Implicit Neural Representations (INRs) have become a powerful paradigm for modeling continuous signals in computer vision, graphics, and scientific computing. However, multilayer perceptrons (MLPs) generally suffer from severe spectral bias, which limits their ability to accurately model high-frequency details and multi-scale structures. To address this challenge, we propose a novel Multi-Scale Sine Activation (MSA), which explicitly introduces multi-scale frequency responses by incorporating multiple sets of sine activations with logarithmically spaced frequencies in parallel at each layer. MSA is further combined with an amplitude modulation mechanism to ensure numerical stability and robust optimization across different frequency channels. We conduct extensive experiments on a series of challenging tasks, including 1D multi-scale function fitting, image representation, video representation, 3D shape representation, and PDEs solving. Experimental results show that MSA outperforms existing state-of-the-art methods in terms of reconstruction accuracy, detail preservation, and training stability.

The quest for analytical solutions to differential equations has traditionally been constrained by the need for extensive mathematical expertise. Machine learning methods like genetic algorithms have shown promise in this domain, but are hindered by significant computational time and the complexity of their derived solutions. This paper introduces **SSDE** (Symbolic Solver for Differential Equations), a novel reinforcement learning-based approach that derives symbolic closed-form solutions for various differential equations. Evaluations across a diverse set of ordinary and partial differential equations demonstrate that SSDE outperforms existing machine learning methods, delivering superior accuracy and efficiency in obtaining analytical solutions.