42 citations · 69 across the 13 of their papers we have counts for
19 papers
Theoretical and Practical Perspectives on what Influence Functions Do
Andrea Schioppa, Katja Filippova, Ivan Titov +1
Influence functions (IF) have been seen as a technique for explaining model predictions through the lens of the training data. Their utility is assumed to be in identifying trainin…
Cross-Lingual Supervision improves Large Language Models Pre-training
Andrea Schioppa, Xavier Garcia, Orhan Firat
The recent rapid progress in pre-training Large Language Models has relied on using self-supervised language modeling objectives like next token prediction or span corruption. On t…
Scaling Up Influence Functions
Andrea Schioppa, Polina Zablotskaia, David Vilar +1
We address efficient calculation of influence functions for tracking predictions back to the training data. We propose and analyze a new approach to speeding up the inverse Hessian…
Distributed Function Minimization in Apache Spark
Andrea Schioppa
We report on an open-source implementation for distributed function minimization on top of Apache Spark by using gradient and quasi-Newton methods. We show-case it with an applicat…
Learning to Transport with Neural Networks
Andrea Schioppa
We compare several approaches to learn an Optimal Map, represented as a neural network, between probability distributions. The approaches fall into two categories: ``Heuristics'' a…
Optimality of the final model found via Stochastic Gradient Descent
Andrea Schioppa
We study convergence properties of Stochastic Gradient Descent (SGD) for convex objectives without assumptions on smoothness or strict convexity. We consider the question of establ…
An example of a doubling "inherently" infinite-dimensional subset of
Andrea Schioppa
We construct a doubling subset of which cannot be biLipschitz embedded in any finite dimensional Euclidean space. This answers a question of Lang and Plaut.
Lipschitz functions with prescribed blowups at many points
Andrea Marchese, Andrea Schioppa
In this paper we prove generalizations of Lusin-type theorems for gradients due to Giovanni Alberti, where we replace the Lebesgue measure with any Radon measure . We apply this…
An example of a differentiability space which is PI-unrectifiable
Andrea Schioppa
We construct a (Lipschitz) differentiability space which has at generic points a disconnected tangent and thus does not contain positive measure subsets isometric to positive measu…
Unrectifiable normal currents in Euclidean spaces
Andrea Schioppa
We construct in a -dimensional simple normal current whose support is purely -unrectifiable. The result is sharp because the support of a normal current ca…
Examples of -unrectifiable normal currents
Andrea Schioppa
We construct new examples of normal (metric) currents using inverse systems of cube complexes. For any we provide examples of -dimensional normal currents whose associa…
The Lip-lip equality is stable under blow-up
Andrea Schioppa
We show that at generic points blow-ups/tangents of differentiability spaces are still differentiability spaces; this implies that an analytic condition introduced by Keith as an i…
PI spaces with analytic dimension 1 and arbitrary topological dimension
Bruce Kleiner, Andrea Schioppa
For every n, we construct a metric measure space that is doubling, satisfies a Poincare inequality in the sense of Heinonen-Koskela, has topological dimension n, and has a measurab…
The Poincaré Inequality does not improve with blow-up
Andrea Schioppa
For each we construct a family of metric measure spaces which is closed under the operation of taking weak-tangents (i.e.~blow-ups), and such that each element of …
Infinitesimal structure of differentiability spaces, and metric differentiation
Jeff Cheeger, Bruce Kleiner, Andrea Schioppa
We prove metric differentiation for differentiability spaces in the sense of Cheeger. As corollaries we give a new proof that the minimal generalized upper gradient coincides with…
Poincaré inequalities for mutually singular measures
Andrea Schioppa
Using an inverse system of metric graphs as in: J. Cheeger and B. Kleiner, "Inverse limit spaces satisfying a Poincaré inequality", we provide a simple example of a metric space $X…
Metric Currents and Alberti representations
Andrea Schioppa
We relate Ambrosio-Kirchheim metric currents to Alberti representations and Weaver derivations. In particular, given a metric current , we show that if the module $\mathscr{X}(\…
Derivations and Alberti representations
Andrea Schioppa
We relate generalized Lebesgue decompositions of measures in terms of curve fragments (Alberti representations) and Weaver derivations. This correspondence leads to a geometric cha…
On the relationship between derivations and measurable differentiable structures on metric measure spaces
Andrea Schioppa
We investigate the relationship between measurable differentiable structures on doubling metric measure spaces and derivations. We prove: [1] a decomposition theorem for the module…