Compiler Transforms for Localizing Non-Local Functions in Reverse-Mode AD
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Solution Overview
Problem
Existing compiler optimizations struggle with non-local transformation problems in dynamic systems, leading to increased memory usage and unnecessary computation, particularly in reverse-mode automatic differentiation, which are not efficiently addressed by traditional methods.
Innovation Solution
The method transforms non-local functions into local functions using dynamic inter-procedural analysis and opaque closures, enabling efficient generation of higher-order derivatives by interleaving transformation and optimization stages, and utilizing optic constructions to maintain composability and optimize data flow.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If reverse-mode or mixed-mode automatic differentiation is used to compute derivatives, then the derivative can be combined with additional information at a later point in execution, but memory usage and computation increase significantly
Solution Approach 1:
The patent segments the non-local derivative computation into local transformation stages using opaque closures. Each closure captures only the necessary local state and transforms it independently, avoiding the need to hold entire non-local computation paths in memory simultaneously. This segmentation reduces memory usage while preserving derivative computation accuracy.
Solution Approach 2:
The patent performs preliminary local transformations on data before it becomes needed for the final derivative computation. By pre-processing and transforming data locally using opaque closures, the system prepares information in advance, reducing the need to store and reprocess large amounts of data during the actual derivative computation, thereby reducing memory usage.
2Measurement precision
If reverse-mode or mixed-mode automatic differentiation is used to compute derivatives, then non-local information flow is enabled, but unnecessary computation increases
Solution Approach 1:
The patent applies local quality by making each transformation stage local rather than non-local. Opaque closures ensure that each transformation operates on localized data with captured environment, allowing the compiler to optimize each local transformation independently. This eliminates unnecessary computation by ensuring each local transformation only processes the specific data it needs, rather than propagating information globally.
Solution Approach 2:
The patent extracts the essential transformation logic into opaque closures that capture only the necessary environment and state. By extracting and isolating the critical computation steps into self-contained closure units, the system eliminates redundant computation steps that would otherwise be required to maintain non-local information flow, improving computation efficiency while preserving derivative accuracy.
3Productivity
If traditional compiler optimizations are applied to non-local transformation problems, then compilation speed may be improved, but the non-local nature of the problem prevents effective optimization
Solution Approach 1:
The patent introduces dynamics by using opaque closures that can adaptively capture and transform environment state. The closures dynamically adjust to the local context in which they are defined, allowing compiler optimizations to work effectively on each local transformation stage. This dynamic approach transforms the rigid non-local problem into flexible local transformations that can be optimized by traditional compiler techniques, improving compilation speed while managing transformation complexity.
Solution Approach 2:
The patent introduces opaque closures as intermediaries between the non-local derivative computation and local optimization passes. These closures act as mediators that encapsulate non-local dependencies, allowing traditional compiler optimizations to operate on the local code without being hindered by non-local constraints. This intermediary layer enables effective optimization while preserving the necessary transformation complexity for accurate derivative computation.
Data Source
AI summary
Systems and methods for using compiler transforms to transform a non-local function into a local function are disclosed. The systems and methods perform a dynamic inter-procedural analysis before performing reverse-mode automatic differentiation. The dynamic inter-procedural analysis is performed to determine a maximum set of computer program information. A non-local to local transformation is applied to the determined maximum set of computer program information, and each original instruction is mapped to an optic that is represented as an opaque closure in the transformed local function.