We introduce a framework for compactly representing light field content with the novel concept of neural subspaces. While the recently proposed neural light field representation achieves great compression results by encoding a light field into a single neural network, the unified design is not optimized for the composite structures exhibited in light fields. Moreover, encoding every part of the light field into one network is not ideal for applications that require rapid transmission and decoding. We recognize this problem's connection to subspace learning. We present a method that uses several small neural networks, specializing in learning the neural subspace for a particular light field segment. Moreover, we propose an adaptive weight sharing strategy among those small networks, improving parameter efficiency. In effect, this strategy enables a concerted way to track the similarity among nearby neural subspaces by leveraging the layered structure of neural networks. Furthermore, we develop a soft-classification technique to enhance the color prediction accuracy of neural representations. Our experimental results show that our method better reconstructs the light field than previous methods on various light field scenes. We further demonstrate its successful deployment on encoding light fields with irregular viewpoint layout and dynamic scene content.