Resource-constrained weight deployment is a task of immense practical importance. Recently, there has been interest in the specific task of Delta Compression, where parties each hold a common base model and only communicate compressed weight updates. However, popular parameter efficient updates such as Low Rank Adaptation (LoRA) face inherent representation limitations - which are especially pronounced when combined with aggressive quantization. To overcome this, we build on recent work that improves LoRA representation capacity by using fixed-frequency sinusoidal functions to increase stable rank without adding additional parameters. We extend this to the quantized setting and present the first theoretical analysis showing how stable rank evolves under quantization. From this, we introduce SineLoRA∆, a principled and effective method for delta compression that improves the expressivity of quantized low-rank adapters by applying a sinusoidal activation. We validate SineLoRA∆ across a diverse variety of domains - including language modeling, vision-language tasks, and text-to-image generation - achieving up to 66% memory reduction with similar performance. We additionally provide a novel application of the canonical Bjøntegaard Delta metric to consistently compare adapter compression changes across the rate-distortion curve.

Low-rank decomposition has emerged as a vital tool for enhancing parameter efficiency in neural network architectures, gaining traction across diverse applications in machine learning. These techniques significantly lower the number of parameters, striking a balance between compactness and performance. However, a common challenge has been the compromise between parameter efficiency and the accuracy of the model, where reduced parameters often lead to diminished accuracy compared to their full-rank counterparts. In this work, we propose a novel theoretical framework that integrates a sinusoidal function within the low-rank decomposition process. This approach not only preserves the benefits of the parameter efficiency characteristic of low-rank methods but also increases the decomposition's rank, thereby enhancing model performance. Our method proves to be a plug in enhancement for existing low-rank models, as evidenced by its successful application in Vision Transformers (ViT), Large Language Models (LLMs), Neural Radiance Fields (NeRF) and 3D shape modelling.

The role of quantization within implicit/coordinate neural networks is still not fully understood. We note that using a canonical fixed quantization scheme during training produces poor performance at low bit-rates due to the network weight distributions changing over the course of training. In this work, we show that a non-uniform quantization of neural weights can lead to significant improvements. Specifically, we demonstrate that a clustered quantization enables improved reconstruction. Finally, by characterising a trade-off between quantization and network capacity, we demonstrate that it is possible (while memory inefficient) to reconstruct signals using binary neural networks. We demonstrate our findings experimentally on 2D image reconstruction and 3D radiance fields; and show that simple quantization methods and architecture search can achieve compression of NeRF to less than 16kb with minimal loss in performance (323x smaller than the original NeRF).