Ganesh Swami

I’ll be at Stanford for the next few days for Hot Chips 20, a symposium on high performance chips. Sessions I’m particularly interested in:

• D.E. Shaw’s specialized ASIC for molecular dynamics which I’ve written about earlier and IBM’s PowerXCell powering Roadrunner.
• Upcoming architectures: AMD’s 780G and Intel’s Nehalem (dot products of special interest to me.)
• Chips tuned for network or IO (Sun’s Rock, Fujitsu’s SPARC64VII and Intel’s Tukwila.)
• Algorithmic content: Roofline models for automatic tuning of kernels (good addition to Demmel’s talk on the future of linear algebra from MMDS.)
• Intel’s Larrabee: response to “the can of whoop-ass” (detailed architectural paper from SIGRAPH.)
• CUDA: useful for a class of algorithms (based on memory access.)

I’m going to be trying something new this time — live blogging. I’ll try to push constant updates to my twitter stream : gane5h.

I’ll be staying at the Sheraton in Palo Alto. Drop me a line if you want to meetup for a chat.

The workshop was a blast! I had an incredible time getting up to speed on the latest and greatest in data analysis research. It was quite humbling to brush shoulders with some of top folks pushing the frontiers of science. There were also many opportunities to network where I could get a peek at the motivations behind some of the projects presented.

Each day had a theme:

• Data Analysis and Data Applications
• Networked Data and Algorithmic Tools
• Statistical, Geometric, and Topological Methods
• Machine Learning and Dimensionality Reduction

The breadth of topics was quite exhaustive. I mostly pushed my own agenda: streaming algorithms. There’s so much to write here that I won’t even attempt to.

Besides streaming algorithms, the presentations on mathematical topics were really interesting. Some of it I’ve previously seen from my day-to-day work, some of it was new. Of particular interest to me were the following:

• Graph Sparsification : Never seen anything like this before.
• Massive Terrain Data : Real smart use of offline datastrutures.
• Symmetries in point cloud data : I’m intimately familiar with this style of mathematics from my previous work.
• Pathway Analysis in Protein Folding : Puts bread on the table.
• Intersection SVMs : Didn’t know this was a well known concept in machine learning known as the kernel trick. Goes by Reproducing Kernel Hilbert Space in my neck of the woods and also a precursor to the above mentioned image matching algorithm.
• Manifold regularization : Fréchet means anyone?
• Sufficient Dimension Reduction
• Semi-definite programming : Some mathematical insights to a couple of engineering problems (where <1e-4 is good enough) that’s making my life difficult.
• Spectral Algorithms
• Matrix/Tensor Factorization
• Future of Parallel Linear Algebra

Thanks to my friend Krishna who let me sleep on the floor in his house, thereby saving me from the grips of boredom.

I know some of my readers are deeply interested in high performance computing and computational physics: this is a post for them. The conference I had mentioned in my previous post was the GROMACS Workshop on Advanced Simulation Methods.

Gromacs is a high performance simulation engine primarily for solving Newtonian dynamics (it also does normal mode analysis, structure minimization and mixed molecular mechanics-quantum mechanics simulations.) It was an industry leader in terms of raw single processor performance for many years, until Desmond from D.E. Shaw Research took over with their super-scalable algorithms (I’ve written about this before.) With Gromacs 4.0, they’ve fixed the scalability problems and with a variety of other algorithmic fixes, they are the top dog once again. Disclaimer: these are all claims by relevant parties and I have not verified them myself, though I’d love to do so unencumbered. Though the Gromacs 4.0 paper is published, I’ll only be writing about it when the actual product is released.

The focus of the workshop was on algorithms, though there were some applications too. I’m sure an applications person would have felt out of place, but I felt I had something to contribute in almost every topic that was discussed. I’m archiving the list of topics here for posterity:

• The new domain decomposition parallelization in Gromacs 4.0, with some tips & tricks to get the most out of your hardware
• Different methods to perform free energy calculations. Slow-growth, perturbations, Bennett Acceptance Ratio. Which protocol is most efficient, and what new things will be in Gromacs 4.0?
• QM/MM. How do you mix Quantum Mechanics with Gromacs?
• Virtual sites for hydrogen motion removal and long time-steps
• Membrane protein simulations
• Replica exchange, and extracting kinetic data from it
• Local pressure extensions to Gromacs
• Gromacs source code walk-through

The take home message: strong coupling between various pieces of the algorithm is anti-thesis to parallel scalability. The CPU industry seems to have hit a brick wall in terms of improving raw computational speed: the future is in multi-core. Therefore, remove the coupling with better algorithms and you are on your way to highly scalable and by definition superbly fast algorithms.

The timestep used in an integrator while solving a set of equations inherently determines the speed of the algorithm. Big timesteps will make the algorithm unstable as you your trajectory will not be able to follow the phase space manifold accurately (as a side note Euler-type integrators also become unstable as you make the timestep smaller, but this is the least of your worries with a non-symplectic integrator.) The Nyquist theorem determines the sampling rate, so removing fast (or high frequency) degrees of motion such as hydrogen bond vibrations with constraints on them is required for a big timestep. Usual constraints algorithms are coupled leading to undesirable non-scalable algorithms. The Gromacs developers have solved this with a new constraints algorithm called P-LINCS.