2 citations · 3 across the 6 of their papers we have counts for
8 papers
When Can One Obtain Certificates of Optimality Using Positivstellensaetze?
Nayoon Kim, Allen Gehret, Shenyuan Ma +1
We study certificates of positivity and optimality for learning problems whose objectives and constraints need not be polynomial. We isolate an axiomatic core of Fischer's construc…
Stochastic Sample Approximations of (Local) Moduli of Continuity
Rodion Nazarov, Allen Gehret, Robert Shorten +1
Modulus of local continuity is used to evaluate the robustness of neural networks and fairness of their repeated uses in closed-loop models. Here, we revisit a connection between g…
Deep Learning as the Disciplined Construction of Tame Objects
Gilles Bareilles, Allen Gehret, Johannes Aspman +2
One can see deep-learning models as compositions of functions within the so-called tame geometry. In this expository note, we give an overview of some topics at the interface of ta…
Dimension theory for the asymptotic couple of the field of logarithmic transseries
Allen Gehret, Elliot Kaplan, Nigel Pynn-Coates
In this paper we completely characterize all dimension functions on all models of the theory of the asymptotic couple of the field of logarithmic transseries (Dimension…
Distality in valued fields and related structures
Matthias Aschenbrenner, Artem Chernikov, Allen Gehret +1
We investigate distality and existence of distal expansions in valued fields and related structures. In particular, we characterize distality in a large class of ordered abelian gr…
Hamel Spaces and Distal Expansions
Allen Gehret, Travis Nell
In this note, we construct a distal expansion for the structure , where is a dense -vector space basis of (a s…
A tale of two Liouville closures
Allen Gehret
An -field is a type of ordered valued differential field with a natural interaction between ordering, valuation, and derivation. The main examples are Hardy fields and fields of…
NIP for the Asymptotic Couple of the Field of Logarithmic Transseries
Allen Gehret
The derivation on the differential-valued field of logarithmic transseries induces on its value group a certain map . The structure $Γ= (Γ_{\log},…