Tik-61.261 Principles of Neural Computing
- An odd sigmoid function is defined by
where denotes a hyperbolic tangent. The limiting values of
this second sigmoid function are and . Show that the derivate
with respect to is given by
What is the value of this derivate at the origin? Suppose that the
slope parameter is made infinitely large. What is the resulting
- Show that the McCulloch-Pitts formal model of
a neuron may be approximated by a sigmoidal neuron (i.e., neuron using
a sigmoid activation function with large synaptic weights).
- Show that a linear neuron may be approximated by a sigmoidal
neuron with small synaptic weights.
- Construct a fully recurrent network with 5 neurons, but with no
- Consider a multilayer feedforward network, all the neurons of
which operate in their linear regions. Justify the statement that such
a network is equivalent to a single-layer feedforward network.
- Figure 1(a) shows the
signal-flow graph of a recurrent network made up of two neurons. Write
the nonlinear difference equation that defines the evolution of
or that of . These two variables define the outputs of the top
and bottom neurons, respectively. What is the order of this equation?
- Figure 1(b) shows the signal-flow graph of a recurrent network
consisting of two neurons with self-feedback. Write the coupled system
of two first-order nonlinear difference equations that describe the
operation of the system.
The signal-flow graphs of the two recurrent networks.