Infinite-dimensional multilayer perceptrons

Date

1996-07-01

Author

Kuzuoğlu, Mustafa
Leblebicioğlu, Mehmet Kemal

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

48
views

0
downloads

In this paper a new multilayer perceptron (MLP) structure is introduced to simulate nonlinear transformations on infinite-dimensional function spaces. This extension is achieved by replacing discrete neurons by a continuum of neurons, summations by integrations and weight matrices by kernels of integral transforms, Variational techniques have been employed for the analysis and training of the infinite-dimensional MLP (IDMLP). The training problem of IDMLP is solved by the Lagrange multiplier technique yielding the coupled state and adjoint state integro-difference equations. A steepest descent-like algorithm is used to construct the required kernel and threshold functions. Finally, some results are presented to show the performance of the new IDMLP.

URI

https://hdl.handle.net/11511/43275

Journal

IEEE TRANSACTIONS ON NEURAL NETWORKS

DOI

https://doi.org/10.1109/72.508932

Collections

Department of Electrical and Electronics Engineering, Article

Suggestions

OpenMETU
Core

Symbolic polynomial interpolation using Mathematica Yazıcı, Adnan; Ergenc, T (2004-01-01) This paper discusses teaching polynomial interpolation with the help of Mathematica. The symbolic power of Mathematica is utilized to prove a theorem for the error term in Lagrange interpolating formula. Derivation of the Lagrange formula is provided symbolically and numerically. Runge phenomenon is also illustrated. A simple and efficient symbolic derivation of cubic splines is also provided.
Algebraic geometric methods in studying splines Sipahi Ös, Neslihan; Bhupal, Mohan Lal; Altınok Bhupal, Selma; Department of Mathematics (2013) In this thesis, our main objects of interest are piecewise polynomial functions (splines). For a polyhedral complex $\Delta$ in $\mathbb{\R}^n$, $C^{r}(\Delta)$ denotes the set of piecewise polynomial functions defined on $\Delta$. Determining the dimension of the space of splines with polynomials having degree at most $k$, denoted by $C^r_k(\Delta)$, is an important problem, which has many applications. In this thesis, we first give an exposition on splines and introduce different algebraic geometric metho...
A 2-D unsteady Navier-Stokes solution method with overlapping/overset moving grids Tuncer, İsmail Hakkı (1996-01-01) A simple, robust numerical algorithm to localize intergrid boundary points and to interpolate unsteady solution variables across 2-D, overset/overlapping, structured computational grids is presented. Overset/ overlapping grids are allowed to move in time relative to each other. The intergrid boundary points are localized in terms of three grid points on the donor grid by a directional search algorithm. The final parameters of the search algorithm give the interpolation weights at the interpolation point. Th...
A 2-0 navier-stokes solution method with overset moving grids Tuncer, İsmail Hakkı (1996-01-01) A simple, robust numerical algorithm to localize moving boundary points and to interpolate uniteady solution variables across 2-D, arbitrarily overset computational grids is presented. Overset grids are allowed to move in time relative to each other. The intergrid boundary points are localized in terms of three grid points on the donor grid by a directional search algorithm. The parameters of the search algorithm give the interpolation weights at the localized boundary point. The method is independent of nu...
Inverse Sturm-Liouville Systems over the whole Real Line Altundağ, Hüseyin; Taşeli, Hasan; Department of Mathematics (2010) In this thesis we present a numerical algorithm to solve the singular Inverse Sturm-Liouville problems with symmetric potential functions. The singularity, which comes from the unbounded domain of the problem, is treated by considering the limiting case of the associated problem on the symmetric finite interval. In contrast to regular problems which are considered on a finite interval the singular inverse problem has an ill-conditioned structure despite of the limiting treatment. We use the regularization t...

Citation Formats

M. Kuzuoğlu and M. K. Leblebicioğlu, “Infinite-dimensional multilayer perceptrons,” IEEE TRANSACTIONS ON NEURAL NETWORKS, pp. 889–896, 1996, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/43275.