3DTurboQuant: Training-Free Near-Optimal Quantization for 3D Reconstruction Models

Every existing method for compressing 3D Gaussian Splatting, NeRF, or transformer-based 3D reconstructors requires learning a data-dependent codebook through per-scene fine-tuning. We show this is unnecessary. The parameter vectors that dominate storage in these models, 45-dimensional spherical harmonics in 3DGS and 1024-dimensional key-value vectors in DUSt3R, fall in a dimension range where a single random rotation transforms any input into coordinates with a known Beta distribution. This makes precomputed, data-independent Lloyd-Max quantization near-optimal, within a factor of 2.7 of the information-theoretic lower bound. We develop 3D, deriving (1) a dimension-dependent criterion that predicts which parameters can be quantized and at what bit-width before running any experiment, (2) norm-separation bounds connecting quantization MSE to rendering PSNR per scene, (3) an entry-grouping strategy extending rotation-based quantization to 2-dimensional hash grid features, and (4) a composable pruning-quantization pipeline with a closed-form compression ratio. On NeRF Synthetic, 3DTurboQuant compresses 3DGS by 3.5x with 0.02dB PSNR loss and DUSt3R KV caches by 7.9x with 39.7dB pointmap fidelity. No training, no codebook learning, no calibration data. Compression takes seconds. The code will be released (https://github.com/JaeLee18/3DTurboQuant)