Joplin is open source, syncing setup between devices is one login to Dropbox, works for free, with native apps on Windows/OSX/Linux/iOS/Android. It has a bunch of plugins too. If you just need markdown files with syncing, use it rather than paying for Obsidian sync.
The 2GB free quota on Dropbox is plenty enough for text (and some screenshots). Or you could self-host obviously. Git while lovely for source code is a hassle for notes.
Many discriminative models converge to same representation space up to a linear transformation. Makes sense that a linear transformation (like PCA) would be able to undo that transformation.
Without properly reading the linked article, if thats all this is, not a particularly new result. Nevertheless this direction of proofs is imo at the core of understanding neural nets.
Edit: actually this paper is the canonical reference (?): https://arxiv.org/abs/2007.00810 models converge to same space up to a linear transformation. Makes sense that a linear transformation (like PCA) would be able to undo that transformation.
You can show for example that siamese encoders for time-series, with MSE loss on similarity, without a decoder, will converge to the the same latent space up to orthogonal transformations (as MSE is kinda like gaussian prior which doesn’t distinguish between different rotations).
Similarly I would expect that transformers trained on the same loss function for predicting the next word, if the data is at all similar (like human language), would converge to approx the same space, up to some, likely linear, transformations. And to represent that same space probably weights are similar, too. Weights in general seem to occupy low-dimensional spaces.
All in all, I don’t think this is that surprising, and I think the theoretical angle should be (have been?) to find mathematical proofs like this paper https://openreview.net/forum?id=ONfWFluZBI
They also have a previous paper (”CEBRA”) published in Nature with similar results.
You can show for example that siamese encoders for time-series, with MSE loss on similarity, without a decoder, will converge to the the same latent space up to orthogonal transformations (as MSE is kinda like gaussian prior which doesn’t distinguish between different rotations).
Similarly I would expect that transformers trained on the same loss function for predicting the next word, if the data is at all similar (like human language), would converge to approx the same space. And to represent that same space probably weights are similar, too. Weights in general seem to occupy low-dimensional spaces.
All in all, I don’t think this is that surprising, and I think the theoretical angle should be (have been?) to find mathematical proofs like this paper https://openreview.net/forum?id=ONfWFluZBI
I don’t believe so. I think all important parts that each need to be scaled to advance significantly in the LLM paradigm are at or near the end of the steep part of the sigmoid:
1) useful training data available in the internet
2) number of humans creating more training data ”manually”
3) parameter scaling
4) ”easy” algorithmic inventions
5) available+buildable compute
”Just” needing a few more algorithmic inventions to keep the graphs exponential is a cop out. It is already obvious that just scaling parameters and compute is not enough.
I personally predict that scaling LLMs for solving all physical tasks (eg cleaning robots) or intellectual pursuits (they suck at multiplication) will not work out.
We will get better specialized tools by collecting data from specific, high economic value, constrained tasks, and automating them, but scaling a (multimodal) LLM to solve everything in a single model will not be economically viable. We will get more natural interfaces for many tasks.
This is how I think right now as a ML researcher, will be interesting to see how wrong was I in 2 years.
EDIT: addition about latest algorithmic advances:
- Deepseek style GRPO requires a ladder of scored problems progressively more difficult and appropriate to get useful gradients. For open-ended problems (like most interesting ones are) we have no ladders for, and it doesn’t work. In particular, learning to generate code for leetcode problems with a good number of well made unit tests is what it is good for.
- Test-time inference is just adding an insane amount of more compute after training to brute-force double-check the sanity of answers
Or would one count any communication between animals as language? In that case almost any interaction would count.