Learned Step Size Quantization

We present here Learned Step Size Quantization, a method for training deep networks such that they can run at inference time using low precision integer matrix multipliers, which offer power and space advantages over high precision alternatives. The essence of our approach is to learn the step size parameter of a uniform quantizer by backpropagation of the training loss, applying a scaling factor to its learning rate, and computing its associated loss gradient by ignoring the discontinuity present in the quantizer. This quantization approach can be applied to activations or weights, using different levels of precision as needed for a given system, and requiring only a simple modification of existing training code. As demonstrated on the ImageNet dataset, our approach achieves better accuracy than all previous published methods for creating quantized networks on several ResNet network architectures at 2-, 3- and 4-bits of precision.

Discovering Low-Precision Networks Close to Full-Precision Networks for Efficient Embedded Inference

To realize the promise of ubiquitous embedded deep network inference, it is essential to seek limits of energy and area efficiency. To this end, low-precision networks offer tremendous promise because both energy and area scale down quadratically with the reduction in precision. Here, for the first time, we demonstrate ResNet-18, ResNet-34, ResNet-50, ResNet-152, Inception-v3, densenet-161, and VGG-16bn networks on the ImageNet classification benchmark that, at 8-bit precision exceed the accuracy of the full-precision baseline networks after one epoch of finetuning, thereby leveraging the availability of pretrained models. We also demonstrate for the first time ResNet-18, ResNet-34, and ResNet-50 4-bit models that match the accuracy of the full-precision baseline networks. Surprisingly, the weights of the low-precision networks are very close (in cosine similarity) to the weights of the corresponding baseline networks, making training from scratch unnecessary. The number of iterations required by stochastic gradient descent to achieve a given training error is related to the square of (a) the distance of the initial solution from the final plus (b) the maximum variance of the gradient estimates. By drawing inspiration from this observation, we (a) reduce solution distance by starting with pretrained fp32 precision baseline networks and fine-tuning, and (b) combat noise introduced by quantizing weights and activations during training, by using larger batches along with matched learning rate annealing. Together, these two techniques offer a promising heuristic to discover low-precision networks, if they exist, close to fp32 precision baseline networks.

Convolutional Networks for Fast, Energy-Efficient Neuromorphic Computing

Deep networks are now able to achieve human-level performance on a broad spectrum of recognition tasks. Independently, neuromorphic computing has now demonstrated unprecedented energy-efficiency through a new chip architecture based on spiking neurons, low precision synapses, and a scalable communication network. Here, we demonstrate that neuromorphic computing, despite its novel architectural primitives, can implement deep convolution networks that i) approach state-of-the-art classification accuracy across 8 standard datasets, encompassing vision and speech, ii) perform inference while preserving the hardware's underlying energy-efficiency and high throughput, running on the aforementioned datasets at between 1200 and 2600 frames per second and using between 25 and 275 mW (effectively > 6000 frames / sec / W) and iii) can be specified and trained using backpropagation with the same ease-of-use as contemporary deep learning. For the first time, the algorithmic power of deep learning can be merged with the efficiency of neuromorphic processors, bringing the promise of embedded, intelligent, brain-inspired computing one step closer.