arXiv subjects

Yumeng Ren

Publications and source records attributed to Yumeng Ren.

5 recordsLinked to original sources

arXiv2026

Adaptively trained Physics-informed Radial Basis Function Neural Networks for Solving Multi-asset Option Pricing Problems

The present study investigates the numerical solution of Black-Scholes partial differential equation (PDE) for option valuation with multiple underlying assets. We develop a physics-informed (PI) machine learning algorithm based on a radial basis function neural network (RBFNN) that concurrently optimizes the network architecture and predicts the target option price. The physics-informed radial basis function neural network (PIRBFNN) combines the strengths of the traditional radial basis function collocation method and the physics-informed neural network machine learning approach to effectively solve PDE problems in the financial context. By employing a PDE residual-based technique to adaptively refine the distribution of hidden neurons during the training process, the PIRBFNN facilitates accurate and efficient handling of multidimensional option pricing models featuring non-smooth payoff conditions. The validity of the proposed method is demonstrated through a set of experiments encompassing a single-asset European put option, a double-asset exchange option, and a four-asset basket call option.

cs.LG↗

arXiv2025

Pusa V1.0: Unlocking Temporal Control in Pretrained Video Diffusion Models via Vectorized Timestep Adaptation

The rapid advancement of video diffusion models has been hindered by fundamental limitations in temporal modeling, particularly the rigid synchronization of frame evolution imposed by conventional scalar timestep variables. While task-specific adaptations and autoregressive models have sought to address these challenges, they remain constrained by computational inefficiency, catastrophic forgetting, or narrow applicability. In this work, we present \textbf{Pusa} V1.0, a versatile model that leverages \textbf{vectorized timestep adaptation (VTA)} to enable fine-grained temporal control within a unified video diffusion framework. Note that VTA is a non-destructive adaptation, which means that it fully preserves the capabilities of the base model. Unlike conventional methods like Wan-I2V, which finetune a base text-to-video (T2V) model with abundant resources to do image-to-video (I2V), we achieve comparable results in a zero-shot manner after an ultra-efficient finetuning process based on VTA. Moreover, this method also unlocks many other zero-shot capabilities simultaneously, such as start-end frames and video extension -- all without task-specific training. Meanwhile, it keeps the T2V capability from the base model. Mechanistic analyses also reveal that our approach preserves the foundation model's generative priors while surgically injecting temporal dynamics, avoiding the combinatorial explosion inherent to the vectorized timestep. This work establishes a scalable, efficient, and versatile paradigm for next-generation video synthesis, democratizing high-fidelity video generation for research and industry alike.

cs.CV↗

arXiv2025

Improving Diffusion Generative Models via Truncated Karhunen--Lo\`eve Expansion

Pretrained diffusion models exhibit a well-known training-sampling mismatch, often attributed to exposure bias and related distribution-shift effects. We provide a quantitative interpretation of this phenomenon through the notion of an effective noise level: empirically, a pretrained denoiser behaves as if trained at a noise level slightly below the nominal schedule. Motivated by this observation, we introduce a training-free sampling strategy based on truncating the Karhunen--Lo\`eve (KL) expansion of the Brownian motion driving the forward stochastic differential equation. Truncation yields a finite-dimensional forward process with a reduced noise level that can be adjusted independently of the time discretization. We prove uniform convergence of the truncated process to the original diffusion. To explain the resulting behaviour, we analyse a toy model in which the denoiser is exact but operates at a reduced effective noise level. The analysis predicts a non-monotone response to the sampling noise with a unique interior optimum, located by a one-dimensional sweep over the truncation order. We implement the approach through corresponding truncated reverse-time and probability-flow equations, without modifying the network architecture. Across CIFAR-10, CelebA, ImageNet, and latent-space Stable Diffusion, the truncation order consistently reveals a sweet spot, improving pretrained models in nearly all tested configurations. Training from scratch at a matched truncation order makes that order the network's own sweet spot, accelerates convergence by about $2.8\times$, and lowers the generation error on CIFAR-10 (Fr\'echet Inception Distance 7.14 to 5.47 at matched epochs; best checkpoint 6.74 to 5.23). A L\'evy--Ciesielski comparison confirms that finite expansion is broadly beneficial.

cs.CV↗

arXiv2024

Redefining Temporal Modeling in Video Diffusion: The Vectorized Timestep Approach

Diffusion models have revolutionized image generation, and their extension to video generation has shown promise. However, current video diffusion models~(VDMs) rely on a scalar timestep variable applied at the clip level, which limits their ability to model complex temporal dependencies needed for various tasks like image-to-video generation. To address this limitation, we propose a frame-aware video diffusion model~(FVDM), which introduces a novel vectorized timestep variable~(VTV). Unlike conventional VDMs, our approach allows each frame to follow an independent noise schedule, enhancing the model's capacity to capture fine-grained temporal dependencies. FVDM's flexibility is demonstrated across multiple tasks, including standard video generation, image-to-video generation, video interpolation, and long video synthesis. Through a diverse set of VTV configurations, we achieve superior quality in generated videos, overcoming challenges such as catastrophic forgetting during fine-tuning and limited generalizability in zero-shot methods.Our empirical evaluations show that FVDM outperforms state-of-the-art methods in video generation quality, while also excelling in extended tasks. By addressing fundamental shortcomings in existing VDMs, FVDM sets a new paradigm in video synthesis, offering a robust framework with significant implications for generative modeling and multimedia applications.

cs.CV↗

arXiv2022

$\ell_1$DecNet+: A new architecture framework by $\ell_1$ decomposition and iteration unfolding for sparse feature segmentation

$\ell_1$ based sparse regularization plays a central role in compressive sensing and image processing. In this paper, we propose $\ell_1$DecNet, as an unfolded network derived from a variational decomposition model incorporating $\ell_1$ related sparse regularization and solved by scaled alternating direction method of multipliers (ADMM). $\ell_1$DecNet effectively decomposes an input image into a sparse feature and a learned dense feature, and thus helps the subsequent sparse feature related operations. Based on this, we develop $\ell_1$DecNet+, a learnable architecture framework consisting of our $\ell_1$DecNet and a segmentation module which operates over extracted sparse features instead of original images. This architecture combines well the benefits of mathematical modeling and data-driven approaches. To our best knowledge, this is the first study to incorporate mathematical image prior into feature extraction in segmentation network structures. Moreover, our $\ell_1$DecNet+ framework can be easily extended to 3D case. We evaluate the effectiveness of $\ell_1$DecNet+ on two commonly encountered sparse segmentation tasks: retinal vessel segmentation in medical image processing and pavement crack detection in industrial abnormality identification. Experimental results on different datasets demonstrate that, our $\ell_1$DecNet+ architecture with various lightweight segmentation modules can achieve equal or better performance than their enlarged versions respectively. This leads to especially practical advantages on resource-limited devices.

eess.IV↗