Bo Lin

Yingjing Xu, Jie Kong, Jiazhi Wang et al.

In this paper, we focus on the task of instruction-based image editing. Previous works like InstructPix2Pix, InstructDiffusion, and SmartEdit have explored end-to-end editing. However, two limitations still remain: First, existing datasets suffer from low resolution, poor background consistency, and overly simplistic instructions. Second, current approaches mainly condition on the text while the rich image information is underexplored, therefore inferior in complex instruction following and maintaining background consistency. Targeting these issues, we first curated the AdvancedEdit dataset using a novel data construction pipeline, formulating a large-scale dataset with high visual quality, complex instructions, and good background consistency. Then, to further inject the rich image information, we introduce a two-stream bridging mechanism utilizing both the textual and visual features reasoned by the powerful Multimodal Large Language Models (MLLM) to guide the image editing process more precisely. Extensive results demonstrate that our approach, InsightEdit, achieves state-of-the-art performance, excelling in complex instruction following and maintaining high background consistency with the original image.

Yige Yuan, Bingbing Xu, Bo Lin et al.

The generalization of neural networks is a central challenge in machine learning, especially concerning the performance under distributions that differ from training ones. Current methods, mainly based on the data-driven paradigm such as data augmentation, adversarial training, and noise injection, may encounter limited generalization due to model non-smoothness. In this paper, we propose to investigate generalization from a Partial Differential Equation (PDE) perspective, aiming to enhance it directly through the underlying function of neural networks, rather than focusing on adjusting input data. Specifically, we first establish the connection between neural network generalization and the smoothness of the solution to a specific PDE, namely "transport equation". Building upon this, we propose a general framework that introduces adaptive distributional diffusion into transport equation to enhance the smoothness of its solution, thereby improving generalization. In the context of neural networks, we put this theoretical framework into practice as $\textbf{PDE+}$ ($\textbf{PDE}$ with $\textbf{A}$daptive $\textbf{D}$istributional $\textbf{D}$iffusion) which diffuses each sample into a distribution covering semantically similar inputs. This enables better coverage of potentially unobserved distributions in training, thus improving generalization beyond merely data-driven methods. The effectiveness of PDE+ is validated through extensive experimental settings, demonstrating its superior performance compared to SOTA methods.

Bo Lin, Qianxiao Li, Weiqing Ren

The invariant distribution, which is characterized by the stationary Fokker-Planck equation, is an important object in the study of randomly perturbed dynamical systems. Traditional numerical methods for computing the invariant distribution based on the Fokker-Planck equation, such as finite difference or finite element methods, are limited to low-dimensional systems due to the curse of dimensionality. In this work, we propose a deep learning based method to compute the generalized potential, i.e. the negative logarithm of the invariant distribution multiplied by the noise. The idea of the method is to learn a decomposition of the force field, as specified by the Fokker-Planck equation, from the trajectory data. The potential component of the decomposition gives the generalized potential. The method can deal with high-dimensional systems, possibly with partially known dynamics. Using the generalized potential also allows us to deal with systems at low temperatures, where the invariant distribution becomes singular around the metastable states. These advantages make it an efficient method to analyze invariant distributions for practical dynamical systems. The effectiveness of the proposed method is demonstrated by numerical examples.