Efficient and Accurate Approximations of Nonlinear Convolutional Networks (1411.4229v1)

Abstract: This paper aims to accelerate the test-time computation of deep convolutional neural networks (CNNs). Unlike existing methods that are designed for approximating linear filters or linear responses, our method takes the nonlinear units into account. We minimize the reconstruction error of the nonlinear responses, subject to a low-rank constraint which helps to reduce the complexity of filters. We develop an effective solution to this constrained nonlinear optimization problem. An algorithm is also presented for reducing the accumulated error when multiple layers are approximated. A whole-model speedup ratio of 4x is demonstrated on a large network trained for ImageNet, while the top-5 error rate is only increased by 0.9%. Our accelerated model has a comparably fast speed as the "AlexNet", but is 4.7% more accurate.

Efficient and Accurate Approximations of Nonlinear Convolutional Networks

The paper presents a novel approach to accelerating the test-time computation of deep Convolutional Neural Networks (CNNs) by accounting for nonlinear components within the networks. This work is distinct from previous studies which mainly focused on linear approximations. The authors minimize the reconstruction error of the nonlinear responses under a low-rank constraint to alleviate computational complexity efficiently, enabling significant reductions in processing time while maintaining accuracy.

The method achieves a speedup factor of 4 on a comprehensive model trained on the ImageNet dataset, with only a marginal top-5 error rate increase of 0.9%. Notably, the accelerated model outperforms the well-known "AlexNet" in accuracy by 4.7%, while maintaining a comparable execution speed.

Key Contributions

1. Nonlinear Response Approximation: By explicitly considering nonlinearities such as Rectified Linear Units (ReLU), the proposed method surpasses existing approaches that overlook these essential network components. The reconstruction strategy focuses on minimizing the error of nonlinear responses, which has been shown to be crucial for maintaining model accuracy.
2. Low-rank Constraint and Optimization: The paper employs a low-rank constraint to reduce the complexity of the convolutional filters. The optimization problem is decomposed into two subproblems and solved iteratively, ensuring that the algorithm is effective in handling complex nonlinearities. Additionally, leveraging asymmetric reconstruction further aids in minimizing accumulated errors when approximating multiple layers consecutively.
3. Theoretical and Practical Gains: Empirical evaluations demonstrate that the method outperforms the linear approximation approach by a noticeable margin in terms of accuracy, especially when operating under significant speedup ratios. This balance between computational savings and accuracy preservation highlights the practical relevance of the method in real-world applications that require fast inference times.
4. Layer-wise and Model-wide Applicability: The algorithm can be applied to individual layers or the entire network. It also includes a rank selection mechanism to optimize across multiple layers, considering the accumulated approximation's effect on overall model performance.

Implications and Future Directions

The implications of this research are both vast and impactful. Practically, the method provides a pathway for deploying more accurate models in environments where computational resources are limited, such as mobile devices or cloud services handling numerous simultaneous requests. Theoretically, the explicit consideration of nonlinear components in network approximation opens new avenues for further research, encouraging exploration into other types of nonlinearities beyond ReLU.

The paper also suggests opportunities for integration with alternative network designs, potentially helping improve efficiency across different types of neural architectures. Future developments could aim to extend the applicability of low-rank constraints as regularizers during training, thus coupling the benefits of accelerated inference directly with improved training processes.

In conclusion, this paper addresses a critical aspect of deploying deep learning models in practice, presenting a balanced approach that prioritizes both speed and accuracy. The findings suggest promising directions for future research in the efficient computation of CNNs and could serve as a foundation for further innovations in the field.