Piecewise Quantization for Neural Network Accuracy
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Solution Overview
Problem
Deep neural networks (DNNs) face challenges in resource-constrained applications due to high computational complexity and energy consumption, with traditional quantization techniques introducing errors that degrade performance, especially in low bit-width deployments.
Innovation Solution
A piecewise linear quantization method that divides the quantization range into non-overlapping regions, applying different quantization functions to each region to minimize quantization error, allowing for efficient deployment in resource-constrained environments without requiring access to the full training dataset.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If uniform quantization with INT8 numbers is used, then near-original FP32 pre-trained model performance is preserved, but resource requirements remain too high for widespread deployment in resource-constrained applications
Solution Approach 1:
The quantization range is divided into multiple non-uniform regions with different quantization granularities. High-precision regions are applied where tensor values have high density (e.g., around zero), while low-precision regions are applied where values are sparse. This segmentation allows the system to use more bits where needed for accuracy and fewer bits where acceptable, reducing overall resource requirements while maintaining model performance.
Solution Approach 2:
Different quantization parameters (bit-width, scale factors) are applied locally to different regions of the tensor value distribution rather than using a single uniform quantization scheme. This allows each region to have the quality appropriate for its characteristics, optimizing the trade-off between precision and resource usage in different parts of the data distribution.
2Quantity of substance
If low bit-width quantization (e.g., 4-bit) is used to reduce resource requirements, then deployment in resource-constrained applications becomes feasible, but quantization error increases and performance degrades to unacceptable levels
Solution Approach 1:
The quantization process is segmented into multiple regions where the first region uses low bit-width quantization (e.g., 4-bit) and the second region uses higher bit-width quantization (e.g., 8-bit or full precision). This allows the system to achieve low resource requirements overall while preserving accuracy in critical regions where high precision is needed.
Solution Approach 2:
The quantization parameters (bit-width, scale factors, offsets) are changed across different regions of the tensor distribution. By adapting these parameters locally rather than using fixed uniform quantization, the system can maintain acceptable performance even when using low bit-width representations in some regions.
3Use of energy by moving object
If quantization is applied to reduce computational complexity and energy consumption, then resource demands are reduced, but quantization errors are introduced that reduce DNN performance
Solution Approach 1:
Different quantization strategies are applied to different regions of the tensor distribution based on their characteristics. Regions with high value density receive finer quantization to minimize information loss, while sparse regions use coarser quantization. This local adaptation minimizes overall quantization error while achieving energy savings.
Solution Approach 2:
The quantization parameters are optimized and varied across different regions rather than using fixed parameters. This allows the system to adapt the quantization precision to the actual data distribution, reducing quantization error in critical regions while maintaining energy efficiency in less critical regions.
Data Source
AI summary
In some embodiments, a method of quantizing an artificial neural network includes dividing a quantization range for a tensor of the artificial neural network into a first region and a second region, and quantizing values of the tensor in the first region separately from values of the tensor in the second region. In some embodiments, linear or nonlinear quantization are applied to values of the tensor in the first region and the second region. In some embodiments, the method includes locating a breakpoint between the first region and the second region by substantially minimizing an expected quantization error over at least a portion of the quantization range. In some embodiments, the expected quantization error is minimized by solving analytically and/or searching numerically.