# Seminars & Events for PACM IDeAS

September 19, 2017
2:30pm - 3:30pm
##### Towards de-mystification of deep learning: function space analysis of the representation layers
###### PACM IDeAS

PLEASE NOTE DIFFERENT DAY (TUESDAY).  We propose a function space approach to Representation Learning [1] and the analysis of the representation layers in deep learning architectures. We show how to compute a weak-type'  Besov smoothness index that quantifies the geometry of the clustering in the feature space. This approach was already applied successfully to improve the performance of machine learning algorithms such as the Random Forest [2] and tree-based Gradient Boosting [3]. Our experiments demonstrate that in well-known and well-performing trained  networks, the Besov smoothness of the training set, measured in the corresponding hidden layer feature map representation, increases from layer to layer which relates to the unfolding' of the clustering in the feature space.

Speaker: Shai Dekel, Tel Aviv University
Location:
Fine Hall 224
September 27, 2017
2:30pm - 3:30pm
##### Stability of some super-resolution problems
###### PACM IDeAS

The problem of computational super-resolution asks to recover an object from its noisy and limited spectrum. In this talk, we consider two inverse problems of this flavor, mainly from the point of view of stability estimates. In the first problem, we assume that the object's spectrum is a finite sum of exponentials modulated by polynomials (extending the well-researched case where the polynomials are constants). We derive upper bounds on the problem condition number and show that the attainable resolution exhibits Hölder-type continuity with respect to the noise level [1,3]. As an application we consider the approximation of a piecewise-smooth function from its Fourier coefficients.

Speaker: Dmitry Batenkov, MIT
Location:
Fine Hall 224
October 11, 2017
2:30pm - 3:30pm
##### TBA - Veit Elser
###### PACM IDeAS
Speaker: Veit Elser, Cornell University
Location:
Fine Hall 224
October 18, 2017
2:30pm - 3:30pm
##### Iron Age Hebrew Epigraphy in the Silicon Age - An Algorithmic Approach To Study Paleo-Hebrew Inscriptions
###### PACM IDeAS

Handwriting comparison and identification, e.g. in the setting of forensics, has been widely addressed over the years. However, even in the case of modern documents, the proposed computerized solutions are quite unsatisfactory. For historical documents, such problems are worsened, due to the inscriptions’ preservation conditions. In the following lecture, we will present an attempt at addressing such a problem in the setting of First Temple Period inscriptions, stemming from the isolated military outpost of Arad (ca. 600 BCE).

Speaker: Barak Sober, Tel Aviv University
Location:
Fine Hall 224
October 25, 2017
2:30pm - 3:30pm
##### TBA - Nicolas Garcia Trillos
###### PACM IDeAS
Speaker: Nicolas Garcia Trillos, Brown University
Location:
Fine Hall 224
November 8, 2017
2:30pm - 3:30pm
##### Provably good convex methods for mapping problems
###### PACM IDeAS

Computing mappings or correspondences between surfaces is an important tool for many applications in computer graphics, computer vision, medical imaging, morphology and related fields. Mappings of least angle distortion (conformal) and distance distortion (isometric) are of particular interest. The problem of finding conformal/isometric mappings between surfaces is typically formulated as a difficult non-convex optimization problem. Convex methods relax the non-convex optimization problem to a convex problem which can then be solved globally. The main issue then is whether the global solution of the convex problem is a good approximation for the original global solution. In this talk we will discuss two families of convex relaxations.

Location:
Fine Hall 224
November 15, 2017
2:30pm - 3:30pm
##### IDeAS Seminar: Computational Algebraic Geometry and Applications to Computer Vision
###### PACM IDeAS

Many models in science and engineering are described by polynomials.  Computational algebraic geometry gives tools to analyze and exploit algebraic structure.  In this talk, we offer a user-friendly introduction to some of these notions, including dimension (formalizing degrees of freedom), degree (formalizing the number of solutions to a polynomial system) and 0-1 laws in algebraic geometry (solution sets to polynomial systems exhibit similar behavior for all but a measure 0 subset of problem instances).  We will also mention algorithms, based on Gröbner bases (symbolic techniques) and homotopy continuation (numerical techniques).

Applied examples are drawn from the structure-from-motion problem in computer vision, where the task of building a 3D model from multiple 2D images leads to nontrivial polynomial systems.

Speaker: Joe Kileel, Princeton University
Location:
Fine Hall 224
November 29, 2017
2:30pm - 3:30pm
##### TBA-Gal Mishne
###### PACM IDeAS
Speaker: Gal Mishne, Yale University
Location:
Fine Hall 224
December 6, 2017
2:30pm - 3:30pm
##### TBA-Ti-Yen Lan
###### PACM IDeAS
Speaker: Ti-Yen Lan, Cornell University
Location:
Fine Hall 224