KAN-CFD: Continual Face Forgery Detection

• The paper presents KAN-CFD, a novel framework that uses localized RBF activations to achieve continual face forgery detection while addressing catastrophic forgetting.
• It employs a Domain-Group KAN Detector (DG-KD) and a feature separation module (FS-KDCP) to maintain accuracy and adapt to sequential, distribution-shifting tasks.
• Empirical evaluations show that KAN-CFD outperforms competing methods with state-of-the-art accuracy and minimal average forgetting across multiple benchmarks.

KAN-based Continual Face Forgery Detection (KAN-CFD) refers to a framework that leverages Kolmogorov-Arnold Networks (KANs) for continual face forgery detection, addressing catastrophic forgetting while operating in a data-free domain-incremental setting. KAN-CFD is structured around a Domain-Group KAN Detector (DG-KD) and a feature separation module (FS-KDCP) that together maintain detection accuracy across sequentially encountered, distribution-shifting face forgery tasks (Zhang et al., 5 Aug 2025).

1. Architectural Foundations: Kolmogorov-Arnold Networks and Domain-Group KAN Detector

KANs employ locally plastic spline-based activations, defined as

$\varphi(x) = \sum_{i=1}^K a_i B_i(x)$

where $B_i(x)$ are (e.g.) cubic B-spline or RBF bases, and $a_i$ are learnable coefficients. The key property—locality—implies that updates to $a_i$ alter only a confined region of $\varphi$'s domain.

For high-dimensional image feature spaces, KAN-CFD replaces splines with Gaussian RBFs:

$$\varphi_{ij}(x_j) = \exp\left(-\frac{(x_j-c_{ij})^2}{2\sigma_{ij}^2}\right)$$

To efficiently map $d_{in}$-dimensional features to $d_{out}$ outputs, input dimensions are grouped (group size $d_g \approx d_{in}/g$), with all $\varphi_{ij}$ in a group sharing a center $B_i(x)$0 and bandwidth $B_i(x)$1.

The DG-KD layer for task $B_i(x)$2 operates as

$B_i(x)$3

with $B_i(x)$4 fixed and only the group-specific RBF parameters $B_i(x)$5 trained per task. After $B_i(x)$6 tasks, each dimension group’s activation is a local sum:

$B_i(x)$7

yielding global output

$B_i(x)$8

This achieves both “locality” (minimal interference) and “local plasticity” (capacity for adaptation).

2. Feature Separation and Drift Compensation: FS-KDCP

Performance on earlier forgery domains typically declines when training on new domains due to feature-space drift—semantic shifts in extracted features from the backbone. KAN-CFD employs FS-KDCP to address both overlap and drift in feature space without storing raw images.

This is accomplished via:

• SUR Selection: For each completed task $B_i(x)$9, a sample of 500 representative $a_i$0-dimensional features is stored: $a_i$1.
• KAN Projection: A projection $a_i$2 (one DG-Layer) aligns old backbone features to the new task space by minimizing

$a_i$3

yielding $a_i$4.

• Contrastive Separation: After projection, features are further separated into non-overlapping clusters through supervised contrastive loss:

$a_i$5

Old and new task features (each annotated with domain/class labels) are pushed apart in feature space; this simulates a convex projection without explicit computation.

3. Unified Loss Function and Optimization

KAN-CFD trains all modules end-to-end with a composite objective:

$a_i$6

where

• $a_i$7: standard binary cross-entropy for classification
• $a_i$8: supervised contrastive separation (with $a_i$9)
• $a_i$0: feature-level distillation to regularize the backbone, defined as

$a_i$1

with $a_i$2.

The projection $a_i$3 is specifically trained with $a_i$4. DG-KD requires no additional regularization due to the intrinsic locality of its RBF structure.

4. Data-Free Continual Learning Protocol

KAN-CFD is strictly data-free in that it refrains from storing or replaying raw images. Instead, it operates as follows:

• After each task, a “feature memory” of 500 vectors (obtained via SUR) captures salient characteristics of that task’s domains.
• Upon encountering a new task, these features are mapped through $a_i$5 to synchronize with the updated backbone, then augmented by Gaussian noise to approximate the prior distribution.
• The augmented and separated features are treated as “pseudo-replay” samples and included alongside new-task features during DG-KD training, ensuring each DG-Layer only covers its task domain’s region in input space.

This strategy prevents catastrophic forgetting even when explicit data replay is infeasible.

5. Experimental Protocols and Empirical Outcomes

KAN-CFD has been evaluated on multiple challenging benchmarks and task protocols:

• Datasets: FF++ (Deepfakes, Face2Face, FaceSwap, NeuralTextures), DFD, DFDC-P, and Celeb-DF v2.
• Protocols:
  • Dataset-Incremental: Each dataset forms a stage ([FF++, DFDC-P, DFD, CDF2]).
  • Forgery-Type-Incremental: Task sequence based on forgery type (e.g., Face-Reenactment, Face-Swap).
  • Long-sequence: 10 tasks sampled from DF40.

Metrics:

• Accuracy (Acc %) or Area Under Curve (AUC %) per task post-training.
• Average Forgetting (AF): $a_i$6.

Key Results

Method	Dataset-Incremental Avg Acc ↑	AF ↓	Forgery-Type Avg AUC ↑	AF ↓
CoReD	81.22	11.42	–	–
DFIL	85.49	7.01	–	–
SUR-LID	91.11	4.39	94.33	2.99
KAN-CFD	91.64	4.08	94.40	2.60

In long-sequence evaluation, KAN-CFD reports average accuracy $a_i$7 and the lowest AF across all compared methods.

Ablations reveal:

• The full system (all loss terms, feature separation + KDCP) yields AF ≈ 4.1%.
• Feature separation without KDCP leads to significantly higher forgetting (AF≈16.04%), underscoring the importance of drift compensation.
• MLPs with global activations show higher AF (28.3%), compared to DG-KD (4.1%), supporting the advantage of localized adaptation.

UMAP visualizations demonstrate that only with full FS-KDCP are task-specific feature clusters both separable and stable across task increments.

6. Context, Limitations, and Interpretive Notes

KAN-CFD’s modular combination of localized functional adaptation (via DG-KD) and explicit separation of evolving feature domains (via FS-KDCP) provides state-of-the-art results in sequential face forgery detection while bypassing the need for raw data replay. This design specifically addresses two critical issues with KANs in high-dimensional, non-stationary settings: difficulty modeling images with splines and repeated overlap/collapse of feature mappings in continual learning scenarios. The empirical comparison against prior methods such as CoReD, DFIL, SUR-LID, and KAC highlights marked improvements in both accuracy and forgetting rates (Zhang et al., 5 Aug 2025).

A plausible implication is that the general structure—local activation functions and data-free drift compensation—can be adapted to other domain-incremental visual tasks, though the number of stored memory vectors and choice of backbone architecture may constrain scalability in more finegrained or open-set problems.

7. Summary Table: Module Functions

Module	Core Mechanism	Continual Learning Contribution
DG-KD	Domain-wise local RBF activations & grouping	Limits interference via “local plasticity”
FS-KDCP	KAN projection + contrastive separation	Maintains domain separation and compensates
		for backbone feature drift

KAN-CFD establishes a paradigm for efficient, data-free continual learning in adversarial image domains, leveraging the unique properties of KANs—locality and plasticity—in conjunction with minimal, memory-based replay and feature space manipulation to suppress catastrophic forgetting and sustain high detection fidelity across evolving face forgery datasets (Zhang et al., 5 Aug 2025).