An Asynchronous Parallel Randomized Kaczmarz Algorithm

We describe an asynchronous parallel variant of the randomized Kaczmarz (RK) algorithm for solving the linear system $Ax=b$. The analysis shows linear convergence and indicates that nearly linear speedup can be expected if the number of processors is bounded by a multiple of the number of rows in $A$

Design of 2D discrete cosine transform using CORDIC architectures in VHDL

The Discrete Cosine Transform is one of the most widely transform techniques in digital signal processing. In addition, this is also most computationally intensive transforms which require many multiplications and additions. Real time data processing necessitates the use of special purpose hardware which involves hardware efficiency as well as high throughput. Many DCT algorithms were proposed in order to achieve high speed DCT. Those architectures which involves multipliers, for example Chen’s algorithm has less regular architecture due to complex routing and requires large silicon area. On the other hand, the DCT architecture based on distributed arithmetic (DA) which is also a multiplier less architecture has the inherent disadvantage of less throughputs because of the ROM access time and the need of accumulator. Also this DA algorithm requires large silicon area if it requires large ROM size. Systolic array architecture for the real-time DCT computation may have the large number of gates and clock skew problem. The other ways of implementation of DCT which involves in multiplierless, thus power efficient and which results in regular architecture and less complicated routing, consequently less area, simultaneously lead to high throughput. So for that purpose CORDIC seems to be a best solution. CORDIC offers a unified iterative formulation to efficiently evaluate the rotation operation. This thesis presents the implementation of 2D Discrete Cosine Transform (DCT) using the Angle Recoded (AR) Cordic algorithm, the new scaling less CORDIC algorithm and the conventional Chen’s algorithm which is multiplier dependant algorithm. The 2D DCT is implemented by exploiting the Separability property of 2D Discrete Cosine Transform. Here first one dimensional DCT is designed first and later a transpose buffer which consists of 64 memory elements, fully pipelined is designed. Later all these blocks are joined with the help of a controller element which is a mealy type FSM which produces some status signals also. The three resulting architectures are all well synthesized in Xilinx 9.1ise, simulated in Modelsim 5.6f and the power is calculated in Xilinx Xpower. Results prove that AR Cordic algorithm is better than Chen’s algorithm, even the new scaling less CORDIC algorithm

Towards Visually Explaining Variational Autoencoders

Recent advances in Convolutional Neural Network (CNN) model interpretability have led to impressive progress in visualizing and understanding model predictions. In particular, gradient-based visual attention methods have driven much recent effort in using visual attention maps as a means for visual explanations. A key problem, however, is these methods are designed for classification and categorization tasks, and their extension to explaining generative models, e.g. variational autoencoders (VAE) is not trivial. In this work, we take a step towards bridging this crucial gap, proposing the first technique to visually explain VAEs by means of gradient-based attention. We present methods to generate visual attention from the learned latent space, and also demonstrate such attention explanations serve more than just explaining VAE predictions. We show how these attention maps can be used to localize anomalies in images, demonstrating state-of-the-art performance on the MVTec-AD dataset. We also show how they can be infused into model training, helping bootstrap the VAE into learning improved latent space disentanglement, demonstrated on the Dsprites dataset

MapToGenome: A Comparative Genomic Tool that Aligns Transcript Maps to Sequenced Genomes

Efforts to generate whole genome assemblies and dense genetic maps have provided a wealth of gene positional information for several vertebrate species. Comparing the relative location of orthologous genes among these genomes provides perspective on genome evolution and can aid in translating genetic information between distantly related organisms. However, large-scale comparisons between genetic maps and genome assemblies can prove challenging because genetic markers are commonly derived from transcribed sequences that are incompletely and variably annotated. We developed the program MapToGenome as a tool for comparing transcript maps and genome assemblies. MapToGenome processes sequence alignments between mapped transcripts and whole genome sequence while accounting for the presence of intronic sequences, and assigns orthology based on user-defined parameters. To illustrate the utility of this program, we used MapToGenome to process alignments between vertebrate genetic maps and genome assemblies 1) self/self alignments for maps and assemblies of the rat and zebrafish genome; 2) alignments between vertebrate transcript maps (rat, salamander, zebrafish, and medaka) and the chicken genome; and 3) alignments of the medaka and zebrafish maps to the pufferfish (Tetraodon nigroviridis) genome. Our results show that map-genome alignments can be improved by combining alignments across presumptive intron breaks and ignoring alignments for simple sequence length polymorphism (SSLP) marker sequences. Comparisons between vertebrate maps and genomes reveal broad patterns of conservation among vertebrate genomes and the differential effects of genome rearrangement over time and across lineages

Learning Similarity Attention

We consider the problem of learning similarity functions. While there has been substantial progress in learning suitable distance metrics, these techniques in general lack decision reasoning, i.e., explaining why the input set of images is similar or dissimilar. In this work, we solve this key problem by proposing the first method to generate generic visual similarity explanations with gradient-based attention. We demonstrate that our technique is agnostic to the specific similarity model type, e.g., we show applicability to Siamese, triplet, and quadruplet models. Furthermore, we make our proposed similarity attention a principled part of the learning process, resulting in a new paradigm for learning similarity functions. We demonstrate that our learning mechanism results in more generalizable, as well as explainable, similarity models. Finally, we demonstrate the generality of our framework by means of experiments on a variety of tasks, including image retrieval, person re-identification, and low-shot semantic segmentation.Comment: 10 pages, 7 figures, 4 table