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Title: WRPN: Wide Reduced-Precision Networks

Paper content:
For computer vision applications, prior works have shown the efficacy of reducing numeric precision of model parameters (network weights) in deep neural networks.
Activation maps, however, occupy a large memory footprint during both the training and inference step when using mini-batches of inputs.
One way to reduce this large memory footprint is to reduce the precision of activations.
However, past works have shown that reducing the precision of activations hurts model accuracy.
We study schemes to train networks from scratch using reduced-precision activations without hurting accuracy.
We reduce the precision of activation maps (along with model parameters) and increase the number of filter maps in a layer, and find that this scheme matches or surpasses the accuracy of the baseline full-precision network.
As a result, one can significantly improve the execution efficiency (e.g. reduce dynamic memory footprint, memory band- width and computational energy) and speed up the training and inference process with appropriate hardware support.
We call our scheme WRPN -- wide reduced-precision networks.
We report results and show that WRPN scheme is better than previously reported accuracies on ILSVRC-12 dataset while being computationally less expensive compared to previously reported reduced-precision networks.
A promising approach to lower the compute and memory requirements of convolutional deeplearning workloads is through the use of low numeric precision algorithms.
Operating in lower precision mode reduces computation as well as data movement and storage requirements.
Due to such efficiency benefits, there are many existing works which propose low-precision deep neural networks (DNNs) BID27 BID12 BID14 BID6 ; BID24 , even down to 2-bit ternary mode BID29 BID11 BID25 and 1-bit binary mode BID28 BID2 BID16 BID23 .
However, majority of existing works in low-precision DNNs sacrifice accuracy over the baseline full-precision networks.
Further, most prior works target reducing the precision of the model parameters (network weights).
This primarily benefits the inference step only when batch sizes are small.We observe that activation maps (neuron outputs) occupy more memory compared to the model parameters for batch sizes typical during training.
This observation holds even during inference when batch size is around eight or more.
Based on this observation, we study schemes for training and inference using low-precision DNNs where we reduce the precision of activation maps as well as the model parameters without sacrificing network accuracy.To improve both execution efficiency and accuracy of low-precision networks, we reduce both the precision of activation maps and model parameters and increase the number of filter maps in a layer.
We call networks using this scheme wide reduced-precision networks (WRPN) and find that this scheme compensates or surpasses the accuracy of the baseline full-precision network.
Although the number of raw compute operations increases as we increase the number of filter maps in a layer, the compute bits required per operation is now a fraction of what is required when using full-precision operations (e.g. going from FP32 AlexNet to 4-bits precision and doubling the number of filters increases the number of compute operations by 4x, but each operation is 8x more efficient than FP32).
WRPN offers better accuracies, while being computationally less expensive compared to previously reported reduced-precision networks.
We report results on AlexNet BID10 , batch-normalized Inception BID8 , and ResNet-34 BID7 on ILSVRC-12 (Russakovsky et al., 2015) dataset.
We find 4-bits to be sufficient for training deep and wide models while achieving similar or better accuracy than baseline network.
With 4-bit activation and 2-bit weights, we find the accuracy to be at-par with baseline full-precision.
Making the networks wider and operating with 1-bit precision, we close the accuracy gap between previously reported binary networks and show state-of-the art results for ResNet-34 (69.85% top-1 with 2x wide) and AlexNet (48.04% top-1 with 1.3x wide).
To the best of our knowledge, our reported accuracies with binary networks and 4-bit precision are highest to date.Our reduced-precision quantization scheme is hardware friendly allowing for efficient hardware implementations.
To this end, we evaluate efficiency benefits of low-precision operations (4-bits to 1-bits) on Titan X GPU, Arria-10 FPGA and ASIC.
We see that FPGA and ASIC can deliver significant efficiency gain over FP32 operations (6.5x to 100x), while GPU cannot take advantage of very low-precision operations.
While most prior works proposing reduced-precision networks work with low precision weights (e.g. work in BID2 BID29 BID28 BID25 ; BID11 ; BID23 ), we find that activation maps occupy a larger memory footprint when using mini-batches of inputs.
Using mini-batches of inputs is typical in training of DNNs and cloud-based batched inference BID9 .
FIG0 shows memory footprint of activation maps and filter maps as batch size changes for 4 different networks (AlexNet, Inception-Resnet-v2 BID22 , during the training and inference steps.
We present the Wide Reduced-Precision Networks (WRPN) scheme for DNNs.
In this scheme, the numeric precision of both weights and activations are significantly reduced without loss of network accuracy.
This result is in contrast to many previous works that find reduced-precision activations to detrimentally impact accuracy; specifically, we find that 2-bit weights and 4-bit activations are sufficient to match baseline accuracy across many networks including AlexNet, ResNet-34 and batchnormalized Inception.
We achieve this result with a new quantization scheme and by increasing the number of filter maps in each reduced-precision layer to compensate for the loss of information capacity induced by reducing the precision.
We believe ours to be the first work to study the interplay between layer width and precision -with widening, the number of neurons in a layer increase; yet with reduced precision, we control overfitting and regularization.We motivate this work with our observation that full-precision activations contribute significantly more to the memory footprint than full-precision weight parameters when using mini-batch sizes common during training and cloud-based inference; furthermore, by reducing the precision of both activations and weights the compute complexity is greatly reduced (40% of baseline for 2-bit weights and 4-bit activations).The
WRPN quantization scheme and computation on low precision activations and weights is hardware friendly making it viable for deeply-embedded system deployments as well as in cloud-based training and inference servers with compute fabrics for low-precision. We
compare Titan X GPU, Arria-10 FPGA and ASIC implementations using WRPN and show our scheme increases performance and energy-efficiency for iso-accuracy across each. Overall
, reducing the precision allows custom-designed compute units and lower buffering requirements to provide significant improvement in throughput.

assistant: text: Lowering precision (to 4-bits, 2-bits and even binary) and widening the filter banks gives as accurate network as those obtained with FP32 weights and activations.