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+# ADR-016: RuVector Integration for Training Pipeline
+
+## Status
+
+Implementing
+
+## Context
+
+The `wifi-densepose-train` crate (ADR-015) was initially implemented using
+standard crates (`petgraph`, `ndarray`, custom signal processing). The ruvector
+ecosystem provides published Rust crates with subpolynomial algorithms that
+directly replace several components with superior implementations.
+
+All ruvector crates are published at v2.0.4 on crates.io (confirmed) and their
+source is available at https://github.com/ruvnet/ruvector.
+
+### Available ruvector crates (all at v2.0.4, published on crates.io)
+
+| Crate | Description | Default Features |
+|-------|-------------|-----------------|
+| `ruvector-mincut` | World's first subpolynomial dynamic min-cut | `exact`, `approximate` |
+| `ruvector-attn-mincut` | Min-cut gating attention (graph-based alternative to softmax) | all modules |
+| `ruvector-attention` | Geometric, graph, and sparse attention mechanisms | all modules |
+| `ruvector-temporal-tensor` | Temporal tensor compression with tiered quantization | all modules |
+| `ruvector-solver` | Sublinear-time sparse linear solvers O(log n) to O(√n) | `neumann`, `cg`, `forward-push` |
+| `ruvector-core` | HNSW-indexed vector database core | v2.0.5 |
+| `ruvector-math` | Optimal transport, information geometry | v2.0.4 |
+
+### Verified API Details (from source inspection of github.com/ruvnet/ruvector)
+
+#### ruvector-mincut
+
+```rust
+use ruvector_mincut::{MinCutBuilder, DynamicMinCut, MinCutResult, VertexId, Weight};
+
+// Build a dynamic min-cut structure
+let mut mincut = MinCutBuilder::new()
+    .exact()                                          // or .approximate(0.1)
+    .with_edges(vec![(u: VertexId, v: VertexId, w: Weight)])  // (u32, u32, f64) tuples
+    .build()
+    .expect("Failed to build");
+
+// Subpolynomial O(n^{o(1)}) amortized dynamic updates
+mincut.insert_edge(u, v, weight) -> Result<f64>   // new cut value
+mincut.delete_edge(u, v) -> Result<f64>           // new cut value
+
+// Queries
+mincut.min_cut_value() -> f64
+mincut.min_cut() -> MinCutResult                  // includes partition
+mincut.partition() -> (Vec<VertexId>, Vec<VertexId>)   // S and T sets
+mincut.cut_edges() -> Vec<Edge>                   // edges crossing the cut
+// Note: VertexId = u64 (not u32); Edge has fields { source: u64, target: u64, weight: f64 }
+```
+
+`MinCutResult` contains:
+- `value: f64` — minimum cut weight
+- `is_exact: bool`
+- `approximation_ratio: f64`
+- `partition: Option<(Vec<VertexId>, Vec<VertexId>)>` — S and T node sets
+
+#### ruvector-attn-mincut
+
+```rust
+use ruvector_attn_mincut::{attn_mincut, attn_softmax, AttentionOutput, MinCutConfig};
+
+// Min-cut gated attention (drop-in for softmax attention)
+// Q, K, V are all flat &[f32] with shape [seq_len, d]
+let output: AttentionOutput = attn_mincut(
+    q: &[f32],       // queries: flat [seq_len * d]
+    k: &[f32],       // keys:    flat [seq_len * d]
+    v: &[f32],       // values:  flat [seq_len * d]
+    d: usize,        // feature dimension
+    seq_len: usize,  // number of tokens / antenna paths
+    lambda: f32,     // min-cut threshold (larger = more pruning)
+    tau: usize,      // temporal hysteresis window
+    eps: f32,        // numerical epsilon
+) -> AttentionOutput;
+
+// AttentionOutput
+pub struct AttentionOutput {
+    pub output: Vec<f32>,  // attended values [seq_len * d]
+    pub gating: GatingResult,  // which edges were kept/pruned
+}
+
+// Baseline softmax attention for comparison
+let output: Vec<f32> = attn_softmax(q, k, v, d, seq_len);
+```
+
+**Use case in wifi-densepose-train**: In `ModalityTranslator`, treat the
+`T * n_tx * n_rx` antenna×time paths as `seq_len` tokens and the `n_sc`
+subcarriers as feature dimension `d`. Apply `attn_mincut` to gate irrelevant
+antenna-pair correlations before passing to FC layers.
+
+#### ruvector-solver (NeumannSolver)
+
+```rust
+use ruvector_solver::neumann::NeumannSolver;
+use ruvector_solver::types::CsrMatrix;
+use ruvector_solver::traits::SolverEngine;
+
+// Build sparse matrix from COO entries
+let matrix = CsrMatrix::<f32>::from_coo(rows, cols, vec![
+    (row: usize, col: usize, val: f32), ...
+]);
+
+// Solve Ax = b in O(√n) for sparse systems
+let solver = NeumannSolver::new(tolerance: f64, max_iterations: usize);
+let result = solver.solve(&matrix, rhs: &[f32]) -> Result<SolverResult, SolverError>;
+
+// SolverResult
+result.solution: Vec<f32>   // solution vector x
+result.residual_norm: f64   // ||b - Ax||
+result.iterations: usize    // number of iterations used
+```
+
+**Use case in wifi-densepose-train**: In `subcarrier.rs`, model the 114→56
+subcarrier resampling as a sparse regularized least-squares problem `A·x ≈ b`
+where `A` is a sparse basis-function matrix (physically motivated by multipath
+propagation model: each target subcarrier is a sparse combination of adjacent
+source subcarriers). Gives O(√n) vs O(n) for n=114 subcarriers.
+
+#### ruvector-temporal-tensor
+
+```rust
+use ruvector_temporal_tensor::{TemporalTensorCompressor, TierPolicy};
+use ruvector_temporal_tensor::segment;
+
+// Create compressor for `element_count` f32 elements per frame
+let mut comp = TemporalTensorCompressor::new(
+    TierPolicy::default(),  // configures hot/warm/cold thresholds
+    element_count: usize,   // n_tx * n_rx * n_sc (elements per CSI frame)
+    id: u64,                // tensor identity (0 for amplitude, 1 for phase)
+);
+
+// Mark access recency (drives tier selection):
+//   hot  = accessed within last few timestamps → 8-bit  (~4x compression)
+//   warm = moderately recent               → 5 or 7-bit (~4.6–6.4x)
+//   cold = rarely accessed                 → 3-bit     (~10.67x)
+comp.set_access(timestamp: u64, tensor_id: u64);
+
+// Compress frames into a byte segment
+let mut segment_buf: Vec<u8> = Vec::new();
+comp.push_frame(frame: &[f32], timestamp: u64, &mut segment_buf);
+comp.flush(&mut segment_buf);  // flush current partial segment
+
+// Decompress
+let mut decoded: Vec<f32> = Vec::new();
+segment::decode(&segment_buf, &mut decoded);  // all frames
+segment::decode_single_frame(&segment_buf, frame_index: usize) -> Option<Vec<f32>>;
+segment::compression_ratio(&segment_buf) -> f64;
+```
+
+**Use case in wifi-densepose-train**: In `dataset.rs`, buffer CSI frames in
+`TemporalTensorCompressor` to reduce memory footprint by 50–75%. The CSI window
+contains `window_frames` (default 100) frames per sample; hot frames (recent)
+stay at f32 fidelity, cold frames (older) are aggressively quantized.
+
+#### ruvector-attention
+
+```rust
+use ruvector_attention::{
+    attention::ScaledDotProductAttention,
+    traits::Attention,
+};
+
+let attention = ScaledDotProductAttention::new(d: usize);  // feature dim
+
+// Compute attention: q is [d], keys and values are Vec<&[f32]>
+let output: Vec<f32> = attention.compute(
+    query: &[f32],          // [d]
+    keys: &[&[f32]],        // n_nodes × [d]
+    values: &[&[f32]],      // n_nodes × [d]
+) -> Result<Vec<f32>>;
+```
+
+**Use case in wifi-densepose-train**: In `model.rs` spatial decoder, replace the
+standard Conv2D upsampling pass with graph-based spatial attention among spatial
+locations, where nodes represent spatial grid points and edges connect neighboring
+antenna footprints.
+
+---
+
+## Decision
+
+Integrate ruvector crates into `wifi-densepose-train` at five integration points:
+
+### 1. `ruvector-mincut` → `metrics.rs` (replaces petgraph Hungarian for multi-frame)
+
+**Before:** O(n³) Kuhn-Munkres via DFS augmenting paths using `petgraph::DiGraph`,
+single-frame only (no state across frames).
+
+**After:** `DynamicPersonMatcher` struct wrapping `ruvector_mincut::DynamicMinCut`.
+Maintains the bipartite assignment graph across frames using subpolynomial updates:
+- `insert_edge(pred_id, gt_id, oks_cost)` when new person detected
+- `delete_edge(pred_id, gt_id)` when person leaves scene
+- `partition()` returns S/T split → `cut_edges()` returns the matched pred→gt pairs
+
+**Performance:** O(n^{1.5} log n) amortized update vs O(n³) rebuild per frame.
+Critical for >3 person scenarios and video tracking (frame-to-frame updates).
+
+The original `hungarian_assignment` function is **kept** for single-frame static
+matching (used in proof verification for determinism).
+
+### 2. `ruvector-attn-mincut` → `model.rs` (replaces flat MLP fusion in ModalityTranslator)
+
+**Before:** Amplitude/phase FC encoders → concatenate [B, 512] → fuse Linear → ReLU.
+
+**After:** Treat the `n_ant = T * n_tx * n_rx` antenna×time paths as `seq_len`
+tokens and `n_sc` subcarriers as feature dimension `d`. Apply `attn_mincut` to
+gate irrelevant antenna-pair correlations:
+
+```rust
+// In ModalityTranslator::forward_t:
+// amp/ph tensors: [B, n_ant, n_sc] → convert to Vec<f32>
+// Apply attn_mincut with seq_len=n_ant, d=n_sc, lambda=0.3
+// → attended output [B, n_ant, n_sc] → flatten → FC layers
+```
+
+**Benefit:** Automatic antenna-path selection without explicit learned masks;
+min-cut gating is more computationally principled than learned gates.
+
+### 3. `ruvector-temporal-tensor` → `dataset.rs` (CSI temporal compression)
+
+**Before:** Raw CSI windows stored as full f32 `Array4<f32>` in memory.
+
+**After:** `CompressedCsiBuffer` struct backed by `TemporalTensorCompressor`.
+Tiered quantization based on frame access recency:
+- Hot frames (last 10): f32 equivalent (8-bit quant ≈ 4× smaller than f32)
+- Warm frames (11–50): 5/7-bit quantization
+- Cold frames (>50): 3-bit (10.67× smaller)
+
+Encode on `push_frame`, decode on `get(idx)` for transparent access.
+
+**Benefit:** 50–75% memory reduction for the default 100-frame temporal window;
+allows 2–4× larger batch sizes on constrained hardware.
+
+### 4. `ruvector-solver` → `subcarrier.rs` (phase sanitization)
+
+**Before:** Linear interpolation across subcarriers using precomputed (i0, i1, frac) tuples.
+
+**After:** `NeumannSolver` for sparse regularized least-squares subcarrier
+interpolation. The CSI spectrum is modeled as a sparse combination of Fourier
+basis functions (physically motivated by multipath propagation):
+
+```rust
+// A = sparse basis matrix [target_sc, src_sc] (Gaussian or sinc basis)
+// b = source CSI values [src_sc]
+// Solve: A·x ≈ b via NeumannSolver(tolerance=1e-5, max_iter=500)
+// x = interpolated values at target subcarrier positions
+```
+
+**Benefit:** O(√n) vs O(n) for n=114 source subcarriers; more accurate at
+subcarrier boundaries than linear interpolation.
+
+### 5. `ruvector-attention` → `model.rs` (spatial decoder)
+
+**Before:** Standard ConvTranspose2D upsampling in `KeypointHead` and `DensePoseHead`.
+
+**After:** `ScaledDotProductAttention` applied to spatial feature nodes.
+Each spatial location [H×W] becomes a token; attention captures long-range
+spatial dependencies between antenna footprint regions:
+
+```rust
+// feature map: [B, C, H, W] → flatten to [B, H*W, C]
+// For each batch: compute attention among H*W spatial nodes
+// → reshape back to [B, C, H, W]
+```
+
+**Benefit:** Captures long-range spatial dependencies missed by local convolutions;
+important for multi-person scenarios.
+
+---
+
+## Implementation Plan
+
+### Files modified
+
+| File | Change |
+|------|--------|
+| `Cargo.toml` (workspace + crate) | Add ruvector-mincut, ruvector-attn-mincut, ruvector-temporal-tensor, ruvector-solver, ruvector-attention = "2.0.4" |
+| `metrics.rs` | Add `DynamicPersonMatcher` wrapping `ruvector_mincut::DynamicMinCut`; keep `hungarian_assignment` for deterministic proof |
+| `model.rs` | Add `attn_mincut` bridge in `ModalityTranslator::forward_t`; add `ScaledDotProductAttention` in spatial heads |
+| `dataset.rs` | Add `CompressedCsiBuffer` backed by `TemporalTensorCompressor`; `MmFiDataset` uses it |
+| `subcarrier.rs` | Add `interpolate_subcarriers_sparse` using `NeumannSolver`; keep `interpolate_subcarriers` as fallback |
+
+### Files unchanged
+
+`config.rs`, `losses.rs`, `trainer.rs`, `proof.rs`, `error.rs` — no change needed.
+
+### Feature gating
+
+All ruvector integrations are **always-on** (not feature-gated). The ruvector
+crates are pure Rust with no C FFI, so they add no platform constraints.
+
+---
+
+## Implementation Status
+
+| Phase | Status |
+|-------|--------|
+| Cargo.toml (workspace + crate) | **Complete** |
+| ADR-016 documentation | **Complete** |
+| ruvector-mincut in metrics.rs | Implementing |
+| ruvector-attn-mincut in model.rs | Implementing |
+| ruvector-temporal-tensor in dataset.rs | Implementing |
+| ruvector-solver in subcarrier.rs | Implementing |
+| ruvector-attention in model.rs spatial decoder | Implementing |
+
+---
+
+## Consequences
+
+**Positive:**
+- Subpolynomial O(n^{1.5} log n) dynamic min-cut for multi-person tracking
+- Min-cut gated attention is physically motivated for CSI antenna arrays
+- 50–75% memory reduction from temporal quantization
+- Sparse least-squares interpolation is physically principled vs linear
+- All ruvector crates are pure Rust (no C FFI, no platform restrictions)
+
+**Negative:**
+- Additional compile-time dependencies (ruvector crates)
+- `attn_mincut` requires tensor↔Vec<f32> conversion overhead per batch element
+- `TemporalTensorCompressor` adds compression/decompression latency on dataset load
+- `NeumannSolver` requires diagonally dominant matrices; a sparse Tikhonov
+  regularization term (λI) is added to ensure convergence
+
+## References
+
+- ADR-015: Public Dataset Training Strategy
+- ADR-014: SOTA Signal Processing Algorithms
+- github.com/ruvnet/ruvector (source: crates at v2.0.4)
+- ruvector-mincut: https://crates.io/crates/ruvector-mincut
+- ruvector-attn-mincut: https://crates.io/crates/ruvector-attn-mincut
+- ruvector-temporal-tensor: https://crates.io/crates/ruvector-temporal-tensor
+- ruvector-solver: https://crates.io/crates/ruvector-solver
+- ruvector-attention: https://crates.io/crates/ruvector-attention