  Deep Neural Networks (DNNs) are extensively employed in safety-critical
applications where ensuring hardware reliability is a primary concern. To
enhance the reliability of DNNs against hardware faults, activation restriction
techniques significantly mitigate the fault effects at the DNN structure level,
irrespective of accelerator architectures. State-of-the-art methods offer
either neuron-wise or layer-wise clipping activation functions. They attempt to
determine optimal clipping thresholds using heuristic and learning-based
approaches. Layer-wise clipped activation functions cannot preserve DNNs
resilience at high bit error rates. On the other hand, neuron-wise clipping
activation functions introduce considerable memory overhead due to the addition
of parameters, which increases their vulnerability to faults. Moreover, the
heuristic-based optimization approach demands numerous fault injections during
the search process, resulting in time-consuming threshold identification. On
the other hand, learning-based techniques that train thresholds for entire
layers concurrently often yield sub-optimal results. In this work, first, we
demonstrate that it is not essential to incorporate neuron-wise activation
functions throughout all layers in DNNs. Then, we propose a hybrid clipped
activation function that integrates neuron-wise and layer-wise methods that
apply neuron-wise clipping only in the last layer of DNNs. Additionally, to
attain optimal thresholds in the clipping activation function, we introduce
ProAct, a progressive training methodology. This approach iteratively trains
the thresholds on a layer-by-layer basis, aiming to obtain optimal threshold
values in each layer separately.
