external memory to run at lower frequencies. Moreover, energy needed to drive off-chip traffic from/to external memory as well as memory read/write energy often contribute significantly to the overall energy consumption [@Vogelsang10; @Lefurgy_etal03]. Reducing memory traffic can thus have significant impact on the overall energy consumption of the learning hardware. In this section, we analyze the savings in memory traffic volume obtained using the learning approach based on local errors that we propose in this paper.

Consider a neural network with $L$ layers. $P^i$ and $A^i$ are the parameters and the mini-batch activations of layer $i$, respectively. $\lvert P^i\rvert$ and $\lvert A^i\rvert$ are the number of elements in $P^i$ and $A^i$. A neuron in layer $i$ has a fanout of $R^i$, i.e, a neuron in layer $i$ projects to $R^i$ neurons in layer $i+1$. In convolutional layers, we ignore any border effects which might cause the neurons at the borders of the feature maps to project to fewer neurons than neurons away from the borders. We divide the training data set into $N_{b}$ mini-batches and train the network for $N_{e}$ epochs. Each weight and each neuron activation takes up one memory word (which we assume is 32 bits).

Figure \[fig:traffic\_a\] 