an isomorphism between the braid variety and the augmentation variety. We also prove that both decompositions coincide with a Deodhar decomposition and another decomposition coming from the microlocal theory of sheaves. Our proof relies on a detailed comparison between weaves and Morse complex sequences. Among other things, we show that the cluster variables of the maximal cluster torus of the augmentation variety can be computed from the Legendrian via Morse complex sequences.

math.SG↗

arXiv2025

Estimating Reeb chords using microlocal sheaf theory

We show that for a closed Legendrian submanifold in a 1-jet bundle, if there is a sheaf with compact support, perfect stalk and singular support on that Legendrian, then (1) the number of Reeb chords has a lower bound by half of the sum of Betti numbers of the Legendrian; (2) the number of Reeb chords between the original Legendrian and its Hamiltonian pushoff has a lower bound in terms of Betti numbers when the oscillation norm of the Hamiltonian is small comparing with the length of Reeb chords. In the proof we develop a duality exact triangle and use the persistence structure (which comes from the action filtration) of microlocal sheaves.

math.SG↗

arXiv2025

Periodic evaluation of defined-contribution pension fund: A dynamic risk measure approach

This paper introduces an innovative framework for the periodic evaluation of defined-contribution pension funds. The performance of the pension fund is evaluated not only at retirement, but also within the interim periods. In contrast to the traditional literature, we set the dynamic risk measure as the criterion and manage the tail risk of the pension fund dynamically. To effectively interact with the stochastic environment, a model-free reinforcement learning algorithm is proposed to search for optimal investment and insurance strategies. Using U.S. data, we calibrate pension members' mortality rates and enhance mortality projections through a Lee-Carter model. Our numerical results indicate that periodic evaluations lead to more risk-averse strategies, while mortality improvements encourage more risk-seeking behaviors.

q-fin.RM↗

arXiv2025

Fine-grained Hierarchical Crop Type Classification from Integrated Hyperspectral EnMAP Data and Multispectral Sentinel-2 Time Series: A Large-scale Dataset and Dual-stream Transformer Method

Fine-grained crop type classification serves as the fundamental basis for large-scale crop mapping and plays a vital role in ensuring food security. It requires simultaneous capture of both phenological dynamics (obtained from multi-temporal satellite data like Sentinel-2) and subtle spectral variations (demanding nanometer-scale spectral resolution from hyperspectral imagery). Research combining these two modalities remains scarce currently due to challenges in hyperspectral data acquisition and crop types annotation costs. To address these issues, we construct a hierarchical hyperspectral crop dataset (H2Crop) by integrating 30m-resolution EnMAP hyperspectral data with Sentinel-2 time series. With over one million annotated field parcels organized in a four-tier crop taxonomy, H2Crop establishes a vital benchmark for fine-grained agricultural crop classification and hyperspectral image processing. We propose a dual-stream Transformer architecture that synergistically processes these modalities. It coordinates two specialized pathways: a spectral-spatial Transformer extracts fine-grained signatures from hyperspectral EnMAP data, while a temporal Swin Transformer extracts crop growth patterns from Sentinel-2 time series. The designed hierarchical classification head with hierarchical fusion then simultaneously delivers multi-level crop type classification across all taxonomic tiers. Experiments demonstrate that adding hyperspectral EnMAP data to Sentinel-2 time series yields a 4.2% average F1-scores improvement (peaking at 6.3%). Extensive comparisons also confirm our method's higher accuracy over existing deep learning approaches for crop type classification and the consistent benefits of hyperspectral data across varying temporal windows and crop change scenarios. Codes and dataset are available at https://github.com/flyakon/H2Crop.

cs.CV↗

arXiv2025

Lagrangian cobordism and shadow distance in Tamarkin category

We study exact Lagrangian cobordisms between exact Lagrangians in a cotangent bundle in the sense of Arnol'd, using microlocal theory of sheaves. We construct a sheaf quantization for an exact Lagrangian cobordism between Lagrangians with conical ends, prove an iterated cone decomposition of the sheaf quantization for cobordisms with multiple ends, and show that the interleaving distance of sheaves is bounded by the shadow distance of the cobordism. Using the result, we prove a rigidity result on Lagrangian intersection by estimating the energy cost of splitting and connecting Lagrangians through cobordisms.

math.SG↗

arXiv2025

Duality and kernels in microlocal geometry

We study the dualizability of sheaves on manifolds with isotropic singular supports $\operatorname{Sh}_Λ(M)$ and microsheaves with isotropic supports $\operatorname{μsh}_Λ(Λ)$ and obtain a classification result of colimit-preserving functors by convolutions of sheaf kernels. Moreover, for sheaves with isotropic singular supports and compact supports $\operatorname{Sh}_Λ^b(M)_0$, the standard categorical duality and Verdier duality are related by the wrap-once functor, which is the inverse Serre functor in proper objects, and we thus show that the Verdier duality extends naturally to all compact objects $\operatorname{Sh}_Λ^c(M)_0$ when the wrap-once functor is an equivalence, for instance, when $Λ$ is a full Legendrian stop or a swappable Legendrian stop.

math.SG↗

arXiv2025

Kolmogorov Arnold Neural Interpolator for Downscaling and Correcting Meteorological Fields from In-Situ Observations

Obtaining accurate weather forecasts at station locations is a critical challenge due to systematic biases arising from the mismatch between multi-scale, continuous atmospheric characteristic and their discrete, gridded representations. Previous works have primarily focused on modeling gridded meteorological data, inherently neglecting the off-grid, continuous nature of atmospheric states and leaving such biases unresolved. To address this, we propose the Kolmogorov Arnold Neural Interpolator (KANI), a novel framework that redefines meteorological field representation as continuous neural functions derived from discretized grids. Grounded in the Kolmogorov Arnold theorem, KANI captures the inherent continuity of atmospheric states and leverages sparse in-situ observations to correct these biases systematically. Furthermore, KANI introduces an innovative zero-shot downscaling capability, guided by high-resolution topographic textures without requiring high-resolution meteorological fields for supervision. Experimental results across three sub-regions of the continental United States indicate that KANI achieves an accuracy improvement of 40.28% for temperature and 67.41% for wind speed, highlighting its significant improvement over traditional interpolation methods. This enables continuous neural representation of meteorological variables through neural networks, transcending the limitations of conventional grid-based representations.

cs.CV↗

arXiv2024

Optimal life insurance and annuity decision under money illusion

This paper investigates the optimal consumption, investment, and life insurance/annuity decisions for a family in an inflationary economy under money illusion. The family can invest in a financial market that consists of nominal bonds, inflation-linked bonds, and a stock index. The breadwinner can also purchase life insurance or annuities that are available continuously. The family's objective is to maximize the expected utility of a mixture of nominal and real consumption, as they partially overlook inflation and tend to think in terms of nominal rather than real monetary values. We formulate this life-cycle problem as a random horizon utility maximization problem and derive the optimal strategy. We calibrate our model to the U.S. data and demonstrate that money illusion increases life insurance demand for young adults and reduces annuity demand for retirees. Our findings indicate that the money illusion contributes to the annuity puzzle and highlights the role of financial literacy in an inflationary environment.

q-fin.PM↗

arXiv2024

Cerberus: Efficient Inference with Adaptive Parallel Decoding and Sequential Knowledge Enhancement

Large language models (LLMs) often face a bottleneck in inference speed due to their reliance on auto-regressive decoding. Recently, parallel decoding has shown significant promise in enhancing inference efficiency. However, we have identified two key issues with existing parallel decoding frameworks: (1) decoding heads fail to balance prediction accuracy and the parallelism of execution, and (2) parallel decoding is not a universal solution, as it can bring unnecessary overheads at some challenging decoding steps. To address these issues, we propose Cerberus, an adaptive parallel decoding framework introduces the gating mechanism to enable the LLMs to adaptively choose appropriate decoding approaches at each decoding step, along with introducing a new paradigm of decoding heads that introduce the sequential knowledge while maintaining execution parallelism. The experiment results demonstrate that the Cerberus can achieve up to 2.12x speed up compared to auto-regressive decoding, and outperforms one of the leading parallel decoding frameworks, Medusa, with a 10% - 30% increase in acceleration and superior generation quality.

cs.CL↗

arXiv2024

MambaDS: Near-Surface Meteorological Field Downscaling with Topography Constrained Selective State Space Modeling

In an era of frequent extreme weather and global warming, obtaining precise, fine-grained near-surface weather forecasts is increasingly essential for human activities. Downscaling (DS), a crucial task in meteorological forecasting, enables the reconstruction of high-resolution meteorological states for target regions from global-scale forecast results. Previous downscaling methods, inspired by CNN and Transformer-based super-resolution models, lacked tailored designs for meteorology and encountered structural limitations. Notably, they failed to efficiently integrate topography, a crucial prior in the downscaling process. In this paper, we address these limitations by pioneering the selective state space model into the meteorological field downscaling and propose a novel model called MambaDS. This model enhances the utilization of multivariable correlations and topography information, unique challenges in the downscaling process while retaining the advantages of Mamba in long-range dependency modeling and linear computational complexity. Through extensive experiments in both China mainland and the continental United States (CONUS), we validated that our proposed MambaDS achieves state-of-the-art results in three different types of meteorological field downscaling settings. We will release the code subsequently.

physics.ao-ph↗

arXiv2024

Relative Calabi-Yau structure on microlocalization

For an oriented manifold $M$ and a compact subanalytic Legendrian $Λ\subseteq S^*M$, we construct a canonical strong smooth relative Calabi--Yau structure on the microlocalization at infinity and its left adjoint $m_Λ^l: \operatorname{μsh}_Λ(Λ) \rightleftharpoons \operatorname{Sh}_Λ(M)_0 : m_Λ$ between compactly supported sheaves on $M$ with singular support on $Λ$ and microsheaves on $Λ$. We also construct a canonical strong Calabi-Yau structure on microsheaves $\operatorname{μsh}_Λ(Λ)$. Our approach does not require local properness and hence does not depend on arborealization. We thus obtain a canonical smooth relative Calabi-Yau structure on the Orlov functor for wrapped Fukaya categories of cotangent bundles with Weinstein stops, such that the wrap-once functor is the inverse dualizing bimodule.

math.SG↗

arXiv2024

Lagrangian cobordism functor in microlocal sheaf theory II

For an exact Lagrangian cobordism $L$ between Legendrians in $J^1(M)$ from $Λ_-$ to $Λ_+$ whose Legendrian lift is $\widetilde{L}$, we prove that sheaves in $Sh_{\widetilde{L}}(M \times \mathbb{R} \times \mathbb{R}_{>0})$ are equivalent to sheaves at the negative end $Sh_{Λ_-}(M \times \mathbb{R})$ together with the data of local systems $Loc({L})$ by studying sheaf quantizations for general noncompact Lagrangians. Thus we interpret the Lagrangian cobordism functor between $Sh_{Λ_\pm}(M \times \mathbb{R})$ as a correspondence parametrized by $Loc({L})$. This enables one to consider generalizations to immersed Lagrangian cobordisms. We also prove that the Lagrangian cobordism functor is action decreasing and recover results on the lengths of embedded Lagrangian cobordisms. Finally, using the construction of Courte-Ekholm, we obtain a family of Legendrians with sheaf categories Morita equivalent to chains of based loop spaces of the Lagrangian fillings.

math.SG↗

arXiv2024

Existence of generating families on Lagrangian cobordisms

For an embedded exact Lagrangian cobordism between Legendrian submanifolds in the 1-jet bundle, we prove that a generating family linear at infinity on the Legendrian at the negative end extends to a generating family linear at infinity on the Lagrangian cobordism after stabilization if and only if the formal obstructions vanish. In particular, a Lagrangian filling with trivial stable Lagrangian Gauss map admits a generating family linear at infinity.

math.SG↗

arXiv2024

Spherical adjunction and Serre functor from microlocalization

For a subanalytic Legendrian $Λ\subseteq S^{*}M$, we prove that when $Λ$ is either swappable or a full Legendrian stop, the microlocalization at infinity $m_Λ: \operatorname{Sh}_Λ(M) \rightarrow \operatorname{μsh}_Λ(Λ)$ is a spherical functor, and the spherical cotwist is the Serre functor on the subcategory $\operatorname{Sh}_Λ^b(M)_0$ of compactly supported sheaves with perfect stalks. This is a sheaf theory counterpart (with weaker assumptions) of the results on the cap functor and cup functors between Fukaya categories. When proving spherical adjunction, we deduce the Sato-Sabloff fiber sequence and construct the Guillermou doubling functor for any Reeb flow.

math.SG↗