[Paper Review] AXNet: ApproXimate computing using an end-to-end trainable neural network

Zhenghao Peng, Xuyang Chen+5 more|arXiv (Cornell University)|Jul 27, 2018

Ferroelectric and Negative Capacitance Devices20 references4 citations

TL;DR

AXNet proposes an end-to-end trainable neural network that fuses an approximator and predictor into a single architecture using multi-task learning with Hadamard product fusion, achieving 50.7% higher invocation rate and up to 90% reduction in training time compared to iterative training methods, while maintaining high approximation quality and energy efficiency.

ABSTRACT

Neural network based approximate computing is a universal architecture promising to gain tremendous energy-efficiency for many error resilient applications. To guarantee the approximation quality, existing works deploy two neural networks (NNs), e.g., an approximator and a predictor. The approximator provides the approximate results, while the predictor predicts whether the input data is safe to approximate with the given quality requirement. However, it is non-trivial and time-consuming to make these two neural network coordinate---they have different optimization objectives---by training them separately. This paper proposes a novel neural network structure---AXNet---to fuse two NNs to a holistic end-to-end trainable NN. Leveraging the philosophy of multi-task learning, AXNet can tremendously improve the invocation (proportion of safe-to-approximate samples) and reduce the approximation error. The training effort also decrease significantly. Experiment results show 50.7% more invocation and substantial cuts of training time when compared to existing neural network based approximate computing framework.

Motivation & Objective

• To address the inefficiency and suboptimal coordination between separate approximator and predictor neural networks in existing approximate computing frameworks.
• To reduce training time and model complexity by fusing the approximator and predictor into a single, jointly trainable network.
• To improve approximation quality control and invocation rate (proportion of safe-to-approximate inputs) through joint optimization.
• To enable efficient deployment in NPU architectures with minimal hardware overhead.
• To provide a novel, scalable fusion mechanism that outperforms iterative training and weight-sharing approaches.

Proposed method

• AXNet fuses the approximator and predictor via a Hadamard product operation between shared control vectors and hidden layer weights, enabling joint optimization.
• The network uses a shared backbone structure where the prediction head is derived from the approximator’s hidden layers through element-wise multiplication with a learnable control vector.
• Training is performed via standard backpropagation with a multi-task loss combining regression loss (for approximation accuracy) and classification loss (for prediction confidence).
• The fusion mechanism allows parameter sharing without architectural constraints, reducing redundancy and model size.
• A cost-effective NPU deployment strategy is proposed, adding minimal hardware cost by extending processing elements with an approximation subnet unit.
• The method is evaluated across multiple benchmarks including Bessel, FFT, JPEG, and Sobel functions to assess scalability and performance.

Experimental results

Research questions

• RQ1 Can a unified neural network architecture jointly optimize approximation accuracy and prediction of safe approximation inputs more effectively than separate training?
• RQ2 Does end-to-end training with joint loss functions reduce training time and improve invocation rate compared to iterative training?
• RQ3 To what extent does the proposed fusion mechanism reduce model parameters and maintain or improve approximation quality?
• RQ4 How does AXNet scale across different neural network topologies and benchmark functions?
• RQ5 Can AXNet be efficiently deployed in a real NPU with minimal hardware modification and significant energy efficiency gains?

Key findings

• AXNet achieves 50.7% higher invocation rate than the iterative training method, indicating a significantly larger proportion of inputs can be safely approximated.
• Training time is reduced by up to 90% compared to iterative training, with 13.8× and 32× speedups observed in Bessel and JPEG benchmarks, respectively.
• AXNet reduces parameter count by 60% on the JPEG benchmark compared to prior methods while maintaining similar true invocation levels.
• The fusion technique using Hadamard product shows no significant performance difference across different fusion locations (first vs. second hidden layer), validating its robustness.
• Energy efficiency is improved across all benchmarks, with AXNet outperforming both iterative and one-pass methods due to higher invocation and lower training cost.
• The proposed NPU deployment adds minimal hardware overhead, with only a small extension to each processing element to support the approximation subnet.