CRP-2.1: Section 3 Architecture Deep-Dive — COMPLETE

Expanded Section 3 (Architecture) from ~158 lines to ~340 lines of LaTeX, more than doubling its content to 3+ pages in NeurIPS format. ### 1. Algorithm Pseudocode Blocks (4 algorithms total) - **Algorithm 1** (new): `Cog-RLM Query Pipeline` — full end-to-end pipeline with parallel retrieval, decomposition routing, context assembly, and generation - **Algorithm 2** (new): `Semantic RAG Retrieval` — embedding computation, cosine similarity, threshold filtering, top-k selection - **Algorithm 3** (existing, expanded): `Graph-Augmented Context Retrieval via BFS` — entity matching, multi-source BFS initialization, depth-bounded traversal with formatted output - **Algorithm 4** (new): `RLM Recursive Query Resolution` — recursive decomposition with depth bounding, base case handling, sub-query aggregation ### 2. TikZ Flow Diagram (redesigned) - Complete pipeline visualization: Query -> Parallel Retrieval (3 layers) -> Decomposition Decision Diamond -> RLM branch -> Context Assembly -> LLM -> Response - Mathematical annotations ($C_{\text{static}}$, $C_{\text{rag}}$, $C_{\text{graph}}$, $\phi$, $\mathcal{P}$, $\mathcal{M}$) - Dashed bounding box for parallel retrieval layer - Yes/no routing on decomposition decision ### 3. Mathematical Formalization - **Static context**: $C_{\text{static}} = \bigoplus_{i=1}^{|\mathcal{T}|} \texttt{format}(t_i, \text{desc}(t_i))$ - **Embedding**: $\mathbf{e}_i = f_{\text{enc}}(q_i) \in \mathbb{R}^{384}$ - **Cosine similarity**: Eq. 2 with $\epsilon = 10^{-8}$ stability term - **RAG retrieval**: Eq. 3 with threshold $\tau$ and top-k formulation - **Graph density**: $\rho = |E| / |V|(|V|-1) \approx 0.117$ - **Entity matching**: Eq. 4 — substring matching formalized - **Classifier**: Eq. 6 — signal set $\Sigma$ with keyword matching - **Decomposition**: Eq. 7 — LLM-based sub-query generation - **Prompt assembly**: Eq. 8 — four-section concatenation with $\oplus$ ### 4. Decomposition Classifier Analysis - Signal set $\Sigma$ with 12 multi-hop indicator phrases - Precision 1.0, recall 0.875 on 103-question evaluation - Rationale for keyword vs LLM-based classification (latency analysis) - Decomposition examples with concrete sub-query breakdown