Robust Few-Shot Online Signature Verification via Bi-Directional-Guided Fusion and Padding-Aware Attention

Abstract

Online signature verification (OSV) remains challenging under few-shot enrollment and multi-posture conditions, where limited reference samples and writing variations increase intra-writer variability and degrade verification performance. Existing methods often rely on simple feature concatenation and insufficiently exploit interactions between global statistical and temporal dynamic representations, while attention mechanisms in variable-length sequences may be affected by invalid padded regions. To address these limitations, this study introduces FT-Transformer, a hybrid CNN–Transformer framework for few-shot online signature verification. The model jointly encodes 18-dimensional local dynamic descriptors and 51-dimensional global statistical features. A bi-directional-guided fusion mechanism is introduced to facilitate interaction between heterogeneous representations, while a closed-loop feedback pathway and padding-aware attention masking are incorporated to improve feature robustness. Experiments on the public SVC2004 benchmark and a custom multi-posture dataset (MPIS-Sig) evaluate the performance of this framework. Under the WD-10/10 protocol, FT-Transformer achieves an Equal Error Rate (EER) of 0.16% on SVC2004 Task 2 and maintains an EER of 2.40% under the more challenging WD-5/5 setting. On MPIS-Sig, the model achieves over 98% verification accuracy across different writing postures. These results demonstrate that FT-Transformer effectively improves OSV robustness under data-scarce and multi-posture conditions.

1. Introduction

Online signature verification (OSV) is a widely studied behavioral biometric technique for identity authentication and has been applied in various security-sensitive scenarios. Unlike physiological biometrics such as fingerprints or facial images, OSV relies on dynamic handwriting signals acquired during the signing process. These signals typically include spatial trajectories, pen pressure, pen orientation, and temporal information recorded by dedicated input devices [1,2]. Compared with static signature images, the dynamic nature of OSV provides additional discriminative information related to writing behavior. In particular, the temporal and kinematic characteristics embedded in the signing process are closely associated with individual writing habits, making them difficult to imitate consistently. Due to these properties, OSV has been increasingly adopted in applications such as financial authentication, electronic governance, and forensic document analysis [3,4].

Despite these advantages, OSV systems remain sensitive to real-world variations. Signing behavior can be affected by external conditions such as writing posture (e.g., standing) and grip style (e.g., high pen grip), which may alter pen trajectories and increase intra-class variability among genuine samples from the same individual [5]. In practical applications, the number of reference samples collected during enrollment is usually limited (e.g., 5–10) due to acquisition cost and user constraints. Under such few-shot settings, limited sample diversity may lead to distribution shift, making it more challenging to distinguish natural variations in genuine signatures from skilled forgeries [6,7].

To address these challenges, feature modeling in OSV has evolved from traditional sequence alignment methods to deep representation learning frameworks. Early studies mainly employed Dynamic Time Warping (DTW) to measure similarity through elastic temporal alignment [8]. However, DTW-based methods are sensitive to local deformations and have limited capacity to handle complex multivariate dynamic features. Subsequently, 1D Convolutional Neural Networks (1D-CNNs) and Recurrent Neural Networks (RNNs) have been introduced to learn representations directly from raw trajectory signals. CNN-based models focus on local patterns, while RNN-based approaches capture temporal dependencies in sequential data [9,10]. More recently, Transformer-based architectures have been applied to OSV, utilizing self-attention mechanisms to model long-range dependencies and global context [11]. In addition, several studies have investigated the integration of synchronous spatial characteristics with learned temporal features to better characterize individual writing behavior from a multi-scale perspective [12].

Despite these advances, existing methods still face several limitations under extremely few-shot and multi-posture conditions. Most approaches rely on late-stage concatenation to combine global statistical descriptors with dynamic temporal features, which does not explicitly account for differences in feature characteristics and semantic granularity. As a result, global information provides limited guidance for modeling fine-grained trajectory variations during feature learning [13]. Furthermore, in batch-processing of variable-length signature sequences, Transformers often suffer from attention dissipation into zero-padded regions, which introduces noise and degrades representation stability [14]. Additionally, most existing hybrid architectures follow a predominantly bottom–up information flow, where the lack of feedback from high-level representations to earlier stages may limit the model’s ability to suppress local noise and minor perturbations [15].

To address these limitations, this work develops FT-Transformer, a few-shot online signature verification framework that integrates hierarchical bi-directional interaction mechanisms to facilitate feature refinement and heterogeneous feature interaction, specifically tailored to these data-scarce behavioral constraints. The model jointly encodes multidimensional local kinetic features and comprehensive global statistical descriptors. A bi-directional guidance mechanism is introduced to facilitate interaction between these heterogeneous representations in a unified latent space. Within a hybrid CNN-Transformer architecture, a feedback pathway from high-level representations to earlier feature extraction stages is incorporated, allowing global structural information to refine local feature encoding. In addition, standard padding–masking operations are adapted to the variable-length characteristics of online signature trajectories. This adaptation prevents attention allocation to invalid padded regions and improves sequence representation stability under limited training samples. The main contributions of this work are summarized below. Rather than introducing a new learning algorithm, loss function, or fundamental Transformer architecture, this work focuses on a task-oriented architectural design for few-shot online signature verification. Specifically:

• An Inner Bi-directional Feedback pathway is incorporated to refine local feature representations through hierarchical interaction with global semantic information.
• A Bi-directional-guided Fusion module is designed to enhance interaction between heterogeneous feature representations prior to feature fusion.
• To bridge the gap in existing public benchmarks regarding physical disturbances, a multi-posture online signature dataset (MPIS-Sig) is constructed to evaluate this method under varying writing conditions and skilled forgery scenarios.
• The experimental results substantiate the effectiveness of the FT-Transformer in few-shot and multi-posture online signature verification. The framework maintains stable performance across diverse writing conditions and presents high discriminative capability against skilled forgery attacks.

1.1. Related Work

1.1.1. Evolution of Feature Modeling in Online Signature Verification

The performance of online signature verification (OSV) largely depends on the effective modeling of dynamic writing trajectories. Early studies primarily relied on Dynamic Time Warping (DTW) and its variants to compute similarity between signature sequences through elastic temporal alignment [8,16]. However, these alignment-based methods are sensitive to local deformations and have limited capability in capturing complex multivariate dynamics.

Subsequently, data-driven representation learning has become the dominant paradigm. Recurrent Neural Networks (RNNs), including Long Short-Term Memory (LSTM) networks, have been widely used to model temporal dependencies in sequential handwriting signals [9]. In parallel, 1D Convolutional Neural Networks (1D-CNNs) have been adopted to extract local patterns from multidimensional trajectory data due to their efficient receptive field design [17,18].

More recently, Transformer architectures [19] have been introduced into OSV to improve long-range dependency modeling via self-attention mechanisms. Gautam et al. leveraged Transformer-based self-attention to capture global relationships in signature sequences, and further proposed the TSOSVNet framework via teacher–student collaborative knowledge distillation to balance the global feature modeling capability and real-time deployment requirements of OSV systems [11], while Vorugunti et al. proposed hybrid CNN–Transformer frameworks to jointly model local and global representations [20]. In addition, several studies have explored integrating convolutional operations with attention mechanisms to enhance feature extraction [14,15]. Unlike these CNN–Transformer hybrid models, which primarily rely on unidirectional feature propagation where high-level representations exert limited influence on earlier stages, the proposed framework introduces hierarchical bi-directional interaction between local dynamic and global statistical representations. This structural design actively counteracts the propagation of localized perturbations and noise, thereby strengthening feature refinement under few-shot conditions.

1.1.2. Few-Shot Biometric Recognition

In practical deployments, OSV systems are often constrained to a limited number of enrollment samples (typically 5–10) due to user convenience and acquisition cost [6]. Such few-shot conditions increase the risk of overfitting in conventional deep learning models.

To mitigate these constraints, metric learning has been widely adopted. For example, SigNet [10] employs a Siamese architecture to reduce intra-class variation in the learned feature space. Prototypical Networks [21] represent each class by the centroid of its support samples and perform classification based on distance metrics. In addition, Model-Agnostic Meta-Learning (MAML) has been explored to improve model adaptability to new tasks with limited samples [22], as summarized in [23]. Such few-shot challenges are also prevalent in other behavioral biometric scenarios. For instance, F²Key [24] and SwipePass [25] realize user authentication with acoustic-sensed dynamic features, and enhance data efficiency under limited enrollment through customized feature modeling and data augmentation. These cross-modal studies corroborate the universality of few-shot biometric recognition problems and provide referable design paradigms for this work.

Within OSV, some studies have introduced lightweight architectures or parameter-efficient designs to alleviate overfitting under data-scarce conditions [7]. However, a small set of enrollment samples often fails to capture the full range of natural variations in genuine signatures caused by different writing conditions (e.g., posture or grip) [5]. As a result, it remains challenging to distinguish between intra-class variability and skilled forgeries under limited supervision.

1.1.3. Feature Fusion and Attention Mechanisms

To comprehensively characterize individual writing behavior, integrating multiple feature types (e.g., spatial and temporal dynamics) has become a common strategy in OSV [12]. Existing approaches typically integrate global statistical descriptors with dynamic temporal features using late-stage concatenation or shallow feature fusion [26,27]. However, these feature types differ significantly in representation form and scale, and simple concatenation may not fully capture their complementary characteristics.

Attention mechanisms have also been widely introduced to enhance sequence modeling. The Swin Transformer demonstrated that local window-based self-attention can preserve structural continuity while reducing computational cost [28]. In time-series analysis, prior studies have indicated that unconstrained global attention may capture less informative dependencies, especially when training data is limited [29]. For online signature data, discriminative information is often concentrated in localized dynamic patterns, such as subtle variations in stroke execution. In such cases, unconstrained global attention may distribute weights across less relevant regions, which can compromise model robustness under few-shot conditions [30].

1.1.4. Summary and Motivation

In summary, despite progress in deep feature modeling and few-shot learning, several challenges remain in OSV under limited-data and varying writing conditions. First, the interaction between global statistical descriptors and dynamic temporal features is insufficiently modeled. Second, standard global attention mechanisms lack structural constraints when applied to limited data, leading to reduced representation stability.

Motivated by these observations, this work proposes a framework that integrates heterogeneous features through a bi-directional guidance mechanism and introduces constrained attention modeling. By enforcing semantic interaction and restricting attention to locally relevant regions, the proposed approach systematically enhances verification robustness in few-shot and multi-condition scenarios.

2. Materials and Methods

To address the structural bottlenecks in online signature verification under few-shot conditions—specifically the tendency to overfit to long-range noise and the semantic gap between heterogeneous features—this paper proposes a deep network architecture based on Hierarchical Bi-directional Interaction named FT-Transformer. This section systematically details the construction paradigm of physical features, the hybrid temporal encoder with a closed-loop feedback mechanism, the padding-aware attention mechanism, and the cross-modal bi-directional-guided fusion strategy.

2.1. Overall Architecture

The system architecture of the FT-Transformer aims to be representative of kinematic characteristics of individual writing behavior from both macroscopic and microscopic scales, and its overall data flow is illustrated in Figure 1.

The processing pipeline encompasses four stages. First, the raw trajectory signals are normalized and differentiated to extract an 18-dimensional local dynamic sequence and a 51-dimensional global statistical feature vector. As traced in Figure 1, the sequential batch input $X_{seq}\in {\mathbb{R}}^{b\times L\times 18}$ is projected into a 128-channel space via a 1D convolutional layer to feed the self-attention mechanism, while the global macro-features $X_{global}\in {\mathbb{R}}^{b\times 51}$ are mapped into a 64-dimensional representation ($b\times 64$) through the global encoder network. Following temporal integration, these aligned dynamic ($b\times 128$) and statistical ($b\times 64$) embeddings are routed into the bi-directional-guided fusion module for cross-modal feature recalibration, before being decoded by the final classification head ($32\to 2$) for verification.

2.2. Multimodal Feature Preprocessing and Construction

The anti-forgery nature of human writing is related to the transient control of the neuromuscular system [29]. To effectively preserve this physical attribute, independent and complementary microscopic sequence and macroscopic statistical feature spaces are constructed.

2.2.1. Trajectory Normalization and High-Order Kinematic Feature Space (${\mathrm{X}}_{\mathrm{s}\mathrm{e}\mathrm{q}}$)

Due to the varying measurement ranges of different acquisition devices, the raw trajectory sequences require geometric normalization before feature extraction. Min-Max Scaling is applied to map the spatial coordinates to a closed interval of [−1, 1], eliminating absolute displacement bias.

According to kinematic theory, high-order derivatives are highly sensitive to muscle contractions and force mutations during writing [31]. Therefore, finite difference methods are introduced to extract high-order derived features on top of the base state features. In addition to first-order velocity and second-order acceleration, the jerk and the instantaneous curvature $\left(\kappa \right)$ of the trajectory are computed. Given the coordinate displacement differentials $\mathrm{d}{\mathrm{x}}_{\mathrm{i}}$, $\mathrm{d}{\mathrm{y}}_{\mathrm{i}}$ and their second-order differentials $dd{x}_i$, $dd{y}_i$ at adjacent sampling points, the mathematical expression for instantaneous curvature is defined as follows:

$${\kappa }_i={\displaystyle \frac{d{x}_i\cdot dd{y}_i-dd{x}_i\cdot d{y}_i}{(d{x}_i^2+d{y}_i^2{)}^{3/2}+ϵ}}$$

(1)

where $\mathsf{ϵ}$ is a very small constant to prevent division by zero anomalies. After high-order derivation and sequence length padding, a single sample’s dynamic trajectory is represented as a feature matrix $X_{seq}\in {\mathbb{R}}^{L\times 18}$, and its specific 18-dimensional feature distribution is detailed in

Table 1. Composition of the 18-dimensional local temporal dynamic features.

Feature Category	Dimension Index	Detailed Feature Description
Basic physical states	1–7	x-coordinate, y-coordinate, timestamp($\mathrm{t}$), button/pressure status (Button), horizontal angle (Azimuth), vertical angle (Altitude), pen tip pressure (Pressure).
First-order differential features	8–11	x-axis displacement difference($\mathrm{d}\mathrm{x}$), y-axis displacement difference($\mathrm{d}\mathrm{y}$), instantaneous tangent direction (Direction), instantaneous movement velocity (Velocity).
High-order kinematic indicators	12–14	Instantaneous acceleration (Acceleration), jerk (Jerk), timestamp-based normalized speed (Speed).
Relative spatiotemporal displacement	15–16	x-axis displacement difference relative to absolute start (${\mathrm{x}}_{\mathrm{r}\mathrm{e}\mathrm{l}}$), y-axis displacement difference relative to absolute start (${\mathrm{y}}_{\mathrm{r}\mathrm{e}\mathrm{l}}$)
Micro-deformation features	17–18	Angular velocity (Angular Velocity), instantaneous curvature (Curvature, $\mathsf{\kappa }$)

.

2.2.2. Global Physical Prior Statistical Space($X_{global}$)

A limited number of registration samples cannot sufficiently cover the probability distribution of a user’s posture deformations in complex physical environments. Relying solely on high-dimensional temporal sequences can easily lead to uncontrollable shifts in the model’s decision boundaries. To address this, a 51-dimensional global statistical feature space $X_{global}\in {\mathbb{R}}^{51}$, independent of time steps, is constructed as a macroscopic physical anchor, as detailed in

Table 2. Composition of the 51-dimensional global statistical features.

Feature Category	Dimensions	Statistical Component Description
Basic sequence statistical moments	42	For the 7-dimensional signals $(x$, $y$, $t$, Button, Azimuth, Altitude, Pressure), calculate their mean ($\mu$), standard deviation $\left(\sigma \right)$, skewness, kurtosis, 25% quartile (Q25), and 75% quartile (Q75) respectively.
Kinematic extremes and fluctuations	4	Expectation and standard deviation of movement velocity (Velocity) and acceleration (Acceleration).
Global behavioral descriptors	4	Total signature duration, total stroke count (Stroke Count), trajectory aspect ratio (Aspect Ratio), horizontal-to-vertical ratio.
Sampling point scale	1	Total number of sampling points of the corresponding signature.

.

Following extraction, Z-score standardization is applied to map these features to a standard normal distribution, ensuring stable convergence in the network backend.

2.2.3. Unified Mapping Strategy for Heterogeneous Datasets

For datasets with incomplete modalities (e.g., SVC2004 Task 1 with only coordinate trajectories), a unified zero-padding mechanism is adopted: missing channels are initialized with a constant value of 0.0. This design allows the hybrid encoder to implicitly perform feature selection by attenuating attention weights on constant channels, enabling seamless compatibility across both tasks under a unified architecture.

2.3. Hybrid Sequence Encoder with Inner Bi-Directional Feedback

To overcome the limitations of conventional deep temporal extraction networks that rely on a bottom–up unidirectional information flow [32], the serial configuration of the 1D-CNN and Transformer is designed according to the hierarchical characteristics of online signature signals, where an inner feedback mechanism is further integrated to connect local convolutions and global attention. The 1D-CNN first captures local temporal patterns from adjacent sampling points, after which the Transformer models long-range contextual dependencies over the refined sequence representation.

2.3.1. Local Topology Prior Extraction and Guidance

Given the input matrix ${\mathrm{X}}_{\mathrm{s}\mathrm{e}\mathrm{q}}$, the model first captures the local deformation topology between adjacent time steps via a 1D convolutional layer (kernel size $k=3$) to obtain the initial local features $H_{conv}^{\left(0\right)}\in {\mathbb{R}}^{L\times D}$. Before entering the Transformer module for global feature interaction, the initial convolution features are linearly embedded, normalized, and mapped via a parameter matrix ${\mathrm{W}}_{\mathrm{c}\to \mathrm{t}}$ (with a dimension of 128 → 128) as a local guidance feature injected into the input of the self-attention layer:

$$X_{attn\_in}=\mathrm{L}\mathrm{a}\mathrm{y}\mathrm{e}\mathrm{r}\mathrm{N}\mathrm{o}\mathrm{r}\mathrm{m}\left(X_{seq}{W}_{embed}\right)+W_{c\to t}\left(H_{conv}^{\left(0\right)}\right)$$

(2)

This mechanism explicitly constrains the Transformer with underlying local physical structures when computing global correlations, preventing attention weights from dissipating excessively on redundant sampling points.

2.3.2. Bottom–up Reconstruction via Global Semantic Feedback

After the multi-layer Transformer blocks extract global semantic features $H_{trans}\in {\mathbb{R}}^{L\times D}$ with long-range dependencies, a top–down feedback pathway is constructed. Specifically, the global structure semantics $H_{trans}$ are mapped back to the bottom–level convolutional space via a feedback projection matrix $W_{t\to c }$ (with a dimension of 128 → 128), acting as a residual calibration term to participate in the reconstruction of the 1D convolutional features:

$$H_{conv\_refined}=\mathrm{L}\mathrm{a}\mathrm{y}\mathrm{e}\mathrm{r}\mathrm{N}\mathrm{o}\mathrm{r}\mathrm{m}\left(ReLU\left(Conv1D\right(X_{seq})+W_{t\to c}(H_{trans}\left)\right)\right)$$

(3)

This residual reconstruction provides an additional mechanism for feature refinement. Because $H_{trans}$ contains macroscopic movement intentions, its feedback signal helps reduce the convolutional layer’s activation response to high-frequency local spikes. Finally, the refined local features $H_{conv\_refined}$ and the Transformer output features undergo masked average pooling across the temporal dimension and are summed to form the local microscopic sequence representation $F_{seq}\in {\mathbb{R}}^D$.

2.4. Padding-Aware Attention Mechanism

In online signature verification, the trajectory lengths (number of sampling points) vary significantly across different users and postures. During parallel batch training, zero-padding is applied to align sequences, which introduces redundant, invalid features. If standard global attention were applied [33], the network may allocate attention weights to these physically meaningless padded regions, introducing noise into the learned global kinematic representations. This problem is particularly prominent in few-shot scenarios with limited training data, and easily leads to overfitting.

To resolve this issue, we adapt the standard Transformer padding–masking strategy to variable-length online signature sequences by preventing padded positions from participating in attention computation. This adaptation reduces the influence of non-informative padded tokens during feature learning while preserving the original attention formulation. During the feature interaction phase, the system dynamically constructs a 2D validity mask matrix $M_{valid}\in R^{L_{max}\times L_{max}}$ based on the actual valid physical length $L_{valid}$ of each signature sample. Its elements are defined as follows:

$$M_{valid}(i,j)=\{\begin{array}{cc}\hfill 1,& \mathrm{i}\mathrm{f} i\le L_{valid} \mathrm{a}\mathrm{n}\mathrm{d} j\le L_{valid}\\ \hfill 0,& \mathrm{o}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r}\mathrm{w}\mathrm{i}\mathrm{s}\mathrm{e}\hfill \end{array}$$

(4)

The scaled dot-product attention formula constrained by the mask is then reconstructed as follows:

$$\mathrm{A}\mathrm{t}\mathrm{t}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}(Q,K,V)=\mathrm{S}\mathrm{o}\mathrm{f}\mathrm{t}\mathrm{m}\mathrm{a}\mathrm{x}\left({\displaystyle \frac{Q{K}^T}{\sqrt{d_k}}}\odot M_{valid}+P\odot (1-M_{valid})\right)V$$

(5)

For positions outside the valid trajectory length, a large negative constant $P$ (set to $-10^9$ in the experiments) is injected. After Softmax activation, the attention weights for invalid padded positions are suppressed to a very low level. This mechanism reduces the interference of invalid padded regions and encourages the model to allocate attention to valid trajectory segments, thereby improving the stability of sequence representation learning under few-shot conditions.

2.5. Cross-Modal Bi-Directional-Guided Fusion

The microscopic sequence features $F_{seq}$ describe transient dynamics, while the macroscopic prior features $F_{global}$ describe overall statistical distributions, creating a heterogeneous semantic gap. To alleviate the semantic mismatch caused by direct concatenation in traditional multimodal fusion [34], a Cross-Modal Bi-directional-Guided Fusion module is introduced to establish reciprocal feature recalibration between local dynamic representations and global statistical priors before dimensionality reduction.

The global statistical features are first encoded by a two-layer projection network (51 → 128 → 64) to obtain the global latent representation. This mechanism utilizes learnable cross-linear projections for mutual compensation. First, the microscopic dynamic features act as kinematic priors to guide the shift in the static global distribution via the projection matrix $W_{seq\to glb}$ (with a dimension of 128 → 64):

$$F_{\mathrm{g}lobal}^{\prime }=F_{\mathrm{g}lobal}+W_{\mathrm{s}eq\to glb}\left(F_{\mathrm{s}eq}\right)$$

(6)

Simultaneously, the global statistical descriptors provide distributional guidance for local dynamic representations via the projection matrix $W_{glb\to seq}$ (with a dimension of 64 → 128), helping alleviate sensitivity to posture-induced trajectory variations and improving consistency between short-term dynamics and long-term statistical characteristics:

$$F_{seq}^{\prime }=F_{seq}+W_{glb\to seq}\left(F_{global}\right)$$

(7)

The proposed design differs from three mainstream multimodal fusion paradigms: cross-attention introduces heavy computational overhead and risks overfitting under few-shot settings; gated fusion lacks explicit statistical prior constraints; residual fusion yields limited gains for heterogeneous features with large semantic gaps. In contrast, our method performs vector-level feature calibration before concatenation, preserves the independence of the two feature spaces, and incorporates statistical priors as implicit constraints, tailored for the heterogeneous feature scenario in OSV.

The semantically aligned features $F_{seq}^{\prime }$ and $F_{\mathrm{g}lobal}^{\prime }$ are then concatenated along the feature dimension and fed into an MLP for non-linear dimensionality reduction. The fusion layer integrates Rectified Linear Unit(ReLU) activation, Layer Normalization, and Dropout ($p=0.2$) to mitigate feature co-adaptation, finally outputting a compact 32-dimensional fused representation $F_{fused}\in {\mathbb{R}}^{32}$.

2.6. Optimization Objective and Model Training Strategy

The signature verification problem is abstracted as a binary classification task, mapping the 32-dimensional feature to 2 classes via a fully connected layer. The model utilizes the Cross-Entropy Loss function with ${\mathrm{L}}_2$ weight decay:

$${\mathcal{L}}_{CE}=-{\displaystyle \frac{1}{B}}{\displaystyle \sum _{i=1}^B}\sum _{c\in \left\{\mathrm{0,1}\right\}}{y}_{i,c}\log ({\widehat{y}}_{i,c})+{\displaystyle \frac{\lambda }{2}}\Vert \mathsf{\Theta }{\Vert }_2^2$$

(8)

where $\mathrm{B}$ is the mini-batch size (set to 8), $y_{i,c}$ is the ground truth label, ${\widehat{y}}_{i,c}$ is the predicted probability from the network, $\Theta$ represents the learnable parameter set, and $\mathsf{\lambda }$ is the regularization coefficient.

For optimization, the AdamW optimizer with decoupled weight decay is adopted to handle complex parameter manifolds [35], which provides more stable regularization for few-shot training compared with standard Adam. A cosine annealing learning rate scheduling strategy is integrated to ensure smooth convergence near the optimal solution in the late training stage and avoid loss oscillation [36]. In line with standard evaluation protocols in the online signature verification field, all hyperparameters are pre-fixed following common practices in the few-shot OSV community, and all models are trained for a fixed number of epochs with a unified configuration. No test set information is involved in the entire training process to eliminate data leakage.

3. Results

To evaluate the proposed FT-Transformer, a series of experiments and comparative analyses are conducted. The evaluations are performed on the public SVC2004 dataset (Task 1 and Task 2) and a self-collected Multi-Posture and Imitation Signature (MPIS-Sig) dataset. This section first introduces the datasets, evaluation metrics, and experimental protocols. It then reports the overall performance of the proposed method, followed by comparisons with existing approaches, ablation studies of key components, multi-posture robustness analysis, and sensitivity analysis with respect to training sample size.

3.1. Experimental Datasets

The experimental evaluations are anchored on the SVC2004 public benchmark and the custom MPIS-Sig dataset. For both datasets, high-fidelity, multidimensional dynamic signature trajectories were acquired via WACOM digitizing tablets.

3.1.1. SVC2004 Public Dataset

The SVC2004 dataset [37], established for the First International Signature Verification Competition hosted by the Hong Kong University of Science and Technology in 2004, is a widely recognized standard benchmark for online signature verification research. It covers both Chinese and English signature samples, with Task 1 comprising 16 Chinese and 24 English signatures, and Task 2 containing 17 Chinese and 23 English signatures. Each sub-task includes 40 subjects, with 20 genuine signatures per subject and 20 corresponding skilled forgeries generated.

Task 1 provides foundational trajectory information, specifically the x-coordinate, y-coordinate, time stamp, and button status. In contrast, Task 2 incorporates a richer set of dynamic features, supplementing the base trajectory with stylus azimuth, altitude, and pen pressure. Figure 2 presents a visual comparison of typical genuine and skilled forgery signature trajectories in this dataset. As shown in the figure, skilled forgeries closely resemble genuine signatures in overall glyph contour and stroke layout, making them difficult to distinguish based solely on static spatial morphology. However, forged samples exhibit less smooth stroke connections and minor local deformations in letter details, reflecting unnatural writing rhythm and pen hesitation induced by deliberate imitation. Such subtle differences in writing fluency correspond to discriminative information in kinematic features such as velocity, pen pressure, and duration. The limited sample size of this dataset further challenges the model’s ability to capture these subtle dynamic differences under few-shot learning settings.

3.1.2. Custom Multi-Posture and Imitation Signature (MPIS-Sig) Dataset

Public datasets for online signature verification (e.g., SVC2004) often lack postural variations and graded forgery complexities, limiting the evaluation of model robustness. To address this, we construct the Multi-Posture and Imitation Signature (MPIS-Sig) dataset, comprising 3300 signature samples from 33 independent university student volunteers aged 18–21 years (18 males and 15 females), with 80 genuine and 20 forged signatures per subject. Prior to data collection, institutional safety review and written informed consent were explicitly obtained from all participants, ensuring rigorous compliance with biometric privacy protocols.

Trajectories were recorded using a Wacom CTL-6100WL/K0-CX tablet and an LP-190-0K stylus (Wacom Co., Ltd., Tokyo, Japan) at a 100 Hz sampling rate. Recorded parameters include x- and y-coordinates (0.001 mm resolution), time stamp (millisecond precision, initialized at 0 with a uniform 10 ms sampling interval), binary pen status (indicating pen-up or pen-down states), normalized pen pressure ([0, 1]), and stroke orientation angle (−180° to +180°). A standardized acquisition protocol was implemented:

• Genuine Signatures: Collected across two sessions separated by at least 3 days to minimize short-term memory bias. In each session, subjects provided 10 signatures under four conditions: (1) Normal Writing (NW): standard sitting posture; (2) Standing Writing (SW); (3) High Position Grip (HPG): gripping the upper half of the stylus; (4) Variable Speed Writing (VSW): writing significantly faster or slower than normal.
• Forged Signatures: Generated by four independent forgers, yielding 12 Random Forgeries (RF) and 8 Skilled Forgeries (SF) per subject [38]. RF samples were produced solely based on the text content of the target name, without prior observation of the genuine trajectory or style. SF samples were executed after at least one week of targeted practice on the genuine dynamics.

Figure 3 presents representative examples of genuine and forged signature trajectories. As shown in panels (a)–(d), genuine signatures produced under different writing conditions exhibit noticeable intra-class morphological variations. When writing in a standing posture or with a high-position grip, diminished pen control leads to local trajectory deformation, looser stroke structure, and increased stroke jitter. Under variable-speed writing, the degree of stroke connection shifts, with distinct variations in stroke rhythm and thickness. From a kinematic perspective, these posture-induced disturbances are directly reflected in pen pressure fluctuations, the uniformity of instantaneous velocity, and the patterns of acceleration variation. Panels (e)–(f) show two categories of forgery samples with different levels of imitation complexity. Random forgeries differ markedly from genuine signatures in overall glyph structure and writing style, but their generation follows natural neuromuscular control rhythms. Skilled forgeries bear high resemblance to genuine signatures in spatial morphology. However, deliberate imitation leads to stiff stroke execution and unnatural transitions at turning points, resulting in distinguishable discrepancies from genuine signatures in dynamic aspects, particularly the distribution characteristics of velocity and pen pressure.

3.2. Evaluation Metrics and Protocol Settings

3.2.1. Metrics and Protocols

The evaluation adopts standard metrics used in biometric verification, including Accuracy (ACC), False Acceptance Rate (FAR), False Rejection Rate (FRR), Equal Error Rate (EER), and Area Under the ROC Curve (AUC) [1,39]. EER is defined as the operating point where FAR equals FRR and is commonly used as a summary indicator of verification performance. AUC measures the overall separability between genuine and forged samples across different decision thresholds. For ACC, FAR, and FRR, a default decision threshold of 0.5 is directly applied to the model output scores without any test-set-based tuning, to demonstrate the raw discriminative ability of the proposed model.

All evaluations follow the Writer-Dependent (WD) setting, including WD-10/10 (standard few-shot) and WD-5/5 (extreme few-shot) protocols. A fixed subject-level sample split scheme is adopted for all experiments to ensure consistent experimental conditions. Taking SVC2004 Task 2 as an example, the dataset contains 40 subjects with 20 genuine and 20 skilled forgery samples per subject. Under the WD-5/5 protocol, 5 genuine and 5 forged samples per subject are fixedly used for fine-tuning, and the remaining 15 genuine and 15 forged samples are used for testing, with no sample overlap between the two sets. The split scheme is consistent with standard practices in the OSV field.

3.2.2. Environment and Hyperparameters

All experiments were conducted on a system equipped with an Intel^® Core™ i9-14900HX CPU (2.20 GHz), 16 GB RAM, and an NVIDIA GeForce RTX 4060 GPU (8 GB GDDR6). The implementation was based on Python 3.13.0 and PyTorch 2.7.1+cu118, with additional libraries including NumPy 1.26.4, SciPy 1.15.3, Pandas 2.3.0, and Scikit-learn 1.7.0.

For training, the AdamW optimizer is adopted with an initial learning rate of 0.001, paired with a CosineAnnealingLR scheduler where ${\mathrm{T}}_{\mathrm{m}\mathrm{a}\mathrm{x}}$ is set to 50. The cross-entropy loss is used as the optimization objective, with a batch size of 8 and a dropout rate of 0.2. All models are trained for a fixed 50 epochs with a unified configuration. We strictly follow the standard fixed subject-level sample split protocol widely used in the OSV field. No test set information is involved in the entire training process to eliminate data leakage.

The key learnable projection matrices in the model follow a unified dimension design aligned with the network’s hidden dimension. All hyperparameters are determined according to standard practices in the few-shot signature verification field, and detailed configurations are provided in

Table 3. Network hyperparameters and training configuration of the proposed FT-Transformer.

Parameter Category	Parameter Name	Symbol	Value
Feature Space	Local dynamic feature dimension	${\mathrm{X}}_{\mathrm{s}\mathrm{e}\mathrm{q}}$	18
	Global statistical feature dimension	${\mathrm{X}}_{\mathrm{g}\mathrm{l}\mathrm{o}\mathrm{b}\mathrm{a}\mathrm{l}}$	51
Network Architecture	1D-CNN output channels	${\mathrm{C}}_{\mathrm{o}\mathrm{u}\mathrm{t}}$	128
	Transformer encoder layers	$\mathrm{N}$	2
	Number of attention heads	${\mathrm{N}}_{\mathrm{h}\mathrm{e}\mathrm{a}\mathrm{d}\mathrm{s}}$	4
	Transformer hidden dimension	${\mathrm{D}}_{\mathrm{h}\mathrm{i}\mathrm{d}\mathrm{d}\mathrm{e}\mathrm{n}}$	128
	Feature fusion hidden dimension	${\mathrm{D}}_{\mathrm{f}\mathrm{u}\mathrm{s}\mathrm{i}\mathrm{o}\mathrm{n}}$	64
Physical Constraint	Spatiotemporal local mask window radius	${\mathrm{w}}_{\mathrm{t}\mathrm{e}\mathrm{m}\mathrm{p}\mathrm{o}\mathrm{r}\mathrm{a}\mathrm{l}}$	10
Training & Optimization	Initial learning rate	$\mathrm{l}\mathrm{r}$	0.001
	Batch size	$\mathrm{b}\mathrm{a}\mathrm{t}\mathrm{c}\mathrm{h}\_\mathrm{s}\mathrm{i}\mathrm{z}\mathrm{e}$	8
	Training epochs	$\mathrm{e}\mathrm{p}\mathrm{o}\mathrm{c}\mathrm{h}\mathrm{s}$	50
	Dropout rate	$\mathrm{d}\mathrm{r}\mathrm{o}\mathrm{p}\mathrm{o}\mathrm{u}\mathrm{t}$	0.2

.

3.3. Overall Model Performance Analysis

To assess the performance of the proposed FT-Transformer, comparative experiments were conducted against five representative sequence-based baselines: Dynamic Time Warping (DTW), 1D-CNN, BiLSTM, InceptionTime and MobileViT, covering traditional dynamic programming, classic recurrent networks, state-of-the-art 1D CNN and lightweight Transformer architectures. Evaluations were performed under both WD-10/10 and WD-5/5 protocols. All methods were implemented under identical data preprocessing and split settings to ensure fair comparison.

3.3.1. Baseline Performance Under the WD-10/10 Protocol

The WD-10/10 protocol uses 10 genuine and 10 forged signatures per user for training. This setting represents a standard few-shot scenario in online signature verification. The experimental results are reported in

Table 4. Performance comparison of baseline methods and the proposed method across various datasets (WD-10/10).

Dataset	Method	ACC (%)	FAR (%)	FRR (%)	EER (%)
SVC2004 Task 1	DTW	94.06	10.00	1.87	11.56
	1D-CNN	86.09	23.75	4.06	8.13
	BiLSTM	79.22	26.25	15.31	18.12
	MobileViT	85.00	14.69	15.31	11.25
	InceptionTime	89.53	11.87	9.06	9.06
	Ours	94.69	7.81	2.81	2.81
SVC2004 Task 2	DTW	59.06	8.44	55.00	17.50
	1D-CNN	60.00	34.06	45.94	28.59
	BiLSTM	89.53	11.87	9.06	10.31
	MobileViT	87.97	13.75	10.31	6.25
	InceptionTime	91.87	11.87	4.37	7.81
	Ours	99.53	0.63	0.31	0.16
MPIS-Sig	DTW	35.94	46.43	50.00	48.21
	1D-CNN	62.50	39.28	37.50	38.39
	BiLSTM	76.56	35.71	37.50	36.61
	MobileViT	81.92	4.58	20.00	10.08
	InceptionTime	95.41	2.08	4.94	2.73
	Ours	98.02	1.98	1.52	1.75

.

On the SVC2004 Task 1 dataset, where only two-dimensional trajectory information is available, the proposed method achieved an EER of 2.81%. 1D-CNN obtained an EER of 8.13%, followed by InceptionTime at 9.06%, MobileViT at 11.25%, DTW at 11.56%, and BiLSTM at 18.12%. The FAR and FRR of the proposed method were 7.81% and 2.81%, respectively. Although the performance gap narrowed compared to Task 2, the results indicate that the proposed method remains effective even when the available feature dimensions are limited.

On the SVC2004 Task 2 dataset, which includes richer dynamic information, the proposed method achieved an ACC of 99.53% and an EER of 0.16%. In comparison, MobileViT and InceptionTime obtained EERs of 6.25% and 7.81%, respectively, followed by BiLSTM at 10.31%, while DTW and 1D-CNN showed significantly higher error rates. The FAR and FRR of the proposed method were 0.63% and 0.31%, respectively, indicating a low error rate on both acceptance and rejection decisions.

On the MPIS-Sig dataset, which introduces variations in writing posture and forgery types, all baseline methods exhibited higher error rates. DTW reached an EER of 48.21%, while 1D-CNN and BiLSTM obtained 38.39% and 36.61%, respectively. MobileViT achieved an EER of 10.08%, and the stronger baseline InceptionTime further reduced the EER to 2.73%. In contrast, the proposed method achieved an ACC of 98.02% with an EER of 1.75%. The corresponding FAR (1.98%) and FRR (1.52%) remained balanced, suggesting stable behavior under more complex data conditions.

Overall, the results in Table 4 show that the proposed method consistently achieves lower EER values across datasets with different characteristics. The performance differences between SVC2004 and MPIS-Sig also suggest that the latter presents a more challenging scenario due to additional variations in writing conditions and forgery strategies.

To further examine performance across different decision thresholds, Figure 4 presents the ROC curves of all methods under the WD-10/10 protocol. AUC is used to summarize the overall discrimination capability independent of a fixed threshold.

As shown in Figure 4a, on the SVC2004 Task 1 dataset, the proposed method achieved an AUC of 0.979. InceptionTime obtained an AUC of 0.961, followed by 1D-CNN at 0.947, MobileViT at 0.926, BiLSTM at 0.875, and DTW at 0.697. The curve of the proposed method remains consistently above all baselines across most false positive rate ranges.

On the SVC2004 Task 2 dataset (Figure 4b), all methods benefited from richer dynamic features. The proposed method attained an AUC of 0.999, while InceptionTime, BiLSTM and MobileViT reached 0.959, 0.951 and 0.949, respectively. The ROC curve of the proposed method shows a steeper rise in the low false positive region, indicating improved discrimination when stricter acceptance conditions are applied.

On the MPIS-Sig dataset (Figure 4c), the difference between methods became more pronounced. The proposed method achieved an AUC of 0.993, whereas BiLSTM reached 0.889, and InceptionTime reached a similarly high AUC of 0.993. MobileViT attained an AUC of 0.954, and 1D-CNN and DTW obtained 0.512 and 0.420, respectively. In this case, the ROC curves of the baseline methods are closer to the diagonal, reflecting weaker separation between genuine and forged samples. Both the proposed method and InceptionTime achieved similarly high AUC values of 0.993, indicating strong ranking capability. However, the proposed method achieved a lower EER (1.75% versus 2.73%), suggesting that it provides more favorable verification performance at the selected operating point.

3.3.2. Baseline Performance Under the WD-5/5 Protocol

To evaluate the proposed method under a more limited writer-dependent setting, experiments were conducted using the WD-5/5 protocol. In this setting, five genuine signatures and five forged signatures from each writer were used for writer-dependent fine-tuning, and the remaining samples were used for testing. Compared with the WD-10/10 protocol, WD-5/5 reduces the amount of writer-specific training data and therefore provides a stricter evaluation of few-shot adaptation. Since forged samples are included during fine-tuning, this setting should be regarded as supervised writer-dependent verification rather than forgery-free enrollment. The results are reported in

Table 5. Performance comparison of baseline methods and the proposed method across various datasets (WD-5/5).

Dataset	Method	ACC (%)	FAR (%)	FRR (%)	EER (%)
SVC2004 Task 1	DTW	91.46	9.79	7.29	15.73
	1D-CNN	79.06	34.17	7.71	15.31
	BiLSTM	74.48	36.04	15.00	24.48
	MobileViT	81.04	27.71	10.21	16.15
	InceptionTime	81.98	22.71	13.33	15.00
	Ours	88.02	18.75	5.21	9.06
SVC2004 Task 2	DTW	58.23	10.83	47.08	18.33
	1D-CNN	55.00	34.58	55.42	38.96
	BiLSTM	86.04	12.92	15.00	11.56
	MobileViT	84.58	20.21	10.62	12.29
	InceptionTime	85.21	17.29	12.29	14.37
	Ours	95.52	7.92	1.04	2.40
MPIS-Sig	DTW	44.19	55.80	55.80	55.80
	1D-CNN	52.31	48.28	48.73	48.51
	BiLSTM	82.19	16.86	18.93	17.90
	MobileViT	73.05	7.22	28.88	20.94
	InceptionTime	88.98	14.44	10.33	11.00
	Ours	94.76	4.94	5.30	5.12

.

As shown in Table 5, the proposed method achieved the lowest EER on all three datasets. On SVC2004 Task 1, it obtained an EER of 9.06%, compared with 15.00% for InceptionTime, 15.31% for 1D-CNN, 15.73% for DTW, 16.15% for MobileViT, and 24.48% for BiLSTM. However, DTW obtained a higher ACC, 91.46% compared with 88.02% for the proposed method, and a lower FAR at the selected threshold. This observation highlights the difference between threshold-dependent and threshold-independent evaluation metrics. ACC is measured at a specific operating threshold, whereas EER reflects the optimal balance between false acceptance and false rejection rates. Therefore, a method may achieve a higher ACC at a particular threshold while still exhibiting inferior overall verification capability.

On SVC2004 Task 2, the proposed method achieved an ACC of 95.52% and an EER of 2.40%. BiLSTM achieves the lowest EER among all baselines on this dataset under the WD-5/5 setting, with an EER of 11.56%, followed by MobileViT at 12.29% and InceptionTime at 14.37%. The proposed method therefore reduced the EER by 79.24% relative to BiLSTM. Its FAR and FRR were 7.92% and 1.04%, respectively, both lower than those of the baseline methods. These results show that the proposed method performs more robustly than the compared baselines under the reduced writer-specific training setting.

On MPIS-Sig, the performance gap was more evident. DTW and 1D-CNN obtained EERs of 55.80% and 48.51%, respectively, while MobileViT and BiLSTM obtained EERs of 20.94% and 17.90%. The stronger baseline InceptionTime further reduced the EER to 11.00%. The proposed method achieved an ACC of 94.76% and an EER of 5.12%. Compared with InceptionTime, it reduced the EER by 53.45%. Its FAR and FRR were 4.94% and 5.30%, respectively, showing a relatively balanced error distribution. These results suggest that the proposed method maintains better verification performance on MPIS-Sig under the WD-5/5 protocol.

Figure 5 presents the ROC curves and AUC values under the WD-5/5 protocol. On SVC2004 Task 1, the proposed method achieved an AUC of 0.939, compared with 0.879 for MobileViT, 0.871 for InceptionTime, 0.868 for 1D-CNN, 0.809 for BiLSTM, and 0.708 for DTW. On SVC2004 Task 2, it obtained an AUC of 0.982, while BiLSTM reached 0.951, followed by MobileViT at 0.903, InceptionTime at 0.900, DTW at 0.852, and 1D-CNN at 0.676. On MPIS-Sig, the proposed method achieved an AUC of 0.980, compared with 0.931 for InceptionTime, 0.854 for MobileViT, 0.834 for BiLSTM, 0.524 for 1D-CNN, and 0.437 for DTW. The low AUC values of DTW and 1D-CNN indicate weak score ranking ability under this setting, and the performance gap between classic baselines and deep learning methods is further widened under the few-shot condition.

Overall, the results in Table 5 and Figure 5 show that the proposed method performs better than the compared baselines under the WD-5/5 protocol, especially on SVC2004 Task 2 and MPIS-Sig. However, the results on SVC2004 Task 1 also show that ACC, FAR, FRR, EER, and AUC may lead to different interpretations when the decision threshold changes. Therefore, these metrics should be analyzed jointly, and threshold calibration remains necessary in practical applications.

3.3.3. Computational Complexity Analysis

Beyond verification performance, computational cost is a critical factor for practical deployment on edge biometric devices. This subsection evaluates the computational complexity of all methods using two hardware-independent, model-level objective metrics: the number of trainable parameters (Params) and floating-point operations (FLOPs).

Since all signature sequences are normalized to a fixed length via unified preprocessing across all datasets and enrollment settings, the input tensor dimension remains consistent throughout all experiments. Params and FLOPs are inherent properties determined by network architecture, and thus do not vary with datasets or the number of enrollment samples. Hence, a single set of complexity results applies to both WD-10/10 and WD-5/5 experimental settings. A detailed comparison is shown in

Table 6. Computational complexity comparison of different models.

Model	Params	FLOPs
DTW	0	1.05 MFLOPs
1D-CNN	32.32 K	19.10 MFLOPs
BiLSTM	530.17 K	1.08 GFLOPs
MobileViT	1.13 M	145.22 MFLOPs
InceptionTime	423.09 K	309.84 MFLOPs
Ours	218.24 K	23.67 MFLOPs

.

As shown in Table 6, DTW, as a conventional dynamic programming algorithm, requires no trainable parameters and incurs the lowest computational cost, but its verification performance degrades sharply on complex datasets with large intra-class variations. Among deep learning baselines, 1D-CNN features the smallest model size and lowest computational overhead, yet its overall verification accuracy lags behind other deep architectures. The proposed method has 218.24 K trainable parameters and 23.67 MFLOPs, maintaining a lightweight model scale.

Compared with the lightweight 1D-CNN baseline, the proposed method only increases FLOPs by 23.9%, but brings substantial performance improvements across datasets. Specifically, under the standard WD-10/10 protocol, it reduces the EER by 99.4% on SVC2004 Task 2 and 95.4% on MPIS-Sig relative to 1D-CNN, achieving remarkable accuracy gain with marginal computational overhead increase.

For higher-performance deep baselines, the proposed method exhibits prominent advantages in computational efficiency. Its FLOPs account for only 7.6% of InceptionTime and 16.3% of MobileViT, and its parameter count is 51.6% that of InceptionTime and 19.3% that of MobileViT. More importantly, on the challenging MPIS-Sig dataset under the strict WD-5/5 setting where InceptionTime achieves the best performance among all baselines, the proposed method further reduces the EER by 53.45%, while cutting parameters by 48.4% and FLOPs by 92.4%, providing a favorable balance between verification accuracy and computational efficiency. In comparison with the classic BiLSTM model (1.08 GFLOPs), the proposed method reduces FLOPs by approximately 97.8% while achieving lower verification error rates across all experimental settings.

3.4. Comparison with State-of-the-Art Works

This section compares the proposed FT-Transformer with recent state-of-the-art (SOTA) methods on the SVC2004 dataset. The evaluation covers both the extreme few-shot (WD-5/5) and standard few-shot (WD-10/10) registration protocols. Table 6 and

Table 7. Comparison of EER (%) with state-of-the-art methods on the SVC2004 Task 1 dataset.

Method	EER (5-Shot) (%)	EER (10-Shot) (%)
Wavelet packet-based [40]	6.65	—
Turning angle & LCS [41]	5.33	—
Hilbert scanning + GMM [42]	—	6.08
Single-template + weighting [43]	4.98	4.26
Ours	9.06	2.81

summarize the quantitative results for Task 1 and Task 2, respectively. All cited SOTA methods follow the Writer-Dependent (WD) verification paradigm and adhere to either the 5-shot or 10-shot registration setting. Entries unavailable in the original literature are indicated by (—).

Table 7 presents the EER of the proposed method and previous SOTA approaches on SVC2004 Task 1. Under the standard 10-shot protocol, the proposed method achieves an EER of 2.81%, lower than 4.26% reported for the single-template weighting method and 6.08% for Hilbert + GMM. Under the extreme 5-shot protocol, several earlier methods relying on handcrafted spatial descriptors obtain lower EERs (e.g., 4.98% for single-template weighting, 5.33% for Turning Angle + LCS) compared with 9.06% for the proposed method. These results indicate that the proposed method benefits from additional registration samples, while under very limited 5-shot conditions, its performance is constrained.

Table 8. Comparison of EER (%) with state-of-the-art methods on the SVC2004 Task 2 dataset.

Method	EER (5-Shot) (%)	EER (10-Shot) (%)
Feature weighting relief [44]	5.31	—
Few-shot learning [7]	5.83	—
1D-CNNs trained cosine similarities [17]	—	2.63
Feature Fusion [18]	5.95	3.93
Multiple DTW distances with gradient boosting [43]	—	2.98
Curvature feature + torsion feature [45]	—	4.38
Feature selection + GhostNet [46]	4.57	2.93
1D-MRSNet + ABSoftmax [47]	11.74	2.33
1D-ACGRNet [14]	4.17	2.12
Ours	2.40	0.16

reports the EER on SVC2004 Task 2, which includes multi-dimensional dynamic features such as pressure and tilt. Under the standard 10-shot protocol, the proposed method achieves an EER of 0.16%, outperforming the latest 1D-ACGRNet (2.12%) and other recent approaches. Under the 5-shot protocol, the proposed method achieves an EER of 2.40%, which is lower than all referenced SOTA methods, including Feature selection + GhostNet (2.93%) and 1D-ACGRNet (4.17%). Overall, the proposed model achieves lower EERs compared to the referenced approaches under both evaluation protocols.

3.5. Ablation Study

To evaluate the contribution of each core component in the FT-Transformer architecture, a series of ablation experiments was conducted under both the WD-10/10 Protocol and the WD-5/5 Protocol. Six model variants (V1–V5 and the full model, Ours) were constructed by progressively incorporating the sequence branch, global branch, bi-directional-guided fusion, closed-loop feedback, and padding-aware attention mechanism. The evaluation metrics include EER, ACC, FAR, FRR, and AUC.

3.5.1. Ablation Study Under WD-10/10 Protocol

The ablation results under the WD-10/10 Protocol are reported in

Table 9. Ablation study results of core modules across three datasets under WD-10/10 Protocol (EER, ACC, FAR, FRR in %, AUC is dimensionless). ‘✓’ indicates that the corresponding module is included, ‘✗’ indicates excluded, and ‘—’ indicates not applicable.

Variants	Sequence Branch	Global Branch	Fusion Method	Closed-Loop Feedback	Padding Masking	Task 1 EER/ACC/FAR/FRR/AUC	Task 2 EER/ACC/FAR/FRR/AUC	MPIS-Sig EER/ACC/FAR/FRR/AUC
V1: Vanilla Transformer	✓	✗	—	✗	✗	8.91/90.47/10.84/7.49/0.934	4.22/95.62/5.47/3.28/0.968	2.85/96.87/3.73/2.56/0.976
V2: Global-only	✗	✓	—	✗	✗	8.44/91.43/9.78/7.34/0.938	3.75/96.09/4.62/3.19/0.971	2.91/97.17/3.37/2.29/0.978
V3: Simple Concat	✓	✓	Concat	✗	✗	7.50/92.47/8.83/6.01/0.948	2.19/97.66/2.91/1.78/0.983	2.70/97.66/2.91/1.78/0.983
V4: + Bi-Fusion	✓	✓	Bi-Guided	✗	✗	5.94/94.23/7.13/4.67/0.961	1.56/98.13/2.07/1.19/0.988	1.97/97.72/2.74/1.82/0.986
V5: + Feedback	✓	✓	Bi-Guided	✓	✗	3.81/94.37/4.82/3.44/0.968	0.94/98.91/1.08/0.66/0.993	1.91/97.97/2.38/1.68/0.987
Ours: + Padding Masking	✓	✓	Bi-Guided	✓	✓	2.81/94.69/7.81/2.81/0.979	0.16/99.53/0.63/0.31/0.999	1.75/98.02/1.98/1.52/0.993

.

To evaluate the individual contributions of each feature component and the effectiveness of the interaction strategy, Variant V1 is configured to represent the local dynamic branch alone, Variant V2 represents the global statistical branch alone, and Variant V3 replaces the proposed bi-directional-guided fusion with simple late-stage feature concatenation. Specifically, in the single-branch baselines, V1 (sequence-only) yields high EERs and relatively lower ACC across all datasets. V2 (global-only) improves the EER on SVC2004 Task 1 (8.44% vs. 8.91%) and Task 2 (3.75% vs. 4.22%) compared to V1, but yields a slightly higher EER on the MPIS-Sig dataset (2.91% vs. 2.85%). This indicates that the two types of features capture different information depending on the dataset characteristics. When the two feature streams are combined through direct concatenation (V3), the verification error decreases, with the EER reduced to 7.50%, 2.19%, and 2.70% on SVC2004 Task 1, Task 2, and MPIS-Sig, respectively, alongside a steady increase in ACC.

After replacing concatenation with the bi-directional-guided fusion mechanism (V4), the EER is further reduced by 1.56 percentage points (pp), 0.63 pp, and 0.73 pp on the three datasets compared to V3, with corresponding decreases in FAR and FRR. This result suggests that guided cross-branch interaction is more effective than direct concatenation for integrating sequential and global representations.

The addition of the closed-loop feedback module (V5) yields further EER reductions of 2.13 pp, 0.62 pp, and 0.06 pp on the three datasets compared to V4. These results indicate that the feedback pathway provides complementary benefits by refining the learned verification features.

The full model (Ours), which incorporates the padding-aware attention mechanism, achieves the lowest EER and highest ACC across all datasets. On SVC2004 Task 2 and MPIS-Sig, the EER is reduced to 0.16% and 1.75%, the ACC increases to 99.53% and 98.02%, and the AUC reaches 0.999 and 0.993, respectively. By masking the zero-padded regions introduced during the batching of variable-length sequences, this mechanism prevents invalid padded positions from participating in attention computation, reducing interference from non-informative tokens.

3.5.2. Ablation Study Under WD-5/5 Protocol

To evaluate the components under more constrained scenarios, the ablation study was repeated under the WD-5/5 Protocol, where only five reference samples are used for registration. The results are summarized in

Table 10. Ablation study results of core modules across three datasets under WD-5/5 Protocol (EER, ACC, FAR, FRR in %, AUC is dimensionless). ‘✓’ indicates that the corresponding module is included, ‘✗’ indicates excluded, and ‘—’ indicates not applicable.

Variants	Sequence Branch	Global Branch	Fusion Method	Closed-Loop Feedback	Padding Masking	Task 1 EER/ACC/FAR/FRR/AUC	Task 2 EER/ACC/FAR/FRR/AUC	MPIS-Sig EER/ACC/FAR/FRR/AUC
V1: Vanilla Transformer	✓	✗	—	✗	✗	18.54/74.10/35.84/19.23/0.907	6.15/92.53/12.82/2.21/0.969	14.96/85.04/14.28/15.72/0.925
V2: Global-only	✗	✓	—	✗	✗	10.94/84.41/22.89/11.56/0.945	4.98/94.20/9.90/1.71/0.975	10.46/89.54/10.13/10.82/0.948
V3: Simple Concat	✓	✓	Concat	✗	✗	10.53/85.33/21.58/11.90/0.947	3.96/95.02/8.66/1.45/0.980	9.33/90.67/9.42/9.66/0.953
V4: + Bi-Fusion	✓	✓	Bi-Guided	✗	✗	10.42/85.97/20.59/10.84/0.948	3.96/95.02/8.66/1.45/0.980	9.33/90.67/9.42/9.66/0.953
V5: + Feedback	✓	✓	Bi-Guided	✓	✗	9.23/87.23/19.25/9.51/0.954	2.67/95.31/8.26/1.21/0.987	7.56/92.44/7.35/7.82/0.962
Ours: + Padding Masking	✓	✓	Bi-Guided	✓	✓	9.06/88.02/18.75/9.06/0.955	2.45/95.52/7.92/1.04/0.988	5.12/94.76/4.94/5.39/0.974

.

With the reference samples halved, the intra-class variation captured by the model is limited, leading to increased error rates across all variants. However, the performance improvement trend remains consistent with the WD-10/10 Protocol. The baseline variant V1 yields EERs of 18.54%, 6.15%, and 14.96%, and ACCs of 74.10%, 92.53%, and 85.04% on the three datasets. The full model (Ours) yields EERs of 9.06%, 2.45%, and 5.12%, corresponding to reductions of 9.48 pp, 3.70 pp, and 9.84 pp compared to V1. The continued performance gains indicate that the guided fusion and feedback modules help mitigate overfitting in few-shot scenarios, while the masking mechanism maintains its effect when processing trajectory sequences of varying lengths.

3.5.3. Parameter and Complexity Analysis

Figure 6 illustrates the EER trajectories under both the WD-10/10 and WD-5/5 protocols, along with the corresponding computational complexity (FLOPs) and model size (Parameters) for each variant.

V2 (global-only) has the lowest parameter count (15.43 K) and computational cost (0.01 M FLOPs) but yields high error rates. The pure Transformer baseline (V1) requires 17.51 M FLOPs and 178.41 K parameters. The simple concatenation variant (V3) exhibits a slight increase in complexity, requiring 17.52 M FLOPs and 193.84 K parameters. Replacing concatenation with the bi-directional-guided fusion (V4) reduces the computational cost to 14.90 M FLOPs and parameters to 182.25 K, indicating that the guided mechanism effectively filters out redundant feature mappings and reduces computation. The addition of the feedback module (V5) brings the FLOPs to 17.56 M and parameters to 198.09 K.

The full model (Ours) operates with 23.67 M FLOPs and 218.24 K parameters. Although the padding-aware attention mechanism introduces a marginal increase in computational overhead compared to V5, the full model consistently yields the lowest EER across all tested datasets and evaluation protocols.

3.6. Multi-Posture Robustness and Specific Forgery Security Analysis

To investigate the model’s robustness against variations in physical writing and its defense capabilities against different attack strategies, an evaluation was conducted using the fine-grained sub-category labels from the MPIS-Sig dataset. The analysis focuses on multi-posture False Rejection Rates (FRRs) and specific forgery False Acceptance Rates (FARs), which are detailed in

Table 11. False Rejection Rate (FRR, %) across distinct writing postures on the MPIS-Sig dataset.

Test Set Sub-Category	Posture Description	FRR (10-Shot) (%)	FRR (5-Shot) (%)
HPG	High Position Grip	1.10	1.38
VSW	Variable Speed Writing	1.75	2.69
NW	Normal Writing	2.94	3.35
SW	Standing Writing	1.74	1.87

and

Table 12. False Acceptance Rate (FAR, %) across specific forgery types on the MPIS-Sig dataset.

Test Set Sub-Category	Forgery Type	FAR (10-Shot) (%)	FAR (5-Shot) (%)
RF	Random Forgery	3.05	14.75
SF	Skilled Forgery	0.00	1.99

, respectively.

Table 11 presents the system’s FRRs across four distinct physical writing conditions. The FT-Transformer demonstrates strong posture invariance. Under the standard WD-10/10 protocol, the FRR remains consistently below 3.00% across all tested conditions. Even when the training set is reduced to the 5-shot protocol, the performance degradation is minimal. The most noticeable fluctuation occurs in Variable Speed Writing (VSW), where the FRR increases from 1.75% to 2.69%. This change aligns with theoretical expectations: intentional variations in speed disrupt the temporal distribution of kinematic features such as velocity and acceleration. However, the maximum FRR is still constrained to 3.35% (Normal Writing), confirming that the padding-aware attention mechanism accommodates variations in intra-class trajectories caused by posture changes.

Table 12 outlines the security performance of the system against specific forgery types. Under the 10-shot protocol, no false acceptances of Skilled Forgeries (SFs) were observed (yielding an empirical FAR of 0.00%), and the FAR remains at 1.99% under the 5-shot protocol. In contrast, Random Forgeries (RFs) exhibit a higher FAR, recording 3.05% under the 10-shot protocol and increasing to 14.75% under the 5-shot protocol.

3.7. Sensitivity Analysis of Training Sample Scale

To quantitatively evaluate the sensitivity of the FT-Transformer to the number of writer-specific training samples, this section compares its performance under the WD-10/10 and WD-5/5 protocols.

Table 13. Sensitivity impact of training sample scale on model performance.

Dataset	Training Scale	ACC (%)	FAR (%)	FRR (%)	EER (%)
SVC2004 Task 1	10-shot	94.69	7.81	2.81	2.81
	5-shot	88.02	18.75	5.21	9.06
SVC2004 Task 2	10-shot	99.53	0.63	0.31	0.16
	5-shot	95.52	7.92	1.04	2.40
MPIS-Sig	10-shot	98.02	1.98	1.52	1.75
	5-shot	94.76	4.94	5.30	5.12

summarizes the results on the three datasets, including ACC, FAR, FRR, and EER. Figure 7 presents the corresponding confusion matrices, which illustrate the changes in hard-decision classification outcomes under different training sample scales.

As shown in Table 13, reducing the training scale from 10-shot to 5-shot leads to higher error rates on all three datasets. However, the degree of performance degradation differs across datasets, suggesting that the influence of training sample scale is related to the available feature information and dataset characteristics.

On SVC2004 Task 1, which contains only 2D spatial coordinates, the model shows the largest sensitivity to the reduction in training samples. When the protocol changes from WD-10/10 to WD-5/5, the ACC decreases from 94.69% to 88.02%, while the EER increases from 2.81% to 9.06%. The FAR also increases from 7.81% to 18.75%, indicating that false acceptances become more frequent under the 5-shot setting. This result suggests that spatial-coordinate information alone may be insufficient to maintain stable verification performance when writer-specific training samples are highly limited.

On SVC2004 Task 2, the model is less affected by the reduction in training samples. Although the ACC decreases from 99.53% to 95.52%, the EER remains relatively low at 2.40% under the WD-5/5 protocol. The FAR and FRR are 7.92% and 1.04%, respectively. Compared with Task 1, the smaller increase in EER indicates that the additional dynamic features in Task 2 provide more discriminative information under limited-sample conditions.

For the MPIS-Sig dataset, the performance degradation is also moderate. When the training scale is reduced from 10-shot to 5-shot, the ACC decreases from 98.02% to 94.76%, and the EER increases from 1.75% to 5.12%. The FAR and FRR under the 5-shot protocol are 4.94% and 5.30%, respectively, showing a relatively balanced error distribution. The corresponding confusion matrix also shows comparable numbers of false acceptances and false rejections. These results indicate that the proposed method maintains stable verification performance on MPIS-Sig despite the reduced number of writer-specific training samples.

Overall, the sensitivity analysis indicates that reducing the training sample scale leads to performance degradation across all datasets, with the impact being more pronounced on SVC2004 Task 1 than on SVC2004 Task 2 and MPIS-Sig.

4. Discussion

4.1. Analysis of Deployment Applicability and Security Properties

All experiments in this study were conducted under the Writer-Dependent (WD) protocol. This protocol introduces both genuine and forgery samples of target users during the fine-tuning phase to quantify the upper discrimination limit of the algorithm under controlled conditions. In specialized high-security applications, the incorporation of forgery samples can be regarded as an adversarial hardening strategy, where high-fidelity attacks are simulated to calibrate decision boundaries for specific users. Nevertheless, the WD protocol differs from the Forgery-free Enrollment paradigm adopted in mainstream consumer authentication systems, where only a limited number of genuine samples are available during registration. Therefore, extending the proposed framework to forgery-free learning paradigms that do not require impostor samples remains an important direction toward broader real-world deployment.

In terms of security analysis, the model achieved a lower False Acceptance Rate (FAR) for Skilled Forgeries than for Random Forgeries on the MPIS-Sig dataset. One possible explanation is that deliberate imitation may introduce additional temporal irregularities, such as pen pauses and fluctuations in kinematic parameters, which can be captured by the learned dynamic representations. However, this phenomenon may be influenced by dataset characteristics and experimental settings and therefore requires further validation on larger public benchmark datasets. Consequently, no universal conclusion is drawn in this study.

In contrast, although Random Forgeries exhibit greater differences in spatial structure, their writing process still follows authentic neuromotor rhythms. Under the extreme 5-shot protocol, the restricted reference sample diversity may be insufficient to fully characterize individual writing variability, resulting in relatively loose decision boundaries. Consequently, some fluently written Random Forgery samples may still be falsely accepted, representing the primary failure case of the system. This observation suggests that stronger spatial discrimination and richer enrollment information are beneficial for reducing false acceptance risk in practical applications.

4.2. Analysis of the Architectural Design

The stable performance exhibited by FT-Transformer under few-shot and multi-posture scenarios can be attributed to the effective adaptation of its architecture to the characteristics of online signature data. Two factors are particularly important.

First, the bi-directional-guided fusion mechanism alleviates intra-class variability caused by posture changes and external disturbances. Variations in writing posture and grip style mainly affect local trajectories, whereas global statistical attributes, such as total duration and trajectory aspect ratio, exhibit stronger writer-specific stability. By enabling semantic interaction before feature concatenation, the proposed mechanism allows global statistical information to complement temporal dynamics, thereby improving feature consistency under posture variations. This advantage becomes more evident on datasets containing richer dynamic information.

Second, the padding-aware attention and closed-loop feedback mechanisms jointly improve feature robustness under few-shot conditions. Since online signatures vary considerably in length, zero-padding regions introduced during batch processing may introduce non-informative noise and aggravate overfitting. The masking mechanism suppresses attention responses to invalid padded regions, while high-level semantic feedback provides additional global guidance for low-level feature learning. Together, these components improve verification performance while maintaining a lightweight architecture. Furthermore, the sample-size sensitivity analysis indirectly supports the effectiveness of the proposed design, as the fusion of multidimensional dynamic features and global statistical priors significantly reduces dependence on the number of enrollment samples.

4.3. Limitations and Future Work

This study still has several limitations that warrant further investigation. First, the current evaluation is based on the supervised WD protocol, and the effectiveness of the proposed architecture under forgery-free enrollment settings remains to be investigated. Future work will explore adapting the framework to forgery-free scenarios through metric-learning approaches, such as prototypical networks and contrastive learning. Second, all experiments were conducted using the same digitizing tablet model. Since different sampling rates and sensor precision may introduce distribution shifts, cross-device domain adaptation will be investigated to improve generalization under heterogeneous hardware conditions. Third, the self-built MPIS-Sig dataset contains a limited number of participants with restricted demographic diversity. Future studies will expand the dataset scale and diversity by including additional subjects and more realistic acquisition conditions, such as touchscreen-based signature input and varying screen friction coefficients.

5. Conclusions

To address the challenges of online signature verification under few-shot enrollment and multi-posture writing scenarios, this study proposed a lightweight FT-Transformer architecture. The proposed model constructs a dual-branch feature space composed of temporal dynamic and global statistical features and incorporates bi-directional-guided fusion, padding-aware attention masking, and a closed-loop feedback mechanism to improve feature robustness under limited training samples.

The experimental results on the public SVC2004 benchmark and the self-built MPIS-Sig dataset demonstrated that the proposed model consistently outperformed mainstream baseline methods under both standard and extreme few-shot settings while exhibiting strong robustness to posture variations and skilled forgery attacks. Moreover, the lightweight design effectively controlled parameter count and computational cost, achieving a favorable trade-off between verification accuracy and efficiency. These findings indicate that the proposed framework provides a feasible lightweight solution for resource-constrained online signature authentication and offers practical insights into heterogeneous feature fusion for behavioral biometric verification tasks.