959 research outputs found
In the footsteps of the "Great Jewish Composer" : Don Harrán, Salamone Rossi: Jewish musician in late Renaissance Mantua. Oxford University Press, 1999, 310 pp. [Rezension]
Genetic analysis of immunological traits in tilapia
The immunological response to handling stress of four tilapia species is evaluated.Polymorphism is examined in genes known to influence immune response in fish
Optimal prefix codes for pairs of geometrically-distributed random variables
Optimal prefix codes are studied for pairs of independent, integer-valued
symbols emitted by a source with a geometric probability distribution of
parameter , . By encoding pairs of symbols, it is possible to
reduce the redundancy penalty of symbol-by-symbol encoding, while preserving
the simplicity of the encoding and decoding procedures typical of Golomb codes
and their variants. It is shown that optimal codes for these so-called
two-dimensional geometric distributions are \emph{singular}, in the sense that
a prefix code that is optimal for one value of the parameter cannot be
optimal for any other value of . This is in sharp contrast to the
one-dimensional case, where codes are optimal for positive-length intervals of
the parameter . Thus, in the two-dimensional case, it is infeasible to give
a compact characterization of optimal codes for all values of the parameter
, as was done in the one-dimensional case. Instead, optimal codes are
characterized for a discrete sequence of values of that provide good
coverage of the unit interval. Specifically, optimal prefix codes are described
for (), covering the range , and
(), covering the range . The described codes produce the expected
reduction in redundancy with respect to the one-dimensional case, while
maintaining low complexity coding operations.Comment: To appear in IEEE Transactions on Information Theor
Separation of Scales and a Thermodynamic Description of Feature Learning in Some CNNs
Deep neural networks (DNNs) are powerful tools for compressing and distilling
information. Their scale and complexity, often involving billions of
inter-dependent parameters, render direct microscopic analysis difficult. Under
such circumstances, a common strategy is to identify slow variables that
average the erratic behavior of the fast microscopic variables. Here, we
identify a similar separation of scales occurring in fully trained finitely
over-parameterized deep convolutional neural networks (CNNs) and fully
connected networks (FCNs). Specifically, we show that DNN layers couple only
through the second moment (kernels) of their activations and pre-activations.
Moreover, the latter fluctuates in a nearly Gaussian manner. For infinite width
DNNs, these kernels are inert, while for finite ones they adapt to the data and
yield a tractable data-aware Gaussian Process. The resulting thermodynamic
theory of deep learning yields accurate predictions in various settings. In
addition, it provides new ways of analyzing and understanding DNNs in general
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