Improving Post Training Neural Quantization: Layer-wise Calibration and Integer Programming (2006.10518v2)

Abstract: Lately, post-training quantization methods have gained considerable attention, as they are simple to use, and require only a small unlabeled calibration set. This small dataset cannot be used to fine-tune the model without significant over-fitting. Instead, these methods only use the calibration set to set the activations' dynamic ranges. However, such methods always resulted in significant accuracy degradation, when used below 8-bits (except on small datasets). Here we aim to break the 8-bit barrier. To this end, we minimize the quantization errors of each layer separately by optimizing its parameters over the calibration set. We empirically demonstrate that this approach is: (1) much less susceptible to over-fitting than the standard fine-tuning approaches, and can be used even on a very small calibration set; and (2) more powerful than previous methods, which only set the activations' dynamic ranges. Furthermore, we demonstrate how to optimally allocate the bit-widths for each layer, while constraining accuracy degradation or model compression by proposing a novel integer programming formulation. Finally, we suggest model global statistics tuning, to correct biases introduced during quantization. Together, these methods yield state-of-the-art results for both vision and text models. For instance, on ResNet50, we obtain less than 1\% accuracy degradation --- with 4-bit weights and activations in all layers, but the smallest two. We open-sourced our code.

Improving Post Training Neural Quantization: Layer-wise Calibration and Integer Programming

The paper presented provides a comprehensive analysis on enhancing post-training neural quantization techniques, specifically breaking the barriers associated with sub-8-bit quantization and mitigating the consequent accuracy degradation. The authors introduce an innovative methodology composed of layer-wise calibration, integer programming, and batch normalization tuning aimed towards improving the efficacy of quantized neural networks, particularly in scenarios where training data is sparse or unavailable due to privacy concerns.

Key Contributions

This paper's central contributions resolve significant limitations associated with existing post-training quantization methods:

• AdaQuant: A novel layer-by-layer optimization, AdaQuant, is proposed which minimizes quantization errors by adjusting the weights and activation parameters per layer, using a minimal calibration dataset. This method adds flexibility by not strictly adhering to conventional MSE objectives typically associated with such quantization tasks. AdaQuant substantially reduces susceptibility to over-fitting, producing superior results even when utilizing a smaller calibration set compared to traditional fine-tuning methods.
• Integer Programming for Bit Allocation: The authors detail a novel integer programming framework for optimizing bit-width allocation across neural network layers. This approach maximizes computational efficiency while constraining the loss in model accuracy. By employing a formal optimization problem, characterized by binary variables, the quantized network achieves an optimal configuration, seamlessly balancing performance improvements with accuracy constraints.
• Batch Normalization Tuning: Recognizing inherent biases resulting from quantization, the research introduces a nuanced approach to recalibrate batch normalization statistics. By tuning batch norm layers after quantization, using calibration data to reconstruct statistics, the framework effectively recovers quantization-induced degradation without additional computational burden.

Empirical Validation

The empirical results indicate substantial improvements over existing methods. Utilizing ResNet50 and MobileNet-V2 among other architectures, the proposed methodologies consistently achieve low precision accuracy degradation. For instance, the system maintains less than 1% accuracy degradation in ResNet50 using 4-bit weights and activations, showcasing the robustness of the technique across both vision and text models, further demonstrating its broad applicability.

Implications and Future Directions

This work introduces a notable advancement in neural network quantization, providing efficient strategies crucial for deploying deep learning models on resource-constrained devices such as smartphones and wearables. By offering a robust framework for layer-specific optimization and effective deployment, the research paves the way towards more practical applications, especially where data availability is limited.

Future developments may explore the integration of additional techniques into the quantization pipeline, such as adaptive learning based on real-world deployment feedback. Additionally, extending applicability to more architectures, including transformer-based models, remains a promising avenue. Continuous improvement in quantization methods will further enhance AI's applicability in diverse domains requiring efficient processing capabilities.

In summary, the paper's contributions present significant progress in overcoming quantization barriers, offering impactful methodologies with practical implications for deploying AI models efficiently across various platforms. The open-source release of the authors’ code further supports replicability and encourages continued exploration in this vital area of AI research.