Discrete Denoising Diffusion Approach to Integer Factorization

Integer factorization is a famous computational problem unknown whether being solvable in the polynomial time. With the rise of deep neural networks, it is interesting whether they can facilitate faster factorization. We present an approach to factorization utilizing deep neural networks and discrete denoising diffusion that works by iteratively correcting errors in a partially-correct solution. To this end, we develop a new seq2seq neural network architecture, employ relaxed categorical distribution and adapt the reverse diffusion process to cope better with inaccuracies in the denoising step. The approach is able to find factors for integers of up to 56 bits long. Our analysis indicates that investment in training leads to an exponential decrease of sampling steps required at inference to achieve a given success rate, thus counteracting an exponential run-time increase depending on the bit-length.Comment: International Conference on Artificial Neural Networks ICANN 202

Quantization and Training of Neural Networks for Efficient Integer-Arithmetic-Only Inference

The rising popularity of intelligent mobile devices and the daunting computational cost of deep learning-based models call for efficient and accurate on-device inference schemes. We propose a quantization scheme that allows inference to be carried out using integer-only arithmetic, which can be implemented more efficiently than floating point inference on commonly available integer-only hardware. We also co-design a training procedure to preserve end-to-end model accuracy post quantization. As a result, the proposed quantization scheme improves the tradeoff between accuracy and on-device latency. The improvements are significant even on MobileNets, a model family known for run-time efficiency, and are demonstrated in ImageNet classification and COCO detection on popular CPUs.Comment: 14 pages, 12 figure

On the efficient representation and execution of deep acoustic models

In this paper we present a simple and computationally efficient quantization scheme that enables us to reduce the resolution of the parameters of a neural network from 32-bit floating point values to 8-bit integer values. The proposed quantization scheme leads to significant memory savings and enables the use of optimized hardware instructions for integer arithmetic, thus significantly reducing the cost of inference. Finally, we propose a "quantization aware" training process that applies the proposed scheme during network training and find that it allows us to recover most of the loss in accuracy introduced by quantization. We validate the proposed techniques by applying them to a long short-term memory-based acoustic model on an open-ended large vocabulary speech recognition task.Comment: Accepted conference paper: "The Annual Conference of the International Speech Communication Association (Interspeech), 2016