Sunset gkr square

[zhiyong1997]

The GKR Square Scheme improves the performance of pow gate. However, it also introduces additional overhead to the ScratchPad, which we found is a major memory bottleneck for ZKML application. We'll temporarily sunset GKR Square, and find a better way to integrate it in the future.

[gemini-code-assist]

Summary of Changes

Hello @zhiyong1997, I'm Gemini Code Assist¹! I'm currently reviewing this pull request and will post my feedback shortly. In the meantime, here's a summary to help you and other reviewers quickly get up to speed!

This pull request deprecates and removes the GKR Square scheme from the project. While the scheme offered performance improvements for 'pow' gates, it introduced substantial memory overhead, which proved to be a critical bottleneck for ZKML applications. The current approach is to sunset this implementation to improve overall memory efficiency, with a commitment to explore and integrate a more optimized version of GKR Square in subsequent development phases.

Highlights

• GKR Square Scheme Sunset: The GKR Square scheme, which previously aimed to improve the performance of 'pow' gates, has been removed from the codebase.
• Memory Optimization Focus: This removal is a strategic decision to alleviate significant memory overhead identified as a major bottleneck for Zero-Knowledge Machine Learning (ZKML) applications.
• Future Reintegration Plans: The team plans to re-evaluate and re-integrate the GKR Square scheme in the future, focusing on a more memory-efficient implementation.
• Codebase Simplification: Associated configurations, benchmark entries, prover/verifier logic, and helper modules specific to GKR Square have been cleaned up or removed, simplifying the codebase.

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[gemini-code-assist]

Code Review

This pull request successfully removes the GKR Square scheme, which was identified as a memory bottleneck. The changes are comprehensive, touching configurations, benchmarks, tests, and the core prover/verifier logic. The removal is clean and also introduces a beneficial memory optimization for the ProverScratchPad. I've identified one critical issue regarding a missing import that would cause a compilation failure, along with a couple of medium-severity refactoring opportunities to simplify the code now that GKRScheme has only one variant.