8 citations · 16 across the 8 of their papers we have counts for
10 papers
You Are What You Eat -- AI Alignment Requires Understanding How Data Shapes Structure and Generalisation
Simon Pepin Lehalleur, Jesse Hoogland, Matthew Farrugia-Roberts +5
In this position paper, we argue that understanding the relation between structure in the data distribution and structure in trained models is central to AI alignment. First, we di…
Geometry of fibers of the multiplication map of deep linear neural networks
Simon Pepin Lehalleur, Richárd Rimányi
We study the geometry of the algebraic set of tuples of composable matrices which multiply to a fixed matrix, using tools from the theory of quiver representations. In particular,…
Exponentiation of coefficient systems and exponential motives
Martin Gallauer, Simon Pepin Lehalleur
We construct new six-functor formalisms capturing cohomological invariants of varieties with potentials. Starting from any six-functor formalism , encoded as a coefficient syste…
Voevodsky motives of stacks of coherent sheaves on a curve
Victoria Hoskins, Simon Pepin Lehalleur
We prove formulae for the motives of stacks of coherent sheaves of fixed rank and degree over a smooth projective curve in Voevodsky's triangulated category of mixed motives with r…
Motives of moduli spaces of rank 3 vector bundles and Higgs bundles on a curve
Lie Fu, Victoria Hoskins, Simon Pepin Lehalleur
We prove formulas for the rational Chow motives of moduli spaces of semistable vector bundles and Higgs bundles of rank 3 and coprime degree on a smooth projective curve. Our appro…
Euler characteristics of homogeneous and weighted-homogeneous hypersurfaces
Marc Levine, Simon Pepin Lehalleur, Vasudevan Srinivas
Let be a field and let be the Grothendieck-Witt ring of virtual non-degenerate symmetric bilinear forms over . We develop methods for computing the quadratic…
On the Voevodsky motive of the moduli space of Higgs bundles on a curve
Victoria Hoskins, Simon Pepin Lehalleur
We study the motive of the moduli space of semistable Higgs bundles of coprime rank and degree on a smooth projective curve C over a field k under the assumption that C has a ratio…
A formula for the Voevodsky motive of the moduli stack of vector bundles on a curve
Victoria Hoskins, Simon Pepin Lehalleur
We prove a formula for the motive of the stack of vector bundles of fixed rank and degree over a smooth projective curve in Voevodsky's triangulated category of mixed motives with…
Constructible 1-motives and exactness
Simon Pepin Lehalleur
We prove that arbitrary pullbacks, as well as Betti and étale realisation functors, are t-exact for the constructible motivic t-structure on the category of cohomological 1-motives…
On the relative motive of a commutative group scheme
Giuseppe Ancona, Annette Huber, Simon Pepin Lehalleur
We prove a canonical Kuenneth decomposition of the relative motive with rational coefficients of a smooth commutative group scheme over a noetherian finite dimensional base. This…