Tensor Graph Splitting for Homomorphic Encryption Efficiency
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Solution Overview
Problem
Existing homomorphic encryption schemes face inefficiencies in performing complex computations due to conflicts in packing shapes during matrix multiplications, leading to costly reshape operations and increased runtime and memory usage.
Innovation Solution
The method involves splitting a graph of operations on tensors into even and odd vertical layers, filling even-even or odd-odd connections using a reshape operation, initializing outputs with a random packing data structure shape, and executing a breadth-first search based on a minimum number of shapes per layer to optimize computations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If homomorphic encryption schemes perform complex computations using traditional methods, then computation can be completed, but runtime and memory usage increase significantly due to reshape operations
Solution Approach 1:
The patent segments the computation graph into even and odd vertical layers, allowing independent optimization of each layer type. This segmentation enables the system to avoid costly reshape operations by keeping even layers connected to even layers and odd layers to odd layers, thereby reducing runtime while maintaining computation completeness
Solution Approach 2:
The patent performs preliminary actions by pre-assigning shapes to even and odd layer outputs before execution. By initializing outputs with predetermined shapes and using breadth-first search to determine optimal shape assignments in advance, the system eliminates the need for runtime reshape operations, significantly reducing execution time
2Productivity
If homomorphic encryption schemes perform complex computations using traditional methods, then computation can be completed, but memory usage increases due to reshape operations
Solution Approach 1:
By dividing the computation into even and odd vertical layers with distinct shape assignments, the patent reduces memory overhead. Each layer type maintains its own shape conventions, eliminating the need to store multiple shape representations for the same tensor, thereby reducing memory usage while preserving computational capabilities
Solution Approach 2:
The patent changes the shape parameter assignments for even and odd layers systematically. By establishing that even layers use one shape convention and odd layers use another, the system avoids the memory overhead of storing multiple shape configurations, reducing memory usage while maintaining computational flexibility
3Reliability
If packing shapes are enforced strictly during matrix multiplications, then data integrity is maintained, but computation cost increases due to reshape operations
Solution Approach 1:
The patent segments the graph into even and odd vertical layers, allowing each layer type to maintain its own shape conventions independently. This segmentation preserves data integrity within each layer type while avoiding costly reshape operations between layers, as even layers connect to even layers and odd layers to odd layers
Solution Approach 2:
Instead of enforcing uniform shape constraints across all layers (traditional approach), the patent inverts the approach by allowing different shape conventions for even and odd layers. This inversion maintains data integrity through consistent shape management within each layer type while eliminating the need for expensive reshape operations
4Ease of manufacture
If uniform shape constraints are applied across all layers, then implementation is simplified, but flexibility in optimizing computation graphs is reduced
Solution Approach 1:
The patent segments the computation graph into even and odd vertical layers, providing a balanced approach between simplicity and flexibility. Each segment follows simple shape conventions, maintaining implementation ease, while the segmented structure enables flexible optimization by allowing different shape assignments for different layer types
Solution Approach 2:
The patent applies local quality by allowing different shape conventions in different parts of the system (even layers versus odd layers). This enables each layer type to be optimized independently with appropriate shape assignments, providing flexibility while maintaining local simplicity through consistent shape management within each layer type
Data Source
AI summary
An example system includes a processor to split a graph of operations on tensors into even and odd vertical layers. In response to detecting even-even or odd-odd connections, the processor can fill the even-even or odd-odd connections using a reshape operation. The processor can also initialize outputs on a same layer type with a random packing data structure shape from a first group. The processor can then execute a breadth-first search backward based on a minimum number of shapes per layer.