Sinusoidal neural networks have been shown effective as implicit neural representations (INRs) of low-dimensional signals, due to their smoothness and high representation capacity. However, initializing and training them remain empirical tasks which lack on deeper understanding to guide the learning process. To fill this gap, our work introduces a theoretical framework that explains the capacity property of sinusoidal networks and offers robust control mechanisms for initialization and training. Our analysis is based on a novel amplitude-phase expansion of the sinusoidal multi-layer perceptron, showing how its layer compositions produce a large number of new frequencies expressed as integer combinations of the input frequencies. This relationship can be directly used to initialize the input neurons, as a form of spectral sampling, and to bound the network’s spectrum while training. Our method, referred to as TUNER (TUNing sinusoidal nEtwoRks), greatly improves the stability and convergence of sinusoidal INR training, leading to detailed reconstructions, while preventing overfitting.

Accurate camera calibration is a fundamental task for 3D perception, especially when dealing with real-world, in-the-wild environments where complex optical distortions are common. Existing methods often rely on pre-rectified images or calibration patterns, which limits their applicability and flexibility. In this work, we introduce a novel framework that addresses these challenges by jointly modeling camera intrinsic and extrinsic parameters using a generic ray camera model. Unlike previous approaches, AlignDiff shifts focus from semantic to geometric features, enabling more accurate modeling of local distortions. We propose AlignDiff, a diffusion model conditioned on geometric priors, enabling the simultaneous estimation of camera distortions and scene geometry. To enhance distortion prediction, we incorporate edge-aware attention, focusing the model on geometric features around image edges, rather than semantic content. Furthermore, to enhance generalizability to real-world captures, we incorporate a large database of ray-traced lenses containing over three thousand samples. This database characterizes the distortion inherent in a diverse variety of lens forms. Our experiments demonstrate that the proposed method significantly reduces the angular error of estimated ray bundles by ~8.2 degrees and overall calibration accuracy, outperforming existing approaches on challenging, real-world datasets.