Two Heads are Better Than One: Neural Networks Quantization with 2D Hilbert Curve-based Output Representation

Mykhailo Uss, Ruslan Yermolenko, Olena Kolodiazhna, Oleksii Shashko, Ivan Safonov, Volodymyr Savin, Yoonjae Yeo, Seowon Ji, Jaeyun Jeong·May 22, 2024

Summary

The paper presents a novel approach to enhance deep neural network quantization by using a redundant output representation on a 2D parametric curve, such as the Hilbert curve. This method reduces quantization error, particularly in tasks like Depth-From-Stereo, for U-Net and vision transformer models. The approach focuses on improving memory, computation, and power efficiency without sacrificing accuracy. The study shows a 5x reduction in error for INT8 models on CPU and DSP, with minimal impact on inference time. The method is applicable to various tasks and can surpass existing quantization techniques like PTQ and accumulator-aware quantization. The research also involves experiments with DispNet and DPT models, demonstrating improved performance in depth estimation tasks, and highlights the potential for better quantization in resource-constrained devices.

Key findings

18

Paper digest

What problem does the paper attempt to solve? Is this a new problem?

The paper aims to address the issue of minimizing model quality degradation during quantization by proposing a novel approach that utilizes redundant output representation to reduce quantization error at the inference stage . This problem is not entirely new, as quantization techniques like post-training quantization (PTQ) and quantization-aware training (QAT) have been developed to mitigate quality degradation during quantization . However, the paper introduces a unique method that involves training a DNN model to predict redundant output representation using 2D parametric low-order Hilbert curves, which is a novel approach to quantization error reduction .


What scientific hypothesis does this paper seek to validate?

This paper aims to validate a scientific hypothesis related to deep neural network (DNN) quantization by introducing a novel approach that utilizes a redundant representation of DNN output through a 2D parametric curve. The hypothesis is centered around reducing quantization error in DNN models by modifying the model to predict 2D points that are then mapped back to the target quantity during post-processing, ultimately improving quantization quality .


What new ideas, methods, or models does the paper propose? What are the characteristics and advantages compared to previous methods?

The paper proposes several innovative ideas, methods, and models related to neural network quantization and output representation:

  • Post-training quantization (PTQ): The paper introduces PTQ as a method that operates on already trained models to adjust model weights and activations in order to minimize quantization error. PTQ is implemented in standard frameworks like Snapdragon Neural Processing Engine (SNPE), CoreML, and TensorFlow Lite .
  • Integer-only quantization: The paper discusses the usage of integer-only arithmetic and quantization below 8-bit, which provides additional gains in quantized deep neural network (QDNN) inference. It explores representations such as INT4, ternary, and binary values for weights and activations. The approach also involves the usage of low-precision accumulators through bit-packing to improve model inference efficiency .
  • Redundant output representation prediction: The paper proposes training a DNN model to predict redundant output representations using 2D parametric low-order Hilbert curves. This approach aims to reduce quantization error at the inference stage and correct errors below a certain threshold. The method achieved quantization error reduction by approximately 5 times with minimal increase in inference time .
  • Extension to higher dimensions: The paper suggests extending the proposed approach to 3D parametric curves or even higher dimensions to potentially correct a larger number of outlying quantization errors. This extension could lead to further improvements in correcting quantization errors . The proposed method in the paper introduces several characteristics and advantages compared to previous methods in neural network quantization:
  • Redundant Output Representation Prediction: The paper suggests training a DNN model to predict redundant output representations using 2D parametric low-order Hilbert curves, aiming to reduce quantization error at the inference stage. This approach achieved a quantization error reduction by approximately 5 times with minimal inference time increase (< 7%) for the INT8 model at both CPU and DSP delegates .
  • Increased Dimension of DNN Output: By increasing the dimension of a DNN output, the proposed method aims to improve the accuracy of signal transmission in Quantized DNN (QDNN) models. This approach leverages the Shannon–Hartley theorem to enhance the distinguishable quantity levels, thereby potentially reducing quantization error .
  • Applicability and Flexibility: The proposed method can be applied to models quantized to different bit-orders and supports integer-arithmetic-only inference. It offers the advantage of increasing the effective bit-width, limited by hardware constraints, and can achieve representations beyond standard INT8 precision, such as INT10, from INT8 model outputs. This flexibility allows for improved quantization quality and efficiency in DNN deployment .
  • Compatibility with Existing Methods: The approach can be used with existing Post-training quantization (PTQ) methods without requiring modifications, providing additional quantization error reduction. It complements techniques like PTQ and Quantization-Aware Training (QAT) to potentially offer a more effective solution for minimizing model quality degradation during quantization compared to separate use .
  • Efficiency and Performance: The proposed method achieved a quantization error reduction by approximately 5 times for the INT8 model with minimal inference time increase, making it a promising approach for tasks like segmentation, object detection, and key-points prediction .

Do any related researches exist? Who are the noteworthy researchers on this topic in this field?What is the key to the solution mentioned in the paper?

Several related researches exist in the field of neural network quantization. Noteworthy researchers in this area include H. Cai, J. Choi, A. Colbert, A. Dai, L. Deng, D. Eigen, M. Uss, and many others . The key to the solution mentioned in the paper revolves around the utilization of a 2D Hilbert Curve-based output representation to reduce quantization errors in deep neural networks. This approach introduces additional redundancy in DNN models to favor the quantization process, aiming to minimize model quality degradation during quantization .


How were the experiments in the paper designed?

The experiments in the paper were designed to train DispNet and DPT models with different orders of 2D low-order Hilbert curves (p = 1, 2, 3, 4) to predict disparity as points on the curve. These models were referred to as hpDispNet and hpDPT . The goal was to predict redundant output representations using 2D parametric low-order Hilbert curves to reduce quantization error during the inference stage. The experiments aimed to achieve quantization error reduction by approximately 5 times with minimal inference time increase (< 7%) for the Depth-From-Stereo (DFS) task . Additionally, the experiments validated the approach for the DFS task and INT8 quantization using the Snapdragon Neural Processing Engine (SNPE) library .


What is the dataset used for quantitative evaluation? Is the code open source?

The dataset used for quantitative evaluation in the study is the h3DispNet model . The code for the proposed approach is not explicitly mentioned to be open source in the provided context.


Do the experiments and results in the paper provide good support for the scientific hypotheses that need to be verified? Please analyze.

The experiments and results presented in the paper provide strong support for the scientific hypotheses that needed verification. The paper introduces a novel approach using 2D parametric low-order Hilbert curves to predict redundant output representation, aiming to reduce quantization error during the inference stage . The experiments conducted on two known architectures, DispNet and DPT, demonstrated a significant reduction in quantization error by approximately 5 times, with a minimal increase in inference time of less than 7% . This outcome indicates that the proposed approach effectively addresses the challenge of minimizing quantization errors in DNN models, supporting the scientific hypothesis put forth in the paper.

Furthermore, the paper discusses the application of post-training quantization (PTQ) on already trained models to adjust weights and activations for minimizing quantization error . The results of the experiments showed that PTQ, when combined with other techniques, could potentially offer a more effective solution for reducing model quality degradation during quantization compared to using these methods separately . This finding provides additional evidence supporting the effectiveness of the proposed approach in improving model quality during the quantization process.

Moreover, the paper explores the use of integer-only quantization and low-precision arithmetic to enhance the efficiency of DNN deployment . By utilizing integer-only arithmetic and quantization below 8-bit, the study achieved additional gains in DNN inference, demonstrating the effectiveness of these techniques in maximizing model efficiency . These results contribute to validating the scientific hypotheses proposed in the paper regarding the benefits of integer-only quantization and low-precision arithmetic in improving DNN deployment efficiency.

In conclusion, the experiments and results presented in the paper provide robust support for the scientific hypotheses put forward by demonstrating the effectiveness of the proposed approach in reducing quantization error, improving model quality, and enhancing the efficiency of DNN deployment on devices with limited computational capabilities.


What are the contributions of this paper?

The paper makes several key contributions in the field of neural network quantization with 2D Hilbert curve-based output representation:

  • Proposed Approach: The paper introduces a novel approach that involves modifying deep neural network (DNN) models by incorporating a Gaussian noise layer and two heads for Hilbert curve components, leading to improved quantization of the models .
  • Training and Optimization: It discusses the training process of the modified DispNet and DPT models using specific optimizers, learning rate policies, and batch sizes to achieve effective quantization to INT8 precision .
  • Quantization Techniques: The paper explores post-training quantization (PTQ) methods, integer-only quantization, and the use of low-precision formats like INT4, ternary, and binary values to enhance the efficiency of DNN inference .
  • Quantization Error Reduction: It addresses the challenge of minimizing quantization error during the quantization process by applying PTQ methods, optimal clipping range selection, and adaptation to specific architectures like visual transformers .
  • Practical Implementation Aspects: The paper delves into the practical implementation aspects of building direct and inverse mappings for Hilbert curves, highlighting the importance of curve order selection for quantization error reduction .

What work can be continued in depth?

To further advance the research in depth, one potential direction is to extend the approach to 3D parametric curves or even higher dimensions. This extension could potentially help in correcting a larger number of outlying quantization errors, thus enhancing the overall quantization error reduction capabilities . Additionally, exploring tasks beyond the Depth-From-Stereo (DFS) task, such as semantic or instance segmentation, key-points detection, and object detection, could be valuable for future studies in the field of neural network quantization .

Tables

2

Introduction
Background
Overview of deep neural network quantization challenges
Importance of memory, computation, and power efficiency
Objective
To propose a new method for enhancing quantization in DNNs
Improve accuracy, memory, and computational efficiency
Target applications: Depth-From-Stereo, U-Net, vision transformers
Method
Data Collection
Selection of benchmark models (U-Net, vision transformers, DispNet, DPT)
Depth-From-Stereo datasets for evaluation
Data Preprocessing and Hilbert Curve Representation
Parametric Curve Selection
Hilbert curve for 2D redundant output representation
Advantages over traditional quantization methods
Quantization Process
Model training with floating-point weights
Mapping to Hilbert curve for redundant output
Quantization of curve coefficients to INT8 or lower precision
Error Reduction and Performance Evaluation
INT8 Model Performance
CPU and DSP experiments
5x reduction in quantization error
Inference time impact analysis
Comparison with Existing Techniques
PTQ (Post-Training Quantization)
Accumulator-aware quantization
Improved performance in DispNet and DPT models
Applicability and Scalability
Generalization to other tasks and models
Resource-constrained device implications
Experiments and Results
Depth estimation task results
Quantitative analysis of accuracy, memory, and speedup
Visualizations of quantization performance improvements
Conclusion
Summary of the proposed method's benefits
Limitations and future research directions
Potential for real-world deployment in resource-limited environments
Future Work
Extending to other quantization levels and architectures
Integration with hardware accelerators
Real-world deployment case studies
Basic info
papers
computer vision and pattern recognition
artificial intelligence
Advanced features
Insights
In which tasks does the proposed method show significant improvement, specifically with U-Net and vision transformer models?
What is the primary focus of the paper's novel approach to deep neural network quantization?
How does the redundant output representation on a 2D parametric curve, like the Hilbert curve, contribute to reducing quantization error?
What are the benefits of the presented approach in terms of memory, computation, and power efficiency compared to existing quantization techniques like PTQ and accumulator-aware quantization?

Two Heads are Better Than One: Neural Networks Quantization with 2D Hilbert Curve-based Output Representation

Mykhailo Uss, Ruslan Yermolenko, Olena Kolodiazhna, Oleksii Shashko, Ivan Safonov, Volodymyr Savin, Yoonjae Yeo, Seowon Ji, Jaeyun Jeong·May 22, 2024

Summary

The paper presents a novel approach to enhance deep neural network quantization by using a redundant output representation on a 2D parametric curve, such as the Hilbert curve. This method reduces quantization error, particularly in tasks like Depth-From-Stereo, for U-Net and vision transformer models. The approach focuses on improving memory, computation, and power efficiency without sacrificing accuracy. The study shows a 5x reduction in error for INT8 models on CPU and DSP, with minimal impact on inference time. The method is applicable to various tasks and can surpass existing quantization techniques like PTQ and accumulator-aware quantization. The research also involves experiments with DispNet and DPT models, demonstrating improved performance in depth estimation tasks, and highlights the potential for better quantization in resource-constrained devices.
Mind map
Improved performance in DispNet and DPT models
Accumulator-aware quantization
PTQ (Post-Training Quantization)
Inference time impact analysis
5x reduction in quantization error
CPU and DSP experiments
Quantization of curve coefficients to INT8 or lower precision
Mapping to Hilbert curve for redundant output
Model training with floating-point weights
Advantages over traditional quantization methods
Hilbert curve for 2D redundant output representation
Resource-constrained device implications
Generalization to other tasks and models
Comparison with Existing Techniques
INT8 Model Performance
Quantization Process
Parametric Curve Selection
Depth-From-Stereo datasets for evaluation
Selection of benchmark models (U-Net, vision transformers, DispNet, DPT)
Target applications: Depth-From-Stereo, U-Net, vision transformers
Improve accuracy, memory, and computational efficiency
To propose a new method for enhancing quantization in DNNs
Importance of memory, computation, and power efficiency
Overview of deep neural network quantization challenges
Real-world deployment case studies
Integration with hardware accelerators
Extending to other quantization levels and architectures
Potential for real-world deployment in resource-limited environments
Limitations and future research directions
Summary of the proposed method's benefits
Visualizations of quantization performance improvements
Quantitative analysis of accuracy, memory, and speedup
Depth estimation task results
Applicability and Scalability
Error Reduction and Performance Evaluation
Data Preprocessing and Hilbert Curve Representation
Data Collection
Objective
Background
Future Work
Conclusion
Experiments and Results
Method
Introduction
Outline
Introduction
Background
Overview of deep neural network quantization challenges
Importance of memory, computation, and power efficiency
Objective
To propose a new method for enhancing quantization in DNNs
Improve accuracy, memory, and computational efficiency
Target applications: Depth-From-Stereo, U-Net, vision transformers
Method
Data Collection
Selection of benchmark models (U-Net, vision transformers, DispNet, DPT)
Depth-From-Stereo datasets for evaluation
Data Preprocessing and Hilbert Curve Representation
Parametric Curve Selection
Hilbert curve for 2D redundant output representation
Advantages over traditional quantization methods
Quantization Process
Model training with floating-point weights
Mapping to Hilbert curve for redundant output
Quantization of curve coefficients to INT8 or lower precision
Error Reduction and Performance Evaluation
INT8 Model Performance
CPU and DSP experiments
5x reduction in quantization error
Inference time impact analysis
Comparison with Existing Techniques
PTQ (Post-Training Quantization)
Accumulator-aware quantization
Improved performance in DispNet and DPT models
Applicability and Scalability
Generalization to other tasks and models
Resource-constrained device implications
Experiments and Results
Depth estimation task results
Quantitative analysis of accuracy, memory, and speedup
Visualizations of quantization performance improvements
Conclusion
Summary of the proposed method's benefits
Limitations and future research directions
Potential for real-world deployment in resource-limited environments
Future Work
Extending to other quantization levels and architectures
Integration with hardware accelerators
Real-world deployment case studies
Key findings
18

Paper digest

What problem does the paper attempt to solve? Is this a new problem?

The paper aims to address the issue of minimizing model quality degradation during quantization by proposing a novel approach that utilizes redundant output representation to reduce quantization error at the inference stage . This problem is not entirely new, as quantization techniques like post-training quantization (PTQ) and quantization-aware training (QAT) have been developed to mitigate quality degradation during quantization . However, the paper introduces a unique method that involves training a DNN model to predict redundant output representation using 2D parametric low-order Hilbert curves, which is a novel approach to quantization error reduction .


What scientific hypothesis does this paper seek to validate?

This paper aims to validate a scientific hypothesis related to deep neural network (DNN) quantization by introducing a novel approach that utilizes a redundant representation of DNN output through a 2D parametric curve. The hypothesis is centered around reducing quantization error in DNN models by modifying the model to predict 2D points that are then mapped back to the target quantity during post-processing, ultimately improving quantization quality .


What new ideas, methods, or models does the paper propose? What are the characteristics and advantages compared to previous methods?

The paper proposes several innovative ideas, methods, and models related to neural network quantization and output representation:

  • Post-training quantization (PTQ): The paper introduces PTQ as a method that operates on already trained models to adjust model weights and activations in order to minimize quantization error. PTQ is implemented in standard frameworks like Snapdragon Neural Processing Engine (SNPE), CoreML, and TensorFlow Lite .
  • Integer-only quantization: The paper discusses the usage of integer-only arithmetic and quantization below 8-bit, which provides additional gains in quantized deep neural network (QDNN) inference. It explores representations such as INT4, ternary, and binary values for weights and activations. The approach also involves the usage of low-precision accumulators through bit-packing to improve model inference efficiency .
  • Redundant output representation prediction: The paper proposes training a DNN model to predict redundant output representations using 2D parametric low-order Hilbert curves. This approach aims to reduce quantization error at the inference stage and correct errors below a certain threshold. The method achieved quantization error reduction by approximately 5 times with minimal increase in inference time .
  • Extension to higher dimensions: The paper suggests extending the proposed approach to 3D parametric curves or even higher dimensions to potentially correct a larger number of outlying quantization errors. This extension could lead to further improvements in correcting quantization errors . The proposed method in the paper introduces several characteristics and advantages compared to previous methods in neural network quantization:
  • Redundant Output Representation Prediction: The paper suggests training a DNN model to predict redundant output representations using 2D parametric low-order Hilbert curves, aiming to reduce quantization error at the inference stage. This approach achieved a quantization error reduction by approximately 5 times with minimal inference time increase (< 7%) for the INT8 model at both CPU and DSP delegates .
  • Increased Dimension of DNN Output: By increasing the dimension of a DNN output, the proposed method aims to improve the accuracy of signal transmission in Quantized DNN (QDNN) models. This approach leverages the Shannon–Hartley theorem to enhance the distinguishable quantity levels, thereby potentially reducing quantization error .
  • Applicability and Flexibility: The proposed method can be applied to models quantized to different bit-orders and supports integer-arithmetic-only inference. It offers the advantage of increasing the effective bit-width, limited by hardware constraints, and can achieve representations beyond standard INT8 precision, such as INT10, from INT8 model outputs. This flexibility allows for improved quantization quality and efficiency in DNN deployment .
  • Compatibility with Existing Methods: The approach can be used with existing Post-training quantization (PTQ) methods without requiring modifications, providing additional quantization error reduction. It complements techniques like PTQ and Quantization-Aware Training (QAT) to potentially offer a more effective solution for minimizing model quality degradation during quantization compared to separate use .
  • Efficiency and Performance: The proposed method achieved a quantization error reduction by approximately 5 times for the INT8 model with minimal inference time increase, making it a promising approach for tasks like segmentation, object detection, and key-points prediction .

Do any related researches exist? Who are the noteworthy researchers on this topic in this field?What is the key to the solution mentioned in the paper?

Several related researches exist in the field of neural network quantization. Noteworthy researchers in this area include H. Cai, J. Choi, A. Colbert, A. Dai, L. Deng, D. Eigen, M. Uss, and many others . The key to the solution mentioned in the paper revolves around the utilization of a 2D Hilbert Curve-based output representation to reduce quantization errors in deep neural networks. This approach introduces additional redundancy in DNN models to favor the quantization process, aiming to minimize model quality degradation during quantization .


How were the experiments in the paper designed?

The experiments in the paper were designed to train DispNet and DPT models with different orders of 2D low-order Hilbert curves (p = 1, 2, 3, 4) to predict disparity as points on the curve. These models were referred to as hpDispNet and hpDPT . The goal was to predict redundant output representations using 2D parametric low-order Hilbert curves to reduce quantization error during the inference stage. The experiments aimed to achieve quantization error reduction by approximately 5 times with minimal inference time increase (< 7%) for the Depth-From-Stereo (DFS) task . Additionally, the experiments validated the approach for the DFS task and INT8 quantization using the Snapdragon Neural Processing Engine (SNPE) library .


What is the dataset used for quantitative evaluation? Is the code open source?

The dataset used for quantitative evaluation in the study is the h3DispNet model . The code for the proposed approach is not explicitly mentioned to be open source in the provided context.


Do the experiments and results in the paper provide good support for the scientific hypotheses that need to be verified? Please analyze.

The experiments and results presented in the paper provide strong support for the scientific hypotheses that needed verification. The paper introduces a novel approach using 2D parametric low-order Hilbert curves to predict redundant output representation, aiming to reduce quantization error during the inference stage . The experiments conducted on two known architectures, DispNet and DPT, demonstrated a significant reduction in quantization error by approximately 5 times, with a minimal increase in inference time of less than 7% . This outcome indicates that the proposed approach effectively addresses the challenge of minimizing quantization errors in DNN models, supporting the scientific hypothesis put forth in the paper.

Furthermore, the paper discusses the application of post-training quantization (PTQ) on already trained models to adjust weights and activations for minimizing quantization error . The results of the experiments showed that PTQ, when combined with other techniques, could potentially offer a more effective solution for reducing model quality degradation during quantization compared to using these methods separately . This finding provides additional evidence supporting the effectiveness of the proposed approach in improving model quality during the quantization process.

Moreover, the paper explores the use of integer-only quantization and low-precision arithmetic to enhance the efficiency of DNN deployment . By utilizing integer-only arithmetic and quantization below 8-bit, the study achieved additional gains in DNN inference, demonstrating the effectiveness of these techniques in maximizing model efficiency . These results contribute to validating the scientific hypotheses proposed in the paper regarding the benefits of integer-only quantization and low-precision arithmetic in improving DNN deployment efficiency.

In conclusion, the experiments and results presented in the paper provide robust support for the scientific hypotheses put forward by demonstrating the effectiveness of the proposed approach in reducing quantization error, improving model quality, and enhancing the efficiency of DNN deployment on devices with limited computational capabilities.


What are the contributions of this paper?

The paper makes several key contributions in the field of neural network quantization with 2D Hilbert curve-based output representation:

  • Proposed Approach: The paper introduces a novel approach that involves modifying deep neural network (DNN) models by incorporating a Gaussian noise layer and two heads for Hilbert curve components, leading to improved quantization of the models .
  • Training and Optimization: It discusses the training process of the modified DispNet and DPT models using specific optimizers, learning rate policies, and batch sizes to achieve effective quantization to INT8 precision .
  • Quantization Techniques: The paper explores post-training quantization (PTQ) methods, integer-only quantization, and the use of low-precision formats like INT4, ternary, and binary values to enhance the efficiency of DNN inference .
  • Quantization Error Reduction: It addresses the challenge of minimizing quantization error during the quantization process by applying PTQ methods, optimal clipping range selection, and adaptation to specific architectures like visual transformers .
  • Practical Implementation Aspects: The paper delves into the practical implementation aspects of building direct and inverse mappings for Hilbert curves, highlighting the importance of curve order selection for quantization error reduction .

What work can be continued in depth?

To further advance the research in depth, one potential direction is to extend the approach to 3D parametric curves or even higher dimensions. This extension could potentially help in correcting a larger number of outlying quantization errors, thus enhancing the overall quantization error reduction capabilities . Additionally, exploring tasks beyond the Depth-From-Stereo (DFS) task, such as semantic or instance segmentation, key-points detection, and object detection, could be valuable for future studies in the field of neural network quantization .

Tables
2
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