111 research outputs found
Evaluation of Explanation Methods of AI -- CNNs in Image Classification Tasks with Reference-based and No-reference Metrics
The most popular methods in AI-machine learning paradigm are mainly black
boxes. This is why explanation of AI decisions is of emergency. Although
dedicated explanation tools have been massively developed, the evaluation of
their quality remains an open research question. In this paper, we generalize
the methodologies of evaluation of post-hoc explainers of CNNs' decisions in
visual classification tasks with reference and no-reference based metrics. We
apply them on our previously developed explainers (FEM, MLFEM), and popular
Grad-CAM. The reference-based metrics are Pearson correlation coefficient and
Similarity computed between the explanation map and its ground truth
represented by a Gaze Fixation Density Map obtained with a psycho-visual
experiment. As a no-reference metric, we use stability metric, proposed by
Alvarez-Melis and Jaakkola. We study its behaviour, consensus with
reference-based metrics and show that in case of several kinds of degradation
on input images, this metric is in agreement with reference-based ones.
Therefore, it can be used for evaluation of the quality of explainers when the
ground truth is not available.Comment: Due to a bug found in the code, all tables and figures were redone.
The new results did not change the main conclusion, except for the best
explainer. FEM has performed better than MLFEM; 25 pages, 16 tables, 16
figures; Submitted to "Advances in Artificial Intelligence and Machine
Learning" (ISSN: 2582-9793
3D Convolutional Networks for Action Recognition: Application to Sport Gesture Recognition
3D convolutional networks is a good means to perform tasks such as video
segmentation into coherent spatio-temporal chunks and classification of them
with regard to a target taxonomy. In the chapter we are interested in the
classification of continuous video takes with repeatable actions, such as
strokes of table tennis. Filmed in a free marker less ecological environment,
these videos represent a challenge from both segmentation and classification
point of view. The 3D convnets are an efficient tool for solving these problems
with window-based approaches.Comment: Multi-faceted Deep Learning, 202
Finding All Solutions of Equations in Free Groups and Monoids with Involution
The aim of this paper is to present a PSPACE algorithm which yields a finite
graph of exponential size and which describes the set of all solutions of
equations in free groups as well as the set of all solutions of equations in
free monoids with involution in the presence of rational constraints. This
became possible due to the recently invented emph{recompression} technique of
the second author.
He successfully applied the recompression technique for pure word equations
without involution or rational constraints. In particular, his method could not
be used as a black box for free groups (even without rational constraints).
Actually, the presence of an involution (inverse elements) and rational
constraints complicates the situation and some additional analysis is
necessary. Still, the recompression technique is general enough to accommodate
both extensions. In the end, it simplifies proofs that solving word equations
is in PSPACE (Plandowski 1999) and the corresponding result for equations in
free groups with rational constraints (Diekert, Hagenah and Gutierrez 2001). As
a byproduct we obtain a direct proof that it is decidable in PSPACE whether or
not the solution set is finite.Comment: A preliminary version of this paper was presented as an invited talk
at CSR 2014 in Moscow, June 7 - 11, 201
Mumford dendrograms and discrete p-adic symmetries
In this article, we present an effective encoding of dendrograms by embedding
them into the Bruhat-Tits trees associated to -adic number fields. As an
application, we show how strings over a finite alphabet can be encoded in
cyclotomic extensions of and discuss -adic DNA encoding. The
application leads to fast -adic agglomerative hierarchic algorithms similar
to the ones recently used e.g. by A. Khrennikov and others. From the viewpoint
of -adic geometry, to encode a dendrogram in a -adic field means
to fix a set of -rational punctures on the -adic projective line
. To is associated in a natural way a
subtree inside the Bruhat-Tits tree which recovers , a method first used by
F. Kato in 1999 in the classification of discrete subgroups of
.
Next, we show how the -adic moduli space of
with punctures can be applied to the study of time series of
dendrograms and those symmetries arising from hyperbolic actions on
. In this way, we can associate to certain classes of dynamical
systems a Mumford curve, i.e. a -adic algebraic curve with totally
degenerate reduction modulo .
Finally, we indicate some of our results in the study of general discrete
actions on , and their relation to -adic Hurwitz spaces.Comment: 14 pages, 6 figure
Scaling limits of a tagged particle in the exclusion process with variable diffusion coefficient
We prove a law of large numbers and a central limit theorem for a tagged
particle in a symmetric simple exclusion process in the one-dimensional lattice
with variable diffusion coefficient. The scaling limits are obtained from a
similar result for the current through -1/2 for a zero-range process with bond
disorder. For the CLT, we prove convergence to a fractional Brownian motion of
Hurst exponent 1/4.Comment: 9 page
Solution sets for equations over free groups are EDT0L languages
© World Scientific Publishing Company. We show that, given an equation over a finitely generated free group, the set of all solutions in reduced words forms an effectively constructible EDT0L language. In particular, the set of all solutions in reduced words is an indexed language in the sense of Aho. The language characterization we give, as well as further questions about the existence or finiteness of solutions, follow from our explicit construction of a finite directed graph which encodes all the solutions. Our result incorporates the recently invented recompression technique of Jez, and a new way to integrate solutions of linear Diophantine equations into the process. As a byproduct of our techniques, we improve the complexity from quadratic nondeterministic space in previous works to NSPACE(n log n) here
A -adic RanSaC algorithm for stereo vision using Hensel lifting
A -adic variation of the Ran(dom) Sa(mple) C(onsensus) method for solving
the relative pose problem in stereo vision is developped. From two 2-adically
encoded images a random sample of five pairs of corresponding points is taken,
and the equations for the essential matrix are solved by lifting solutions
modulo 2 to the 2-adic integers. A recently devised -adic hierarchical
classification algorithm imitating the known LBG quantisation method classifies
the solutions for all the samples after having determined the number of
clusters using the known intra-inter validity of clusterings. In the successful
case, a cluster ranking will determine the cluster containing a 2-adic
approximation to the "true" solution of the problem.Comment: 15 pages; typos removed, abstract changed, computation error remove
Hydrodynamic limit for a boundary driven stochastic lattice gas model with many conserved quantities
We prove the hydrodynamic limit for a particle system in which particles may
have different velocities. We assume that we have two infinite reservoirs of
particles at the boundary: this is the so-called boundary driven process. The
dynamics we considered consists of a weakly asymmetric simple exclusion process
with collision among particles having different velocities
Ground state at high density
Weak limits as the density tends to infinity of classical ground states of
integrable pair potentials are shown to minimize the mean-field energy
functional. By studying the latter we derive global properties of high-density
ground state configurations in bounded domains and in infinite space. Our main
result is a theorem stating that for interactions having a strictly positive
Fourier transform the distribution of particles tends to be uniform as the
density increases, while high-density ground states show some pattern if the
Fourier transform is partially negative. The latter confirms the conclusion of
earlier studies by Vlasov (1945), Kirzhnits and Nepomnyashchii (1971), and
Likos et al. (2007). Other results include the proof that there is no Bravais
lattice among high-density ground states of interactions whose Fourier
transform has a negative part and the potential diverges or has a cusp at zero.
We also show that in the ground state configurations of the penetrable sphere
model particles are superposed on the sites of a close-packed lattice.Comment: Note adde
Rigorous Probabilistic Analysis of Equilibrium Crystal Shapes
The rigorous microscopic theory of equilibrium crystal shapes has made
enormous progress during the last decade. We review here the main results which
have been obtained, both in two and higher dimensions. In particular, we
describe how the phenomenological Wulff and Winterbottom constructions can be
derived from the microscopic description provided by the equilibrium
statistical mechanics of lattice gases. We focus on the main conceptual issues
and describe the central ideas of the existing approaches.Comment: To appear in the March 2000 special issue of Journal of Mathematical
Physics on Probabilistic Methods in Statistical Physic
- …