We propose a novel value-aware quantization which applies aggressively reduced precision to the majority of data while separately handling a small amount of large data in high precision, which reduces total quantization errors under very low precision. We present new techniques to apply the proposed quantization to training and inference. The experiments show that our method with 3-bit activations (with 2 of large ones) can give the same training accuracy as full-precision one while offering significant (41.6 and 53.7 ) reductions in the memory cost of activations in ResNet-152 and Inception-v3 compared with the state-of-the-art method. Our experiments also show that deep networks such as Inception-v3, ResNet-101 and DenseNet-121 can be quantized for inference with 4-bit weights and activations (with 1 16-bit data) within 1 top-1 accuracy drop.
Recently, there have been presented several methods of memory-efficient training. In @cite_4 , propose a checkpointing method of storing intermediate activations of some layers to reduce memory cost of storing activations and re-calculating the other activations during back-propagation. In @cite_6 , present a reversible network which, during back-propagation, re-computes input activations utilizing output activations thereby minimizing the storage of intermediate activations. The existing methods of checkpointing and reversible network are effective in reducing memory cost. However, they have a common critical limitation, the additional computation to re-compute activations during back-propagation. Considering that computation cost determines runtime and energy consumption of training on GPUs, the additional computation cost needs to be minimized. As will be explained in the experiments, our proposed quantization method gives much smaller cost in both memory and computation than the state-of-the-art ones. More importantly, it has a potential of offering less computation cost than the conventional training method.
@cite_4 @cite_6
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In this paper, we propose quantized densely connected U-Nets for efficient visual landmark localization. The idea is that features of the same semantic meanings are globally reused across the stacked U-Nets. This dense connectivity largely improves the information flow, yielding improved localization accuracy. However, a vanilla dense design would suffer from critical efficiency issue in both training and testing. To solve this problem, we first propose order-K dense connectivity to trim off long-distance shortcuts; then, we use a memory-efficient implementation to significantly boost the training efficiency and investigate an iterative refinement that may slice the model size in half. Finally, to reduce the memory consumption and high precision operations both in training and testing, we further quantize weights, inputs, and gradients of our localization network to low bit-width numbers. We validate our approach in two tasks: human pose estimation and face alignment. The results show that our approach achieves state-of-the-art localization accuracy, but using ( )70 fewer parameters, ( )98 less model size and saving ( )32 ( ) training memory compared with other benchmark localizers. We propose a systematic approach to reduce the memory consumption of deep neural network training. Specifically, we design an algorithm that costs O( √ n) memory to train a n layer network, with only the computational cost of an extra forward pass per mini-batch. As many of the state-of-the-art models hit the upper bound of the GPU memory, our algorithm allows deeper and more complex models to be explored, and helps advance the innovations in deep learning research. We focus on reducing the memory cost to store the intermediate feature maps and gradients during training. Computation graph analysis is used for automatic in-place operation and memory sharing optimizations. We show that it is possible to trade computation for memory giving a more memory efficient training algorithm with a little extra computation cost. In the extreme case, our analysis also shows that the memory consumption can be reduced to O(logn) with as little as O(n logn) extra cost for forward computation. Our experiments show that we can reduce the memory cost of a 1,000-layer deep residual network from 48G to 7G on ImageNet problems. Similarly, significant memory cost reduction is observed in training complex recurrent neural networks on very long sequences. As the failure frequency is increasing with the components count in modern and future supercomputers, resilience is becoming critical for extreme scale systems. The association of failure prediction with proactive checkpointing seeks to reduce the effect of failures in the execution time of parallel applications. Unfortunately, proactive checkpointing does not systematically avoid restarting from scratch. To mitigate this issue, failure prediction and proactive checkpointing can be coupled with periodic checkpointing. However, blind use of these techniques does not always improves system efficiency, because everyone of them comes with a mix of overheads and benefits. In order to study and understand the combination of these techniques and their improvement in the system's efficiency, we developed: (i) a prototype combining state of the art failure prediction, fast proactive checkpointing and preventive checkpointing; (ii) a mathematical model that reflects the expected computing efficiency of the combination and computes the optimal checkpointing interval in this context; (iii) a discrete event simulator to evaluate the computing efficiency of the combination for system parameters corresponding to the current and projected large scale HPC systems. We evaluate our proposed technique on a large supercomputer (i.e. TSUBAME2) with production-level HPC applications and we show that failure prediction, proactive and preventive checkpointing can be coupled successfully, imposing only about 2 to 6 of overhead in comparison with preventive checkpointing only. Moreover, our model-based simulations show that the optimal solution improves the computing efficiency up to 30 in comparison with classic periodic checkpointing. We show that the prediction recall has a much higher impact on execution efficiency than the prediction precision. This result suggests that researchers on failure prediction algorithms should focus on improving the recall. We also show that the combination of these techniques can significantly improve (by a factor 2, for a particular configuration) the mean time between failures (MTBF) perceived by the application. In this paper, we leverage the efficiency of Binarized Neural Networks (BNNs) to learn complex state transition models of planning domains with discretized factored state and action spaces. In order to directly exploit this transition structure for planning, we present two novel compilations of the learned factored planning problem with BNNs based on reductions to Weighted Partial Maximum Boolean Satisfiability (FD-SAT-Plan+) as well as Binary Linear Programming (FD-BLP-Plan+). Theoretically, we show that our SAT-based Bi-Directional Neuron Activation Encoding is asymptotically the most compact encoding in the literature and maintains the generalized arc-consistency property through unit propagation -- an important property that facilitates efficiency in SAT solvers. Experimentally, we validate the computational efficiency of our Bi-Directional Neuron Activation Encoding in comparison to an existing neuron activation encoding and demonstrate the effectiveness of learning complex transition models with BNNs. We test the runtime efficiency of both FD-SAT-Plan+ and FD-BLP-Plan+ on the learned factored planning problem showing that FD-SAT-Plan+ scales better with increasing BNN size and complexity. Finally, we present a finite-time incremental constraint generation algorithm based on generalized landmark constraints to improve the planning accuracy of our encodings through simulated or real-world interaction.