Another cute way I thought for deriving e^ax as the derivative operator eigenfunctions, after seeing the Functions as Vectors post today
Readit Newsrtolsma commented on Derivative Eigenfunctions ryantolsma.com/thoughts/2... · Posted by u/rtolsma
The Linux repository has ~50M tokens, which goes beyond the 1M token limit for Gemini 2.5 Pro.
I think there are two paths forward: (1) decompose the repository into smaller parts (e.g., kernel, shell, file system, etc.), or (2) wait for larger-context models with a 50M+ input limit.
You can use the AST for some languages to identify modular components that are smaller and can fit into the 1M window
rtolsma commented on Memos – An open source Rewinds / Recall github.com/arkohut/memos... · Posted by u/arkohut
strongly recommend you check out the built in Swift APIs for screen capture and OCR. They’re heavily optimized for energy usage, and allow much finer grained controls on what apps are white/blacklisted for privacy
rtolsma commented on Topological Problems in Voting ryantolsma.com/thoughts/2... · Posted by u/rtolsma
I'm not quite sure why one would use a sphere, unless you were specifically trying to get a version of Arrow's theorem.
If anything it looks like it fails precisely because the space is not homologically trivial, but I'm a bit unsure how to make that precise. A similar set up with just [0,1]^n as preference space works perfectly fine just by averaging all the scores for each candidate.
I kind of sense that requiring a function X^k -> X to exist is somehow hard if X is not 'simple', but I'm not yet sure what the obstruction is.
Yea I think one reason to restrict to spheres is because the voting function takes as input the relative preferences (like in [0,1]^n how does all 0s differ from all 1s), which implies the vectors should be normalized
rtolsma commented on Topological Problems in Voting ryantolsma.com/thoughts/2... · Posted by u/rtolsma
Hmm, is this author related to the Physics for the Birds YouTube channel?
That channel just released a video on the same topic.
Yes, I saw that! Inspired me to look at the original paper.
The video takes a slightly different approach from the paper and uses a retraction on the möbius strip to its boundary as a contradiction.
That particular argument doesn’t generalize as well in higher dimensions (in particular, the symmetric product won't always have a boundary to retract to), so I followed the original paper’s one instead. I'll add a link to that video as well
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rtolsma commented on High-Dimensional Probability and Applications in Data Science math.uci.edu/~rvershyn/te... · Posted by u/gone35
The High Dimensional Probability textbook is one of my all time favorites. The elegant mix of probability, geometry, and linear algebra can generate some really non-intuitive insights. The intuitions developed are also pretty useful for reasoning about modeling in a lot of applications
rtolsma commented on Show HN: Use Code Llama as Drop-In Replacement for Copilot Chat continue.dev/docs/walkthr... · Posted by u/sestinj
When will tools/models like these start integrating with code servers and linters in IDEs instead of just yielding supercharged autocomplete?