Improving the interpretability and performance of neural networks with Wavelet-integrated Kolmogorov-Arnold Networks (Wav-KAN)

Advances in ai have given rise to competent systems that make unclear decisions, raising concerns about the deployment of untrustworthy ai in daily life and the economy. Understanding neural networks is vital for trust, ethical concerns such as algorithmic bias, and scientific applications that require model validation. Multilayer perceptrons (MLPs) are widely used but lack interpretability compared to attention layers. The model renewal aims to improve interpretability with specially designed components. Based on Kolmogorov-Arnold Networks (KAN), it offers improved interpretability and accuracy based on the Kolmogorov-Arnold theorem. Recent work extends KANs to arbitrary widths and depths using B-splines, known as Spl-KAN.

Researchers at Boise State University have developed Wav-CAN, a neural network architecture that improves interpretability and performance by using wavelet functions within the KAN framework. Unlike traditional MLPs and Spl-KAN, Wav-KAN efficiently captures high- and low-frequency data components, improving training speed, accuracy, robustness, and computational efficiency. By adapting to the data structure, Wav-KAN avoids overfitting and improves performance. This work demonstrates the potential of Wav-KAN as a powerful and interpretable neural network tool with applications in various fields and implementations in frameworks such as PyTorch and TensorFlow.

Wavelets and B-splines are key methods for function approximation, each with unique advantages and drawbacks in neural networks. B-splines offer smooth, locally controlled approximations, but have problems with high-dimensional data. Excelling at multi-resolution analysis, wavelets handle high- and low-frequency data, making them ideal for feature extraction and efficient neural network architectures. Wav-KAN outperforms Spl-KAN and MLP in speed, accuracy, and robustness of training by using wavelets to capture data structure without overfitting. Wav-KAN's parameter efficiency and lack of dependence on grid spaces make it superior for complex tasks, supported by batch normalization to improve performance.

KANs are inspired by the Kolmogorov-Arnold representation theorem, which states that any multivariate function can be decomposed into the sum of univariate functions of sums. In KANs, instead of traditional weights and fixed activation functions, each “weight” is a learnable function. This allows KANs to transform inputs through adaptive functions, leading to more accurate function approximation with fewer parameters. During training, these functions are optimized to minimize the loss function, improving the accuracy and interpretability of the model by directly learning relationships from the data. Therefore, KANs offer a flexible and efficient alternative to traditional neural networks.

Experiments with the KAN model on the MNIST data set using various wavelet transforms showed promising results. The study used 60,000 training images and 10,000 test images, with wave types including Mexican hat, Morlet, derivative of Gauss (DOG), and Shannon. Wav-KAN and Spl-KAN employed batch normalization and had a structure of (28*28,32,10) nodes. The models were trained for 50 epochs in five trials. Using the AdamW optimizer and cross-entropy loss, the results indicated that wavelets such as DOG and Mexican hat outperformed Spl-KAN in effectively capturing essential features and maintaining robustness against noise, emphasizing the critical role of wavelet selection. wavelets.

In conclusion, Wav-KAN, a new neural network architecture, integrates wavelet functions into KAN to improve interpretability and performance. Wav-KAN captures complex data patterns using multi-resolution wavelet analysis more effectively than traditional MLP and Spl-KAN. Experiments show that Wav-KAN achieves higher accuracy and faster training speeds due to its unique combination of wavelet transforms and the Kolmogorov-Arnold representation theorem. This structure improves parameter efficiency and model interpretability, making Wav-KAN a valuable tool for various applications. Future work will further optimize the architecture and expand its implementation in machine learning frameworks such as PyTorch and TensorFlow.

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