Deep learning has made enormous leaps forward thanks to GPU hardware. But much Big Data analysis is still done with classical methods on *sparse data*. Tasks like click prediction, personalization, recommendation, search ranking, etc. still account for most of the revenue from commercial data analysis. The role of GPUs in that realm has been less clear. In the BIDMach project (part of the BID Data Project at UC Berkeley), we have been exploring general machine learning with GPUs. The results are remarkable: not only do we see order-of-magnitude speedups for most problems, but our system also outperforms today’s cluster computing systems running up to several hundred nodes on typical workloads. As well as the incentives to adopt GPU technology for deep learning tasks, there is now a strong incentive for organizations to migrate to GPUs for the remainder of their analytics workload.

## Roofline Design

To build the fastest system, we borrowed the approach of *roofline design* from computer architecture. Roofline design involves designing to fundamental limits (e.g. ALU throughput, memory speed, network speed, I/O speed etc). A rooflined system is fast, and no other system can be much faster, since both have to respect the same hardware limits. A roofline diagram for matrix multiply is shown below:

The y-axis shows the potential throughput in arithmetic operations/second. The x-axis is “operational intensity” which is the number of operations applied to each data value (in units of operations per byte). The intensity is much lower for sparse operations – e.g. sparse matrix multiply typically involves only a multiply and add for each input datum, while dense matrix multiply uses each datum many times. The horizontal lines reflect the maximum ALU throughput for each type of processor (the graph is drawn for Intel i7 and NVIDIA GeForce GTX 680 processors). GPUs have much higher ALU throughput since the GPU chip area is almost entirely ALU. For dense matrix multiply, GPUs are10x faster thanks to this higher computing area.

The diagonal lines reflect memory bandwidth. Since bandwidth is flow in bytes/second it defines a linear relationship between the x-axis (flops/byte) and the y-axis (in flops/sec). A less well-known feature of GPUs is their higher main-memory bandwidth. This leads to a (potential) 10x gap in sparse matrix operations, which are the most important for many machine learning tasks. CuSparse achieves this ceiling for typical scientific data, but we found it was less well fit to very sparse data (text, web logs etc.). We wrote our own sparse kernels and were able to get them close to the roofline limits over a full range of sparseness. These kernels form the basis for the high throughput in most of BIDMach’s algorithms. Continue reading