Designing spectral convolutional networks is a challenging problem in graph learning. ChebNet, one of the early attempts, approximates the spectral graph convolutions using Chebyshev polynomials.

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Designing spectral convolutional networks is a challenging problem in graph learning. ChebNet, one of the early attempts, approximates the spectral graph convolutions using Chebyshev polynomials.

ABSTRACT Inertial odometry (IO) relies exclusively on signals from an inertial measurement unit (IMU) for localization and offers a promising avenue for consumer-grade positioning. However, accurate modeling of the nonlinear motion patterns present in IMU signals remains the principal limitation on IO accuracy. To address this challenge, we propose CKANIO, an IO framework that integrates Chebyshev-based Kolmogorov-Arnold Networks (Chebyshev KAN). To the best of our knowledge, this work represents the first application of an interpretable KAN model to IO. Experimental results on five publicly available datasets demonstrate the effectiveness of CKANIO. Index T erms-- Chebyshev KAN, Inertial Odometry, Inertial Measurement Unit signals 1. INTRODUCTION Inertial odometry (IO) estimates the position and orientation of an IMU-equipped platform using acceleration and angular velocity signals provided by the inertial measurement unit (IMU) [1].

Modeling long-range interactions, the propagation of information across distant parts of a graph, is a central challenge in graph machine learning. Graph wavelets, inspired by multi-resolution signal processing, provide a principled way to capture both local and global structures. However, existing wavelet-based graph neural networks rely on finite-order polynomial approximations, which limit their receptive fields and hinder long-range propagation. We propose Long-Range Graph Wavelet Networks (LR-GWN), which decompose wavelet filters into complementary local and global components. Local aggregation is handled with efficient low-order polynomials, while long-range interactions are captured through a flexible spectral-domain parameterization. This hybrid design unifies short- and long-distance information flow within a principled wavelet framework. Experiments show that LR-GWN achieves state-of-the-art performance among wavelet-based methods on long-range benchmarks, while remaining competitive on short-range datasets.