19,379 research outputs found
A novel iterative method to approximate structured singular values
A novel method for approximating structured singular values (also known as
mu-values) is proposed and investigated. These quantities constitute an
important tool in the stability analysis of uncertain linear control systems as
well as in structured eigenvalue perturbation theory. Our approach consists of
an inner-outer iteration. In the outer iteration, a Newton method is used to
adjust the perturbation level. The inner iteration solves a gradient system
associated with an optimization problem on the manifold induced by the
structure. Numerical results and comparison with the well-known Matlab function
mussv, implemented in the Matlab Control Toolbox, illustrate the behavior of
the method
Matrix Completion on Graphs
The problem of finding the missing values of a matrix given a few of its
entries, called matrix completion, has gathered a lot of attention in the
recent years. Although the problem under the standard low rank assumption is
NP-hard, Cand\`es and Recht showed that it can be exactly relaxed if the number
of observed entries is sufficiently large. In this work, we introduce a novel
matrix completion model that makes use of proximity information about rows and
columns by assuming they form communities. This assumption makes sense in
several real-world problems like in recommender systems, where there are
communities of people sharing preferences, while products form clusters that
receive similar ratings. Our main goal is thus to find a low-rank solution that
is structured by the proximities of rows and columns encoded by graphs. We
borrow ideas from manifold learning to constrain our solution to be smooth on
these graphs, in order to implicitly force row and column proximities. Our
matrix recovery model is formulated as a convex non-smooth optimization
problem, for which a well-posed iterative scheme is provided. We study and
evaluate the proposed matrix completion on synthetic and real data, showing
that the proposed structured low-rank recovery model outperforms the standard
matrix completion model in many situations.Comment: Version of NIPS 2014 workshop "Out of the Box: Robustness in High
Dimension
Approximate FPGA-based LSTMs under Computation Time Constraints
Recurrent Neural Networks and in particular Long Short-Term Memory (LSTM)
networks have demonstrated state-of-the-art accuracy in several emerging
Artificial Intelligence tasks. However, the models are becoming increasingly
demanding in terms of computational and memory load. Emerging latency-sensitive
applications including mobile robots and autonomous vehicles often operate
under stringent computation time constraints. In this paper, we address the
challenge of deploying computationally demanding LSTMs at a constrained time
budget by introducing an approximate computing scheme that combines iterative
low-rank compression and pruning, along with a novel FPGA-based LSTM
architecture. Combined in an end-to-end framework, the approximation method's
parameters are optimised and the architecture is configured to address the
problem of high-performance LSTM execution in time-constrained applications.
Quantitative evaluation on a real-life image captioning application indicates
that the proposed methods required up to 6.5x less time to achieve the same
application-level accuracy compared to a baseline method, while achieving an
average of 25x higher accuracy under the same computation time constraints.Comment: Accepted at the 14th International Symposium in Applied
Reconfigurable Computing (ARC) 201
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