Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fractional-order Backpropagation Neural Networks: Modified
  Fractional-order Steepest Descent Method for Family of Backpropagation Neural
  Networks   This paper offers a novel mathematical approach, the modified
Fractional-order Steepest Descent Method (FSDM) for training BackPropagation
Neural Networks (BPNNs); this differs from the majority of the previous
approaches and as such. A promising mathematical method, fractional calculus,
has the potential to assume a prominent role in the applications of neural
networks and cybernetics because of its inherent strengths such as long-term
memory, nonlocality, and weak singularity. Therefore, to improve the
optimization performance of classic first-order BPNNs, in this paper we study
whether it could be possible to modified FSDM and generalize classic
first-order BPNNs to modified FSDM based Fractional-order Backpropagation
Neural Networks (FBPNNs). Motivated by this inspiration, this paper proposes a
state-of-the-art application of fractional calculus to implement a modified
FSDM based FBPNN whose reverse incremental search is in the negative directions
of the approximate fractional-order partial derivatives of the square error. At
first, the theoretical concept of a modified FSDM based FBPNN is described
mathematically. Then, the mathematical proof of the fractional-order global
optimal convergence, an assumption of the structure, and the fractional-order
multi-scale global optimization of a modified FSDM based FBPNN are analysed in
detail. Finally, we perform comparative experiments and compare a modified FSDM
based FBPNN with a classic first-order BPNN, i.e., an example function
approximation, fractional-order multi-scale global optimization, and two
comparative performances with real data. The more efficient optimal searching
capability of the fractional-order multi-scale global optimization of a
modified FSDM based FBPNN to determine the global optimal solution is the major
advantage being superior to a classic first-order BPNN.

24
The categories of this paper are: dg-ga
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
23
The categories of this paper are: solv-int
20
The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
21
The categories of this paper are: adap-org
32
The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc