7,707 research outputs found
Cognitive Deficit of Deep Learning in Numerosity
Subitizing, or the sense of small natural numbers, is an innate cognitive
function of humans and primates; it responds to visual stimuli prior to the
development of any symbolic skills, language or arithmetic. Given successes of
deep learning (DL) in tasks of visual intelligence and given the primitivity of
number sense, a tantalizing question is whether DL can comprehend numbers and
perform subitizing. But somewhat disappointingly, extensive experiments of the
type of cognitive psychology demonstrate that the examples-driven black box DL
cannot see through superficial variations in visual representations and distill
the abstract notion of natural number, a task that children perform with high
accuracy and confidence. The failure is apparently due to the learning method
not the CNN computational machinery itself. A recurrent neural network capable
of subitizing does exist, which we construct by encoding a mechanism of
mathematical morphology into the CNN convolutional kernels. Also, we
investigate, using subitizing as a test bed, the ways to aid the black box DL
by cognitive priors derived from human insight. Our findings are mixed and
interesting, pointing to both cognitive deficit of pure DL, and some measured
successes of boosting DL by predetermined cognitive implements. This case study
of DL in cognitive computing is meaningful for visual numerosity represents a
minimum level of human intelligence.Comment: Accepted for presentation at the AAAI-1
A Sharp upper bound for the spectral radius of a nonnegative matrix and applications
In this paper, we obtain a sharp upper bound for the spectral radius of a
nonnegative matrix. This result is used to present upper bounds for the
adjacency spectral radius, the Laplacian spectral radius, the signless
Laplacian spectral radius, the distance spectral radius, the distance Laplacian
spectral radius, the distance signless Laplacian spectral radius of a graph or
a digraph. These results are new or generalize some known results.Comment: 16 pages in Czechoslovak Math. J., 2016. arXiv admin note: text
overlap with arXiv:1507.0705
Bis(ethylenediamine-κ2 N,N′)(nitrato-κ2 O,O′)cobalt(III) hydroxide nitrate
The Co ion in the title salt, [Co(NO3)(H2NCH2CH2NH2)2](OH)(NO3), has oxidation state + III and is coordinated by four N atoms from two ethylenediamine molecules and two O atoms from a nitrate anion in a distorted octahedral geometry. The charge of the complex cation is balanced by a hydroxide anion and a nitrate anion. The cations and anions are connected by N—H⋯O and O—H⋯O hydrogen bonds, resulting in a three-dimensional supramolecular framework. There are two independent ion pairs with similar configurations in the unit cell. Both uncoordinated nitrate counter-anions are disordered
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