Add backlog item for parameter tying investigation and CIP creation

backlog/infrastructure/2025-08-15_parameter-tying-framework.md

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+---
+id: "parameter-tying-framework"
+title: "Design parameter tying framework for GPy multioutput kernels"
+status: "Ready"
+priority: "High"
+created: "2025-08-15"
+last_updated: "2025-08-15"
+owner: "Neil Lawrence"
+github_issue: ""
+dependencies: ""
+tags:
+- parameter-tying
+- multioutput
+- kernel-framework
+- architecture
+---
+
+# Investigate parameter tying limitations and create CIP for discussion
+
+## Description
+
+During LFM kernel code review, we identified that GPy lacks systematic parameter tying capabilities compared to GPmat's `modelTieParam()` functionality. This limitation affects combination kernels such as multiouptut or additive kernels. We need to investigate the scope of this problem and create a CIP to discuss potential solutions with the community.
+
+## Problem Statement
+
+- **Current Limitation**: GPy's parameter system doesn't support tying parameters across different kernel components
+- **Impact on LFM**: Forces complex parameter handling in EQ_ODE1 and EQ_ODE2 kernels
+- **Broader Impact**: May affect other multiple kernel scenarios where parameters should be shared
+- **Comparison**: GPmat has `modelTieParam()` functionality that GPy lacks
+
+## Investigation Needed
+
+### 1. Scope Assessment
+- [ ] Search existing GitHub issues for parameter tying discussions
+- [ ] Identify other kernels/models that could benefit from parameter tying
+- [ ] Assess impact on current GPy codebase
+
+
+### 2. Community Input
+- [ ] Create GitHub issue and associated CIP to discuss parameter tying needs
+- [ ] Gather feedback from GPy maintainers and users
+- [ ] Identify use cases beyond LFM kernels
+- [ ] Assess priority relative to other GPy improvements
+
+### 3. Technical Analysis
+- [ ] Analyze GPmat's parameter tying implementation
+- [ ] Review GPy's current parameter system architecture
+- [ ] Identify potential integration points
+- [ ] Assess complexity and maintenance burden
+
+## Acceptance Criteria
+
+- [ ] Complete investigation of existing GitHub issues and discussions
+- [ ] Document scope of parameter tying needs across GPy
+- [ ] Create CIP for parameter tying framework discussion
+- [ ] Gather community feedback on approach and priority
+- [ ] Provide recommendations for next steps
+
+## Implementation Notes
+
+- Focus on problem identification and community discussion
+- Avoid prescribing specific solutions until community input is gathered
+- Consider whether this should be a separate CIP or part of broader multioutput improvements
+- Document trade-offs between different approaches
+
+## Related
+
+- CIP: 0001 (LFM kernel implementation) - may depend on parameter tying
+- GPy parameter system design
+- GPmat parameter tying implementation
+- Multioutput kernel architecture discussions
+
+## Progress Updates
+
+### 2025-08-15
+Task created after identifying parameter tying as a potential limitation during LFM kernel code review. Need to investigate scope and create CIP for community discussion.