I'm finishing up my PhD on tensor network algorithms at the University of Queensland, Australia, under Ian McCulloch. I've also proposed a new definition of wavefunction branches using quantum circuit complexity.
Predictably, I'm moving into AI safety work. See my post on graphical tensor notation for interpretability. I also attended the Machine Learning for Alignment Bootcamp in Berkeley in 2022, did a machine learning/ neuroscience internship in 2020/2021, and also wrote a post exploring the potential counterfactual impact of AI safety work.
My website: https://sites.google.com/view/jordantensor/
Contact me: jordantensor [at] gmail [dot] com Also see my CV, LinkedIn, or Twitter.
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I'm keen to hear how you think your work relates to "Activation plateaus and sensitive directions in LLMs". Presumably should be chosen just large enough to get out of an activation plateau? Perhaps it might also explain why gradient based methods for MELBO alone might not work nearly as well as methods with a finite step size, because the effect is reversed if is too small?
Couldn't you do something like fit a Gaussian to the model's activations, then restrict the steered activations to be high likelihood (low Mahalanobis distance)? Or (almost) equivalently, you could just do a whitening transformation to activation space before you constrain the L2 distance of the perturbation.
(If a gaussian isn't expressive enough you could model the manifold in some other way, eg. with a VAE anomaly detector or mixture of gaussians or whatever)
There are many articles on quantum cellular automata. See for example "A review of Quantum Cellular Automata", or "Quantum Cellular Automata, Tensor Networks, and Area Laws".
I think compared to the literature you're using an overly restrictive and nonstandard definition of quantum cellular automata. Specifically, it only makes sense to me to write as a product of operators like you have if all of the terms are on spatially disjoint regions.
Consider defining quantum cellular automata instead as local quantum circuits composed of identical two-site unitary operators everywhere:
If you define them like this, then basically any kind of energy and momentum conserving local quantum dynamics can be discretized into a quantum cellular automata, because any two-site time and space independent quantum Hamiltonian can be decomposed into steps with identical unitaries like this using the Suzuki-Trotter decomposition.
This seems easy to try and a potential point to iterate from, so you should give it a go. But I worry that and will be dense and very uninterpretable:
- contains no information about which actual tokens each SAE feature activated on right? Just the token positions? So activations in completely different contexts but with the same features active in the same token positions cannot be distinguished by ?
- I'm not sure why you expect to have low-rank structure. Being low-rank is often in tension with being sparse, and we know that is a very sparse matrix.
- Perhaps it would be better to utilize the fact that is a very sparse matrix of positive entries? Maybe permutation matrices or sparse matrices would be more apt than general orthogonal matrices (which can be negative)? (Then you might have to settle for something like a block-diagonal central matrix, rather than a diagonal matrix of singular values).
I'm keen to see stuff in this direction though! I certainly think you could construct some matrix or tensor of SAE activations such that some decomposition of it is interpretable in an interesting way.
Special relativity is not such a good example here when compared to general relativity, which was much further ahead of its time. See, for example, this article: https://bigthink.com/starts-with-a-bang/science-einstein-never-existed/
Regarding special relativity, Einstein himself said:[1]
There is no doubt, that the special theory of relativity, if we regard its development in retrospect, was ripe for discovery in 1905. Lorentz had already recognized that the transformations named after him are essential for the analysis of Maxwell's equations, and Poincaré deepened this insight still further. Concerning myself, I knew only Lorentz's important work of 1895 [...] but not Lorentz's later work, nor the consecutive investigations by Poincaré. In this sense my work of 1905 was independent. [..] The new feature of it was the realization of the fact that the bearing of the Lorentz transformation transcended its connection with Maxwell's equations and was concerned with the nature of space and time in general. A further new result was that the "Lorentz invariance" is a general condition for any physical theory.
As for general relativity, the ideas and the mathematics required (Riemannian Geometry) were much more obscure and further afield. The only people who came close, Nordstrom and Hilbert, arguably did so because they were directly influenced by Einstein's ongoing work on general relativity (not just special relativity).
https://www.quora.com/Without-Einstein-would-general-relativity-be-discovered-by-now
1Thanks for the kind words! Sadly I just used inkscape for the diagrams - nothing fancy. Though hopefully that could change soon with the help of code like yours. Your library looks excellent! (though I initially confused it with https://github.com/wangleiphy/tensorgrad due to the name).
I like how you represent functions on the tensors, like you're peering inside them. I can see myself using it often, both for visualizing things, and for computing derivatives.
The difficulty in using it for final diagrams may be in getting the positions of the tensors arranged nicely. Do you use a force-directed layout like networkx for that currently? Regardless, a good thing about exporting tixz code is that you can change the positions manually, as long as the positions are set up as nice tikz variables rather than "hardcoded" numbers everywhere.
Anyway, I love it. Here's an image for others to get the idea:
Nice, I forgot about ZX (and ZXW) calculus. I've never seriously engaged with it, despite it being so closely related to tensor networks. The fact that you can decompose any multilinear equation into so few primitive building blocks is interesting.
Oops, yep. I initially had the tensor diagrams for that multiplication the other way around (vector then matrix). I changed them to be more conventional, but forgot that. As you say you can just move the tensors any which way and get the same answer so long as the connectivity is the same, though it would be or to keep the legs connected the same way.
This is an interesting and useful overview, though it's important not to confuse their notation with the Penrose graphical notation I use in this post, since lines in their notation seem to represent the message-passing contributions to a vector, rather than the indices of a tensor.
That said, there are connections between tensor network contractions and message passing algorithms like Belief Propagation, which I haven't taken the time to really understand. Some references are:
Duality of graphical models and tensor networks - Elina Robeva and Anna Seigal
Tensor network contraction and the belief propagation algorithm - R. Alkabetz and I. Arad
Tensor Network Message Passing - Yijia Wang, Yuwen Ebony Zhang, Feng Pan, Pan Zhang
Gauging tensor networks with belief propagation - Joseph Tindall, Matt Fishman
Fixed links:
https://huggingface.co/oliverdk/codegen-350M-mono-measurement_pred
https://github.com/oliveradk/measurement-pred