Add LFM kernel implementation backlog items

- Add code review task for existing LFM implementations
- Add design task for modern LFM kernel architecture
- Add implementation task for core LFM kernel functionality
- Establish clear task dependencies and acceptance criteria
- Link to CIP-0001 and relevant papers

backlog/features/2025-08-15_lfm-kernel-code-review.md

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+---
+id: "lfm-kernel-code-review"
+title: "Review existing LFM kernel implementations"
+status: "Ready"
+priority: "High"
+created: "2025-08-15"
+last_updated: "2025-08-15"
+owner: "Neil Lawrence"
+dependencies: []
+tags:
+- lfm
+- kernel
+- code-review
+- documentation
+---
+
+# Review existing LFM kernel implementations
+
+## Description
+Conduct a comprehensive review of existing LFM (Latent Force Model) kernel implementations in both GPy and MATLAB to understand the current state, design decisions, and limitations.
+
+## Background
+- GPy has existing ODE-based kernels (`EQ_ODE1`, `EQ_ODE2`) that implement LFM concepts
+- MATLAB implementation in GPmat provides a more complete LFM framework
+- Need to understand differences and identify modernization opportunities
+
+## Tasks
+- [ ] Review `GPy/kern/src/eq_ode1.py` and `eq_ode2.py` implementations
+- [ ] Analyze MATLAB LFM implementation structure and patterns
+- [ ] Document current limitations and inconsistencies
+- [ ] Identify reusable components and design patterns
+- [ ] Compare parameter handling approaches
+- [ ] Review cross-kernel computation methods
+- [ ] Document mathematical foundations and implementation details
+
+## Acceptance Criteria
+- [ ] Complete documentation of existing implementations
+- [ ] Clear understanding of design differences between GPy and MATLAB versions
+- [ ] Identified list of modernization opportunities
+- [ ] Documentation of mathematical foundations
+- [ ] Assessment of current limitations and bugs
+
+## Implementation Notes
+- Focus on understanding the mathematical foundations from the papers
+- Pay attention to parameter tying and multi-output handling
+- Document the differential equation structure and kernel computation
+- Identify opportunities for using GPy's modern multioutput kernel approach
+
+## Related
+- CIP: 0001 (LFM kernel implementation)
+- Papers: Álvarez et al. (2009, 2012), Lawrence et al. (2006)