26,647 research outputs found
Why are probabilistic laws governing quantum mechanics and neurobiology?
We address the question: Why are dynamical laws governing in quantum
mechanics and in neuroscience of probabilistic nature instead of being
deterministic? We discuss some ideas showing that the probabilistic option
offers advantages over the deterministic one.Comment: 40 pages, 8 fig
Stationary probability density of stochastic search processes in global optimization
A method for the construction of approximate analytical expressions for the
stationary marginal densities of general stochastic search processes is
proposed. By the marginal densities, regions of the search space that with high
probability contain the global optima can be readily defined. The density
estimation procedure involves a controlled number of linear operations, with a
computational cost per iteration that grows linearly with problem size
Deep Unsupervised Learning using Nonequilibrium Thermodynamics
A central problem in machine learning involves modeling complex data-sets
using highly flexible families of probability distributions in which learning,
sampling, inference, and evaluation are still analytically or computationally
tractable. Here, we develop an approach that simultaneously achieves both
flexibility and tractability. The essential idea, inspired by non-equilibrium
statistical physics, is to systematically and slowly destroy structure in a
data distribution through an iterative forward diffusion process. We then learn
a reverse diffusion process that restores structure in data, yielding a highly
flexible and tractable generative model of the data. This approach allows us to
rapidly learn, sample from, and evaluate probabilities in deep generative
models with thousands of layers or time steps, as well as to compute
conditional and posterior probabilities under the learned model. We
additionally release an open source reference implementation of the algorithm
On the Probabilistic Interpretation of the Evolution Equations with Pomeron Loops in QCD
We study some structural aspects of the evolution equations with Pomeron
loops recently derived in QCD at high energy and for a large number of colors,
with the purpose of clarifying their probabilistic interpretation. We show
that, in spite of their appealing dipolar structure and of the self-duality of
the underlying Hamiltonian, these equations cannot be given a meaningful
interpretation in terms of a system of dipoles which evolves through
dissociation (one dipole splitting into two) and recombination (two dipoles
merging into one). The problem comes from the saturation effects, which cannot
be described as dipole recombination, not even effectively. We establish this
by showing that a (probabilistically meaningful) dipolar evolution in either
the target or the projectile wavefunction cannot reproduce the actual evolution
equations in QCD.Comment: 31 pages, 2 figure
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