Instant Neural Graphics Primitives with a Multiresolution Hash Encoding

### Instant Neural Graphics Primitives with Multiresolution Hash Encoding Multiresolution hash encoding is a technique that allows the representation of high-frequency details in neural fields, such as images or volumes, while maintaining efficiency during training and inference. This method divides space into multiple resolutions using an octree structure to efficiently store information at different levels of detail[^1]. The core idea behind instant neural graphics primitives (INGP) lies in combining multiresolution grid-based feature vectors encoded through hashing techniques. By mapping spatial coordinates into discrete indices within grids, this approach can capture intricate patterns without requiring excessive memory resources. The use of hash tables enables fast lookups when accessing these features. For implementing INGP: - **Octree Construction**: An adaptive octree is constructed based on scene complexity; finer divisions occur where more detail exists. - **Feature Vectors Storage**: Each node contains low-dimensional learnable parameters representing local geometry properties. - **Hash Function Application**: Spatial positions are transformed via modulo operations followed by random projections onto higher dimensions before being fed into networks for learning purposes. This combination results in models capable of generating highly detailed outputs from compact representations learned directly from data samples provided during training phases. ```python import torch.nn.functional as F def get_grid_coordinates(xyz, level): """Convert continuous xyz coordinates to integer grid cell ids.""" scale = 2**(level - 1) coords = ((xyz + 1.) * scale).long() return coords % (scale*2) def apply_hashing(coords, table_size=1<<20): """Apply simple modular arithmetic hashing function""" hashed_coords = [] primes = [1, 2654435761, 805459861] for i in range(3): h = int((coords[:,i]*primes[i])%table_size) hashed_coords.append(h) return torch.stack(hashed_coords,dim=-1) ```