test+bins: flash grad-check, flash==composed, PyTorch parity, --flash flag

autograd: flash_attention_batched_bwd (dQ/dK/dV finite-diff, seq>tile)
+ flash_matches_composed_fwd. model/tests/flash.rs: flash==composed
on-vs-off (logits/loss/every param grad), fp32 + bf16. parity_dump:
XTRAIN_PARITY_FLASH dumps the flash path for the same parity.py oracle
(PyTorch SDPA parity at B>1). train + train_ddp get the --flash flag.

Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>

crates/xtrain-autodiff/tests/autograd.rs

@@ -625,6 +625,104 @@ fn attention_batched_bwd() {
     );
 }
 
+// ---- fused FLASH causal attention (the T14 op) ----
+// Same structure as attention_batched_bwd, but exercises ops::flash_attention.
+// q,k,v: [bh, seq, hd]. Grad-check dq/dk/dv against finite-diff of L=sum(W∘out).
+// seq=40 > FA_TILE=32 so the online-softmax tile-rescale path is exercised (not
+// just a single KV tile).
+#[test]
+fn flash_attention_batched_bwd() {
+    require_gpu();
+    let (bh, seq, hd) = (2, 40, 16);
+    let n = bh * seq * hd;
+    let scale = 1.0 / (hd as f32).sqrt();
+    let q_h = fill(n, 241);
+    let k_h = fill(n, 242);
+    let v_h = fill(n, 243);
+    let w = fill(n, 244);
+
+    let q = Var::leaf(cuda(&q_h, &[bh, seq, hd]));
+    let k = Var::leaf(cuda(&k_h, &[bh, seq, hd]));
+    let v = Var::leaf(cuda(&v_h, &[bh, seq, hd]));
+    let out = ops::flash_attention(&q, &k, &v, scale);
+    scalar_loss(&out, &w).backward();
+
+    let dq = q.grad().unwrap().to_device(Device::Cpu);
+    let dk = k.grad().unwrap().to_device(Device::Cpu);
+    let dv = v.grad().unwrap().to_device(Device::Cpu);
+
+    let fwd = move |qh: &[f32], kh: &[f32], vh: &[f32]| -> f32 {
+        let qv = cuda(qh, &[bh, seq, hd]);
+        let kv = cuda(kh, &[bh, seq, hd]);
+        let vv = cuda(vh, &[bh, seq, hd]);
+        let (o, _) = qv.flash_attention(&kv, &vv, scale);
+        weighted_sum(&o, &w)
+    };
+    let (kf, vf, ff) = (k_h.clone(), v_h.clone(), fwd.clone());
+    let lq = move |x: &[f32], _s: &[usize]| ff(x, &kf, &vf);
+    report(
+        "flash dQ",
+        &grad_check(
+            &q_h,
+            &[bh, seq, hd],
+            &lq,
+            dq.as_slice::<f32>(),
+            cfg_nonlinear(),
+        ),
+    );
+    let (qf, vf, ff) = (q_h.clone(), v_h.clone(), fwd.clone());
+    let lk = move |x: &[f32], _s: &[usize]| ff(&qf, x, &vf);
+    report(
+        "flash dK",
+        &grad_check(
+            &k_h,
+            &[bh, seq, hd],
+            &lk,
+            dk.as_slice::<f32>(),
+            cfg_nonlinear(),
+        ),
+    );
+    let (qf, kf, ff) = (q_h.clone(), k_h.clone(), fwd.clone());
+    let lv = move |x: &[f32], _s: &[usize]| ff(&qf, &kf, x);
+    report(
+        "flash dV",
+        &grad_check(
+            &v_h,
+            &[bh, seq, hd],
+            &lv,
+            dv.as_slice::<f32>(),
+            cfg_linear(),
+        ),
+    );
+}
+
+// flash forward must equal the composed attention forward (same SDPA math).
+#[test]
+fn flash_matches_composed_fwd() {
+    require_gpu();
+    let (bh, seq, hd) = (2, 40, 16);
+    let n = bh * seq * hd;
+    let scale = 1.0 / (hd as f32).sqrt();
+    let q = cuda(&fill(n, 341), &[bh, seq, hd]);
+    let k = cuda(&fill(n, 342), &[bh, seq, hd]);
+    let v = cuda(&fill(n, 343), &[bh, seq, hd]);
+    let (oc, _) = q.attention(&k, &v, scale);
+    let (of, _) = q.flash_attention(&k, &v, scale);
+    let oc = oc.to_device(Device::Cpu);
+    let of = of.to_device(Device::Cpu);
+    let max_rel = oc
+        .as_slice::<f32>()
+        .iter()
+        .zip(of.as_slice::<f32>())
+        .map(|(c, f)| (c - f).abs() / (c.abs() + 1e-6))
+        .fold(0.0f32, f32::max);
+    println!("flash-vs-composed fwd max rel: {max_rel:.3e}");
+    assert!(
+        max_rel < 1e-4,
+        "flash fwd diverges from composed: {max_rel:.3e}"
+    );
+}
+
 // --- test helpers ---
 
 // Scalar loss node L = sum(W ∘ out): wraps a fixed-weight Var and reduces. We

crates/xtrain-distributed/src/bin/train_ddp.rs

@@ -89,6 +89,9 @@ fn main() {
     // rank checkpoints its own forward/backward; exact grads, lower peak activation
     // memory (lets dim1024 batch32 fit). Opt-in; default off.
     let recompute = args.iter().any(|a| a == "--recompute");
+    // Fused flash-attention (Phase T14): single fused SDPA kernel, online softmax,
+    // no materialized [bh,S,S] scores. Opt-in; default off keeps the composed path.
+    let flash = args.iter().any(|a| a == "--flash");
     let ckpt: Option<PathBuf> = args
         .iter()
         .position(|a| a == "--ckpt")
@@ -174,6 +177,9 @@ fn main() {
     if recompute {
         println!("activation recompute: ON (per-block gradient checkpointing)");
     }
+    if flash {
+        println!("flash-attention: ON (fused SDPA kernel, no materialized scores)");
+    }
     let results = launch(
         &devices,
         &train_corpus,
@@ -187,6 +193,9 @@ fn main() {
             if recompute {
                 m = m.with_recompute(true);
             }
+            if flash {
+                m = m.with_flash(true);
+            }
             m
         },
     );

crates/xtrain-model/tests/flash.rs

@@ -0,0 +1,157 @@
+// T14 flash-attention correctness gate: the fused flash SDPA core must match the
+// composed T10 path (cublasSgemmStridedBatched×2 + causal-softmax kernel) in
+// forward logits, loss, AND every parameter gradient — flash is the SAME SDPA
+// math (online softmax never materializes the [bh,S,S] scores), so it differs
+// from composed only by reduction order (in-kernel fp32 FMA vs cuBLAS, and the
+// dK/dV atomicAdd order in backward). This test makes that a closed on-GPU loop:
+//
+//   build two identical models (same init), one with `--flash` on, one off, run
+//   the SAME batched loss + backward on both, and assert
+//     1. the forward logits match within tolerance
+//     2. the loss matches
+//     3. EVERY parameter's grad matches within tolerance
+//
+// Parameterised over fp32 AND bf16 (T12). bf16 just adds the bf16 rounding band on
+// top — flash's bf16 path upcasts Q/K/V to fp32 for the kernel exactly like the
+// composed path's fp32 softmax, so the two are still the same softmax numerics.
+#![cfg(not(no_cuda))]
+
+use xtrain_cuda::device;
+use xtrain_model::{Config, TinyTransformer, batched_ids_tensor};
+use xtrain_tensor::{DType, Device};
+
+fn fill(n: usize, seed: u64, scale: f32) -> Vec<f32> {
+    let mut state = seed
+        .wrapping_mul(2862933555777941757)
+        .wrapping_add(3037000493);
+    (0..n)
+        .map(|_| {
+            state = state
+                .wrapping_mul(6364136223846793005)
+                .wrapping_add(1442695040888963407);
+            (((state >> 33) as f32 / (1u64 << 31) as f32) - 0.5) * 2.0 * scale
+        })
+        .collect()
+}
+
+fn build(cfg: Config, device: Device, dtype: DType, flash: bool) -> TinyTransformer {
+    let mut seed = 1u64;
+    let m = TinyTransformer::new(cfg, device, |shape| {
+        seed = seed.wrapping_add(1);
+        let n: usize = shape.iter().product();
+        if shape.len() == 1 {
+            fill(n, seed, 0.02).iter().map(|v| v + 1.0).collect()
+        } else {
+            fill(n, seed, 0.08)
+        }
+    });
+    m.with_compute_dtype(dtype).with_flash(flash)
+}
+
+fn host(t: &xtrain_tensor::Tensor) -> Vec<f32> {
+    t.to_dtype(DType::F32)
+        .to_device(Device::Cpu)
+        .as_slice::<f32>()
+        .to_vec()
+}
+
+fn run(dtype: DType, logit_tol: f32, grad_tol: f32) {
+    assert!(device::device_count().unwrap() > 0, "no CUDA device");
+    device::set_device(0).unwrap();
+    let device = Device::Cuda(0);
+
+    // seq=40 > FA_TILE=32 so the online-softmax tile-rescale path is exercised.
+    let mut cfg = Config::tiny();
+    cfg.vocab = 16;
+    cfg.n_layers = 4;
+    let batch = 3usize;
+    let seq = 40usize;
+    let seqs: Vec<Vec<i32>> = (0..batch)
+        .map(|b| {
+            (0..seq)
+                .map(|i| ((b * 7 + i * 3 + 1) % cfg.vocab) as i32)
+                .collect()
+        })
+        .collect();
+    let tgts: Vec<Vec<i32>> = (0..batch)
+        .map(|b| {
+            (0..seq)
+                .map(|i| ((b * 5 + i * 2 + 2) % cfg.vocab) as i32)
+                .collect()
+        })
+        .collect();
+    let ids = batched_ids_tensor(&seqs, device);
+    let tgt = batched_ids_tensor(&tgts, device);
+
+    // --- flash OFF (composed reference) ---
+    let off = build(cfg, device, dtype, false);
+    let off_logits = host(&off.forward_batched(&ids, batch).value());
+    let off_loss = off.loss_batched(&ids, &tgt, batch);
+    let off_loss_val = host(&off_loss.value())[0];
+    off_loss.backward();
+    let off_grads: Vec<Vec<f32>> = off
+        .params()
+        .iter()
+        .map(|p| host(&p.grad().expect("off grad")))
+        .collect();
+
+    // --- flash ON ---
+    let on = build(cfg, device, dtype, true);
+    let on_logits = host(&on.forward_batched(&ids, batch).value());
+    let on_loss = on.loss_batched(&ids, &tgt, batch);
+    let on_loss_val = host(&on_loss.value())[0];
+    on_loss.backward();
+    let on_grads: Vec<Vec<f32>> = on
+        .params()
+        .iter()
+        .map(|p| host(&p.grad().expect("on grad")))
+        .collect();
+
+    // 1. Forward logits.
+    let logit_rel = off_logits
+        .iter()
+        .zip(&on_logits)
+        .map(|(a, b)| (a - b).abs() / a.abs().max(1e-4))
+        .fold(0.0f32, f32::max);
+    // 2. Loss.
+    let loss_rel = (off_loss_val - on_loss_val).abs() / off_loss_val.abs().max(1e-4);
+    println!(
+        "[{dtype:?}] flash on/off: loss {off_loss_val:.6}/{on_loss_val:.6} (rel {loss_rel:.2e}), \
+         logits max rel {logit_rel:.2e}"
+    );
+    assert!(
+        logit_rel < logit_tol,
+        "[{dtype:?}] logits diverged: {logit_rel:.2e}"
+    );
+    assert!(
+        loss_rel < logit_tol,
+        "[{dtype:?}] loss diverged: {loss_rel:.2e}"
+    );
+
+    // 3. Every parameter grad — the load-bearing gate.
+    let mut max_grad_rel = 0.0f32;
+    for (off_g, on_g) in off_grads.iter().zip(&on_grads) {
+        for (a, b) in off_g.iter().zip(on_g) {
+            let rel = (a - b).abs() / a.abs().max(1e-3);
+            max_grad_rel = max_grad_rel.max(rel);
+        }
+    }
+    println!("[{dtype:?}] flash on/off: grad max rel err = {max_grad_rel:.3e}");
+    assert!(
+        max_grad_rel < grad_tol,
+        "[{dtype:?}] flash grads diverged from composed: {max_grad_rel:.3e}"
+    );
+}
+
+#[test]
+fn flash_matches_composed_fp32() {
+    // fp32: same SDPA math, differs only by reduction order (in-kernel fp32 FMA vs
+    // cuBLAS, dK/dV atomicAdd order). Tight but not bit-exact.
+    run(DType::F32, 1e-3, 2e-2);
+}
+
+#[test]
+fn flash_matches_composed_bf16() {
+    // bf16 (T12 composition): bf16 rounding band on top of the fp32-softmax core.
+    run(DType::BF16, 2e-2, 5e-2);
+}

crates/xtrain-model/tests/parity_dump.rs

@@ -67,7 +67,7 @@ fn dump_for_parity() {
 
     // Same deterministic init as the overfit test.
     let mut seed = 1u64;
-    let model = TinyTransformer::new(cfg, device, |shape| {
+    let mut model = TinyTransformer::new(cfg, device, |shape| {
         seed = seed.wrapping_add(1);
         let n: usize = shape.iter().product();
         if shape.len() == 1 {
@@ -76,6 +76,14 @@ fn dump_for_parity() {
             fill(n, seed, 0.08)
         }
     });
+    // T14: with XTRAIN_PARITY_FLASH set, dump from the fused flash-attention path.
+    // flash is the SAME SDPA math, so the SAME parity.py PyTorch oracle is the
+    // reference for both paths — running this once per path checks flash against
+    // PyTorch at B>1 (forward logits + every parameter grad).
+    if std::env::var("XTRAIN_PARITY_FLASH").is_ok() {
+        model = model.with_flash(true);
+        println!("parity: FLASH attention path");
+    }
 
     // config + ids
     {

crates/xtrain-train/src/bin/train.rs

@@ -116,6 +116,9 @@ fn main() {
     // exact grads, lower peak activation memory (lets dim1024 batch32 fit). Opt-in;
     // default off stores every activation (unchanged numerics).
     let recompute = args.iter().any(|a| a == "--recompute");
+    // Fused flash-attention (Phase T14): single fused SDPA kernel, online softmax,
+    // no materialized [bh,S,S] scores. Opt-in; default off keeps the composed path.
+    let flash = args.iter().any(|a| a == "--flash");
     let ckpt: PathBuf = PathBuf::from(
         args.iter()
             .position(|a| a == "--ckpt")
@@ -183,6 +186,10 @@ fn main() {
         model = model.with_recompute(true);
         println!("activation recompute: ON (per-block gradient checkpointing)");
     }
+    if flash {
+        model = model.with_flash(true);
+        println!("flash-attention: ON (fused SDPA kernel, no materialized scores)");
+    }
 
     // Eval-only mode: load a checkpoint and score it on the held-out val set, then
     // exit. Used to put an EXISTING model (e.g. v0) and a new one on the same