Abstract

Accurate modeling and forecasting of complex sequential data, spanning diverse applications from 3D human motion prediction to multivariate time series forecasting, remains a fundamental challenge in computer vision and machine learning. Existing approaches, including Transformer- and MLP-based models, have demonstrated strong empirical performance but often struggle with balancing prediction accuracy, computational complexity, and model interpretability. Transformers are constrained by quadratic complexity and positional encoding limitations, whereas MLPs suffer from spectral bias, hindering their ability to capture fine-grained temporal dynamics essential for high-fidelity predictions. This thesis addresses these limitations by leveraging the expressive power of Kolmogorov-Arnold Networks (KANs), which utilize polynomial-based learnable activation functions to enhance model efficiency and interpretability. The thesis contributions are two-fold: The first contribution introduces LuKAN, an effective and computationally efficient model designed for 3D human motion prediction. LuKAN utilizes the Discrete Wavelet Transform to encode temporal information, and at its core, employs a Temporal Dependency Learner built on a KAN layer parameterized by Lucas polynomial activations. The second contribution introduces HaKAN, a versatile and lightweight framework for long-term multivariate time series forecasting. HaKAN is composed of a stack of Hahn-KAN blocks, where fixed activations are replaced with Hahn polynomial-based learnable functions to enhance both interpretability and adaptability, which not only mitigates spectral bias but also enables the model to effectively capture both global and local temporal patterns. HaKAN integrates channel independence, patching, a bottleneck structure, and residual connections, ensuring both strong generalization and a minimal architectural footprint. Extensive experiments on benchmark datasets for 3D motion prediction and long-term time series forecasting tasks demonstrate that both LuKAN and HaKAN consistently outperform competing state-of-the-art methods in terms of prediction accuracy and computational cost. Notably, their polynomial-based KAN architecture offers a unique advantage in interpretability and efficiency, as validated through comprehensive quantitative and ablation studies.