This paper presents an approximate floating-point computing framework TorctiAxf1 that enables fast simulation of various approximate deep neural network (DNN) models, including spiking neural networks (SNNs), using various types of approximate adders and multipliers. Additionally, it supports the standard reduced precision floating-point formats, such as bfloat16, and any user-customized precision representation. TorchAxf leverages GPU acceleration to expedite approximate DNN training and inference running on the PyTorch framework. Any arbitrary approximate arithmetic algorithm with C/C++ behavioral models can be readily integrated with TorchAxf to emulate approximate DNN accelerators. Through extensive experiments, we reveal an appropriate degree of the floating-point arithmetic that can be approximated for DNN models without any significant accuracy loss. We also show that approximate-aware re-training can recover errors and refine pre-trained DNN models under reduced precision formats. Besides, TorchAxf running on GPU enables the simulation time of complex DNN models using approximate arithmetic to reduce up to$43.17\times$compared to the baseline optimized CPU implementation.

This paper presents a novel early training termination technique that significantly improves the training speed and energy efficiency of unsupervised learning-based spiking neural networks (SNNs) by skipping redundant training samples. To achieve early termination, we leveraged the key observation that unsupervised SNNs tend to stably maintain previously learned information and systematically analyze the spike firing activity of the network during training. To make a training termination decision, we exploit the difference between the number of spikes generated by the previous and current input training samples. Our termination algorithm is adopted in an SNN using the spike-timing-dependent plasticity (STDP) learning rule for a pattern classification application. The proposed scheme made an early termination decision with insignificant accuracy performance loss by adequately ignoring redundant training samples. Specifically, it enhances the training speedup and energy efficiency by up to 5.07 × and 5.14 × , respectively, with less than 1 percent points (pp) accuracy loss compared to the baseline counterparts by skipping up to 80% of the training samples. Additionally, when employed in a VLSI-based neuromorphic chip environment, it exhibits up to 4.95 × better energy efficiency than the baseline.