C. L. Giles, R. Griffin and T. Maxwell. Encoding geometric invariances in higher order neural networks. Neural Information Processing Systems, American Institute of Physics, New York, pp. 301-309, 1988.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... method for the calculation of invariant features is the averaging A of monomials f over the transformation group [8] f(g(m) 1) All monomials of equal form and order are summed to form one feature; e.g. for the group of cyclic translations on a four dimensional pattern (m[0] m[1] m[2]; m[3] T the average of the monomial f(m) m[0] Delta m[1] is A[f] m) m[0] Delta m[1] m[1] Delta m[2] m[2] Delta m[3] m[3] Delta m[0] 2) This averaging technique is also used in higher order neural networks [2] The output y i of a neuron i is the weighted sum of several ....

.... [8] f(g(m) 1) All monomials of equal form and order are summed to form one feature; e.g. for the group of cyclic translations on a four dimensional pattern (m[0] m[1] m[2] m[3] T the average of the monomial f(m) m[0] Delta m[1] is A[f] m) m[0] Delta m[1] m[1] Delta m[2] m[2] Delta m[3] m[3] Delta m[0] 2) This averaging technique is also used in higher order neural networks [2] The output y i of a neuron i is the weighted sum of several averages of monomials which is processed by a nonlinear thresholding element Theta. Equation (3) shows this for ....

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C.L. Giles, R.D. Griffin, T. Maxwell, Encoding geometric invariances in higher-order neural networks, Neural Information Processing Systems, American Institute of Physics, Conference Proceedings, pp. 301-309, 1988

....cycle only. 1 Introduction Structured feedforward neural networks have shown promising results in speech processing applications [9] and the field of shift and rotation invariant pattern recognition [1, 5, 6] see Fig. 1. Also higher order neural networks belong to this class of networks [2, 8]. Their Figure 1: The same object: original, and shifted and rotated characteristic is that the invariance property is directly built into their architecture by the use of nodes with shared weight vectors. Since they are of feedforward type it is common to apply a modified backpropagation ....

C.L. Giles, R.D. Griffin, T. Maxwell, Encoding geometric invariances in higher-order neural networks, Neural Information Processing Systems, American Inst. of Physics, Conference Proceedings, pp. 301-309, 1988

....under shifts and small rotations of the input image. In neural nets, there are several ways to achieve this invariance 1. In neural networks, the invariance can be hard wired by weight sharing in the case of summation nodes [1] or by constraints similar to weight sharing in higher order nodes [2]. 2. One can enhance the training ensemble by adding examples of inputs transformed under the desired invariance group, while maintaining the same targets as for the raw data. 3. One can add to the cost function a regularizer that penalizes changes in the output when the input is transformed by ....

C.L. Giles, R.D. Griffin, and T. Maxwell. Encoding geometric invariances in higherorder neural networks. In D.Z.Anderson, editor, Neural Information Processing Systems, pages 301--309. American Institute of Physics, 1988.

....equilateral triangles than is biologically possible. The spatial relationships which define equilateralness will have to be discovered for each position, scale, and orientation of the triangle. Techniques have been proposed for introducing translation and rotational invariance into networks (Giles et al. 1987) which eliminate the need for independent feature detectors at every location. Unfortunately these methods require that every unit have a large (quadratic) number of connections with complicated weight linkages between them. Furthermore, positional information is lost in these representations ....

Giles, C.L., Griffin, R.D., & Maxwell, T. (1987). Encoding Geometric Invariances in Higher Order Neural Networks. In "Advances in Neural Information Processing", David Touretzky, Ed. Morgan Kaufmann.

....the use of Fourier amplitude coefficients, rather than pixel intensities, provides invariance under translations. 2. In neural networks, the invariance can be hard wired by weight sharing in the case of summation nodes [1] or by constraints similar to weight sharing in higher order nodes [2]. 3. One can enhance the training ensemble by adding examples of inputs transformed under the desired invariance group, while maintaining the same targets as for the raw data. 4. One can add to the cost function a regularizer that penalizes changes in the output when the input is transformed by ....

C.L. Giles, R.D. Griffin, and T. Maxwell. Encoding geometric invariances in higherorder neural networks. In D.Z.Anderson, editor, Neural Information Processing Systems, pages 301--309. American Institute of Physics, 1988.

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C. L. Giles, R. Griffin and T. Maxwell. Encoding geometric invariances in higher order neural networks. Neural Information Processing Systems, American Institute of Physics, New York, pp. 301-309, 1988.

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