Chemical Reaction Neural Networks (CRNNs) have emerged as an interpretable machine learning framework for discovering reaction kinetics directly from data, while strictly adhering to the Arrhenius and mass action laws. However, standard CRNNs cannot represent pressure-dependent or mixture-based rate behavior, which is critical in many combustion and chemical systems and typically requires empirical falloff formulations such as Troe or SRI, or data-based interpolation or polynomial fits such as PLOG or Chebyshev Polynomials. Here, we develop Kolmogorov-Arnold Chemical Reaction Neural Networks (KA-CRNNs) that generalize CRNNs by modeling each kinetic parameter as a learnable function of third-body concentrations using Kolmogorov-Arnold activations. This structure maintains the Arrhenius and mass action interpretability and physical constraints of a vanilla CRNN while enabling assumption-free inference of global and collider-specific pressure effects directly from data. Two proof-of-concept reaction studies are presented to highlight the capability of KA-CRNNs to accurately reproduce pressure-dependent and collider-specific kinetics across a range of temperatures, pressures, and bath gas mixtures, extracting meaningful and generalizable models from sparse training data and significantly outperforming interpolative approaches (2.88x reduction in MSE). The framework establishes a foundation for data-driven discovery of extended kinetic behaviors in complex reacting systems, advancing interpretable and physics-constrained approaches for chemical model inference.