Double-branch counterfeit watermark tracking detection model based on Kolmogorov-Arnold network and differential perception

Abstract

The invention discloses a dual-branch counterfeit watermark tracking detection model based on a Kolmogorov-Arnold network and differential perception. The dual-branch counterfeit watermark tracking detection model is characterized in that the detection model comprises a traceability branch and a counterfeit detector branch; the traceability branch comprises an encoder, the encoder is used for receiving a real face image CF (Clean face) and binary watermark information Wm (Watermark message), and a face image EF (Encoded face) with a watermark is generated; the forgery detector branch decoder extracts WFD from common distorted and depfake distorted images respectively, whether the WFD is forged or not is determined through consistency comparison, and the branch constructs an SAEM to improve the sensitivity to a damaged area; the traceability branch comprises an MSPD discriminator arranged between the encoder and the counterfeited object detector branch. Compared with the prior art, the method has the advantages that the robustness of tampering watermarks to traceability can be ensured, the traceability is ensured, and the accuracy of counterfeited object detection is improved by a counterfeited object detector branch.

Description

Technical Field

[0001] The present invention relates to the technical field of watermark tracing and detection, in particular to a double-branch forged watermark tracing and detection model based on a Kolmogorov-Arnold network and differential perception. Background Art

[0002] The concept of watermarking in active forensics originates from digital watermarking technology. Its core idea is to embed invisible watermarks during the content generation process to enable the traceability and verification of forged content. With the rapid development of deepfake technology, watermarking technology has been widely used in deepfake tracing and detection, and has made significant progress in multiple fields.

[0003] While active forensics has made progress in forgery detection and content tracing, existing approaches still face several technical challenges. First, many existing methods couple detection and tracing functions within a single network architecture, leading to performance conflicts and making it difficult to strike a balance between robustness and sensitivity. This coupling makes it difficult for systems to maintain high robustness against complex forgeries while also failing to maintain high sensitivity against more subtle forgeries.

[0004] Second, existing watermarking methods lack semantic modeling, making them susceptible to interference from deepfakes (such as deepfakes). This not only reduces the robustness of the watermark but also severely impacts its traceability. Deepfakes, through sophisticated generation and modification, can easily undermine the effectiveness of traditional watermarking techniques, making it even more difficult to trace the forged content.

[0005] Furthermore, existing methods lack a robust response mechanism to localized tampering, making watermarking particularly vulnerable to subtle structural changes in images. Localized tampering typically manifests as subtle changes in image details, but these changes are often difficult to capture effectively using traditional watermark embedding and extraction techniques, resulting in the watermark being unable to detect and identify these forgeries.

[0006] In summary, although existing active forensics technologies have made some progress in many aspects, with the continuous development of forgery technology, existing methods still face many challenges in terms of robustness, sensitivity, and local tampering detection. These problems indicate that future research needs to further optimize and innovate in terms of watermark robustness, resistance to deep forgeries, and the ability to perceive subtle tampering. Summary of the Invention

[0007] The technical problem to be solved by the present invention is to overcome the above technical defects.

[0008] In order to solve the above problems, the technical solution of the present invention is: a dual-branch forged watermark tracing detection model based on Kolmogorov-Arnold network and differential perception, wherein the detection model includes a tracing branch and a forged object detector branch;

[0009] The tracing branch includes an encoder, which receives a real face image CF (Clean face) and binary watermark information Wm (Watermark message) to generate a watermarked face image EF (Encoded face). EF is then input into a forged noise pool to introduce common distortion and deepfake distortion to produce a diverse distorted image NF (Noisy face). The decoder recovers the robust watermark information WST from NF. This branch integrates the Tok-KAN module for complex semantic modeling and the SDM module for enhancing the robustness of edges and high-frequency areas.

[0010] The forgery detector branch is trained under common distortions to maintain the "fragility" of the watermark and avoid co-adaptation with deepfake noise. The watermark is distorted or lost during the forgery process, forming a detectable difference signal. The decoder extracts WFD from the images with common distortion and deepfake distortion, respectively, and determines whether it is forged through consistency comparison. This branch constructs SAEM to improve sensitivity to damaged areas;

[0011] The provenance branch includes an MSPD discriminator between the encoder and the forgery detector branch, which performs multi-scale perceptual comparison between the original image CF and the watermarked image EF to help the collaborative optimization of the two branches in terms of visual quality and hiding.

[0012] Furthermore, the traceability branch includes a Tok-KAN module;

[0013] The feature modeling capability is enhanced through tokenized feature sequences and adaptive B-spline transformation. Tok-KAN includes tokenization and KANBlock, which are responsible for feature embedding and nonlinear refinement.

[0014] Token: In the tokenized KAN phrase process, the deep two-dimensional feature map output by the convolution stage is first divided into a series of fixed-size tokens through patch embedding and mapped into a high-dimensional feature space. This tokenization process mainly converts the output feature XL of the convolution stage into a series of flat two-dimensional patches, which can be mathematically expressed as follows:

[0015]

[0016] P×P is the size of each block, CL represents the number of input channels, is the total number of feature blocks, where HL and WL represent the height and width of the input feature map respectively;

[0017] Each tokenized feature block Through a trainable linear transformation matrix is mapped into a high-dimensional embedding space to obtain feature representation:

[0018]

[0019] Among them, Z0∈R N×D is the resulting tag sequence, where each tag is mapped to a D-dimensional vector through linear projection to form a complete tag sequence;

[0020] KANBlock: The input is first normalized through the layer to enhance data stability and alleviate the vanishing gradient problem. KANLayer alternately applies KANLinear interpolation and depthwise separable convolution (DWConv) to optimize feature maps, improving expressiveness and computational efficiency.

[0021] During feature conversion, the DropPath mechanism randomly discards paths to improve generalization and reduce overfitting. The residual connection fuses the input features with the transformation results, ensuring stable gradient propagation and improving training stability and convergence. The whole process can be expressed as:

[0022] X′=X+DropPath(KANLayer(LayerNorm(X),H,W))

[0023] The input feature is represented by X, while H and W represent the height and width of the feature map. LayerNorm normalizes the input, KANLayer combines B-spline interpolation and DWConv for feature mapping, DropPath randomly deletes the calculation path to enhance generalization, and residual connection ensures stable gradient propagation;

[0024] KANLayer: Processes the tokenized feature sequence Z0 from the tokenized KAN phrase as the first step of feature transformation. KANLayer combines KANLinear and depthwise separable convolution (DWConv) to enhance the robustness of the watermark against various attacks and forgeries, as well as the concealment of the watermark embedding, while improving the model's adaptability to tampering attacks.

[0025] KANLinear performs nonlinear mapping to give the input data a complex feature distribution, thereby improving watermark embedding and resisting Deepfake attacks. Subsequently, DWConv reduces computation by using channel grouping convolution and combines batch normalization and ReLU to improve efficiency and versatility, ensuring effective watermark extraction under various interference conditions.

[0026] In the calculation process of KANLayer, the input feature X undergoes three layers of alternating KANLinear and DWConv operations to produce the output feature X'. First, X0 = X is used as the initial input of KANLayer. At each layer k (k = 1, 2, 3), KANLinear performs nonlinear transformations to make the feature map better fit the complex data distribution. This is followed by DWConv, which extracts local features and enhances the nonlinear representation. The calculation process can be expressed as:

[0027] Z k =LayerNorm(Z k-1 )+DropPath(D k (KANLinear k (Z k-1 )),k=1,2,3

[0028] Finally, after three layers of transformation, the output feature is X'=Z3;

[0029] KANLinear: In watermark embedding tasks, the balance between robustness and stealth ensures that watermarks resist various tampering attacks without degrading image quality. Traditional linear transformations are difficult to adapt to complex data distributions, limiting the effectiveness of watermark modeling. KANLinear is an adaptive nonlinear transformation method based on B-spline interpolation. KANLinear optimizes interpolation by dynamically adjusting grid control points and adjusting the grid according to the input data distribution, improving the versatility of various tampering methods and preventing over-adaptation to specific attack patterns.

[0030] For the input feature vector X∈R B×D , where B is the batch size and D is the input feature dimension. KANLinear maps features through a combination of standard linear projection and adaptive B-spline interpolation. This transformation is expressed as:

[0031] Z=W base ·σ(X)+W spline ·B(X)

[0032] in, Represents the weight matrix of the standard linear transformation, σ(X) uses the Luce activation function, and It is a trainable B-spline interpolation weight. B(X) calculates the projection of the input data on the B-spline control points to describe the interpolation relationship.

[0033] In KANLinear, the B-spline activation function is expressed as a weighted sum of learnable margin functions φ(x), given by:

[0034]

[0035] Among them B i (x) represents the i-th basis function, c i is its learnable coefficient. The number of basis functions depends on the control points. The term n′>n conditionally increases the number of basis functions during grid expansion, thereby increasing the control point density and ensuring a smooth transition between coarse and fine grids.

[0036] Traditional fixed-grid interpolation methods have difficulty handling complex data distributions. B-spline control points are optimized based on the data distribution, combining uniform and adaptive grids to maintain global consistency while flexibly adjusting local interpolation.

[0037] The uniform grid is constructed based on the minimum and maximum values ​​of the input data x, which ensures that the grid points are evenly distributed:

[0038]

[0039]

[0040] Where ε is the boundary expansion term used to ensure smooth transitions at the boundaries, and K is the number of grid control points. The index k determines the grid position and the points are evenly distributed in [x min -ε,x max +ε], where k is in [0, K];

[0041] To enhance the adaptability to different data distributions, we introduce adaptive grids. By sorting the input data and selecting non-uniform grid points based on the data distribution, we adjust the grid layout to better match the data distribution:

[0042] X′ sorted =sort(X)

[0043]

[0044] Where X is the input data, X′ sorted is the sorted data, G adaptive represents a dynamically selected grid point;

[0045] Finally, we use the weight parameter to fuse the uniform and adaptive grids:

[0046] G=αG uniform +(1-α)G adaptive

[0047] This parameter α controls the weight distribution and optimizes the selection of control points to make the interpolation more consistent with the data distribution, thereby enhancing the cartographic expression ability of the features;

[0048] On the optimized grid G, we use the De Boor recursive formula to calculate the B-spline basis function, which ensures numerical stability and smooth interpolation. The B-spline transformation improves feature modeling by dynamically adjusting the control points, enhancing the robustness and adaptability of the watermark. The overall transformation is expressed as:

[0049] S=B(X)∈R B×D×C

[0050] S represents the feature representation after B-spline transformation, B(X) projects the input data X onto the control points, B is the batch size, D is the feature size, C is the number of control points, and De Boor recursive formula is used to calculate the interpolation between control points;

[0051]

[0052] Among them B i,k (x) represents the B-spline weight at the i-th control point and order k, G i is the i-th control point, and x is the input data point. This recursion ensures smooth interpolation and improves the robustness and visual imperceptibility of the watermark.

[0053] The advantages of the present invention compared with the existing technology are:

[0054] The present invention consists of two branch models: the source tracing branch accurately tracks the watermark information under various distortions to ensure that the extraction is not affected; the forgery detector branch introduces selective vulnerability, maintains a low bit error rate under common distortions, and exhibits a higher bit error rate under malicious forgery, and uses the consistency difference before and after watermark extraction to achieve forgery detection. Under common distortions (for example, compression, blur, noise, etc.), the BER of the source tracker branch is close to 0), showing excellent robustness, ensuring the accurate extraction and traceability of watermark information. DETAILED DESCRIPTION

[0055] In order to make the contents of the present invention more clearly understood, the technical solutions in the embodiments of the present invention will be clearly and completely described below in combination with the embodiments of the present invention.

[0056] A dual-branch forged watermark tracing and detection model based on the Kolmogorov-Arnold network and differential perception, wherein the detection model includes a tracing branch and a forgery detector branch;

[0057] The tracing branch includes an encoder, which receives a real face image CF (Clean face) and binary watermark information Wm (Watermark message) to generate a watermarked face image EF (Encoded face). EF is then input into a forged noise pool to introduce common distortion and deepfake distortion to produce a diverse distorted image NF (Noisy face). The decoder recovers the robust watermark information WST from NF. This branch integrates the Tok-KAN module for complex semantic modeling and the SDM module for enhancing the robustness of edges and high-frequency areas.

[0058] The forgery detector branch is trained under common distortions to maintain the "fragility" of the watermark and avoid co-adaptation with deepfake noise. The watermark is distorted or lost during the forgery process, forming a detectable difference signal. The decoder extracts WFD from the images with common distortion and deepfake distortion, respectively, and determines whether it is forged through consistency comparison. This branch constructs SAEM to improve sensitivity to damaged areas;

[0059] The provenance branch includes an MSPD discriminator between the encoder and the forgery detector branch, which performs multi-scale perceptual comparison between the original image CF and the watermarked image EF to help the collaborative optimization of the two branches in terms of visual quality and hiding.

[0060] The traceability branch includes the Tok-KAN module; the feature modeling capability is enhanced through tokenized feature sequences and adaptive B-spline transformation. Tok-KAN includes tokenization and KANBlock, which are responsible for feature embedding and nonlinear refinement.

[0061] Token: In the tokenized KAN phrase process, the deep two-dimensional feature map output by the convolution stage is first divided into a series of fixed-size tokens through patch embedding and mapped into a high-dimensional feature space. This tokenization process mainly converts the output feature XL of the convolution stage into a series of flat two-dimensional patches, which can be mathematically expressed as follows:

[0062]

[0063] P×P is the size of each block, CL represents the number of input channels, is the total number of feature blocks, where HL and WL represent the height and width of the input feature map respectively;

[0064] Each tokenized feature block Through a trainable linear transformation matrix is mapped into a high-dimensional embedding space to obtain feature representation:

[0065]

[0066] Among them, Z0∈R N×D is the resulting tag sequence, where each tag is mapped to a D-dimensional vector through linear projection to form a complete tag sequence;

[0067] KANBlock: The input is first normalized through the layer to enhance data stability and alleviate the vanishing gradient problem. KANLayer alternately applies KANLinear interpolation and depthwise separable convolution (DWConv) to optimize feature maps, improving expressiveness and computational efficiency.

[0068] During feature conversion, the DropPath mechanism randomly discards paths to improve generalization and reduce overfitting. The residual connection fuses the input features with the transformation results, ensuring stable gradient propagation and improving training stability and convergence. The whole process can be expressed as:

[0069] X′=X+DropPath(KANLayer(LayerNorm(X),H,W))

[0070] The input feature is represented by X, while H and W represent the height and width of the feature map. LayerNorm normalizes the input, KANLayer combines B-spline interpolation and DWConv for feature mapping, DropPath randomly deletes the calculation path to enhance generalization, and residual connection ensures stable gradient propagation;

[0071] KANLayer: Processes the tokenized feature sequence Z0 from the tokenized KAN phrase as the first step of feature transformation. KANLayer combines KANLinear and depthwise separable convolution (DWConv) to enhance the robustness of the watermark against various attacks and forgeries, as well as the concealment of the watermark embedding, while improving the model's adaptability to tampering attacks.

[0072] KANLinear performs nonlinear mapping to give the input data a complex feature distribution, thereby improving watermark embedding and resisting Deepfake attacks. Subsequently, DWConv reduces computation by using channel grouping convolution and combines batch normalization and ReLU to improve efficiency and versatility, ensuring effective watermark extraction under various interference conditions.

[0073] In the calculation process of KANLayer, the input feature X undergoes three layers of alternating KANLinear and DWConv operations to produce the output feature X'. First, X0 = X is used as the initial input of KANLayer. At each layer k (k = 1, 2, 3), KANLinear performs nonlinear transformations to make the feature map better fit the complex data distribution. This is followed by DWConv, which extracts local features and enhances the nonlinear representation. The calculation process can be expressed as:

[0074] Z k =LayerNorm(Z k-1 )+DropPath(D k (KANLinear k (Z k-1 )),k=1,2,3

[0075] Finally, after three layers of transformation, the output feature is X'=Z3;

[0076] KANLinear: In watermark embedding tasks, the balance between robustness and stealth ensures that watermarks resist various tampering attacks without degrading image quality. Traditional linear transformations are difficult to adapt to complex data distributions, limiting the effectiveness of watermark modeling. KANLinear is an adaptive nonlinear transformation method based on B-spline interpolation. KANLinear optimizes interpolation by dynamically adjusting grid control points and adjusting the grid according to the input data distribution, improving the versatility of various tampering methods and preventing over-adaptation to specific attack patterns.

[0077] For the input feature vector X∈R B×D , where B is the batch size and D is the input feature dimension. KANLinear maps features through a combination of standard linear projection and adaptive B-spline interpolation. This transformation is expressed as:

[0078] Z=W base ·σ(X)+W spline ·B(X)

[0079] in, Represents the weight matrix of the standard linear transformation, σ(X) uses the Luce activation function, and It is a trainable B-spline interpolation weight. B(X) calculates the projection of the input data on the B-spline control points to describe the interpolation relationship.

[0080] In KANLinear, the B-spline activation function is expressed as a weighted sum of learnable margin functions φ(x), given by:

[0081]

[0082] Among them B i (x) represents the i-th basis function, c i is its learnable coefficient. The number of basis functions depends on the control points. The term n′>n conditionally increases the number of basis functions during grid expansion, thereby increasing the control point density and ensuring a smooth transition between coarse and fine grids.

[0083] Traditional fixed-grid interpolation methods have difficulty handling complex data distributions. B-spline control points are optimized based on the data distribution, combining uniform and adaptive grids to maintain global consistency while flexibly adjusting local interpolation.

[0084] The uniform grid is constructed based on the minimum and maximum values ​​of the input data x, which ensures that the grid points are evenly distributed:

[0085]

[0086] Where ε is the boundary expansion term used to ensure smooth transitions at the boundaries, and K is the number of grid control points. The index k determines the grid position and the points are evenly distributed in [x min -ε,x max +ε], where k is in [0, K];

[0087] To enhance the adaptability to different data distributions, we introduce adaptive grids. By sorting the input data and selecting non-uniform grid points based on the data distribution, we adjust the grid layout to better match the data distribution:

[0088] X′ sorted =sort(X)

[0089]

[0090] Where X is the input data, X′ sorted is the sorted data, G adaptive represents a dynamically selected grid point;

[0091] Finally, we use the weight parameter to fuse the uniform and adaptive grids:

[0092] G=αG uniform +(1-α)G adaptive

[0093] This parameter α controls the weight distribution and optimizes the selection of control points to make the interpolation more consistent with the data distribution, thereby enhancing the cartographic expression ability of the features;

[0094] On the optimized grid G, we use the De Boor recursive formula to calculate the B-spline basis function, which ensures numerical stability and smooth interpolation. The B-spline transformation improves feature modeling by dynamically adjusting the control points, enhancing the robustness and adaptability of the watermark. The overall transformation is expressed as:

[0095] S=B(X)∈R B×D×C

[0096] S represents the feature representation after B-spline transformation, B(X) projects the input data X onto the control points, B is the batch size, D is the feature size, C is the number of control points, and De Boor recursive formula is used to calculate the interpolation between control points;

[0097]

[0098] Among them B i,k (x) represents the B-spline weight at the i-th control point and order k, G i is the i-th control point, and x is the input data point. This recursion ensures smooth interpolation and improves the robustness and visual imperceptibility of the watermark.

[0099] In specific use,

[0100] Detection and tracking functions are coupled in a single network architecture, resulting in a performance conflict between robustness and sensitivity. Existing methods typically integrate detection and tracking functions into the same network architecture. This design makes it difficult for the system to find a balance between robustness and sensitivity, which in turn affects its detection accuracy for deepfake content.

[0101] To address this issue, we proposed a dual-branch network architecture, which separates source tracing and forgery detection into two independent branches. Each branch focuses on optimizing its own task objectives. The source tracing branch focuses on image robustness, ensuring that the watermark can be stably extracted after various perturbations (such as compression, cropping, and deepfakes). The forgery detection branch, on the other hand, focuses on improving sensitivity to subtle forgeries, ensuring that it can detect even the slightest changes introduced by deepfakes. This separate design allows us to more effectively balance robustness and sensitivity, improving the overall detection performance of the system.

[0102] The lack of semantic modeling makes the watermark vulnerable to interference from deep fakes, weakening the traceability of the watermark. Existing watermarking technology usually relies on low-level features of the image (such as texture, edges, etc.) to embed the watermark, while ignoring the high-level semantic information of the image, which makes the watermark vulnerable to interference in the face of deep fake attacks, thereby affecting the traceability of the forged content.

[0103] To address this issue, we propose the Tok-KAN module and the Structure-aware Difference Module (SDM) module, which aim to improve the robustness and traceability of watermarks by incorporating high-level semantic information and structural features of the image. The Tok-KAN module leverages the Kolmogorov-Arnold network (KAN) to enhance the robustness and adaptability of watermarks against complex forgeries, such as deepfakes. This module first divides the image into multiple semantic blocks and independently optimizes each block, enabling Tok-KAN to model the image's high-level semantic features. By preserving this semantic information, Tok-KAN ensures the stability of the watermark under deepfake interference, thereby enhancing its traceability. Furthermore, the nonlinear mapping process ensures that these features remain stable during image forgery, effectively improving the watermark's embedding and extraction capabilities. The Structure-aware Difference Module (SDM) improves the robustness of the watermark by enhancing the perception of image structural features, particularly the modeling of high-frequency regions. SDM uses a multi-branch structure to process different local regions in the image and adaptively adjusts according to the fine-grained structure of the image (such as edges and textures), effectively mitigating distortions caused by common operations such as compression, noise, or deep fakes. The module fuses these differential information into a unified representation, ensuring that the watermark remains stable under various noise conditions, making it more resistant to interference when combating image tampering.

[0104] Lack of response mechanism to local tampering, making it difficult to perceive fine-grained structural changes. Existing watermarking technologies generally lack response mechanisms to local tampering (such as forgery of image details or local areas). This makes it impossible for watermarks to effectively identify and repair tampering in these areas when faced with fine-grained structural changes.

[0105] The core goal of the Structure-Aware Enhancement Module (SAEM) is to enhance sensitivity to watermark corruption, particularly in the face of deepfakes, enabling effective detection and identification of watermark tampering. By introducing a position feature extraction module and a channel feature extraction module, SAEM enhances the network's ability to model key image regions, particularly high-frequency regions like edges and textures. These features enable SAEM to better capture fine-grained structural features in images, increasing the network's sensitivity to destructive forgeries and enabling accurate detection even after watermark corruption or tampering.

[0106] The above description of the present invention and its embodiments is non-limiting, and the actual structure is not limited thereto. In short, if a person skilled in the art is inspired by the above description and, without departing from the purpose of the present invention, designs a structure and embodiment similar to the technical solution without creatively designing, they shall fall within the scope of protection of the present invention.

Claims

1. A dual-branch forged watermark tracking and detection model based on the Kolmogorov-Arnold network and differential perception, characterized by: The detection model includes a provenance branch and a forgery detector branch; The tracing branch includes an encoder, which receives a real face image CF (Clean face) and binary watermark information Wm (Watermark message) to generate a watermarked face image EF (Encoded face). EF is then input into a forged noise pool to introduce common distortion and deepfake distortion to produce a diverse distorted image NF (Noisyface). The decoder recovers the robust watermark information WST from NF. This branch integrates the Tok-KAN module for complex semantic modeling and the SDM module for enhancing the robustness of edges and high-frequency areas. The forgery detector branch is trained under common distortions to maintain the "fragility" of the watermark and avoid co-adaptation with deepfake noise. The watermark is distorted or lost during the forgery process, forming a detectable difference signal. The decoder extracts the WFD from the images with common distortion and deepfake distortion, respectively, and determines whether it is forged through consistency comparison. This branch constructs the SAEM to improve sensitivity to damaged areas. The provenance branch includes an MSPD discriminator between the encoder and the forgery detector branch, which performs multi-scale perceptual comparison between the original image CF and the watermarked image EF to help the collaborative optimization of the two branches in terms of visual quality and hiding.

2. The dual-branch forged watermark tracking and detection model based on Kolmogorov-Arnold network and differential perception according to claim 1 is characterized by: The traceability branch includes a Tok-KAN module; The feature modeling capability is enhanced through tokenized feature sequences and adaptive B-spline transformation. Tok-KAN includes tokenization and KANBlock, which are responsible for feature embedding and nonlinear refinement. Token: In the tokenized KAN phrase process, the deep two-dimensional feature map output by the convolution stage is first divided into a series of fixed-size tokens through patch embedding and mapped into a high-dimensional feature space. This tokenization process mainly converts the output feature XL of the convolution stage into a series of flat two-dimensional patches, which can be mathematically expressed as follows: P×P is the size of each block, CL represents the number of input channels, is the total number of feature blocks, where HL and WL represent the height and width of the input feature map respectively; Each tokenized feature block Through a trainable linear transformation matrix is mapped into a high-dimensional embedding space to obtain feature representation: Among them, Z0∈R N×D is the resulting tag sequence, where each tag is mapped to a D-dimensional vector through linear projection to form a complete tag sequence; KANBlock: The input is first normalized through the layer to enhance data stability and alleviate the vanishing gradient problem. KANLayer alternately applies KANLinear interpolation and depthwise separable convolution (DWConv) to optimize feature maps, improving expressiveness and computational efficiency. During feature conversion, the DropPath mechanism randomly discards paths to improve generalization and reduce overfitting. The residual connection fuses the input features with the transformation results, ensuring stable gradient propagation and improving training stability and convergence. The whole process can be expressed as: X ′ =X+DropPath(KANLayer(LayerNorm(X),H,W)) The input feature is represented by X, while H and W represent the height and width of the feature map. LayerNorm normalizes the input, KANLayer combines B-spline interpolation and DWConv for feature mapping, DropPath randomly deletes the calculation path to enhance generalization, and residual connection ensures stable gradient propagation; KANLayer: Processes the tokenized feature sequence Z0 from the tokenized KAN phrase as the first step of feature transformation. KANLayer combines KANLinear and depthwise separable convolution (DWConv) to enhance the robustness of the watermark against various attacks and forgeries, as well as the concealment of the watermark embedding, while improving the model's adaptability to tampering attacks. KANLinear performs nonlinear mapping to give the input data a complex feature distribution, thereby improving watermark embedding and resisting Deepfake attacks. Subsequently, DWConv reduces computation by using channel grouping convolution and combines batch normalization and ReLU to improve efficiency and versatility, ensuring effective watermark extraction under various interference conditions. In the calculation process of KANLayer, the input feature X undergoes three layers of alternating KANLinear and DWConv operations to produce the output feature X'. First, X0 = X is used as the initial input of KANLayer. At each layer k (k = 1, 2, 3), KANLinear performs nonlinear transformations to make the feature map better fit the complex data distribution. This is followed by DWConv, which extracts local features and enhances the nonlinear representation. The calculation process can be expressed as: Z k =LayerNorm(Z k-1 )+DropPath(D k (KANLinear k (Z k-1 )),k=1,2,3 Finally, after three layers of transformation, the output feature is X'=Z3; KANLinear: In watermark embedding tasks, the balance between robustness and stealth ensures that watermarks resist various tampering attacks without degrading image quality. Traditional linear transformations are difficult to adapt to complex data distributions, limiting the effectiveness of watermark modeling. KANLinear is an adaptive nonlinear transformation method based on B-spline interpolation. KANLinear optimizes interpolation by dynamically adjusting grid control points and adjusting the grid according to the input data distribution, improving the versatility of various tampering methods and preventing over-adaptation to specific attack patterns. For the input feature vector X∈R B×D , where B is the batch size and D is the input feature dimension. KANLinear maps features through a combination of standard linear projection and adaptive B-spline interpolation. This transformation is expressed as: Z=W base ·σ(X)+W spline ·B(X) in, Represents the weight matrix of the standard linear transformation, σ(X) uses the Luce activation function, and It is a trainable B-spline interpolation weight. B(X) calculates the projection of the input data on the B-spline control points to describe the interpolation relationship. In KANLinear, the B-spline activation function is expressed as a weighted sum of learnable margin functions φ(x), given by: Among them B i (x) represents the i-th basis function, c i is its learnable coefficient, the number of basis functions depends on the control points, n ′ The >n term conditionally increases the number of basis functions during mesh expansion, thereby increasing the control point density and ensuring a smooth transition between coarse and fine meshes; Traditional fixed-grid interpolation methods have difficulty handling complex data distributions. B-spline control points are optimized based on the data distribution, combining uniform and adaptive grids to maintain global consistency while flexibly adjusting local interpolation. The uniform grid is constructed based on the minimum and maximum values ​​of the input data x, which ensures that the grid points are evenly distributed: Where ε is the boundary expansion term used to ensure smooth transitions at the boundaries, and K is the number of grid control points. The index k determines the grid position and the points are evenly distributed in [x min -ε,x max +ε], where k is in [0, K]; To enhance the adaptability to different data distributions, we introduce adaptive grids. By sorting the input data and selecting non-uniform grid points based on the data distribution, we adjust the grid layout to better match the data distribution: X′ sorted =sort(X) Where X is the input data, X′ sorted is the sorted data, G adaptive represents a dynamically selected grid point; Finally, we use the weight parameter to fuse the uniform and adaptive grids: G=αG uniform +(1-α)G adaptive This parameter α controls the weight distribution and optimizes the selection of control points to make the interpolation more consistent with the data distribution, thereby enhancing the cartographic expression ability of the features; On the optimized grid G, we use the De Boor recursive formula to calculate the B-spline basis function, which ensures numerical stability and smooth interpolation. The B-spline transformation improves feature modeling by dynamically adjusting the control points, enhancing the robustness and adaptability of the watermark. The overall transformation is expressed as: S=B(X)∈R B×D×C S represents the feature representation after B-spline transformation, B(X) projects the input data X onto the control points, B is the batch size, D is the feature size, C is the number of control points, and De Boor recursive formula is used to calculate the interpolation between control points; Among them B i,k (x) represents the B-spline weight at the i-th control point and order k, G i is the i-th control point, and x is the input data point. This recursion ensures smooth interpolation and improves the robustness and visual imperceptibility of the watermark.

Images