# What effect does a negative output of a neuron have on neighbouring neurons?

Artificial neural networks are composed of multiple neurons that are connected to each other. When the output of an artificial neuron is zero, it does not have any effect on neighboring neurons. When the output is positive, the neuron has an effect on neighboring neurons.

What does it mean when the output of a neuron is negative (which can e.g. occur when the activation function of a neuron is the hyperbolic tangent)? What effect would this output have on neighboring neurons?

Do biological neural networks also have this property?

• To be honest is somewhat unclear. Neural Nets can mean both artificial/biological NN. So I would suggest you edit the question to show where you are talking about biological (instead of the term 'real') NN and where artificial NN.
– user9947
Dec 18 '19 at 15:52
• I mean both of them Dec 18 '19 at 17:57
• I think you might be misinterpreting what a neural network is doing with its outputs. The most an output of a neuron can generally mean, is how sensitive it is to a certain feature of the input. If you were to look at a 100 layer neural network, and saw an individual neuron was negative, there is very little you can infer from this. It doesn't really mean anything tangible. If you were to research this particular frozen state of the network, you could eventually interpret exactly what the network is doing, but for all intents and purposes, a negative output from a neuron doesnt tell you much Dec 19 '19 at 6:28

In the case of artificial neural networks, your question can be (partially) answered by looking at the definition of the operation that an artificial neuron performs. An artificial neuron is usually defined as a linear combination of its inputs, followed by the application of a non-linear activation function (e.g. the hyperbolic tangent or ReLU). More formally, a neuron $$i$$ in layer $$l$$ performs the following operation

\begin{align} o_i^l = \sigma \left(\sum_{j=1}^N w_j o_j^{l-1} \right) \tag{1}\label{1}, \end{align}

where $$o_j^{l-1}$$ is the output from neuron $$j$$ in layer $$l-1$$ (the previous layer), $$w_j$$ the corresponding weight, $$\sigma$$ an activation function and $$N$$ the number of neurons from layer $$l-1$$ connected to neuron $$i$$ in layer $$l$$.

Let's assume that $$\sigma$$ is the ReLU, which is defined as follows

$$\sigma(x)=\max(0, x)$$

which means that all negative numbers become $$0$$ and all non-negative numbers become themselves.

In equation \ref{1}, if $$w_j$$ and $$o_j^{l-1}$$ have the same sign, then the product $$w_j o_j^{l-1}$$ is non-negative (positive or zero), else it is negative (or zero). Therefore, the sign of the output of neuron $$j$$ in layer $$l-1$$ alone does not fully determine the effect on $$o_i^l$$, but the sign of the $$w_j$$ is also required.

Let's suppose that the product $$w_j o_j^{l-1}$$ is negative, then, of course, this will negatively contribute to the sum in equation \ref{1}. In any case, even if the sum $$\sum_{j=1}^N w_j o_j^{l-1}$$ is negative, if $$\sigma$$ is the ReLU, no matter the magnitude of the negative number, $$o_i^l$$ will always be zero. However, if the activation function is hyperbolic tangent, the magnitude of a negative $$\sum_{j=1}^N w_j o_j^{l-1}$$ affects the magnitude of $$o_i^l$$. More precisely, the more negative the sum is, the closest $$o_i^l$$ is to $$-1$$.

To conclude, in general, the effect of the sign of an output of an artificial neuron on neighboring neurons depends on the activation function and the learned weights, which depend on the error the neural network is making (assuming the neural network is trained with gradient descent combined with back-propagation), which in turn depends on the training dataset, the loss function, the architecture of the neural network, etc.

Biological neurons and synapses are more complex than artificial ones. Nevertheless, biological synapses are usually classified as either excitatory or inhibitory, so they can have an excitatory or inhibitory effect on connected neurons.

• So what means when we receive a negative in next neuron? Could you give me an example Dec 18 '19 at 22:41
• @MehdiAmrollahi I am exactly explaining this in my answer. Please, read it again until you understand it.
– nbro
Dec 18 '19 at 22:43
• Maybe I do not understand the question - isn't it the case the the artificial neurons in layer X are only affected by those in layer X-1 (providing inputs), not other neurons in layer X? Dec 20 '19 at 3:40
• @GeorgeWhite I think this is a nice question you should ask on the main website. I'll answer it (if nobody does it).
– nbro
Dec 20 '19 at 16:06