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Danyu Yang

Publications and source records attributed to Danyu Yang.

18 recordsLinked to original sources
arXiv2026

Online Signature Verification Using Augmented Path Signature and T-Mamba

Handwritten signature verification is vital for personal authentication across commercial and financial applications. Although deep learning methods are widely adopted for online signature verification (OSV), they often struggle with capturing highly discriminative features and modelling long-range dependencies. To address these issues, we propose a novel framework that integrates the augmented path signature (APS) descriptor with the T-Mamba model. The APS descriptor first applies time and basepoint augmentations, then computes sliding-window path signatures. The path signature is a non-parametric feature map from rough path theory that effectively captures geometric structures and nonlinear inter-channel interactions. Inspired by the efficacy of state space models (SSMs) in sequence modelling, our T-Mamba model employs a hybrid design combining two temporal convolutional network (TCN) blocks with a time-scanning Mamba. This design enables the model to learn both local temporal patterns and global long-range dependencies, substantially improving verification accuracy. Our framework achieves state-of-the-art EERs on three public benchmark datasets (MCYT-100, SVC-2004 Task 2, DeepSignDB), validating its effectiveness and robustness, especially when the training data is limited. Our code is publicly available at https://github.com/DLRL04/OSV-using-APS-and-T-Mamba.

cs.LG↗
arXiv2026

Rotation-free Online Handwritten Character Recognition Using Linear Recurrent Units

Online handwritten character recognition leverages stroke order and dynamic features, which generally provide higher accuracy and robustness compared with offline recognition. However, in practical applications, rotational deformations can disrupt the spatial layout of strokes, substantially reducing recognition accuracy. Extracting rotation-invariant features therefore remains a challenging open problem. In this work, we employ the Sliding Window Path Signature (SW-PS) to capture local structural features of characters, and introduce the lightweight Linear Recurrent Units (LRU) as the classifier. The LRU combine the fast incremental processing capability of recurrent neural networks (RNN) with the efficient parallel training of state space models (SSM), while reliably modelling dynamic stroke characteristics. We conducted recognition experiments with random rotation angle up to $\pm 180^{\circ}$ on three subsets of the CASIA-OLHWDB1.1 dataset: digits, English upper letters, and Chinese radicals. The accuracies achieved after ensemble learning were $99.62\%$, $96.67\%$, and $94.33\%$, respectively. Experimental results demonstrate that the proposed SW-PS+LRU framework consistently surpasses competing models in both convergence speed and test accuracy.

cs.CV↗
arXiv2026

Integration of branched rough paths

When the one-form is $Lip\left(\gamma-1\right) $ with $\gamma >p\geq 1$, we construct the integral of a branched $p$-rough path, which defines another branched $p$-rough path. We derive a quantitative bound for this integral and prove that it depends continuously on the driving branched rough path in rough path metric. Moreover, we prove that the first level branched rough integral coincides with a first level integral of the associated $\Pi$-rough path.

math.PR↗
arXiv2023

Taylor estimate for differential equations driven by $\Pi $-rough paths

We obtain a remainder estimate for the truncated Taylor expansion for differential equations driven by weakly geometric $\Pi $-rough paths for $\Pi =\left( p_{1},\cdots ,p_{k}\right) $, $p_{i}\geq 1$. When there exists $ p\geq 1$ such that $p_{i}=pk_{i}^{-1}\ $for some $k_{i}\in \left\{ 1,\dots , \left[ p\right] \right\} $, we obtain a refined Taylor remainder estimate that contains a factorial decay component. The remainder estimates are in the right order as they are comparable to the next term in the Taylor expansion.

math.CA↗
arXiv2016

Integration of geometric rough paths

We build a connection between rough path theory and noncommutative algebra, and interpret the integration of geometric rough paths as an example of a non-abelian Young integration. We identify a class of slowly-varying one-forms, and prove that the class is stable under basic operations. In particular rough path theory is extended to allow a natural class of time varying integrands.

math.CA↗
arXiv2015

The theory of rough paths via one-forms and the extension of an argument of Schwartz to rough differential equations

We give an overview of the recent approach to the integration of rough paths that reduces the problem to classical Young integration. As an application, we extend an argument of Schwartz to rough differential equations, and prove the existence, uniqueness and continuity of the solution, which is applicable when the driving path takes values in nilpotent Lie group or Butcher group.

math.CA↗
arXiv2014

Integration of time-varying cocyclic one-forms against rough paths

We embed the rough integration in a larger geometrical/algebraic framework of integrating one-forms against group-valued paths, and reduce the rough integral to an inhomogeneous analogue of the classical Young integral. We define dominated paths as integrals of one-forms, and demonstrate that they are stable under basic operations.

math.CA↗
arXiv2014

The Signature of a Rough Path: Uniqueness

In the context of controlled differential equations, the signature is the exponential function on paths. B. Hambly and T. Lyons proved that the signature of a bounded variation path is trivial if and only if the path is tree-like. We extend Hambly-Lyons' result and their notion of tree-like paths to the setting of weakly geometric rough paths in a Banach space. At the heart of our approach is a new definition for reduced path and a lemma identifying the reduced path group with the space of signatures.

math.CA↗
arXiv2014

Rough differential equation in Banach space driven by weak geometric p-rough path

By using an explicit ordinary differential equation to approximate the exponential solution flow, we extend the universal limit theorem to rough differential equation in Banach space driven by weak geometric rough path, and give the quantitative dependence of solution in term of the initial value, vector field and driving rough path.

math.CA↗
arXiv2013

Dimension-free Euler estimates of rough differential equations

We give a dimension-free Euler estimation of solution of rough differential equations in term of the driving rough path. In the meanwhile, we prove that, the solution of rough differential equation is close to the exponential of a Lie series, with a concrete error bound.

math.CA↗
arXiv2013

On It\^o differential equation in rough path theory

The solution of rough differential equation, driven by the It\^o signature of a continuous local martingale, exists uniquely a.s. when the vector field is Lip(\beta) for \beta > 1, and coincides a.s. with the It\^o signature of the solution of parallel stochastic differential equation. Moreover, the It\^o solution can be recovered pathwisely by concatenating discounted Stratonovich solutions.

math.PR↗
arXiv2013

G-Brownian Motion as Rough Paths and Differential Equations Driven by G-Brownian Motion

The present paper is devoted to the study of sample paths of G-Brownian motion and stochastic differential equations (SDEs) driven by G-Brownian motion from the view of rough path theory. As the starting point, we show that quasi-surely, sample paths of G-Brownian motion can be enhanced to the second level in a canonical way so that they become geometric rough paths of roughness 2 < p < 3. This result enables us to introduce the notion of rough differential equations (RDEs) driven by G-Brownian motion in the pathwise sense under the general framework of rough paths. Next we establish the fundamental relation between SDEs and RDEs driven by G-Brownian motion. As an application, we introduce the notion of SDEs on a differentiable manifold driven by GBrownian motion and construct solutions from the RDE point of view by using pathwise localization technique. This is the starting point of introducing G-Brownian motion on a Riemannian manifold, based on the idea of Eells-Elworthy-Malliavin. The last part of this paper is devoted to such construction for a wide and interesting class of G-functions whose invariant group is the orthogonal group. We also develop the Euler-Maruyama approximation for SDEs driven by G-Brownian motion of independent interest.

math.PR↗
arXiv2012

Notes on area operator, geometric 2-rough paths and Young integral when p^-1+q^-1=1

1.When equipped with 2-rough norm and restricted to continuous paths with bounded variation, the area operator is a closable unbounded operator. 2.The area defined through Riemann-Stieltjes integral is the only possible candidate to enhance a path with vanishing 2-variation into a geometric 2-rough path. 3.Young integral is extended to p^-1+q^-1=1 by assigning a finer scale continuity.

math.CA↗