学習モデルにおける補題の証明 (Computer Algebra --Theory and its Applications)

Abstract

学習モデルを中間ユニット数がHの3層パーセプトロンとする. 真の分布を実現するパラメータの集合は, 活性化関数を級数展開させると, 有限個の多項式の零点集合として表される. 初めに, H=2のとき, 真の分布が中間ユニット数が0と1で実現されるときの集合を求める. 次に, 一般のHに対して, 真の分布より少ない中間ユニット数H0<Hで実現されるときの集合を考える.

The statistical model is a three-layer neural network with H hidden units. (By using taylor expansion of activation function , t he set of parameters that true density function is realizable by a statistical model is a common zero points defined by finite polynomials. First, in this case of hidden units equals two, we calculate equations defining equation of the algebraic set. The algebraic set is the set of parameters such that true density function is realizable by a statistical model with zero or one hidden unit. Next, for the general case, we determine equations define the algebraic set. The algebraic set is the set of parameters that true density function is realizable by a statistical model with Ho is less than H hidden unit.