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Sebastian Raschka points out the chain of inspiration from LatentMoE back to eigendecomposition through MLA, LoRA, and SVD.
This paper performs full Jacobian eigendecomposition across production-scale LLMs, revealing a learned spectral gradient from rotation-dominated early layers to symmetric late layers, along with a low-rank bottleneck that compresses perturbations. The results link perturbation propagation and compression to network functional topology.
After 8 years, the author rewrote the open-source pytorch-hessian-eigenthings library, providing efficient eigendecomposition of Hessian and other curvature matrices for PyTorch models using iterative methods like Lanczos.