Signatory: differentiable computations of the signature and logsignature transforms, on both CPU and GPU (2001.00706v2)

Abstract: Signatory is a library for calculating and performing functionality related to the signature and logsignature transforms. The focus is on machine learning, and as such includes features such as CPU parallelism, GPU support, and backpropagation. To our knowledge it is the first GPU-capable library for these operations. Signatory implements new features not available in previous libraries, such as efficient precomputation strategies. Furthermore, several novel algorithmic improvements are introduced, producing substantial real-world speedups even on the CPU without parallelism. The library operates as a Python wrapper around C++, and is compatible with the PyTorch ecosystem. It may be installed directly via \texttt{pip}. Source code, documentation, examples, benchmarks and tests may be found at \texttt{\url{https://github.com/patrick-kidger/signatory}}. The license is Apache-2.0.

• The paper introduces innovative algorithmic improvements that drastically reduce computation times for signature and logsignature transforms.
• It pioneers a GPU-capable approach with OpenMP-driven parallelism, achieving orders of magnitude speedup over CPU-only methods.
• Backward integration with PyTorch and efficient precomputation strategies ensure practical applicability for high-dimensional sequential data.

Overview of "Signatory: Differentiable Computations of the Signature and Logsignature Transforms, on both CPU and GPU"

The paper presents "Signatory," a computational library designed for efficient calculation and application of the signature and logsignature transforms. These transforms are pivotal in rough path theory and have significant applications in machine learning, particularly for tasks involving sequential data like time series.

Key Contributions

1. Innovative Computational Improvements: The authors introduce novel algorithmic approaches that significantly improve the computational efficiency of calculating the signature and logsignature transforms. Notably, a fused multiply-exponentiate operation is proposed, which optimizes both the computational complexity and the number of required multiplications.
2. First GPU-Capable Library: Signatory is distinguished as the first library to offer GPU support for these operations. This feature provides substantial speedups over previous CPU-only implementations, such as esig and iisignature, which can be a bottleneck during the training of deep learning models.
3. Parallelism and Efficiency: The library utilizes OpenMP for parallelism on CPU operations and leverages existing GPU frameworks to further accelerate computations. This is strategically crucial for deep networks that operate on machines with high parallel computational power.
4. Backward Compatibility and Integrability: Specialized handwritten backward operations ensure efficient backpropagation, key for integrating these transforms into deep learning workflows. Direct compatibility with the PyTorch ecosystem enhances its usability for machine learning researchers and practitioners.
5. Extensive Precomputation Strategies: Signatory implements strategies to efficiently precompute signature values over a sequence and offers constant-time querying over arbitrary intervals, improving on the logarithmic-time methods previously available.

Numerical and Theoretical Implications

The paper provides extensive benchmarking to quantify the performance improvement of Signatory over existing solutions. These benchmarks show orders of magnitude improvements, particularly on larger computations. The library’s speedup is due to both GPU accessibility and computational optimizations, reaffirming its impact on practical machine learning applications.

Theoretically, Signatory’s approach to logsignature basis provides a more computationally efficient representation, facilitating high-dimensional data operations inherent in modern machine learning tasks. The authors note that the choice of basis in the logsignature operation can be made computationally lighter, capitalizing on the typically subsequent linear transformations in learning models.

Future Directions

Signatory sets a precedent for future work on computationally efficient signature and logsignature operations. Potential future developments could include further optimization of memory usage, integration of additional functionalities relevant to advanced path space computations, and enhancements in auto-differentiation techniques that may streamline future model training processes. Moreover, expanding the library to encompass a broader class of path-defined operations, potentially leveraging advancements in adaptive systems, could further enhance its utility.

Signatory's integration into the deep learning framework opens new avenues for its application in complex domains such as finance, genomics, and other areas where understanding sequential and temporal dependencies is critical. As machine learning models and the datasets they operate on continue to grow in complexity and size, such efficient computational tools will be integral to processing and learning from data that could otherwise be computationally prohibitive.

In conclusion, this paper presents a comprehensive tool that effectively bridges theoretical rough path concepts and practical machine learning demands, offering researchers a robust platform for advanced signature-based methods in AI applications. The combination of technical depth and practical utility makes Signatory a noteworthy addition to the computational libraries available in the machine learning landscape.