Modelling Long Range Dependencies in $N$D: From Task-Specific to a General Purpose CNN (2301.10540v2)

Abstract: Performant Convolutional Neural Network (CNN) architectures must be tailored to specific tasks in order to consider the length, resolution, and dimensionality of the input data. In this work, we tackle the need for problem-specific CNN architectures. We present the Continuous Convolutional Neural Network (CCNN): a single CNN able to process data of arbitrary resolution, dimensionality and length without any structural changes. Its key component are its continuous convolutional kernels which model long-range dependencies at every layer, and thus remove the need of current CNN architectures for task-dependent downsampling and depths. We showcase the generality of our method by using the same architecture for tasks on sequential ($1{\rm D}$), visual ($2{\rm D}$) and point-cloud ($3{\rm D}$) data. Our CCNN matches and often outperforms the current state-of-the-art across all tasks considered.

• The paper introduces continuous convolutional kernels that generate adaptable filters, eliminating the need for task-specific CNN designs.
• It proposes a unified CCNN architecture that consistently handles 1D, 2D, and 3D data with high parameter efficiency.
• Empirical results show state-of-the-art performance on sequence modeling and competitive outcomes on image and point-cloud tasks.

Overview of "Modelling Long Range Dependencies in $N$D: From Task-Specific to a General Purpose CNN"

The paper presents a novel architecture, the Continuous Convolutional Neural Network (CCNN), designed to overcome the limitations of task-specific CNN architectures by enabling the modeling of data across arbitrary resolutions, dimensionalities, and lengths. This work addresses a fundamental challenge in current convolutional neural networks: the need to customize CNN architectures based on input data properties, such as length and resolution.

Key Contributions

1. Continuous Convolutional Kernels: The paper introduces continuous convolutional kernels, parameterized by a small neural network, which allow the formation of convolutional kernels of any size in a parameter-efficient manner. This alleviates the necessity for task-specific architectures by decoupling the parameter count from kernel size.
2. Unified CNN Architecture: The CCNN serves as a general-purpose architecture that seamlessly adapts across different types of data, be it sequential (1D), visual (2D), or point-cloud (3D) data. This unification is significant because it enables consistent performance without architectural modifications.
3. Empirical Evaluation: The CCNN architecture is evaluated on various datasets with varying dimensionality, achieving state-of-the-art results in sequence modeling tasks and competitive outcomes in image processing tasks. The paper notably demonstrates zero-shot generalization across different data resolutions.
4. Efficient Handling of Long-Range Dependencies: By employing continuous convolutional kernels, the CCNN efficiently handles long-range dependencies, a critical factor for the comprehension and processing of complex data, without resorting to task-dependent strategies like downsampling or depth adjustments.

Experimental Results

The paper’s empirical results reveal the CCNN’s performance benefits across a broad array of tasks. On sequences like Sequential and Permuted MNIST, and Sequential CIFAR10, the CCNN achieved state-of-the-art performance, underscoring its ability to model long-range dependencies effectively. In visual tasks, though the CCNN’s performance was competitive with established large-scale architectures, it demonstrated superior parameter efficiency. An interesting facet of the CCNN’s flexibility was showcased by its successful deployment on 3D point-cloud data, surpassing the performance of some point-cloud-specific models.

Technical Insights

• Parameterization of Convolutional Kernels: The kernel generator network is crucial as it transforms position inputs into kernel values, making it possible to use a single neural network for generating kernels for various input types. This allows the CCNN to maintain consistent performance across different input resolutions and dimensionalities.
• Pointwise and Global Operations: The paper distinguishes between components in CNN architectures: pointwise operations, which are naturally data-independent, and global operations, which are reused without modification. Local operations, typically data-dependent, are reimagined through the aforementioned continuous parameterization.
• Computational Aspects: While the use of large, continuous kernels could introduce computational challenges, the paper discusses strategies like Fourier domain exploitation to mitigate the overhead, thereby maintaining feasibility in large-scale applications.

Implications and Future Directions

The CCNN presents implications for applications requiring flexible and adaptive neural network models across heterogeneous data. Practically, this research opens avenues for architectures capable of cross-modal training and data fusion, given the adaptability inherent in the CCNN's design. Theoretically, it suggests a paradigm where the semantics of the data, rather than its synthetic representation such as resolution or dimensionality, drive architectural design.

Future research could investigate further computational optimizations, potentially looking into self-adjusting architectures for handling irregular data. Additionally, inquiries into cross-modal applications and data fusion could verify the CCNN's practical capabilities in real-world, mixed-data environments.

In conclusion, the paper puts forth a compelling solution to a long-standing challenge in CNN architecture design, contributing significantly to the quest for versatile, high-performing neural models. Its innovative use of continuous convolutional kernels marks a forward step in both the practical application and theoretical understanding of convolutional neural networks.