3 ms·
awesome - spent couple of years deep in this space for dissertation using graph theory to boost linear algebra computes; lots of room to extend our discrete res
by aghilmort 5y ago
awesome - spent couple of years deep in this space for dissertation using graph theory to boost linear algebra computes; lots of room to extend our discrete result into approximate / continuous computes and boost AI, GPUs, etc.
similar result came out around the same time using category theory as basis; our work was intentionally simpler / more applied, partly to make it more accessible from an algorithmic perspective and also to put it into practice, etc.
* www - https://scholar.afit.edu/etd/2632/ https://scholar.afit.edu/etd/2632/
* pdf - https://www.sagemath.org/files/thesis/augeri-thesis-2008.pdf https://www.sagemath.org/files/thesis/augeri-thesis-2008.pdf
- aghilmort 5y agop.s. my user name from that work -- aghilmort is canonical alpha sort / scrabble sort of algorithm and logarithm
- orange3xchicken 5y agoThat's really cool. These days similar strategies based on graph coarsening and vertex ordering are really popular for improving the sparsity pattern of preconditioners- e.g. incomplete lu decompositions for iterative linear solvers.
- aghilmort 5y agoyeah, there's so much room to extend this work in terms of graph coarsening / sparsifying, especially for progressive / approximate approaches there's lots of overlap with entropy binning as well and likely some sort of combo for win -- figure out "max frequency" with some sort of FFT / wavelet like meta technique or somehow bin edges based on entropy contribution, etc. or, lots of pathways to make coontinuous / numerical in JPEG like way basically JPEGs for graphs -- with big impacts in AI / ML computes