Neural Texture Compression using Hypernetworks

Primitive-based methods such as 3D Gaussian Splatting have recently become the state-of-the-art for novel-view synthesis and related reconstruction tasks. Compared to neural fields, these representations are more flexible, adaptive, and scale better to large scenes. However, the limited expressivity of individual primitives makes modeling high-frequency detail challenging. We introduce Neural Harmonic Textures, a neural representation approach that anchors latent feature vectors on a virtual scaffold surrounding each primitive. These features are interpolated within the primitive at ray intersection points. Inspired by Fourier analysis, we apply periodic activations to the interpolated features, turning alpha blending into a weighted sum of harmonic components. The resulting signal is then decoded in a single deferred pass using a small neural network, significantly reducing computational cost. Neural Harmonic Textures yield state-of-the-art results in real-time novel view synthesis while bridging the gap between primitive- and neural-field-based reconstruction. Our method integrates seamlessly into existing primitive-based pipelines such as 3DGUT, Triangle Splatting, and 2DGS. We further demonstrate its generality with applications to 2D image fitting and semantic reconstruction.

Neural networks are thought to represent concepts as directions in their activation space, and superposition lets them encode more concepts than they have dimensions. It is natural to ask whether they can also compute more functions than they have neurons, i.e., perform computation in superposition. In this regime many functions of sparse inputs are evaluated by a layer with fewer neurons than there are functions to compute. Representation in superposition is by now fairly well understood, but computation in superposition is not, and there are few toy models of it arising through training rather than being hand designed. As a toy model of computation in superposition we study the compressed-computation setup: a single-hidden-layer ReLU network with 50 neurons that must compute the ReLU of each of 100 sparse input features. We show that training it under an $L^4$ loss (the mean fourth power of the error), rather than the usual $L^2$, elicits a solution that appears to compute all features in superposition. We then reverse-engineer this solution. We find that the network assigns each feature a sparse binary codeword over neurons and decodes it with a pseudoinverse of the encoder. Given these codewords, a description with only three scalars recovers most of the network's performance, and we validate it by building equivalent networks from hand-designed codes.

Neural networks suffer from shortcut learning, where learned features generalize well to the training set but not to in-distribution (ID) or out-of-distribution (OOD) test sets. Existing studies are all based on a few standard benchmarks, which are shape-driven. Numerous application domains, however, are texture-driven. In this work, we present shortcut learning analysis for texture-driven domains, and compare it with that of a standard benchmark. We show that texture-driven domains suffer from low-frequency shortcuts. They make the majority of their decisions based on a few low-frequency components (LFCs) with a skewed spectral behavior, despite that their classification information is in higher-frequency, fine-grained details. Pruning LFCs from training and test sets eliminates the shortcut and provides a more balanced spectral behavior, improving the ID accuracy by up to 8%. We show that low-frequency shortcuts make the models highly vulnerable to OOD corruptions, leading up to 70% accuracy drop compared to the ID accuracy. Pruning LFCs significantly improves robustness to low-frequency corruptions, by up to 40%, and introduces a trade-off for high-frequency corruptions; the balanced spectral behavior provides a better generalization performance, whereas the increased dependence on high-frequency features reduces it. OOD accuracy depends on the interaction between these two factors.