# GeoXGB Optimization Ideas (Fitting Speed)

This document outlines architectural and engineering strategies to accelerate GeoXGB fitting, specifically for the high-round counts (e.g., 2,000+) used with low learning rates (e.g., 0.02) where standard models would typically overfit.

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### 1. Adaptive Geometric Refitting (Geometric "Momentum")
The current `refit_interval` is static. At high round counts, the gradient landscape often stabilizes, making frequent HVRT geometry updates redundant.

*   **Mechanism:** Monitor the **Cosine Similarity** between the current gradient vector $
abla L_i$ and the gradient vector from the last refit $
abla L_{refit}$. 
*   **Strategy:** Skip the scheduled HVRT refit if similarity remains high (e.g., $>0.98$). 
*   **Impact:** Reduces $O(N^2 D)$ HVRT geometry calculations by 50–80% in the later stages of boosting without sacrificing the "freshness" of the sample distribution.

### 2. SIMD-Vectorized Tree Traversal (C++ Backend)
In the high-round regime, the $O(N \cdot 	ext{n\_rounds})$ prediction update step dominates the total runtime.

*   **Mechanism:** Implement **horizontal bit-parallel tree traversal** using AVX-512 or AVX2 in the C++ backend.
*   **Strategy:** Process 8 (AVX2) or 16 (AVX512) samples in parallel. Pack split thresholds and feature indices into registers and use mask-registers to handle branching.
*   **Impact:** Speeds up the `preds_on_X += lr * tree.predict(X)` step by 4–6x, which is the most frequent operation in the loop.

### 3. Cache-Friendly Histogram Re-use
The C++ backend bins $X$ once, but subsetting the `X_bin_full_` matrix during every refit can cause significant cache misses due to random memory access.

*   **Mechanism:** Sort the `red_idx` vector before performing the subsetting operation.
*   **Strategy:** Ensures linear memory access patterns during `X_bin_r.row(s) = X_bin_full_.row(red_idx[s])`.
*   **Impact:** Improves cache locality during the data-intensive tree-building phase, reducing memory latency.

### 4. Geometric "Warm-starting" for HVRT
Currently, each `HVRT.fit()` in the `do_resample` call performs a full whitening and partition tree build from scratch.

*   **Mechanism:** Use the previous round's partition tree as a **Warm-Start** for the next.
*   **Strategy:** Instead of re-building the tree, update only the **leaf statistics** (mean-abs-z, variance) based on the new gradients. Only "re-grow" or "prune" branches where the variance shift exceeds a threshold.
*   **Impact:** Converts an $O(N \log N)$ tree build into an $O(N)$ update for most refit intervals.

### 5. Multi-Level Pipeline Parallelism
The C++ backend uses OpenMP for `predict_from_trees` (parallelizing over trees), but the main `fit_boosting` loop remains sequential.

*   **Mechanism:** Parallelize the **Gradient + Prediction Update** step using a background thread.
*   **Strategy:** While the weak learner is fitting on the current subset $X_r$, use a background thread to calculate `predict(X)` for the *previous* round's tree.
*   **Impact:** Hides the latency of updating predictions on the full dataset, effectively making the $O(N)$ prediction step "free" if the tree-fit on the subset takes longer.

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**Recommended Implementation Order:**
1.  **Strategy 1 (Adaptive Refit):** Largest algorithmic reduction in $O(N^2)$ operations.
2.  **Strategy 2 (SIMD Traversal):** Largest engineering speedup for the bottleneck $O(N \cdot 	ext{Rounds})$ step.
