Continuous Relaxation Quantization for Deep Neural Networks
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Solution Overview
Problem
Conventional neural network quantization methods face challenges in reducing computational costs on resource-constrained devices, as they introduce discontinuity and make gradient-based optimization infeasible due to the lossy and non-invertible nature of discretization, leading to performance degradation.
Innovation Solution
A method for continuous relaxation of quantization is introduced, where noise is modeled and grid values are assigned based on a local fixed-point quantization grid, enabling gradient-based updates and improving the accuracy of discretized deep neural networks by transforming continuous distributions to categorical distributions over the quantization grid.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Use of energy by moving object
If conventional quantization methods are applied to reduce computational costs, then device resource consumption is reduced, but gradient-based optimization becomes infeasible due to discontinuity
Solution Approach 1:
The patent transforms the discrete quantization parameter space into a continuous parameter space by introducing a temperature parameter T. This allows the quantization function to become differentiable, enabling gradient-based optimization while maintaining the essential quantization effect. The continuous relaxation is achieved by replacing the discrete assignment with a softmax-based continuous approximation.
Solution Approach 2:
The patent introduces a continuous relaxation function as an intermediary between the discrete quantization operation and the gradient computation. This intermediary function (using softmax with temperature parameter) bridges the gap by providing a differentiable approximation that preserves the quantization behavior while enabling gradient flow through the otherwise discontinuous operation.
2Productivity
If discretization is applied to reduce computational complexity, then processing speed is improved, but accuracy degrades due to lossy and non-invertible nature
Solution Approach 1:
The patent applies preliminary action by performing continuous relaxation during the training phase, allowing the network to learn optimal quantization parameters in a continuous space. This preliminary training with continuous parameters enables the network to adapt to quantization effects before the actual discrete quantization is applied during inference, thereby reducing accuracy degradation.
Solution Approach 2:
The patent introduces dynamics by making the quantization process adaptive through the temperature parameter T. During training, T is gradually reduced (annealing) to transition from a soft continuous approximation to a harder discrete assignment. This dynamic adjustment allows the network to first learn in a more flexible continuous space and then converge to the discrete quantized solution, improving final accuracy.
3Device complexity
If fixed-point quantization grid is used to simplify computation, then device complexity is reduced, but adaptability to different noise distributions is limited
Solution Approach 1:
The patent enhances adaptability by introducing learnable parameters that characterize the noise distribution (mean and variance). These parameters are optimized during training to match the actual noise characteristics of the data, allowing the fixed-point quantization grid to adapt to different noise distributions without changing its fundamental simple structure. This maintains low device complexity while achieving high adaptability.
Data Source
AI summary
A method for quantizing a neural network includes modeling noise of parameters of the neural network. The method also includes assigning grid values to each realization of the parameters according to a concrete distribution that depends on a local fixed-point quantization grid and the modeled noise and. The method further includes computing a fixed-point value representing parameters of a hard fixed-point quantized neural network.