GR4DGS: Sparse-View 4D Gaussian Compression via Temporal Grid Prediction

4D Gaussian representations enable free-viewpoint video, but their frame-wise scene updates incur substantial storage and transmission costs. We investigate this compression challenge under sparse-view capture. In our three-view evaluation of a grid-based streaming codec, motion grids account for about 99% of P-frame payloads, although consecutive quantized grids remain highly correlated. Independent per-frame grid coding therefore repeatedly transmits information that is predictable from the decoder's preceding state. We propose GR4DGS to exploit this redundancy through temporal motion-grid prediction. GR4DGS transmits integer differences from the previously decoded grid, recovering the current quantized grid exactly while retaining the other rendering inputs. To further reduce payloads, GR4DGS-E2E combines residual-domain rate optimization with occupancy-aware initialization: unqueried cells inherit the preceding decoded values, while queried cells restart from a shared warm-up. Across six Neural 3D Video scenes of 300 frames each under three-view training, lossless prediction reduces P-frame payloads by 65–72% relative to the default independently coded 4DGC baseline. The separately trained GR4DGS-E2E variant reduces them by 88–93%, with per-scene mean PSNR differences within 0.03 dB. Including the shared uncompressed keyframe once, E2E reduces sequence payloads by 81–86%.