BlakeHastings Recursive Learning Models (RLM)
Overview
This skill enables deep exploration of Recursive Learning Models — a paradigm shift in machine learning that empowers systems to iteratively refine their outputs through multi-step reasoning, feedback loops, self-correction mechanisms, and preference-based optimization. RLM represents the evolution from static feed-forward approaches to dynamic, iterative learning systems capable of deeper cognitive processing.
Core Capabilities
1. PRefLexOR Analysis
- Preference-Based Recursive Language Modeling for exploratory optimization of reasoning and agentic thinking
- Thinking tokens framework with iterative feedback loops
- Multi-stage training: preference alignment + rejection sampling refinement
- Dynamic knowledge graph construction through question generation from text chunks
- Rejection sampling for in-situ training data generation while masking reasoning steps
2. Mixture-of-Recursions (MoR) Analysis
- Learning Dynamic Recursive Depths for adaptive token-level computation
- Unified recursive transformer framework with shared layers across recursion steps
- Lightweight routers assigning different recursion depths to individual tokens
- Selective caching of key-value pairs for memory efficiency
- KV sharing variants reusing cached representations from first recursion
3. Vertical LoRA Analysis
- Dense Expectation-Maximization Interpretation of transformers as recursive Bayesian networks
- Each layer recursively learning increments based on prior layer computations
- Orthogonal low-rank adaptation combining with existing LoRA methods
- Dramatic parameter reduction while preserving model performance
4. Graph-PReFLexOR Analysis
- In-situ graph reasoning and knowledge expansion using symbolic abstraction
- Category theory-inspired concept encoding as nodes with relationship edges
- Hierarchical inference through isomorphic representations
- Knowledge garden growth strategy for interdisciplinary connections
- Hypothesis generation, materials design, creative cross-domain reasoning
Research Foundations
Original Papers
- RET-LLM (arXiv:2305.14322) - Initial write-read memory framework with triplet-based knowledge extraction and Davidsonian semantics inspiration
- MemLLM - Evolved, thoroughly evaluated successor to RET-LLM
Key Derivations Timeline
| Year | Paper | arXiv ID | Primary Contribution |
|---|---|---|---|
| 2009 | Stochastic Recursive Learning (Finance) | 0910.1166 | Convergence guarantees for stochastic recursive procedures |
| 2010 | Optimized RNN Algorithm | 1004.1997 | Matrix operations for online learning without manual rate selection |
| 2021 | Transfer-Recursive Ensemble (COVID) | 2108.09131 | Multi-day forecasting with recursive refinement |
| 2022 | Recursive 3D Segmentation | 2203.07846 | Iterative label improvement for medical imaging |
| 2023 | Koopman Operator Learning | 2309.04074 | Data-driven nonlinear system representation |
| 2024 | Stability-Certified LQR | 2403.05367 | Lyapunov-based stability guarantees for recursive learning |
| 2024 | Vertical LoRA | 2406.09315 | EM interpretation of transformers as recursive BNs |
| 2024 | PRefLexOR | 2410.12375 | Preference-based recursive language modeling |
| 2025 | Graph-PReFLexOR | 2501.08120 | Symbolic abstraction with graph reasoning |
| 2025 | Mixture-of-Recursions | 2507.10524 | Adaptive token-level computation depths |
Control Systems Applications
- Tiwari et al. (arXiv:2309.04074): Koopman operator theory with deep learning recursive representation for system identification
- Sforni et al. (arXiv:2403.05367): Stability-certified LQR via recursive least squares + policy gradient with Lyapunov guarantees
Domain Applications Summary
| Domain | Application | Key Innovation |
|---|---|---|
| Medical Imaging | 3D Shoulder Joint Segmentation | Iterative label refinement reducing segmentation errors |
| Time Series | COVID-19 Multi-Day Forecasting | Transfer learning + recursive ensemble predictions |
| Control Systems | Aircraft LQR with Drifting Parameters | Stability-certified on-policy learning |
| State-Space Models | Online Variational Inference | Sequential Monte Carlo for streaming data |
Analysis Frameworks
Iterative Refinement Loop Pattern
Initial Output → Critique/Feedback → Adjustment → Re-evaluation → Final Output
Recursive State Updates
- Each iteration builds upon previous computations
- Contextual information maintained through recursive state variables
- Progressive improvement rather than single-pass processing
Feedback Loop Architectures
- Closed-loop refinement: Continuous feedback within single inference pass
- Multi-round sampling: Multiple independent generation attempts with selection
- Cross-model ensemble: Combining predictions from different model instances
Methodological Components
| Component | Description | Use Case |
|---|---|---|
| Thinking Tokens | Explicit modeling of intermediate computational states | Reflective processing, self-correction |
| Rejection Sampling | Quality control mechanism for iterative refinement | Ensuring output quality across iterations |
| Preference Optimization | RL-style optimization with preferred/non-preferred response comparison | Aligning reasoning paths with accurate solutions |
| Dynamic Depth Selection | Router-based assignment of different recursion depths per token | Computational efficiency optimization |
| Graph Reasoning Integration | Symbolic abstraction supporting hierarchical inference | Cross-domain knowledge connection and expansion |
Available Operations
analyze-paper [paper-name]
Analyze a specific RLM paper or derivation in depth, extracting methodology, key innovations, theoretical foundations, and practical implications.
Example: /rml analyze-paper PRefLexOR
compare-methods [method1] [method2] ...
Compare multiple RLM approaches side-by-side, highlighting differences in architecture, computational efficiency, applicability domains, and trade-offs.
Example: /rml compare-methods Mixture-of-Recursions Vertical-LoRA PRefLexOR
design-recursive-system [domain]
Design a recursive learning system for a specific application domain (e.g., scientific discovery, control systems, time series forecasting).
Example: /rml design-recursive-system materials-science-discovery
troubleshoot-convergence [issue-description]
Diagnose convergence issues in recursive learning algorithms, providing theoretical explanations and practical solutions.
Example: /rml troubleshoot-convergence error-propagation-through-deep-recursion-layers
evaluate-applicability [use-case]
Evaluate whether RLM approaches are suitable for a specific use case, recommending the most appropriate framework and identifying potential challenges.
Example: /rml evaluate-applicability multi-modal-reasoning-vision-language-models
Process for Analysis
- Discovery: Parse arguments to identify target(s) and operation type
- Literature Search: Use WebFetch to retrieve