Amir Gholami is a postdoctoral research fellow in
BAIR Lab working under supervision of Prof. Kurt
Keutzer. He received his PhD in Computational Science
and Engineering Mathematics from UT Austin, working
with Prof. George Biros on novel methods for automatic tumor-bearing
image analysis (thesis can be found here).
Amir has extensive experience in second-order optimization methods, image registration, inverse problems, and large scale parallel computing,
developing codes that
have been scaled up to 200K cores. He is a Melosh Medal finalist,
recipient of best student paper award in SC'17 and Gold Medal in the ACM Student Research Competition,
as well as best student paper finalist in SC’14.
His current research includes large scale
training of Neural Networks, stochastic second-order
optimization methods, and robust optimization
(resume).
Characterizing the generalization performance of Neural Network at different points in the optimization space is an active area of research. In particular, the network's performance highly depends on the mini-batch size used for training. But what is different in the quality of the solution for large and small batch size that leads to this difference? We study this through the lens of the Hessian operator and show an interesting interleaved connection with robustness of the Neural Network and mini-batch size. For details please see this paper.
Segmenting a tumor-bearing image, is the task of decomposing the image into disjoint regions. We present a framework for fully automatic segmentation of brain MRI bearing gliomas, which includes three main steps: (1) preprocessing of the input MRI to normalize intensities and transport them in a common atlas space; (2) using supervised machine learning to create initial segmentation and probability maps for the target classes (whole tumor, edema, tumor core, and enhancing tumor); (3) combining these probabilities with an atlas-based segmentation algorithm in which we use a tumor growth model to improve on the segmentation and probability maps from the supervised learning scheme. The result of this work will be presented in MICCAI 2017.
I worked on this project during my internship at NVIDIA. The goal was to perform the whole training pipeline using half-float precision. This is very challenging due to the limited range of expressible numerical values in half-precision. The limitted precision, severeley affect the vanishing and exploding gradient problem in Neural Networks. Existing approaches, included use of stochastic rounding, which even for shallow networks cannot achieve the baseline accuracy. We developed a novel approach that achieves same accuracy as the baseline, with all the calculations and storage in half-float. We successfully tested the method on deep networks such as AlexNet and GoogLeNet. This work has resulted in a pending patent application.
Image registration is a process in which a mapping from a reference image to a target image is sought. It is key in many different applications ranging from medical imaging to machine learning. We have develoepd a state-of-the-art parallel registration solver that has been scaled up to 8,192 cores, and have been able to solve a record 3D image registration problem with 200 billion unknowns in less than 4 minutes. The code that we have developed is based on AccFFT along with a novel parallel high-order interpolation kernel. The result of this work will appear in SC'17( best student paper finalist [pdf]).
Accelerated FFT (AccFFT) is a new parallel FFT library for computing distributed Fast Fourier Transforms on GPU and CPU architectures. The library has been designed with the goal of achieving maximum performance, without making the user interface complicated. AccFFT supports parallel FFTs distributed with slab or pencil decomposition for both CPU and GPU architectures. The library's scalability has been tested upto 131K CPU cores, and upto 4K GPUs [pdf].
Stokes equation is one of the most important equations derived from Navier-Stokes. Numerical solutions and discretization of the Stokes equation is challenging. For instance, one cannot use arbitrary discretization spaces for velocity and pressure. Moreover, it is an elliptic but indefinite problem, which further complicates the construction of fast linear algebraic solvers and preconditioners, especially for problems with highly variable coefficients or high-order discretizations. We are using a novel adaptive fast multipole method (pvfmm), which uses an integral formulation scheme that can circumvent most of the difficulties with the Stokes equation. Compared to finite element methods, our formulation decouples the velocity and pressure, and generates fields that are by construction divergence free [pdf].
The need for large scale parallel solvers for elliptic partial differential equations (PDES) pervades across a spectrum of problems with resolution requirements that cannot be accommodated on current systems. Poisson solvers must scale to trillions of unknowns. Example of methods that scale well are the FFT (based on spectral discretizations), the Fast Multipole Method, and multigrid methods (for stencil-based discretizations). We have benchmarked these methods and compared their parallel efficiency as well as the corresponding cost per unknowns for different test cases. FFT is tested with p3dfft, FMM with pvfmm, AMG with ML package, and GMG with an in house code [pdf].
Gliomas are tumors that arise from Glial cells in the brain. They account for 29% of all brain and central nervous system (CNS) tumors, and 80% of all malignant tumors out of about 60,000 cases diagnosed each year in the United States. Despite advances in surgery, chemo/radio therapy, the median survival rate of high grade Gliomas has remained about one year in the past 30 years. One of the key parameters in increasing the survival rate of patients is how well the tumor invasion boundaries are detectable. With the current imaging technologies only the bulk of the tumor abnormalities, can be detected, and the infiltrated tumor cells get masked. I am trying to approximate the extent of tumor infiltration by coupling the imaging data with tumor growth dynamics [pdf].