equivariance

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!), * Show more 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.