arXiv subjects

Shuhan Zhou

Publications and source records attributed to Shuhan Zhou.

10 recordsLinked to original sources

arXiv2026

Generalised stochastic curvature flow in $d \geq 2$, and sharp interface limit for the stochastic Allen-Cahn equation with nonlinear diffusion

We construct the local-in-time solution of the generalised anisotropic direction-dependent curvature flow in dimension $d \geq 2$ forced by a white-in-time and smooth-in-space Gaussian noise. This seems to be the first construction with a white-in-time noise which also allows spatial dependence, even in the simpler case of isotropic stochastic mean curvature flow. The main difficulty is that the stochastic PDE describing the flow has a multiplicative noise depending nonlinearly on both the solution and its gradient. The key technique is a transform developed in \cite{BKMZ20} based on rough characteristics that removes this rough multiplicative term. We also illustrate the relationship of this transform with previously known special situations. As an application of the construction, we show that in a short time interval, the sharp interface limit of the stochastic Allen-Cahn equation with nonlinear diffusion and the same noise (slightly smoothened in time) is given by the above direction-dependent stochastic curvature flow.

math.PR↗

arXiv2025

Interface fluctuations for $1$D stochastic Allen-Cahn equation -- singular regime

We study interface fluctuations for the $1$D stochastic Allen-Cahn equation perturbed by half a spatial derivative of the spacetime white noise. This half derivative makes the solution distribution-valued, so that proper renormalization is needed to make sense of the solution. We show that if the noise is sufficiently small, then an analogue of the classical results by \cite{Fun95,BBDMP98} holds in this singular regime. More precisely, for initial data close to the traveling wave solution of the deterministic equation, under proper long time scaling, the solution still stays close to the family of traveling waves, and the interface location moves according to an approximate diffusion process. There is one interesting difference between our singular regime and the classical situation: even if the solution and its approximate phase separation point are both well defined, the intended diffusion describing the movement of the canonical candidate of the phase point is not (even for fixed $\eps$). Two infinite quantities arise from the derivation of such an SDE, one due to singularity of the noise, and the other from renormalization. Magically, it turns out that they cancel out each other, thus making the derivation of the interface SDE valid in the $\eps \rightarrow 0$ limit.

math.PR↗

arXiv2024

MCTS: A Multi-Reference Chinese Text Simplification Dataset

Text simplification aims to make the text easier to understand by applying rewriting transformations. There has been very little research on Chinese text simplification for a long time. The lack of generic evaluation data is an essential reason for this phenomenon. In this paper, we introduce MCTS, a multi-reference Chinese text simplification dataset. We describe the annotation process of the dataset and provide a detailed analysis. Furthermore, we evaluate the performance of several unsupervised methods and advanced large language models. We additionally provide Chinese text simplification parallel data that can be used for training, acquired by utilizing machine translation and English text simplification. We hope to build a basic understanding of Chinese text simplification through the foundational work and provide references for future research. All of the code and data are released at https://github.com/blcuicall/mcts/.

cs.CL↗

arXiv2024

Interface fluctuations for $1$D stochastic Allen-Cahn equation revisited

We revisit the interface fluctuation problem for the $1$D Allen-Cahn equation perturbed by a small space-time white noise. We show that if the initial data is a standing wave solution to the deterministic equation, then under proper long time scale, the solution is still close to the family of traveling wave solutions. Furthermore, the motion of the interface converges to an explicit stochastic differential equation. This extends the classical result in \cite{Fun95} to full small noise regime, and recovers the result in \cite{BBDMP98}. The proof builds on the analytic framework in \cite{Fun95}. Our main novelty is the construction of a series of functional correctors that are designed to recursively cancel potential divergences. Moreover, to show these correctors are well-behaved, we develop a systematic decomposition of Fr\'echet derivatives of the deterministic Allen-Cahn flow of all orders. This decomposition is of its own interest, and may be useful in other situations as well.

math.PR↗

arXiv2023

I run as fast as a rabbit, can you? A Multilingual Simile Dialogue Dataset

A simile is a figure of speech that compares two different things (called the tenor and the vehicle) via shared properties. The tenor and the vehicle are usually connected with comparator words such as "like" or "as". The simile phenomena are unique and complex in a real-life dialogue scene where the tenor and the vehicle can be verbal phrases or sentences, mentioned by different speakers, exist in different sentences, or occur in reversed order. However, the current simile research usually focuses on similes in a triplet tuple (tenor, property, vehicle) or a single sentence where the tenor and vehicle are usually entities or noun phrases, which could not reflect complex simile phenomena in real scenarios. In this paper, we propose a novel and high-quality multilingual simile dialogue (MSD) dataset to facilitate the study of complex simile phenomena. The MSD is the largest manually annotated simile data ($\sim$20K) and it contains both English and Chinese data. Meanwhile, the MSD data can also be used on dialogue tasks to test the ability of dialogue systems when using similes. We design 3 simile tasks (recognition, interpretation, and generation) and 2 dialogue tasks (retrieval and generation) with MSD. For each task, we provide experimental results from strong pre-trained or state-of-the-art models. The experiments demonstrate the challenge of MSD and we have released the data/code on GitHub.

cs.CL↗

arXiv2023

Multi-Path Transformer is Better: A Case Study on Neural Machine Translation

For years the model performance in machine learning obeyed a power-law relationship with the model size. For the consideration of parameter efficiency, recent studies focus on increasing model depth rather than width to achieve better performance. In this paper, we study how model width affects the Transformer model through a parameter-efficient multi-path structure. To better fuse features extracted from different paths, we add three additional operations to each sublayer: a normalization at the end of each path, a cheap operation to produce more features, and a learnable weighted mechanism to fuse all features flexibly. Extensive experiments on 12 WMT machine translation tasks show that, with the same number of parameters, the shallower multi-path model can achieve similar or even better performance than the deeper model. It reveals that we should pay more attention to the multi-path structure, and there should be a balance between the model depth and width to train a better large-scale Transformer.

cs.CL↗

arXiv2022

ODE Transformer: An Ordinary Differential Equation-Inspired Model for Sequence Generation

Residual networks are an Euler discretization of solutions to Ordinary Differential Equations (ODE). This paper explores a deeper relationship between Transformer and numerical ODE methods. We first show that a residual block of layers in Transformer can be described as a higher-order solution to ODE. Inspired by this, we design a new architecture, {\it ODE Transformer}, which is analogous to the Runge-Kutta method that is well motivated in ODE. As a natural extension to Transformer, ODE Transformer is easy to implement and efficient to use. Experimental results on the large-scale machine translation, abstractive summarization, and grammar error correction tasks demonstrate the high genericity of ODE Transformer. It can gain large improvements in model performance over strong baselines (e.g., 30.77 and 44.11 BLEU scores on the WMT'14 English-German and English-French benchmarks) at a slight cost in inference efficiency.

cs.CL↗

arXiv2021

The NiuTrans Machine Translation Systems for WMT21

This paper describes NiuTrans neural machine translation systems of the WMT 2021 news translation tasks. We made submissions to 9 language directions, including English$\leftrightarrow$$\{$Chinese, Japanese, Russian, Icelandic$\}$ and English$\rightarrow$Hausa tasks. Our primary systems are built on several effective variants of Transformer, e.g., Transformer-DLCL, ODE-Transformer. We also utilize back-translation, knowledge distillation, post-ensemble, and iterative fine-tuning techniques to enhance the model performance further.

cs.CL↗

arXiv2021

ODE Transformer: An Ordinary Differential Equation-Inspired Model for Neural Machine Translation

It has been found that residual networks are an Euler discretization of solutions to Ordinary Differential Equations (ODEs). In this paper, we explore a deeper relationship between Transformer and numerical methods of ODEs. We show that a residual block of layers in Transformer can be described as a higher-order solution to ODEs. This leads us to design a new architecture (call it ODE Transformer) analogous to the Runge-Kutta method that is well motivated in ODEs. As a natural extension to Transformer, ODE Transformer is easy to implement and parameter efficient. Our experiments on three WMT tasks demonstrate the genericity of this model, and large improvements in performance over several strong baselines. It achieves 30.76 and 44.11 BLEU scores on the WMT'14 En-De and En-Fr test data. This sets a new state-of-the-art on the WMT'14 En-Fr task.

cs.CL↗

arXiv2019

A graph inequality on the common neighbourhood

In this note we prove a graph inequality based on the sizes of the common neighbourhoods. We also characterize the extremal graphs that achieve the equality. The result was first discovered as a consequence of the classical Forster's theorem in electric networks. We also present a short combinatorial proof that was inspired by a similar inequality related to the celebrated Turán's theorem.

math.CO↗