test(temporal): dense-vs-sparse numerical A/B baseline (ADR-096 §5, #513)

Establishes the kernel-level output-divergence envelope between the
two backends — what §5's downstream-metric gate (contrastive loss,
rank-1, Spearman) would calibrate against. Two regimes:

1. Saturated pattern (window ≥ N, block ≥ N): sparse and dense visit
   the same edge set, so divergence reflects only float accumulation
   order. **Asserted < 1e-4** at N=32, heads=4, dim=16. Tight bound.

2. Realistic sparse (window=16, block=32, N=256): real approximation,
   real divergence. **Measured max_abs_err = 5.22e-3, mean = 1.79e-3**
   on the deterministic test inputs. Sanity-checked finite + < 1.0
   so structural breakage (NaN, softmax overflow) trips a panic, but
   the specific numbers are *baseline data* not a hard contract — the
   §5 gate cares about downstream task metrics, not bit-equality.

Why this is in the test suite rather than a benchmark:
- It runs in <0.2s, no need to gate behind --release.
- The saturated-pattern bound IS a hard contract — if that breaks
  the kernel changed semantics in a way the API hides, and we want
  CI to catch it.
- Printing the realistic-pattern numbers (eprintln, visible with
  --nocapture) gives a known-good reference point to compare future
  builds against.

Test count is now 21/21 across the crate (6 smoke + 8 weight blob +
2 blob e2e + 3 streaming + 2 dense-vs-sparse).

Co-Authored-By: claude-flow <ruv@ruv.net>

v2/crates/wifi-densepose-temporal/tests/dense_vs_sparse.rs

@@ -0,0 +1,184 @@
+//! Numerical A/B test for ADR-096 §5: do Dense and SparseGqa produce
+//! comparable outputs on the same input?
+//!
+//! Background. Sparse attention is *structurally* an approximation —
+//! it skips edges that the local window + log-stride + landmark
+//! pattern decided wouldn't matter. The §5 validation gate cares
+//! about whether that approximation degrades downstream metrics
+//! (contrastive loss, rank-1 accuracy, Spearman correlation), not
+//! whether outputs are bit-equal. This file establishes the *direct*
+//! output-level error envelope so the gate can be calibrated against
+//! it.
+//!
+//! Two regimes:
+//!
+//! 1. **Sparse pattern is dense.** When window ≥ N AND block_size ≥ N
+//!    AND every position is global, sparse and dense visit the same
+//!    edge set. Output divergence then reflects only floating-point
+//!    accumulation order, which is a tight bound (~1e-5 for f32 sums
+//!    of ~100 terms at 0.1 magnitude).
+//!
+//! 2. **Sparse pattern is sparse.** Default config drops most edges
+//!    at long N. Output divergence here is the *real* approximation
+//!    error — and the §5 gate's tolerances apply downstream of it.
+
+use ruvllm_sparse_attention::Tensor3;
+use wifi_densepose_temporal::{
+    AetherTemporalHead, TemporalBackendKind, TemporalHeadConfig,
+};
+
+fn make_qkv(seq: usize, heads: usize, dim: usize) -> (Tensor3, Tensor3, Tensor3) {
+    let mut q = Tensor3::zeros(seq, heads, dim);
+    let mut k = Tensor3::zeros(seq, heads, dim);
+    let mut v = Tensor3::zeros(seq, heads, dim);
+    for s in 0..seq {
+        for h in 0..heads {
+            for d in 0..dim {
+                let qv = ((s * 31 + h * 7 + d) as f32).sin() * 0.1;
+                let kv = (((s * 17 + h * 3 + d) as f32).cos()) * 0.1;
+                q.set(s, h, d, qv);
+                k.set(s, h, d, kv);
+                v.set(s, h, d, kv * 0.5);
+            }
+        }
+    }
+    (q, k, v)
+}
+
+fn max_abs_err(a: &Tensor3, b: &Tensor3) -> f32 {
+    let (s, h, d) = a.shape();
+    assert_eq!((s, h, d), b.shape(), "shape mismatch");
+    let mut max_err = 0.0f32;
+    for ti in 0..s {
+        for hi in 0..h {
+            for di in 0..d {
+                let e = (a.get(ti, hi, di) - b.get(ti, hi, di)).abs();
+                if e > max_err {
+                    max_err = e;
+                }
+            }
+        }
+    }
+    max_err
+}
+
+fn mean_abs_err(a: &Tensor3, b: &Tensor3) -> f32 {
+    let (s, h, d) = a.shape();
+    let mut sum = 0.0f32;
+    let mut n = 0usize;
+    for ti in 0..s {
+        for hi in 0..h {
+            for di in 0..d {
+                sum += (a.get(ti, hi, di) - b.get(ti, hi, di)).abs();
+                n += 1;
+            }
+        }
+    }
+    sum / n.max(1) as f32
+}
+
+#[test]
+fn dense_and_sparse_agree_when_sparse_pattern_is_dense() {
+    // Saturate the sparse pattern: window ≥ N means the local-window
+    // primitive includes every causal predecessor, so the attention
+    // edge set is identical to dense MHA's. The remaining gap is
+    // floating-point accumulation order (sparse goes
+    // window-then-stride-then-landmark, dense goes naive 0..i).
+    let seq = 32;
+    let heads = 4;
+    let dim = 16;
+    let (q, k, v) = make_qkv(seq, heads, dim);
+
+    let dense_cfg = TemporalHeadConfig {
+        backend: TemporalBackendKind::Dense,
+        q_heads: heads,
+        kv_heads: heads,
+        head_dim: dim,
+        window: seq, // saturate
+        block_size: seq,
+        causal: true,
+    };
+    let sparse_cfg = TemporalHeadConfig {
+        backend: TemporalBackendKind::SparseGqa,
+        ..dense_cfg.clone()
+    };
+
+    let dense = AetherTemporalHead::new(&dense_cfg).expect("dense");
+    let sparse = AetherTemporalHead::new(&sparse_cfg).expect("sparse");
+
+    let d = dense.forward(&q, &k, &v).expect("dense forward");
+    let s = sparse.forward(&q, &k, &v).expect("sparse forward");
+
+    let max_err = max_abs_err(&d, &s);
+    let mean_err = mean_abs_err(&d, &s);
+
+    // 1e-4 covers a generous f32-summation-order envelope at 0.1
+    // input magnitude. If this ever blows up, either the saturation
+    // assumption is wrong (window/block_size no longer covers
+    // everything) or the kernel changed semantics.
+    assert!(
+        max_err < 1.0e-4,
+        "saturated-pattern max_abs_err exceeds 1e-4: max={max_err} mean={mean_err}"
+    );
+}
+
+#[test]
+fn dense_and_sparse_diverge_predictably_at_long_n() {
+    // The interesting case: real sparse pattern (window << N), real
+    // approximation. We don't assert a specific error bound here —
+    // that's what ADR-096 §5's validation gate calibrates. We only
+    // check the numbers come out finite and plausible (per-position
+    // outputs stay within a few × the input magnitude after
+    // attention-weighted averaging — softmax can't blow them up).
+    let seq = 256;
+    let heads = 4;
+    let dim = 16;
+    let (q, k, v) = make_qkv(seq, heads, dim);
+
+    let dense_cfg = TemporalHeadConfig {
+        backend: TemporalBackendKind::Dense,
+        q_heads: heads,
+        kv_heads: heads,
+        head_dim: dim,
+        window: seq, // dense — placeholder; ignored by Dense backend
+        block_size: seq,
+        causal: true,
+    };
+    let sparse_cfg = TemporalHeadConfig {
+        backend: TemporalBackendKind::SparseGqa,
+        q_heads: heads,
+        kv_heads: heads,
+        head_dim: dim,
+        window: 16,    // realistic sparse window
+        block_size: 32,
+        causal: true,
+    };
+
+    let dense = AetherTemporalHead::new(&dense_cfg).expect("dense");
+    let sparse = AetherTemporalHead::new(&sparse_cfg).expect("sparse");
+
+    let d = dense.forward(&q, &k, &v).expect("dense forward");
+    let s = sparse.forward(&q, &k, &v).expect("sparse forward");
+
+    let max_err = max_abs_err(&d, &s);
+    let mean_err = mean_abs_err(&d, &s);
+
+    // Sanity bounds. Inputs are scaled to 0.1, attention is a softmax
+    // average so outputs stay in roughly [-0.1, 0.1]. If max_err > 1.0
+    // something is structurally broken (NaN, underflow, etc).
+    assert!(
+        max_err.is_finite() && mean_err.is_finite(),
+        "non-finite error: max={max_err} mean={mean_err}"
+    );
+    assert!(
+        max_err < 1.0,
+        "implausibly large divergence: max={max_err} mean={mean_err}"
+    );
+
+    // Print the numbers so they're visible when running `cargo test --
+    // --nocapture`. These are what ADR-096 §5's gate would calibrate
+    // against on real AETHER inputs.
+    eprintln!(
+        "dense_vs_sparse @ N={seq}, window=16, block=32: max_abs_err={max_err:.6e}, mean_abs_err={mean_err:.6e}"
+    );
+}