This paper presents a comprehensive methodology for implementing scalable 2D convolution layers in the MindsEye neural network framework. We address the fundamental challenge of processing large-scale inputs that exceed GPU memory constraints through a novel multi-tiered implementation strategy. Our approach combines reference implementations for validation, optimized native library integration, and dynamic partitioning algorithms that enable processing of arbitrarily large inputs. The proposed system demonstrates successful scaling from standard inputs to 1024×1024 images with 1024-band convolutions through intelligent tile-based decomposition, achieving approximately 4096 elemental operations distributed across heterogeneous GPU architectures.

Keywords: deep learning, convolution layers, GPU acceleration, scalability, partitioning algorithms

1. Introduction

Modern deep neural networks require convolution layers capable of processing increasingly large inputs while maintaining computational efficiency and memory constraints. Traditional implementations face significant limitations when dealing with high-resolution images and high-dimensional feature maps, often exceeding available GPU memory or compute unit scaling limits. This paper presents a systematic approach to developing scalable 2D convolution layers that addresses these constraints through hierarchical implementation strategies and dynamic partitioning.

The primary contributions of this work include:

Existing convolution implementations typically rely on highly optimized libraries such as cuDNN or custom CUDA kernels for GPU acceleration. While these approaches achieve excellent performance for standard-sized inputs, they encounter scalability limitations with very large tensors. Previous work has addressed memory constraints through techniques such as gradient checkpointing and model parallelism, but few approaches provide transparent scaling for arbitrarily large inputs within a single layer implementation.

3. Methodology

3.1 Multi-Tiered Implementation Strategy

Our approach employs a three-tier implementation hierarchy:

Tier 1: Reference Implementation We begin with a pure Java implementation optimized for clarity rather than performance. This reference serves as the ground truth for validation, capturing the mathematical semantics of 2D convolution in a verifiable form. Test-driven development ensures correctness and provides a baseline for comparing optimized implementations.

Tier 2: Native Library Integration Optimized implementations leverage existing high-performance libraries including BLAS and cuDNN. Additionally, we explore Aparapi-based implementations that transpile Java code to OpenCL, providing cross-platform GPU acceleration with acceptable performance characteristics.

Tier 3: Dynamic Partitioning Implementation For inputs exceeding hardware constraints, we implement a sophisticated partitioning strategy that decomposes large operations into manageable sub-problems.

3.2 Dynamic Partitioning Algorithm

The core innovation addresses scalability through a two-dimensional partitioning strategy:

Spatial Partitioning: Large input images are divided into overlapping tiles. For a 1024×1024 input, we generate 64 tiles of 128×128 pixels each, with appropriate overlap to maintain convolution boundary conditions.

Channel Partitioning: High-dimensional convolution kernels are decomposed similarly to block matrix operations. A 1024-band convolution is partitioned into 64 sub-convolutions of 128 bands each.

The combined partitioning strategy transforms a single large operation into approximately N×M elemental convolutions, where N and M represent the number of spatial and channel partitions respectively.

3.3 Runtime Adaptation

The system implements dynamic threshold-based switching between implementation tiers. At evaluation time, the convolution layer analyzes input dimensions and automatically selects the appropriate implementation strategy. For inputs exceeding predefined thresholds, the system dynamically constructs a select-process-reassemble network architecture.

4. Implementation Details

4.1 Memory Management

Our implementation leverages CUDA 6/Pascal managed memory architecture, enabling efficient data movement between CPU and GPU memory spaces. The partitioning strategy ensures that individual tiles remain within GPU memory constraints while maintaining overall computational efficiency.

4.2 Multi-GPU Distribution

The elemental convolution operations generated by partitioning provide natural parallelization opportunities. We distribute computations across heterogeneous GPU configurations, balancing load based on device capabilities and memory availability.

4.3 Network Construction

The dynamic network generation subsystem creates specialized processing graphs at runtime. These networks implement the select-process-reassemble pattern, ensuring that results from individual tiles are correctly aggregated to produce mathematically equivalent outputs to monolithic implementations.

5. Experimental Results

Testing demonstrates successful scaling from standard convolution operations to extreme cases such as 1024×1024 inputs with 1024-band kernels. The partitioning strategy successfully decomposes these operations into approximately 4096 manageable convolutions while maintaining numerical accuracy within acceptable tolerances.

Performance analysis shows that while individual tile processing introduces overhead, the overall system achieves better throughput than memory-constrained implementations that would otherwise fail entirely.

6. Discussion

6.1 Scalability Analysis

The proposed partitioning strategy provides theoretically unlimited scalability, bounded only by available computational resources and acceptable processing time. The O(N×M) decomposition ensures that arbitrarily large inputs can be processed through sufficient partitioning.

6.2 Accuracy Considerations

Tile-based processing introduces potential numerical differences due to boundary effects and floating-point accumulation order. Our validation framework ensures that these differences remain within acceptable bounds for practical applications.

6.3 Software Architecture Implications

This work highlights the need for new software development paradigms in deep learning frameworks. The dynamic, data-dependent network construction represents a fundamentally different computational model that requires specialized development tools and design patterns.

7. Conclusion

We present a comprehensive approach to scalable 2D convolution layer implementation that addresses the growing demands of modern neural network architectures. The multi-tiered strategy provides a clear development path from reference implementations to highly optimized, scalable solutions. The dynamic partitioning algorithm successfully enables processing of arbitrarily large inputs while maintaining correctness and computational efficiency.

Future work will explore adaptive partitioning strategies that optimize tile sizes based on hardware characteristics and input statistics. Additionally, extending this approach to other computationally intensive layers such as attention mechanisms presents promising research directions.

Acknowledgments

The authors acknowledge the use of heterogeneous GPU configurations supporting CUDA 6/Pascal managed memory architecture in the development and testing of this work.

References

[References would be included here in a real academic paper, citing relevant work on neural network optimization, GPU computing, and scalable deep learning implementations]