[math-ias] Theoretical Computer Science/Discrete Math Seminars -- Week of September 30, 2013

[Anthony V. Pulido]

INSTITUTE FOR ADVANCED STUDY
School of Mathematics
Princeton, NJ 08540

Theoretical Computer Science/Discrete Math Seminars
Week of September 30, 2013




Monday, September 30

Computer Science/Discrete Mathematics Seminar I
Topic:         Some provable bounds for deep learning
Speaker:     Sanjeev Arora
Time/Room:     11:15am - 12:15pm/S-101
Abstract:    See below



Tuesday, October 1

Computer Science/Discrete Mathematics Seminar II
Topic:         Small set expander flows
Speaker:     Ali Kemal Sinop, Institute for Advanced Study; Member, School 
of Mathematics
Time/Room:     10:30am - 12:30pm/S-101
Abstract:    See below

1 Some provable bounds for deep learning
   Sanjeev Arora

Deep learning, a modern version of neural nets, is increasingly seen as a 
promising way to implement AI tasks such as speech recognition and image 
recognition. Most current algorithms are heuristic and have no provable 
guarantees. This talk will describe provable learning of an interesting 
class of deep networks which are neural nets. Here a deep net is viewed as 
a generative model for a probability distribution on inputs, using the 
"denoising autoencoder" framework of Vincent et al. The talk will be 
self-contained. (Joint work with Aditya Bhaskara, Rong Ge, Tengyu Ma)

2 Small set expander flows
   Ali Kemal Sinop

A common way for lower bounding the expansion of a graph is by looking the 
second smallest eigenvalue of its Laplacian matrix. Also known as the easy 
direction of Cheeger's inequality, this bound becomes too weak when the 
expansion is o(1). In 2004, Arora, Rao and Vazirani proved the existence of 
"expander flows", which are certificates of graph expansion up to a factor 
of O(sqrt{log n}). In this talk, I will describe a generalization of these 
for small set, "small set expander (SSE) flows", and I will describe an 
application of such flows for finding near optimal sparse cuts on graphs 
with certain isoperimetric profiles. This is joint work with Sanjeev Arora 
and Rong Ge.

Computer Science/Discrete Math Seminars can be found on our web page:

http://www.math.ias.edu/csdm
http://www.math.ias.edu
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