Acceleration Method for Learning Fine-Layered Optical Neural Networks

An optical neural network (ONN) is a promising system due to its high-speed and low-power operation. Its linear unit performs a multiplication of an input vector and a weight matrix in optical analog circuits. Among them, a circuit with a multiple-layered structure of programmable Mach-Zehnder interferometers (MZIs) can realize a specific class of unitary matrices with a limited number of MZIs as its weight matrix. The circuit is effective for balancing the number of programmable MZIs and ONN performance. However, it takes a lot of time to learn MZI parameters of the circuit with a conventional automatic differentiation (AD), which machine learning platforms are equipped with. To solve the time-consuming problem, we propose an acceleration method for learning MZI parameters. We create customized complex-valued derivatives for an MZI, exploiting Wirtinger derivatives and a chain rule. They are incorporated into our newly developed function module implemented in C++ to collectively calculate their values in a multi-layered structure. Our method is simple, fast, and versatile as well as compatible with the conventional AD. We demonstrate that our method works 20 times faster than the conventional AD when a pixel-by-pixel MNIST task is performed in a complex-valued recurrent neural network with an MZI-based hidden unit.

Structured Inverted-File k-Means Clustering for High-Dimensional Sparse Data

This paper presents an architecture-friendly k-means clustering algorithm called SIVF for a large-scale and high-dimensional sparse data set. Algorithm efficiency on time is often measured by the number of costly operations such as similarity calculations. In practice, however, it depends greatly on how the algorithm adapts to an architecture of the computer system which it is executed on. Our proposed SIVF employs invariant centroid-pair based filter (ICP) to decrease the number of similarity calculations between a data object and centroids of all the clusters. To maximize the ICP performance, SIVF exploits for a centroid set an inverted-file that is structured so as to reduce pipeline hazards. We demonstrate in our experiments on real large-scale document data sets that SIVF operates at higher speed and with lower memory consumption than existing algorithms. Our performance analysis reveals that SIVF achieves the higher speed by suppressing performance degradation factors of the number of cache misses and branch mispredictions rather than less similarity calculations.

Inverted-File k-Means Clustering: Performance Analysis

This paper presents an inverted-file k-means clustering algorithm (IVF) suitable for a large-scale sparse data set with potentially numerous classes. Given such a data set, IVF efficiently works at high-speed and with low memory consumption, which keeps the same solution as a standard Lloyd's algorithm. The high performance arises from two distinct data representations. One is a sparse expression for both the object and mean feature vectors. The other is an inverted-file data structure for a set of the mean feature vectors. To confirm the effect of these representations, we design three algorithms using distinct data structures and expressions for comparison. We experimentally demonstrate that IVF achieves better performance than the designed algorithms when they are applied to large-scale real document data sets in a modern computer system equipped with superscalar out-of-order processors and a deep hierarchical memory system. We also introduce a simple yet practical clock-cycle per instruction (CPI) model for speed-performance analysis. Analytical results reveal that IVF suppresses three performance degradation factors: the numbers of cache misses, branch mispredictions, and the completed instructions.