Realistic sound propagation is essential for immersion in a virtual scene, yet physically accurate wave-based simulations remain computationally prohibitive for real-time applications. Wave coding methods address this limitation by precomputing and compressing impulse responses of a given scene into a set of scalar acoustic parameters, which can reach unmanageable sizes in large environments with many source-receiver pairs. We introduce Reciprocal Latent Fields (RLF), a memory-efficient framework for encoding and predicting these acoustic parameters. The RLF framework employs a volumetric grid of trainable latent embeddings decoded with a symmetric function, ensuring acoustic reciprocity. We study a variety of decoders and show that leveraging Riemannian metric learning leads to a better reproduction of acoustic phenomena in complex scenes. Experimental validation demonstrates that RLF maintains replication quality while reducing the memory footprint by several orders of magnitude. Furthermore, a MUSHRA-like subjective listening test indicates that sound rendered via RLF is perceptually indistinguishable from ground-truth simulations.

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