Optimizing Sampling Pattern Correlations for Neural Field Training

Neural fields are optimized from samples of a source signal whose locations can often be chosen freely. While existing approaches exploit this freedom by adapting individual sample locations to the signal, we investigate a complementary question: how should the samples be spatially correlated? We characterize these correlations through sampling-pattern power spectra and explore this space to identify patterns that optimize the outcome of neural field fitting. By evaluating sampling patterns through the resulting neural field, our approach accounts for the complete fitting process rather than integration accuracy alone. The optimized patterns outperform IID uniform sampling as well as correlated patterns designed for numerical integration, with particularly pronounced benefits under limited sampling budgets. Moreover, the patterns transfer across source signals, enabling inexpensive proxy signals to drive their optimization for more costly settings. We analyze the resulting sampling structures and characterize how they depend on the neural field fitting problem. Together, our results establish optimized sampling correlations as an effective tool for improving neural field fitting.