34,104 research outputs found
Fast, Exact and Multi-Scale Inference for Semantic Image Segmentation with Deep Gaussian CRFs
In this work we propose a structured prediction technique that combines the
virtues of Gaussian Conditional Random Fields (G-CRF) with Deep Learning: (a)
our structured prediction task has a unique global optimum that is obtained
exactly from the solution of a linear system (b) the gradients of our model
parameters are analytically computed using closed form expressions, in contrast
to the memory-demanding contemporary deep structured prediction approaches that
rely on back-propagation-through-time, (c) our pairwise terms do not have to be
simple hand-crafted expressions, as in the line of works building on the
DenseCRF, but can rather be `discovered' from data through deep architectures,
and (d) out system can trained in an end-to-end manner. Building on standard
tools from numerical analysis we develop very efficient algorithms for
inference and learning, as well as a customized technique adapted to the
semantic segmentation task. This efficiency allows us to explore more
sophisticated architectures for structured prediction in deep learning: we
introduce multi-resolution architectures to couple information across scales in
a joint optimization framework, yielding systematic improvements. We
demonstrate the utility of our approach on the challenging VOC PASCAL 2012
image segmentation benchmark, showing substantial improvements over strong
baselines. We make all of our code and experiments available at
{https://github.com/siddharthachandra/gcrf}Comment: Our code is available at https://github.com/siddharthachandra/gcr
Unmasking Clever Hans Predictors and Assessing What Machines Really Learn
Current learning machines have successfully solved hard application problems,
reaching high accuracy and displaying seemingly "intelligent" behavior. Here we
apply recent techniques for explaining decisions of state-of-the-art learning
machines and analyze various tasks from computer vision and arcade games. This
showcases a spectrum of problem-solving behaviors ranging from naive and
short-sighted, to well-informed and strategic. We observe that standard
performance evaluation metrics can be oblivious to distinguishing these diverse
problem solving behaviors. Furthermore, we propose our semi-automated Spectral
Relevance Analysis that provides a practically effective way of characterizing
and validating the behavior of nonlinear learning machines. This helps to
assess whether a learned model indeed delivers reliably for the problem that it
was conceived for. Furthermore, our work intends to add a voice of caution to
the ongoing excitement about machine intelligence and pledges to evaluate and
judge some of these recent successes in a more nuanced manner.Comment: Accepted for publication in Nature Communication
Solution of large linear systems of equations on the massively parallel processor
The Massively Parallel Processor (MPP) was designed as a special machine for specific applications in image processing. As a parallel machine, with a large number of processors that can be reconfigured in different combinations it is also applicable to other problems that require a large number of processors. The solution of linear systems of equations on the MPP is investigated. The solution times achieved are compared to those obtained with a serial machine and the performance of the MPP is discussed
Image classification by visual bag-of-words refinement and reduction
This paper presents a new framework for visual bag-of-words (BOW) refinement
and reduction to overcome the drawbacks associated with the visual BOW model
which has been widely used for image classification. Although very influential
in the literature, the traditional visual BOW model has two distinct drawbacks.
Firstly, for efficiency purposes, the visual vocabulary is commonly constructed
by directly clustering the low-level visual feature vectors extracted from
local keypoints, without considering the high-level semantics of images. That
is, the visual BOW model still suffers from the semantic gap, and thus may lead
to significant performance degradation in more challenging tasks (e.g. social
image classification). Secondly, typically thousands of visual words are
generated to obtain better performance on a relatively large image dataset. Due
to such large vocabulary size, the subsequent image classification may take
sheer amount of time. To overcome the first drawback, we develop a graph-based
method for visual BOW refinement by exploiting the tags (easy to access
although noisy) of social images. More notably, for efficient image
classification, we further reduce the refined visual BOW model to a much
smaller size through semantic spectral clustering. Extensive experimental
results show the promising performance of the proposed framework for visual BOW
refinement and reduction
Report from the MPP Working Group to the NASA Associate Administrator for Space Science and Applications
NASA's Office of Space Science and Applications (OSSA) gave a select group of scientists the opportunity to test and implement their computational algorithms on the Massively Parallel Processor (MPP) located at Goddard Space Flight Center, beginning in late 1985. One year later, the Working Group presented its report, which addressed the following: algorithms, programming languages, architecture, programming environments, the way theory relates, and performance measured. The findings point to a number of demonstrated computational techniques for which the MPP architecture is ideally suited. For example, besides executing much faster on the MPP than on conventional computers, systolic VLSI simulation (where distances are short), lattice simulation, neural network simulation, and image problems were found to be easier to program on the MPP's architecture than on a CYBER 205 or even a VAX. The report also makes technical recommendations covering all aspects of MPP use, and recommendations concerning the future of the MPP and machines based on similar architectures, expansion of the Working Group, and study of the role of future parallel processors for space station, EOS, and the Great Observatories era
Faster Inversion and Other Black Box Matrix Computations Using Efficient Block Projections
Block projections have been used, in [Eberly et al. 2006], to obtain an
efficient algorithm to find solutions for sparse systems of linear equations. A
bound of softO(n^(2.5)) machine operations is obtained assuming that the input
matrix can be multiplied by a vector with constant-sized entries in softO(n)
machine operations. Unfortunately, the correctness of this algorithm depends on
the existence of efficient block projections, and this has been conjectured. In
this paper we establish the correctness of the algorithm from [Eberly et al.
2006] by proving the existence of efficient block projections over sufficiently
large fields. We demonstrate the usefulness of these projections by deriving
improved bounds for the cost of several matrix problems, considering, in
particular, ``sparse'' matrices that can be be multiplied by a vector using
softO(n) field operations. We show how to compute the inverse of a sparse
matrix over a field F using an expected number of softO(n^(2.27)) operations in
F. A basis for the null space of a sparse matrix, and a certification of its
rank, are obtained at the same cost. An application to Kaltofen and Villard's
Baby-Steps/Giant-Steps algorithms for the determinant and Smith Form of an
integer matrix yields algorithms requiring softO(n^(2.66)) machine operations.
The derived algorithms are all probabilistic of the Las Vegas type
Weighted maximal regularity estimates and solvability of non-smooth elliptic systems I
We develop new solvability methods for divergence form second order, real and
complex, elliptic systems above Lipschitz graphs, with boundary data. The
coefficients may depend on all variables, but are assumed to be close to
coefficients that are independent of the coordinate transversal to the
boundary, in the Carleson sense defined by Dahlberg. We obtain a
number of {\em a priori} estimates and boundary behaviour results under
finiteness of . Our methods yield full characterization of weak
solutions, whose gradients have estimates of a non-tangential maximal
function or of the square function, via an integral representation acting on
the conormal gradient, with a singular operator-valued kernel. Also, the
non-tangential maximal function of a weak solution is controlled in by
the square function of its gradient. This estimate is new for systems in such
generality, and even for real non-symmetric equations in dimension 3 or higher.
The existence of a proof {\em a priori} to well-posedness, is also a new fact.
As corollaries, we obtain well-posedness of the Dirichlet, Neumann and
Dirichlet regularity problems under smallness of and
well-posedness for , improving earlier results for real symmetric
equations. Our methods build on an algebraic reduction to a first order system
first made for coefficients by the two authors and A. McIntosh in order
to use functional calculus related to the Kato conjecture solution, and the
main analytic tool for coefficients is an operational calculus to prove
weighted maximal regularity estimates.Comment: This is an extended version of the paper, containing some new
material and a road map to proofs on suggestion from the referee
Decimated generalized Prony systems
We continue studying robustness of solving algebraic systems of Prony type
(also known as the exponential fitting systems), which appear prominently in
many areas of mathematics, in particular modern "sub-Nyquist" sampling
theories. We show that by considering these systems at arithmetic progressions
(or "decimating" them), one can achieve better performance in the presence of
noise. We also show that the corresponding lower bounds are closely related to
well-known estimates, obtained for similar problems but in different contexts
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