Building a Neural Network with 555

It was a few months ago that I had finished my classes of Artificial Neural Networks in my postgraduate course when Jack Ganssle published his column about the “555 Contest”, and the first thing a thought after reading it was: is it possible to build an artificial neuron using 555, so you can combine them to make a complex neuron network by hardware? Well after spending some time thinking about it I’ve arrived to a conclusion that yes, 555 is flexible and powerful enough to build such modern and complex structures.

An artificial neuron is a mathematical model of a neuron cell. It is the building block to a neuron network. It can be described by 3 basic elements: weighted inputs, an adder and an activation function.

The overall sum of each input(x_n) multiplied by a weight(w_n) is passed as an argument of the activation function ( f(s) ), resulting in the output (y).

To begin with, I’ve chosen to implement a very simple neuron model, it is referred to in the literature as the McCulloch-Pitts model, in recognition of the pioneering work done by McCulloch and Pits in 1943. In this model the activation function is nothing more than a threshold function:

Where t is the desired threshold.

A very simple example is an implementation of an AND port. It utilizes only one neuron.

Therefore the output y will only be activated, or equal to ‘1’, only when both inputs are ‘1’. That’s because s=2 that is higher than the threshold t=1.5.

Now we are going to implement this example in hardware using 555 timer operating as monostable.

In this circuit V₁ and V₂, are the inputs, which 10V represents a high level and 5V a low level, and are connected to the control pin of the IC.

In the first 555, U₁, the capacitor C2 will charge until it reaches the voltage set by V₁, resulting in a pulse with the same duration, at the output pin. After reaching the threshold, the discharge pin will go low triggering the second 555, U₂, through R₅ and C₅, which starts charging C₃ through R₃ until reach the voltage set in V_2. So at each output we’ll have timing pulses proportional to the voltages applied. Theses pulses will be summed by D₂ and D₃, and any glitches will be filtered by C_6. The summed pulse will be used to charge a RC network formed by R₁₀ and C₈. The voltage V₃ sets the threshold of the activation function or when C₈ will stop to charge. If the pulse is wide enough, C₈ reaches the control voltage and the output pin of U₃ goes low otherwise it’ll be in high state. It actually implements a NAND gate, a little bit different of the preceding example, but if you invert the output you‘ll have an AND gate.

Representing the 15V power supply voltage by V_CC and t₁ as the duration of the output pulse in U₁ we can have the following general equations:

Putting t₁ in the right side of the equation,

Similarly,

For the case showed before V₁ and V₂ can assume 5V ou 10V, or 1/3V_CC and 2/3 V_cc, respectively (considering V_CC=15V). Now we can compute substitute this values, and have:

So the product RC will work as the weights in the neuron network, changing them can change the relevance you give for such input.

For the third 555, we have this equation:

Where V_o is the voltage at the junction point of D₂ and D₃. And t₃ is the sum of t₁ and t₂. When the two inputs are high, t₃ must be at least 1.5 times t_1H, to charge C₈ enough to reach threshold and make the output low. So substituting t₃ and the preceding equation:

We will make R₂=R₁₀ and C₂=C₈, so we can take them out of the equation, and so we have:

So since the output of the 555 generally swings from 0 to 13.5V, when powered by a 15V, and considering a 1V drop at the diode D₂ and D₃, a good estimate for V_o will be 12.5V:

Which gives our threshold voltage.

The diode D₁ serves to isolate U₁from U₂ but gives an undesired effect, C₂ only discharges to 0.7V, to compensate this, R₂ was chosen to be slightly higher than R₃ and R₈.

The circuit was simulated to verify his behavior. One of the main advantages of neural networks is that minor changes in inputs values don’t affect the output. That was verified when I applied in V₁=8V and V₂=9V, in this case, since the two inputs are close to a high level voltage (10V) the circuit behaves as having two high levels in the output.

One drawback of this implementation is that we can’t have negative values for weights. But it’s possible to build big networks for classification, or to take complex decision in hardware.

Bibliography: Haykin, S.; Neural Networks: A comprehensive foundation; Second Edition; Prentice Hall; 1999.