A Differentiable Programming System to Bridge Machine Learning and Scientific Computing (1907.07587v2)

Abstract: Scientific computing is increasingly incorporating the advancements in machine learning and the ability to work with large amounts of data. At the same time, machine learning models are becoming increasingly sophisticated and exhibit many features often seen in scientific computing, stressing the capabilities of machine learning frameworks. Just as the disciplines of scientific computing and machine learning have shared common underlying infrastructure in the form of numerical linear algebra, we now have the opportunity to further share new computational infrastructure, and thus ideas, in the form of Differentiable Programming. We describe Zygote, a Differentiable Programming system that is able to take gradients of general program structures. We implement this system in the Julia programming language. Our system supports almost all language constructs (control flow, recursion, mutation, etc.) and compiles high-performance code without requiring any user intervention or refactoring to stage computations. This enables an expressive programming model for deep learning, but more importantly, it enables us to incorporate a large ecosystem of libraries in our models in a straightforward way. We discuss our approach to automatic differentiation, including its support for advanced techniques such as mixed-mode, complex and checkpointed differentiation, and present several examples of differentiating programs.

• The paper presents a Julia-based differentiable programming system that integrates automatic differentiation to bridge machine learning and scientific computing.
• The system supports complex constructs like recursion, control flow, and mutation while generating high-performance code without user-side adjustments.
• Practical applications include differentiable simulations, neural stochastic differential equations, and quantum hardware modeling, highlighting cross-disciplinary innovation.

Bridging Machine Learning and Scientific Computing through Differentiable Programming

The paper "$\partial P$: A Differentiable Programming System to Bridge Machine Learning and Scientific Computing" presents an integrated approach to unify the methodologies of machine learning and scientific computing. This research is rooted in the growing convergence of both fields, driven by their reliance on numerical linear algebra and their shared infrastructure demands. The authors propose a system that empowers the Julia programming language with differentiable programming capabilities, enabling a seamless transition between scientific computing and machine learning tasks. This system leverages automatic differentiation as a first-class feature, supporting complex constructs and high-performance code generation without the need for user-side adjustments.

The core contribution of the paper is in showcasing how Differentiable Programming ($\partial P$) infrastructure can facilitate shared development across these domains. A significant aspect is the implementation of a source-to-source automatic differentiation (AD) system within Julia, known for its strong base in both scientific and machine learning applications. By focusing on this singular language, the complexity is reduced, and existing packages can be utilized without altering their underlying structures.

Key Features and Applications

1. Comprehensive Language Features: The $\partial P$ system supports overarching language constructs like recursion, control flows, and mutation, offering flexibility and performance without code refactoring.
2. Advanced Differentiation Techniques: The system integrates mixed-mode, complex, and checkpointed differentiation, optimizing computational efficiency.
3. Real-world Integration: The paper provides practical examples, merging machine learning with scientific simulations—experimenting with models like differentiable ray tracing, neural stochastic differential equations, probabilistic programming, and quantum hardware simulations.
4. Performance with Minimal Overhead: The differentiation system introduces negligible runtime overhead beyond the necessary computations of the backward pass, suggesting high compatibility with existing scientific frameworks and ML models.
5. Potential for Two-way Innovation: Machine learning frameworks stand to benefit from scientific computing's robust adjoint sensitivity analyses, inverse problem-solving, and probabilistic modeling. Conversely, scientific computing can harness machine learning techniques for surrogate modeling and optimization.

Implications and Future Developments

The system's potential to blend two historically parallel fields introduces new realms of possibility for researchers and practitioners. In machine learning, this could lead to improved algorithmic performance with more sophisticated models that incorporate dynamic, data-driven constructs typically seen in scientific computing. On the scientific front, bridging with machine learning technologies can result in dramatically increased simulation speeds, new methods for solving complex differential equations, and a more nuanced understanding of physical phenomena through data-driven approaches.

The paper's contribution also extends into practical implementations, setting a precedent for using high-level languages like Julia to achieve technical advancements within AI research. The authors lay the foundation for more integrated and complex cross-disciplinary collaborations in future computational methodologies.

Moving forward, researchers should explore further optimizations and the potential expansion of these techniques across other languages and platforms. There is a large scope for developing domain-specific tools that leverage this shared infrastructure, potentially leading to significant advances in high-performance computing, scalable machine learning models, and nuanced simulations of complex systems.

In conclusion, this paper provides a strategic pathway toward a more holistic computational approach, leveraging the synergies between machine learning and scientific computing through automated differentiation in Julia. This approach not only enhances performance but also opens a spectrum of innovative applications across numerous research domains.