On Information Geometry and Iterative Optimization in Model Compression: Operator Factorization
The ever-increasing parameter counts of deep learning models necessitate effective compression techniques for deployment on resource-constrained devices. This paper explores the application of information geometry, the study of density-induced metrics on parameter spaces, to analyze existing methods within the space of model compression, primarily focusing on operator factorization. Adopting this perspective highlights the core challenge: defining an optimal low-compute submanifold (or subset) and projecting onto it. We argue that many successful model compression approaches can be understood…
A recent paper from Apple researchers, "The Super Weight in Large Language Models," reveals that an extremely small subset of parameters in LLMs (in some cases, a single parameter) can exert a disproportionate influence on an LLM’s overall functionality (see Figure 1). This work highlights the critical role of these…
In 1991, Brenier proved a theorem that generalizes the polar decomposition for square matrices -- factored as PSD ×times× unitary -- to any vector field F:Rd→RdF:mathbb{R}^drightarrow mathbb{R}^dF:Rd→Rd. The theorem, known as the polar factorization theorem, states that any field FFF can be recovered as the composition of the gradient of…
This paper was accepted at the IEEE Workshop on Applications of Signal Processing to Audio and Acoustics (WASPAA) 2025 Non-negative Matrix Factorization (NMF) is a powerful technique for analyzing regularly-sampled data, i.e., data that can be stored in a matrix. For audio, this has led to numerous applications using time-frequency…