arXiv subjects

Shengyan Li

Publications and source records attributed to Shengyan Li.

3 recordsLinked to original sources

arXiv2026

E$^3$mo-Bench: A Scalable Benchmark for Multimodal Evoked and Expressed Emotion Understanding via Bayesian Pairwise Alignment

Understanding both expressed and evoked emotions is critical for multimodal large language models (MLLMs) to achieve comprehensive affect-aware interactions. However, existing benchmarks typically examine expressed and evoked emotions in isolation or are constrained to coarse-grained and incomplete affective characterizations. To bridge this gap, we introduce E$^3$mo-Bench, a scalable benchmark comprising $12{,}314$ question-answer pairs across $2{,}524$ videos with predefined affective perspectives. It evaluates evoked and expressed emotion understanding via $3$ complementary tasks: emotion perception, open-vocabulary recognition, and valence-arousal-dominance (VAD) assessment. To efficiently scale reliable continuous annotations, we propose Bayesian Pairwise Alignment, which aggregates sparse, low-burden pairwise judgments into anchor-referenced VAD estimates. Furthermore, we develop E$^3$mo-Score, a training-free agent that aggregates complementary judgments from a five-model committee to improve VAD estimation. Extensive experiments validate the effectiveness of our framework and expose a pronounced performance skew between evoked and expressed emotion paradigms. These findings, coupled with MLLMs' persistent deficits in fine-grained recognition and dimensional assessment, chart a clear course for advancing multimodal emotional intelligence.

cs.CV↗

arXiv2025

Learning Singularity-Encoded Green's Functions with Application to Iterative Methods

Green's function provides an inherent connection between theoretical analysis and numerical methods for elliptic partial differential equations, and general absence of its closed-form expression necessitates surrogate modeling to guide the design of effective solvers. Unfortunately, numerical computation of Green's function remains challenging due to its doubled dimensionality and intrinsic singularity. In this paper, we present a novel singularity-encoded learning approach to resolve these problems in an unsupervised fashion. Our method embeds the Green's function within a one-order higher-dimensional space by encoding its prior estimate as an augmented variable, followed by a neural network parametrization to manage the increased dimensionality. By projecting the trained neural network solution back onto the original domain, our deep surrogate model exploits its spectral bias to accelerate conventional iterative schemes, serving either as a preconditioner or as part of a hybrid solver. The effectiveness of our proposed method is empirically verified through numerical experiments with two and four dimensional Green's functions, achieving satisfactory resolution of singularities and acceleration of iterative solvers.

math.NA↗

arXiv2024

Neural Green's Function Accelerated Iterative Methods for Solving Indefinite Boundary Value Problems

Neural operators, which learn mappings between the function spaces, have been applied to solve boundary value problems in various ways, including learning mappings from the space of the forcing terms to the space of the solutions with the substantial requirements of data pairs. In this work, we present a data-free neural operator integrated with physics, which learns the Green kernel directly. Our method proceeds in three steps: 1. The governing equations for the Green's function are reformulated into an interface problem, where the delta Dirac function is removed; 2. The interface problem is embedded in a lifted space of higher-dimension to handle the jump in the derivative, but still solved on a two-dimensional surface without additional sampling cost; 3. Deep neural networks are employed to address the curse of dimensionality caused by this lifting operation. The approximate Green's function obtained through our approach is then used to construct preconditioners for the linear systems allowed by its mathematical properties. Furthermore, the spectral bias of it revealed through both theoretical analysis and numerical validation contrasts with the smoothing effects of traditional iterative solvers, which motivates us to propose a hybrid iterative method that combines these two solvers. Numerical experiments demonstrate the effectiveness of our approximate Green's function in accelerating iterative methods, proving fast convergence for solving indefinite problems even involving discontinuous coefficients.

math.NA↗