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Implicit Gradient Regularization

- D. Barrett, B. Dherin
- Computer ScienceICLR
- 23 September 2020

TLDR

On the Origin of Implicit Regularization in Stochastic Gradient Descent

- Samuel L. Smith, B. Dherin, D. Barrett, Soham De
- Computer ScienceICLR
- 28 January 2021

TLDR

Symplectic microgeometry I: micromorphisms

- A. Cattaneo, B. Dherin, A. Weinstein
- Mathematics
- 21 May 2009

We introduce the notion of symplectic microfolds and symplectic micromorphisms between them. They form a symmetric monoidal category, which is a version of the “category” of symplectic manifolds and… Expand

Symplectic microgeometry II: generating functions

- A. Cattaneo, B. Dherin, A. Weinstein
- Mathematics
- 3 March 2011

We adapt the notion of generating functions for lagrangian submanifolds to symplectic microgeometry. We show that a symplectic micromorphism always admits a global generating function. As an… Expand

Formal Symplectic Groupoid

- A. Cattaneo, B. Dherin, G. Felder
- Mathematics
- 19 December 2003

The multiplicative structure of the trivial symplectic groupoid over ℝd associated to the zero Poisson structure can be expressed in terms of a generating function. We address the problem of… Expand

Integration of Lie algebroid comorphisms

- A. Cattaneo, B. Dherin, A. Weinstein
- Mathematics
- 16 October 2012

We show that the path construction integration of Lie algebroids by Lie groupoids is an actual equivalence from the of integrable Lie algebroids and complete Lie algebroid comorphisms to the of… Expand

Symplectic microgeometry III: monoids

- A. Cattaneo, B. Dherin, A. Weinstein
- Mathematics
- 22 September 2011

We show that the category of Poisson manifolds and Poisson maps, the category of symplectic microgroupoids and Lagrangian submicrogroupoids (as morphisms), and the category of monoids and monoid… Expand

Tensor products of representations up to homotopy

- C. A. Abad, M. Crainic, B. Dherin
- Mathematics
- 29 September 2010

We study the construction of tensor products of representations up to homotopy, which are the A-infinity version of ordinary representations. We provide formulas for the construction of tensor… Expand

Symplectic microgeometry, IV: Quantization

- A. Cattaneo, B. Dherin, A. Weinstein
- MathematicsPacific Journal of Mathematics
- 16 July 2020

We construct a special class of semiclassical Fourier integral operators whose wave fronts are symplectic micromorphisms. These operators have very good properties: they form a category on which the… Expand

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