[continuing from previous screenshot]
...assumptions accurately capture physical reality remains an empirical question. That is why we fabricated and tested the results.
We generated four actuator classes by crossing two stimuli - humidity and heat - with two responses: bending and twisting. The fourth, thermal twisting, required no new pipeline and no separate derivation within the framework. It emerged by composing a thermal stimulus module already validated in one case with a twisting module validated in another. The generated G-code produced the intended motion without manual redesign, and all four predictions fell within one experimental standard deviation of the measured response.
Why this matters:
1. For AI in science, this provides a physics-aware type system against which generative proposals can be checked - and rejected at the interface - before expensive simulation, fabrication, or experiment. It is roughly analogous to proof checking, but for the composition of physical mechanisms.
2. For engineering, the accessible design space can scale with a library of validated components rather than with the number of individually derived cases.
3. The mathematics, category theory, carries all the way into a physical object on a print bed. This points toward scientific knowledge as executable infrastructure: models that are not only described in papers, but typed, composable, verifiable, and able to compile into experiments.
Excellent work led by my student @leemmarom with @SkylarTibbits & @GioeleZardini.
Note from Claude Sonnet 5
Conclusion of Markus Buehler's X thread: describes an experiment generating four actuator classes (humidity/heat stimuli x bending/twisting responses) where the fourth class (thermal twisting) emerged automatically by composing two already-validated modules, with predictions matching experiment within one standard deviation. Argues this gives AI-for-science a category-theoretic 'physics-aware type system' analogous to proof checking, letting design space scale with a library of validated components. Credits student @leemmarom with @SkylarTibbits and @GioeleZardini.
ai for sciencematerials sciencecategory theorybioinspired engineeringtwittermit
Petar Veličković @PetarV_93 · 6h
in case you were wondering why i have "monoids" in my bio --
this paper offers a monoid-equivariant model.
monoids strike a 'sweet spot' which i particularly like:
* they offer a framework more general than geometric dl (your transforms no longer need to be invertible!),
*
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Quoted tweet, Petar Veličko... @PetarV_... · 19h
one for my theory friends:
filter equivariant functions
[Paper image, two-panel]:
Left panel: "Filter Equivariant Functions" — "...ric account of length-general extrapolation" [title cut off], authors "...is², Neil Ghani³,⁴*, Andrew Dudzik¹, Christos Perivolaro... Razvan Pascanu¹ and Petar Veličković¹" — affiliations "¹Google DeepMind ²Goodfire AI ³Kodamai ⁴University of Strathclyde *Work done at Google DeepMi[nd]". Abstract text partially visible: "...function that extrapolates beyond known input/output examples look lik[e]...to answer in general, as any function matching the outputs on those exam[ples]...correct extrapolant. We argue that a "good" extrapolant should follow c[ertain]...ere we study a particularly appealing criterion for rule-following in lis[ts]...on should behave predictably even when certain elements are removed. I[n]...a standard way to express such removal operations is by using a filt[er]...ur paper introduces a new semantic class of functions – the filter equivarian[t]...this class contains interesting examples, prove some basic theorems ab[out]...well-known class of map equivariant functions. We also present a geomet[ric]...riants, showing how they correspond naturally to certain simplicial struc[tures]...t is the amalgamation algorithm, which constructs any filter-equivarian[t]...tudying how it behaves on sublists of the input, in a way that extrapolat[es]"
Right panel: diagram showing equivariance — boxes labeled x3, x4, x5 (colored) mapping via function f to y1, y2, ... and a second row x3, x4 mapping via f to y1, ... illustrating equivariance producing the same results.
Note from Claude Sonnet 5
NOT-ARCHIVE-MATERIAL (mostly): a DeepMind researcher (Petar Veličković, known for geometric deep learning / GNN theory) sharing a theoretical ML paper on "filter equivariant functions" for length-general extrapolation, co-authored with researchers at Goodfire AI (an interpretability company Nathan tracks — GoodFire SAE feature findings are in Nathan's memory notes) and Google DeepMind. Mostly abstract math/ML theory, low direct relevance beyond the Goodfire AI co-authorship link.
twittermachine learning theoryequivariancegeometric deep learningdeepmindgoodfire aicategory theory
