42,476 research outputs found
Improved Asymmetric Locality Sensitive Hashing (ALSH) for Maximum Inner Product Search (MIPS)
Recently it was shown that the problem of Maximum Inner Product Search (MIPS)
is efficient and it admits provably sub-linear hashing algorithms. Asymmetric
transformations before hashing were the key in solving MIPS which was otherwise
hard. In the prior work, the authors use asymmetric transformations which
convert the problem of approximate MIPS into the problem of approximate near
neighbor search which can be efficiently solved using hashing. In this work, we
provide a different transformation which converts the problem of approximate
MIPS into the problem of approximate cosine similarity search which can be
efficiently solved using signed random projections. Theoretical analysis show
that the new scheme is significantly better than the original scheme for MIPS.
Experimental evaluations strongly support the theoretical findings.Comment: arXiv admin note: text overlap with arXiv:1405.586
Spin-Boson Hamiltonian and Optical Absorption of Molecular Dimers
An analysis of the eigenstates of a symmetry-broken spin-boson Hamiltonian is
performed by computing Bloch and Husimi projections. The eigenstate analysis is
combined with the calculation of absorption bands of asymmetric dimer
configurations constituted by monomers with nonidentical excitation energies
and optical transition matrix elements. Absorption bands with regular and
irregular fine structures are obtained and related to the transition from the
coexistence to a mixing of adiabatic branches in the spectrum. It is shown that
correlations between spin states allow for an interpolation between absorption
bands for different optical asymmetries.Comment: 15 pages, revTeX, 8 figures, accepted for publication in Phys. Rev.
Learning Edge Representations via Low-Rank Asymmetric Projections
We propose a new method for embedding graphs while preserving directed edge
information. Learning such continuous-space vector representations (or
embeddings) of nodes in a graph is an important first step for using network
information (from social networks, user-item graphs, knowledge bases, etc.) in
many machine learning tasks.
Unlike previous work, we (1) explicitly model an edge as a function of node
embeddings, and we (2) propose a novel objective, the "graph likelihood", which
contrasts information from sampled random walks with non-existent edges.
Individually, both of these contributions improve the learned representations,
especially when there are memory constraints on the total size of the
embeddings. When combined, our contributions enable us to significantly improve
the state-of-the-art by learning more concise representations that better
preserve the graph structure.
We evaluate our method on a variety of link-prediction task including social
networks, collaboration networks, and protein interactions, showing that our
proposed method learn representations with error reductions of up to 76% and
55%, on directed and undirected graphs. In addition, we show that the
representations learned by our method are quite space efficient, producing
embeddings which have higher structure-preserving accuracy but are 10 times
smaller
Breaking the waves: asymmetric random periodic features for low-bitrate kernel machines
Many signal processing and machine learning applications are built from
evaluating a kernel on pairs of signals, e.g. to assess the similarity of an
incoming query to a database of known signals. This nonlinear evaluation can be
simplified to a linear inner product of the random Fourier features of those
signals: random projections followed by a periodic map, the complex
exponential. It is known that a simple quantization of those features
(corresponding to replacing the complex exponential by a different periodic map
that takes binary values, which is appealing for their transmission and
storage), distorts the approximated kernel, which may be undesirable in
practice. Our take-home message is that when the features of only one of the
two signals are quantized, the original kernel is recovered without distortion;
its practical interest appears in several cases where the kernel evaluations
are asymmetric by nature, such as a client-server scheme. Concretely, we
introduce the general framework of asymmetric random periodic features, where
the two signals of interest are observed through random periodic features:
random projections followed by a general periodic map, which is allowed to be
different for both signals. We derive the influence of those periodic maps on
the approximated kernel, and prove uniform probabilistic error bounds holding
for all signal pairs from an infinite low-complexity set. Interestingly, our
results allow the periodic maps to be discontinuous, thanks to a new
mathematical tool, i.e. the mean Lipschitz smoothness. We then apply this
generic framework to semi-quantized kernel machines (where only one signal has
quantized features and the other has classical random Fourier features), for
which we show theoretically that the approximated kernel remains unchanged
(with the associated error bound), and confirm the power of the approach with
numerical simulations
Jellyfish galaxies with the IllustrisTNG simulations: I. Gas-stripping phenomena in the full cosmological context
We use IllustrisTNG, a suite of gravity and MHD simulations, to study the
demographics and properties of jellyfish galaxies in the full cosmological
context. By jellyfish galaxies, we mean satellites orbiting in massive groups
and clusters that exhibit highly asymmetric distributions of gas and gas tails.
We use the TNG100 run and select galaxies at redshifts with stellar
mass exceeding and with host halo masses of
. Among more than about 6000 (2600) galaxies
with stars (and some gas), we identify 800 jellyfish galaxies by visually
inspecting their gas and stellar mass maps in random projections. About
of cluster satellites are found with signatures of ram-pressure stripping and
gaseous tails stemming from the main luminous bodies. This is a lower limit,
since the random orientation entails a loss of about of galaxies that in
an optimal projection would otherwise be identified as jellyfish. The
connection with ram-pressure stripping is further confirmed by a series of
findings: jellyfish galaxies are more frequent at intermediate and large
cluster-centric distances (); they move through the
ICM with larger bulk velocities and Mach numbers than the general cluster
population, typically orbiting supersonically and experiencing larger ram
pressures. Furthermore, the gaseous tails usually extend in opposite directions
to the galaxy trajectory, with no relation between tail orientation and the
host's center. The frequency of jellyfish galaxies shows a very weak dependence
on redshift but larger fractions of disturbed gaseous
morphologies occur in more massive hosts and at smaller satellite masses.
Finally, jellyfish galaxies are late infallers ( Gyrs ago, at )
and the emergence of gaseous tails correlates well with the presence of bow
shocks in the ICM.Comment: 25 pages, 15 figures, Accepted for publication on MNRAS after minor
revision
Anticollusion solutions for asymmetric fingerprinting protocols based on client side embedding
In this paper, we propose two different solutions for making a recently proposed asymmetric fingerprinting protocol based on client-side embedding robust to collusion attacks. The first solution is based on projecting a client-owned random fingerprint, securely obtained through existing cryptographic protocols, using for each client a different random matrix generated by the server. The second solution consists in assigning to each client a Tardos code, which can be done using existing asymmetric protocols, and modulating such codes using a specially designed random matrix. Suitable accusation strategies are proposed for both solutions, and their performance under the averaging attack followed by the addition of Gaussian noise is analytically derived. Experimental results show that the analytical model accurately predicts the performance of a realistic system. Moreover, the results also show that the solution based on independent random projections outperforms the solution based on Tardos codes, for different choices of parameters and under different attack models
Random Growth Models
The link between a particular class of growth processes and random matrices
was established in the now famous 1999 article of Baik, Deift, and Johansson on
the length of the longest increasing subsequence of a random permutation.
During the past ten years, this connection has been worked out in detail and
led to an improved understanding of the large scale properties of
one-dimensional growth models. The reader will find a commented list of
references at the end. Our objective is to provide an introduction highlighting
random matrices. From the outset it should be emphasized that this connection
is fragile. Only certain aspects, and only for specific models, the growth
process can be reexpressed in terms of partition functions also appearing in
random matrix theory.Comment: Review paper; 24 pages, 4 figures; Minor correction
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