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🏛️ Architect: Extract generic optimization module#625

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architect-optimization-refactor-8598226063567658698
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🏛️ Architect: Extract generic optimization module#625
fderuiter wants to merge 2 commits intomainfrom
architect-optimization-refactor-8598226063567658698

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This PR performs a "Module Extraction" refactoring by moving the mathematical implementation of optimization algorithms (SGD, Adam) from the AI-specific modules (ai::optimization, ai::sds::training) to a new, generic pure_math::optimization module.

Changes:

  1. New Module: math_explorer/src/pure_math/optimization.rs defines a generic Optimizer<P> trait and implements SGD and Adam structs that work with nalgebra types (DMatrix, DVector).
  2. Refactoring: math_explorer/src/ai/optimization.rs now delegates the mathematical updates to the new module, while maintaining its layer-based state management logic.
  3. Cleanup: Duplicate implementations in math_explorer/src/ai/sds/training.rs were removed and replaced with the core primitives.
  4. Verification: All tests passed (cargo test pure_math::optimization, cargo test ai).

Impact:

  • Reduces code duplication.
  • Decouples optimization logic from neural network topology.
  • Makes optimization algorithms reusable for other domains (e.g., Physics simulations, Curve fitting).

PR created automatically by Jules for task 8598226063567658698 started by @fderuiter

- Extracted `SGD` and `Adam` to `math_explorer/src/pure_math/optimization.rs`.
- Defined generic `Optimizer<P>` trait.
- Refactored `math_explorer/src/ai/optimization.rs` to wrap core primitives.
- Refactored `math_explorer/src/ai/sds/training.rs` to use `pure_math` implementations.
- Removed duplicated code and improved error handling.
- Added architectural decision record in `.jules/architect.md`.

Co-authored-by: google-labs-jules[bot] <161369871+google-labs-jules[bot]@users.noreply.github.com>
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… formatting

- Extracted `SGD` and `Adam` to `math_explorer/src/pure_math/optimization.rs`.
- Defined generic `Optimizer<P>` trait.
- Refactored `math_explorer/src/ai/optimization.rs` to wrap core primitives.
- Refactored `math_explorer/src/ai/sds/training.rs` to use `pure_math` implementations.
- Removed duplicated code and improved error handling.
- Fixed `cargo fmt` errors in modified files.
- Added architectural decision record in `.jules/architect.md`.

Co-authored-by: google-labs-jules[bot] <161369871+google-labs-jules[bot]@users.noreply.github.com>
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