SMPConv: Self-moving Point Representations for Continuous Convolution (2304.02330v1)

Abstract: Continuous convolution has recently gained prominence due to its ability to handle irregularly sampled data and model long-term dependency. Also, the promising experimental results of using large convolutional kernels have catalyzed the development of continuous convolution since they can construct large kernels very efficiently. Leveraging neural networks, more specifically multilayer perceptrons (MLPs), is by far the most prevalent approach to implementing continuous convolution. However, there are a few drawbacks, such as high computational costs, complex hyperparameter tuning, and limited descriptive power of filters. This paper suggests an alternative approach to building a continuous convolution without neural networks, resulting in more computationally efficient and improved performance. We present self-moving point representations where weight parameters freely move, and interpolation schemes are used to implement continuous functions. When applied to construct convolutional kernels, the experimental results have shown improved performance with drop-in replacement in the existing frameworks. Due to its lightweight structure, we are first to demonstrate the effectiveness of continuous convolution in a large-scale setting, e.g., ImageNet, presenting the improvements over the prior arts. Our code is available on https://github.com/sangnekim/SMPConv

• The paper introduces SMPConv, which uses self-moving point representations to implement continuous convolution without relying on MLPs.
• It achieves high parameter efficiency and captures high-frequency data by dynamically adjusting point positions during training.
• Empirical results show superior performance on benchmarks like sequential MNIST, CIFAR10, and ImageNet compared to traditional convolution models.

Analysis of SMPConv: Self-Moving Point Representations for Continuous Convolution

The paper introduces SMPConv, a novel approach to continuous convolution that departs from the conventional reliance on neural networks such as MLPs. This method is particularly significant given the computational inefficiencies and limitations associated with MLP-based approaches in continuous convolution scenarios. Continuous convolution addresses the limitations of discrete convolution by efficiently handling irregularly sampled data and constructing large convolution kernels, enabling better modeling of long-term dependencies.

Methodological Advancements

SMPConv utilizes self-moving point representations as a core innovation. Each point in this representation includes learnable parameters for position, weight, and radius, which are interpolated to implement continuous convolution kernels. This contrasts with existing methodologies that employ neural networks to approximate continuous convolution. The proposed method replaces the complexity of MLP-based architectures with computationally light point representations.

The self-moving points have an inherent flexibility; their positions are not static and can adjust during training, optimally covering various frequencies in the data. This flexibility is critical for capturing high-frequency elements without being constrained by spectral bias, a common challenge faced when using MLPs. High parameter efficiency is maintained by reducing the number of points required compared to the total possible size of large kernels, which contrasts with the parameter explosion typical in traditional large-kernel convolutions.

Empirical Results and Performance

In experimental validations, SMPConv showcases superior performance across a range of tasks, demonstrating its robustness and ability to handle diverse data types. Specifically, it achieves state-of-the-art results on sequential image datasets such as sequential MNIST (sMNIST) and permuted MNIST (pMNIST), and competitive performance on time-series datasets. In these experiments, SMPConv's lightweight structure allows it to manage long-term dependencies effectively with less computational overhead compared to MLP-based alternatives. Furthermore, on the CIFAR10 image dataset, SMPConv surpasses traditional convolution models like ResNet-44, validating its ability to match and exceed the performance of established architectures with fewer parameters.

One of the most notable accomplishments of SMPConv is its application on the ImageNet dataset. The experiments prove that continuous convolution, as executed by SMPConv, can be applied efficiently at scale, achieving results on par with state-of-the-art models like ConvNeXt-B and Swin-B. This forms an essential contribution to deep learning as it demonstrates that continuous convolution is viable in practical, large-scale scenarios, where previous applications were mainly limited to smaller datasets or theoretical discussions.

Practical and Theoretical Implications

The promise of SMPConv stems from its ability to combine parameter efficiency with computational simplicity, making it attractive for deployment in resource-limited environments without sacrificing performance. The continuous kernel framework also highlights new directions for efficient architecture designs in AI, encouraging the exploration of alternatives to heavily parameterized and computationally expensive neural network models.

Future Prospects

Given the strengths demonstrated by SMPConv, future work could focus on its broader application across other domains requiring efficient large-kernel transformations, such as video processing and three-dimensional data processing in point clouds. Additionally, exploring the integration of SMPConv into hybrid models that leverage both neural fields and lightweight convolutions could yield more versatile architectures.

In conclusion, the approach posited by SMPConv marks a strategic advancement in convolutional architectures, offering a successful synthesis of computational efficiency and performance while sidestepping some of the common drawbacks associated with neural network-heavy solutions. Its development holds the potential to propel further innovations in the processing of complex data streams in artificial intelligence.