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Scaling of geometric phase versus band structure in cluster-Ising models
We study the phase diagram of a class of models in which a generalized
cluster interaction can be quenched by Ising exchange interaction and external
magnetic field. We characterize the various phases through winding numbers.
They may be ordinary phases with local order parameter or exotic ones, known as
symmetry protected topologically ordered phases. Quantum phase transitions with
dynamical critical exponents z = 1 or z = 2 are found. Quantum phase
transitions are analyzed through finite-size scaling of the geometric phase
accumulated when the spins of the lattice perform an adiabatic precession. In
particular, we quantify the scaling behavior of the geometric phase in relation
with the topology and low energy properties of the band structure of the
system
Discrete Factorization Machines for Fast Feature-based Recommendation
User and item features of side information are crucial for accurate
recommendation. However, the large number of feature dimensions, e.g., usually
larger than 10^7, results in expensive storage and computational cost. This
prohibits fast recommendation especially on mobile applications where the
computational resource is very limited. In this paper, we develop a generic
feature-based recommendation model, called Discrete Factorization Machine
(DFM), for fast and accurate recommendation. DFM binarizes the real-valued
model parameters (e.g., float32) of every feature embedding into binary codes
(e.g., boolean), and thus supports efficient storage and fast user-item score
computation. To avoid the severe quantization loss of the binarization, we
propose a convergent updating rule that resolves the challenging discrete
optimization of DFM. Through extensive experiments on two real-world datasets,
we show that 1) DFM consistently outperforms state-of-the-art binarized
recommendation models, and 2) DFM shows very competitive performance compared
to its real-valued version (FM), demonstrating the minimized quantization loss.
This work is accepted by IJCAI 2018.Comment: Appeared in IJCAI 201
Nanocomposites Preparation Method Based on Bubbles Explosion and Nanocomposites Capability Evaluation Method Base on Fractal Theory and TEM Image
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