8,133 research outputs found
Hints and the VC Dimension
Learning from hints is a generalization of learning from examples that allows for a variety of information about the unknown function to be used in the learning process. In this paper, we use the VC dimension, an established tool for analyzing learning from examples, to analyze learning from hints. In particular, we show how the VC dimension is affected by the introduction of a hint. We also derive a new quantity that defines a VC dimension for the hint itself. This quantity is used to estimate the number of examples needed to "absorb" the hint. We carry out the analysis for two types of hints, invariances and catalysts. We also describe how the same method can be applied to other types of hints
Invariance Hints and the VC Dimension
We are interested in having a neural network learn an unknown function f. If the function satisfies an invariant of some sort, such as f is an odd function, then we want to be able to take advantage of this information and not have the network deduce the invariant based on an example of f. The invariant might be defined in terms of an explicit transformation of the input space under which f is constant. In this case it is possible to build a network thatnecessarily satisfies the invariant. In general, we define the invariant in terms of a partition of
the input space such that if x, x' are in the same partition element then f (x) = f (x'). An example of the invariant would be a pair (x, x') taken from a single partition element. We can combine examples of the invariant with examples of the function in the learning process. The goal is to substitute examples of the invariant for examples of the function; the extent to which we can actually do this depends on the appropriate VC dimensions. Simulations verify, at least in simple cases, that examples of the invariant do aid the learning process
Hints
The systematic use of hints in the learning-from-examples paradigm is the subject of this review. Hints are the properties of the target function that are known to us independently of the training examples. The use of hints is tantamount to combining rules and data in learning, and is compatible with different learning models, optimization techniques, and regularization techniques. The hints are represented to the learning process by virtual examples, and the training examples of the target function are treated on equal footing with the rest of the hints. A balance is achieved between the information provided by the different hints through the choice of objective functions and learning schedules. The Adaptive Minimization algorithm achieves this balance by relating the performance on each hint to the overall performance. The application of hints in forecasting the very noisy foreign-exchange markets is illustrated. On the theoretical side, the information value of hints is contrasted to the complexity value and related to the VC dimension
Stochastic collective dynamics of charged--particle beams in the stability regime
We introduce a description of the collective transverse dynamics of charged
(proton) beams in the stability regime by suitable classical stochastic
fluctuations. In this scheme, the collective beam dynamics is described by
time--reversal invariant diffusion processes deduced by stochastic variational
principles (Nelson processes). By general arguments, we show that the diffusion
coefficient, expressed in units of length, is given by ,
where is the number of particles in the beam and the Compton
wavelength of a single constituent. This diffusion coefficient represents an
effective unit of beam emittance. The hydrodynamic equations of the stochastic
dynamics can be easily recast in the form of a Schr\"odinger equation, with the
unit of emittance replacing the Planck action constant. This fact provides a
natural connection to the so--called ``quantum--like approaches'' to beam
dynamics. The transition probabilities associated to Nelson processes can be
exploited to model evolutions suitable to control the transverse beam dynamics.
In particular we show how to control, in the quadrupole approximation to the
beam--field interaction, both the focusing and the transverse oscillations of
the beam, either together or independently.Comment: 15 pages, 9 figure
Weakly supervised 3D Reconstruction with Adversarial Constraint
Supervised 3D reconstruction has witnessed a significant progress through the
use of deep neural networks. However, this increase in performance requires
large scale annotations of 2D/3D data. In this paper, we explore inexpensive 2D
supervision as an alternative for expensive 3D CAD annotation. Specifically, we
use foreground masks as weak supervision through a raytrace pooling layer that
enables perspective projection and backpropagation. Additionally, since the 3D
reconstruction from masks is an ill posed problem, we propose to constrain the
3D reconstruction to the manifold of unlabeled realistic 3D shapes that match
mask observations. We demonstrate that learning a log-barrier solution to this
constrained optimization problem resembles the GAN objective, enabling the use
of existing tools for training GANs. We evaluate and analyze the manifold
constrained reconstruction on various datasets for single and multi-view
reconstruction of both synthetic and real images
Spin-charge coupling in quantum wires at zero magnetic field
We discuss an approximation for the dynamic charge response of nonlinear
spin-1/2 Luttinger liquids in the limit of small momentum. Besides accounting
for the broadening of the charge peak due to two-holon excitations, the
nonlinearity of the dispersion gives rise to a two-spinon peak, which at zero
temperature has an asymmetric line shape. At finite temperature the spin peak
is broadened by diffusion. As an application, we discuss the density and
temperature dependence of the Coulomb drag resistivity due to long-wavelength
scattering between quantum wires.Comment: 16 pages, 5 figures. This is an extended version of "Coulomb drag
from spin-charge coupling at zero magnetic field
Spin-charge separation and localization in one-dimension
We report on measurements of quantum many-body modes in ballistic wires and
their dependence on Coulomb interactions, obtained from tunneling between two
parallel wires in a GaAs/AlGaAs heterostructure while varying electron density.
We observe two spin modes and one charge mode of the coupled wires, and map the
dispersion velocities of the modes down to a critical density, at which
spontaneous localization is observed. Theoretical calculations of the charge
velocity agree well with the data, although they also predict an additional
charge mode that is not observed. The measured spin velocity is found to be
smaller than theoretically predicted.Comment: There are minor textual differences between this version and the
version that has been published in Science (follow the DOI link below to
obtain it). In addition, here we have had to reduce figure quality to save
space on the serve
New constraints on Planck-scale Lorentz Violation in QED from the Crab Nebula
We set constraints on O(E/M) Lorentz Violation in QED in an effective field
theory framework. A major consequence of such assumptions is the modification
of the dispersion relations for electrons/positrons and photons, which in turn
can affect the electromagnetic output of astrophysical objects. We compare the
information provided by multiwavelength observations with a full and
self-consistent computation of the broad-band spectrum of the Crab Nebula. We
cast constraints of order 10^{-5} at 95% confidence level on the lepton Lorentz
Violation parameters.Comment: 23 pages, 9 figures. v2: added comments and references, matches
version accepted by JCA
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