Ruixun Zhang

Minshuo Chen, Renyuan Xu, Yumin Xu et al.

Financial scenario simulation is essential for risk management and portfolio optimization, yet it remains challenging especially in high-dimensional and small data settings common in finance. We propose a diffusion factor model that integrates latent factor structure into generative diffusion processes, bridging econometrics with modern generative AI to address the challenges of the curse of dimensionality and data scarcity in financial simulation. By exploiting the low-dimensional factor structure inherent in asset returns, we decompose the score function--a key component in diffusion models--using time-varying orthogonal projections, and this decomposition is incorporated into the design of neural network architectures. We derive rigorous statistical guarantees, establishing nonasymptotic error bounds for both score estimation at O(d^{5/2} n^{-2/(k+5)}) and generated distribution at O(d^{5/4} n^{-1/2(k+5)}), primarily driven by the intrinsic factor dimension k rather than the number of assets d, surpassing the dimension-dependent limits in the classical nonparametric statistics literature and making the framework viable for markets with thousands of assets. Numerical studies confirm superior performance in latent subspace recovery under small data regimes. Empirical analysis demonstrates the economic significance of our framework in constructing mean-variance optimal portfolios and factor portfolios. This work presents the first theoretical integration of factor structure with diffusion models, offering a principled approach for high-dimensional financial simulation with limited data. Our code is available at https://github.com/xymmmm00/diffusion_factor_model.

Haoyang Cao, Jesse Hoekstra, Renyuan Xu et al.

Bi-causal optimal transport (OT) is a natural framework for comparing and coupling stochastic processes under nonanticipative information constraints, with important applications in robust finance, sequential uncertainty quantification, and multistage stochastic optimization. In particular, a learned bi-causal coupling naturally serves as a simulator for generating joint sample paths that respect both prescribed marginal laws and the underlying information flow. Its practical use, however, is limited by the computational difficulty of enforcing bi-causal coupling constraints over path space, especially for continuous distributions and long horizons. We develop a scalable stochastic-optimization framework for computing bi-causal OT couplings under general marginals. Our approach introduces a Kullback--Leibler (KL)-penalized relaxation that replaces hard marginal constraints with tractable divergence penalties while preserving the recursive structure of the problem. We establish dynamic programming principles for both the original and relaxed formulations, prove that the relaxed problem converges to the original bi-causal OT problem as the penalty grows, and derive explicit policy-gradient representations for the relaxed objective. Building on these results, we propose a practical policy-gradient algorithm with unbiased mini-batch estimators, variance reduction, and nonasymptotic regret guarantees. Numerical experiments show that the method accurately captures marginal laws and temporal dependence, and performs well in applications including robust subhedging and time series statistical downscaling. These results provide a scalable computational approach to bi-causal OT and broaden its applicability in settings where nonanticipative information constraints are essential.

Xinni Jiang, Zengsheng Kuang, Chunle Guo et al.

Guided depth super-resolution (GDSR) involves restoring missing depth details using the high-resolution RGB image of the same scene. Previous approaches have struggled with the heterogeneity and complementarity of the multi-modal inputs, and neglected the issues of modal misalignment, geometrical misalignment, and feature selection. In this study, we rethink some essential components in GDSR networks and propose a simple yet effective Dynamic Dual Alignment and Aggregation network (D2A2). D2A2 mainly consists of 1) a dynamic dual alignment module that adapts to alleviate the modal misalignment via a learnable domain alignment block and geometrically align cross-modal features by learning the offset; and 2) a mask-to-pixel feature aggregate module that uses the gated mechanism and pixel attention to filter out irrelevant texture noise from RGB features and combine the useful features with depth features. By combining the strengths of RGB and depth features while minimizing disturbance introduced by the RGB image, our method with simple reuse and redesign of basic components achieves state-of-the-art performance on multiple benchmark datasets. The code is available at https://github.com/JiangXinni/D2A2.

Yangxinyu Xie, Xiang Li, Tanwi Mallick et al.

Watermarking language models is essential for distinguishing between human and machine-generated text and thus maintaining the integrity and trustworthiness of digital communication. We present a novel green/red list watermarking approach that partitions the token set into ``green'' and ``red'' lists, subtly increasing the generation probability for green tokens. To correct token distribution bias, our method employs maximal coupling, using a uniform coin flip to decide whether to apply bias correction, with the result embedded as a pseudorandom watermark signal. Theoretical analysis confirms this approach's unbiased nature and robust detection capabilities. Experimental results show that it outperforms prior techniques by preserving text quality while maintaining high detectability, and it demonstrates resilience to targeted modifications aimed at improving text quality. This research provides a promising watermarking solution for language models, balancing effective detection with minimal impact on text quality.

Zixi Chen, Yumin Xu, Ruixun Zhang

The nonlinear two-time-scale stochastic approximation is widely studied under conditions of bounded variances in noise. Motivated by recent advances that allow for variability linked to the current state or time, we consider state- and time-dependent noises. We show that the Lyapunov function exhibits polynomial convergence rates in both cases, with the rate of polynomial delay depending on the parameters of state- or time-dependent noises. Notably, if the state noise parameters fully approach their limiting value, the Lyapunov function achieves an exponential convergence rate. We provide two numerical examples to illustrate our theoretical findings in the context of stochastic gradient descent with Polyak-Ruppert averaging and stochastic bilevel optimization.

Xin Guo, Binnan Wang, Ruixun Zhang et al.

Signatures are iterated path integrals of continuous and discrete-time processes, and their universal nonlinearity linearizes the problem of feature selection in time series data analysis. This paper studies the consistency of signature using Lasso regression, both theoretically and numerically. We establish conditions under which the Lasso regression is consistent both asymptotically and in finite sample. Furthermore, we show that the Lasso regression is more consistent with the Itô signature for time series and processes that are closer to the Brownian motion and with weaker inter-dimensional correlations, while it is more consistent with the Stratonovich signature for mean-reverting time series and processes. We demonstrate that signature can be applied to learn nonlinear functions and option prices with high accuracy, and the performance depends on properties of the underlying process and the choice of the signature.

Xian Fang, Jinchao Zhu, Ruixun Zhang et al.

Salient object detection is a fundamental topic in computer vision. Previous methods based on RGB-D often suffer from the incompatibility of multi-modal feature fusion and the insufficiency of multi-scale feature aggregation. To tackle these two dilemmas, we propose a novel multi-modal and multi-scale refined network (M2RNet). Three essential components are presented in this network. The nested dual attention module (NDAM) explicitly exploits the combined features of RGB and depth flows. The adjacent interactive aggregation module (AIAM) gradually integrates the neighbor features of high, middle and low levels. The joint hybrid optimization loss (JHOL) makes the predictions have a prominent outline. Extensive experiments demonstrate that our method outperforms other state-of-the-art approaches.