diff --git a/crates/xtrain-autodiff/tests/autograd.rs b/crates/xtrain-autodiff/tests/autograd.rs
index ff15be4..0ed9a41 100644
--- a/crates/xtrain-autodiff/tests/autograd.rs
+++ b/crates/xtrain-autodiff/tests/autograd.rs
@@ -1177,3 +1177,94 @@ fn clipped_pg_loss_bwd_and_degenerate() {
     assert!((gotb - wantb).abs() < 1e-5, "β=0 loss mismatch: {gotb} vs {wantb}");
     println!("clipped_pg_loss OK: grad-check (active + A=0) + degenerate (ε→∞ vanilla, β=0 no KL)");
 }
+
+// clipped_pg_loss_batched (M2d): N ragged completions packed + right-padded into ONE
+// forward must equal the looped per-sample path Σ_s (1/N)·clipped_pg_loss_s. The
+// per-row CE backward is row-local, so folding weight = 1/(N·n_s) into the batched
+// op reproduces the looped gradient and weighted-sum loss bit-for-bit (f32 path).
+#[test]
+fn clipped_pg_loss_batched_matches_looped() {
+    require_gpu();
+    let (n, lmax, cols) = (3usize, 5usize, 10usize);
+    let rows = n * lmax;
+    let x_h = fill(rows * cols, 909);
+    // Per sample: row 0 = prompt (-100); rows 1..real_len = completion; rest = pad
+    // (-100). Different real_len ⇒ n_s = {2, 3, 1} completion rows.
+    let real_len = [3usize, 4, 2];
+    let adv_s = [0.7f32, -0.5, 0.3];
+    let mut targets = vec![-100i32; rows];
+    for s in 0..n {
+        for r in 1..real_len[s] {
+            let t = s * lmax + r;
+            targets[t] = ((t * 3) % cols) as i32;
+        }
+    }
+    let mk_target = || Tensor::from_slice(&targets, &[rows]).to_device(Device::Cuda(0));
+
+    // logp_old ≈ logπθ at base logits (ρ≈1), logp_ref offset to exercise the KL term.
+    let (_, per_row0) = cuda(&x_h, &[rows, cols]).cross_entropy(&mk_target());
+    let logp_old: Vec<f32> = per_row0
+        .to_device(Device::Cpu)
+        .as_slice::<f32>()
+        .iter()
+        .map(|p| -p)
+        .collect();
+    let logp_ref: Vec<f32> = logp_old.iter().map(|l| l - 0.3).collect();
+    let (eps, beta) = (0.2f32, 0.1f32);
+
+    // Per-row advantage (sample's A) + per-row weight 1/(N·n_s) (full normaliser).
+    let n_of = |s: usize| (0..lmax).filter(|&r| targets[s * lmax + r] >= 0).count() as f32;
+    let mut advantage = vec![0f32; rows];
+    let mut weight = vec![0f32; rows];
+    for s in 0..n {
+        let w = (1.0 / n as f32) * (1.0 / n_of(s));
+        for r in 0..lmax {
+            advantage[s * lmax + r] = adv_s[s];
+            weight[s * lmax + r] = w;
+        }
+    }
+
+    // Batched: one packed [R, vocab] forward + one backward.
+    let xb = Var::leaf(cuda(&x_h, &[rows, cols]));
+    let lb = ops::clipped_pg_loss_batched(
+        &xb, &mk_target(), &logp_old, &logp_ref, &advantage, &weight, eps, beta,
+    );
+    lb.backward();
+    let gb = xb.grad().unwrap().to_device(Device::Cpu).as_slice::<f32>().to_vec();
+    let lb_val = lb.value().to_device(Device::Cpu).as_slice::<f32>()[0];
+
+    // Looped reference: per-sample slice → clipped_pg_loss → scale(1/N) → backward.
+    let mut g_ref = vec![0f32; rows * cols];
+    let mut loss_ref = 0f32;
+    for s in 0..n {
+        let r0 = s * lmax;
+        let xs_h = x_h[r0 * cols..(r0 + lmax) * cols].to_vec();
+        let tgt_s: Vec<i32> = targets[r0..r0 + lmax].to_vec();
+        let lo_s = logp_old[r0..r0 + lmax].to_vec();
+        let lr_s = logp_ref[r0..r0 + lmax].to_vec();
+        let xs = Var::leaf(cuda(&xs_h, &[lmax, cols]));
+        let tgt = Tensor::from_slice(&tgt_s, &[lmax]).to_device(Device::Cuda(0));
+        let ls = ops::clipped_pg_loss(&xs, &tgt, &lo_s, &lr_s, adv_s[s], eps, beta);
+        let scaled = ops::scale(&ls, 1.0 / n as f32);
+        scaled.backward();
+        let gs = xs.grad().unwrap().to_device(Device::Cpu).as_slice::<f32>().to_vec();
+        g_ref[r0 * cols..(r0 + lmax) * cols].copy_from_slice(&gs);
+        loss_ref += scaled.value().to_device(Device::Cpu).as_slice::<f32>()[0];
+    }
+
+    let max_g = gb
+        .iter()
+        .zip(&g_ref)
+        .map(|(a, b)| (a - b).abs())
+        .fold(0.0f32, f32::max);
+    assert!(
+        (lb_val - loss_ref).abs() < 1e-5,
+        "batched loss {lb_val} vs looped {loss_ref}"
+    );
+    assert!(max_g < 1e-5, "batched grad vs looped: max|Δ| = {max_g}");
+    println!(
+        "clipped_pg_loss_batched OK: loss Δ={:.2e}, grad max|Δ|={:.2e} (== looped Σ_s 1/N·pg_s)",
+        (lb_val - loss_ref).abs(),
+        max_g
+    );
+}
diff --git a/crates/xtrain-model/tests/ragged_batch.rs b/crates/xtrain-model/tests/ragged_batch.rs
new file mode 100644
index 0000000..7d8e201
--- /dev/null
+++ b/crates/xtrain-model/tests/ragged_batch.rs
@@ -0,0 +1,97 @@
+// M2d gate: does forward_batched on RIGHT-PADDED ragged sequences reproduce the
+// per-sequence single-seq forward on the real (non-pad) rows? The batched GRPO
+// training-side forwards depend on this "right-pad is free under causal attention"
+// property — a real completion row is at an earlier position than the trailing pad,
+// and causal masking forbids attending forward, so its logits should be unchanged.
+//
+// Tested in fp32 (exact) over both SDPA cores (composed + fused flash), since the
+// bench uses flash and a kernel could in principle leak the pad keys into the online
+// softmax.
+#![cfg(not(no_cuda))]
+
+use xtrain_cuda::device;
+use xtrain_model::{Config, TinyTransformer, ids_tensor};
+use xtrain_tensor::{DType, Device, Tensor};
+
+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: &Tensor) -> Vec<f32> {
+    t.to_dtype(DType::F32).to_device(Device::Cpu).as_slice::<f32>().to_vec()
+}
+
+#[test]
+fn forward_batched_ragged_matches_looped() {
+    if device::device_count().unwrap_or(0) == 0 {
+        eprintln!("no CUDA device; skipping");
+        return;
+    }
+    device::set_device(0).unwrap();
+    let device = Device::Cuda(0);
+
+    let mut cfg = Config::tiny();
+    cfg.vocab = 32;
+    cfg.n_layers = 2;
+    let vocab = cfg.vocab;
+
+    // Ragged lengths incl. one crossing the flash tile (>32) and short ones.
+    let lens = [6usize, 40, 9, 4];
+    let lmax = *lens.iter().max().unwrap();
+    let n = lens.len();
+    let seqs: Vec<Vec<i32>> = lens
+        .iter()
+        .enumerate()
+        .map(|(b, &l)| (0..l).map(|i| ((b * 7 + i * 3 + 1) % vocab) as i32).collect())
+        .collect();
+
+    for (dtype, tol) in [(DType::F32, 2e-3f32), (DType::BF16, 3e-1f32)] {
+      for flash in [false, true] {
+        let m = build(cfg, device, dtype, flash);
+        // Looped: each sequence on its own (the ground truth).
+        let looped: Vec<Vec<f32>> = seqs.iter().map(|s| host(&m.forward(&ids_tensor(s, device)).value())).collect();
+
+        // Batched: right-pad each to lmax (pad id 0), one forward_batched(batch = n).
+        let mut flat = vec![0i32; n * lmax];
+        for (i, s) in seqs.iter().enumerate() {
+            flat[i * lmax..i * lmax + s.len()].copy_from_slice(s);
+        }
+        let ids = Tensor::from_slice(&flat, &[n * lmax]).to_device(device);
+        let batched = host(&m.forward_batched(&ids, n).value()); // [n*lmax, vocab]
+
+        let mut dmax = 0f32;
+        for (i, s) in seqs.iter().enumerate() {
+            for r in 0..s.len() {
+                for c in 0..vocab {
+                    let a = looped[i][r * vocab + c];
+                    let b = batched[(i * lmax + r) * vocab + c];
+                    dmax = dmax.max((a - b).abs());
+                }
+            }
+        }
+        println!("dtype={dtype:?} flash={flash}: ragged right-pad vs looped, max|Δlogit| (real rows) = {dmax:.3e}");
+        assert!(dmax < tol, "dtype={dtype:?} flash={flash}: right-pad NOT free under causal — max|Δ| = {dmax}");
+      }
+    }
+    println!("forward_batched_ragged_matches_looped OK: right-pad is free under causal (fp32+bf16, composed + flash)");
+}
diff --git a/crates/xtrain-train/src/bin/bench_grpo_batch.rs b/crates/xtrain-train/src/bin/bench_grpo_batch.rs
new file mode 100644
index 0000000..dc57e58
--- /dev/null
+++ b/crates/xtrain-train/src/bin/bench_grpo_batch.rs
@@ -0,0 +1,268 @@
+//! Micro-benchmark + closeness gate for the M2d batched GRPO training-side forwards.
+//!
+//! After M2b/M2c the GRPO *step* is no longer rollout-bound — it is the `N = B·G`
+//! per-sample full-sequence forwards (the `per_token_logp` captures + the inner
+//! clipped-PG forward/backwards). This bin isolates exactly that, weight-independently
+//! (step wall-clock depends on shapes + launch counts, not on what the weights are), by
+//! synthesising `N` realistic ragged samples and A/B-timing the looped vs batched path
+//! for BOTH phases — plus asserting they agree numerically (the looped-vs-batched
+//! closeness gate; per-row bit-equivalence of the loss op is pinned by the autograd
+//! test `clipped_pg_loss_batched_matches_looped`).
+//!
+//!   bench_grpo_batch <tokenizer.json> --init-ckpt <base.ckpt> <arch flags> \
+//!       --n 48 --plen 12 --clen 24 --micro 16 --reps 3
+
+#[cfg(no_cuda)]
+fn main() {
+    eprintln!("bench_grpo_batch: built without CUDA (no_cuda); run on a GPU host.");
+}
+
+#[cfg(not(no_cuda))]
+use xtrain_cuda::device;
+#[cfg(not(no_cuda))]
+use xtrain_model::{Config, TinyTransformer};
+#[cfg(not(no_cuda))]
+use xtrain_tensor::{DType, Device, Tensor};
+#[cfg(not(no_cuda))]
+use xtrain_train::grpo_batch::{PgSample, inner_pg_step_batched, inner_pg_step_looped, per_token_logp, per_token_logp_batched};
+
+#[cfg(not(no_cuda))]
+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()
+}
+
+#[cfg(not(no_cuda))]
+fn flag<T: std::str::FromStr>(args: &[String], name: &str, default: T) -> T {
+    args.iter().position(|a| a == name).and_then(|i| args.get(i + 1)).and_then(|s| s.parse().ok()).unwrap_or(default)
+}
+
+#[cfg(not(no_cuda))]
+fn flag_value(args: &[String], name: &str) -> Option<String> {
+    args.iter().position(|a| a == name).and_then(|i| args.get(i + 1)).cloned()
+}
+
+#[cfg(not(no_cuda))]
+fn load_model(cfg: Config, device: Device, ckpt: &str) -> 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, 0.04)
+        }
+    })
+    .with_compute_dtype(DType::BF16)
+    .with_flash(true);
+    xtrain_train::checkpoint::load_into(std::path::Path::new(ckpt), &m.params()).expect("load ckpt");
+    m.eval();
+    m
+}
+
+#[cfg(not(no_cuda))]
+fn elapsed_ms<F: FnMut()>(reps: usize, mut f: F) -> f32 {
+    let start = std::time::Instant::now();
+    for _ in 0..reps {
+        f();
+    }
+    start.elapsed().as_secs_f32() * 1e3 / reps as f32
+}
+
+/// Per-position argmax of the model over each ragged `input` (one `forward_batched`
+/// per `micro`-chunk). Used to teacher-force WELL-CONDITIONED targets (the top-1 token,
+/// high prob) so the closeness gate's logp isn't the ~−20 of a random token — where
+/// `−log p` amplifies bf16 noise. This matches real GRPO (targets are model samples).
+#[cfg(not(no_cuda))]
+fn model_argmax(model: &TinyTransformer, device: Device, inputs: &[Vec<i32>], vocab: usize, micro: usize) -> Vec<Vec<i32>> {
+    let mut out = Vec::with_capacity(inputs.len());
+    for chunk in inputs.chunks(micro.max(1)) {
+        let m = chunk.len();
+        let lmax = chunk.iter().map(|s| s.len()).max().unwrap();
+        let mut flat = vec![0i32; m * lmax];
+        for (i, s) in chunk.iter().enumerate() {
+            flat[i * lmax..i * lmax + s.len()].copy_from_slice(s);
+        }
+        let ids = Tensor::from_slice(&flat, &[m * lmax]).to_device(device);
+        let logits = model.forward_batched(&ids, m).value().to_dtype(DType::F32).to_device(Device::Cpu);
+        let v = logits.as_slice::<f32>();
+        for (i, s) in chunk.iter().enumerate() {
+            let mut row = Vec::with_capacity(s.len());
+            for r in 0..s.len() {
+                let base = (i * lmax + r) * vocab;
+                let mut best = 0usize;
+                for c in 1..vocab {
+                    if v[base + c] > v[base + best] {
+                        best = c;
+                    }
+                }
+                row.push(best as i32);
+            }
+            out.push(row);
+        }
+    }
+    out
+}
+
+#[cfg(not(no_cuda))]
+fn main() {
+    use xserv_tokenizer::Tokenizer;
+
+    let args: Vec<String> = std::env::args().collect();
+    let positionals: Vec<&String> = args[1..].iter().filter(|a| !a.starts_with("--")).collect();
+    let tok_path = positionals.first().expect("usage: bench_grpo_batch <tokenizer.json> [flags]");
+
+    let n_heads = flag(&args, "--heads", 52usize);
+    let head_dim = flag(&args, "--head-dim", 32usize);
+    let n_layers = flag(&args, "--layers", 22usize);
+    let ffn = flag(&args, "--ffn", 6656usize);
+    let kv_heads = flag(&args, "--kv-heads", n_heads);
+    let n: usize = flag(&args, "--n", 48); // B·G samples per step
+    let plen: usize = flag(&args, "--plen", 12); // prompt tokens
+    let clen: usize = flag(&args, "--clen", 24); // max completion tokens
+    let micro: usize = flag(&args, "--micro", 16);
+    let reps: usize = flag(&args, "--reps", 3);
+    let (eps, beta) = (flag(&args, "--eps", 0.2f32), flag(&args, "--beta", 0.0f32));
+    let init_ckpt = flag_value(&args, "--init-ckpt").expect("--init-ckpt <base.ckpt> required");
+
+    assert!(device::device_count().unwrap() > 0, "no CUDA device");
+    device::set_device(0).unwrap();
+    let device = Device::Cuda(0);
+    let tok = Tokenizer::from_file(std::path::Path::new(tok_path.as_str()));
+    let vocab = tok.vocab_size();
+    let cfg = Config::from_arch(vocab, n_heads, head_dim, n_layers, ffn).with_kv_heads(kv_heads);
+    let policy = load_model(cfg, device, &init_ckpt);
+    let params = policy.params();
+
+    // --- Synthesise N ragged samples (frame-shaped: prompt masked, ragged completion).
+    // Token IDs are random-but-valid; only the SHAPES drive the forward cost.
+    let mut rng = 0xC0FFEEu64;
+    let mut next = || {
+        rng = rng.wrapping_mul(6364136223846793005).wrapping_add(1442695040888963407);
+        (rng >> 33) as usize
+    };
+    let mut io: Vec<(Vec<i32>, Vec<i32>)> = Vec::with_capacity(n);
+    let mut advs: Vec<f32> = Vec::with_capacity(n);
+    for _ in 0..n {
+        let pl = plen.saturating_sub(2) + next() % 5; // jitter prompt length a little
+        let cl = 4 + next() % clen.max(1); // completion 4..=clen
+        let total = pl + cl;
+        let toks: Vec<i32> = (0..total).map(|_| (next() % vocab) as i32).collect();
+        let mut labels = vec![-100i32; pl]; // prompt masked
+        labels.extend_from_slice(&toks[pl..]);
+        let l = toks.len();
+        io.push((toks[..l - 1].to_vec(), labels[1..l].to_vec())); // target masked at [..pl-1]
+        advs.push(if next() % 2 == 0 { 0.7 } else { -0.7 });
+    }
+    let toklens: Vec<usize> = io.iter().map(|(i, _)| i.len()).collect();
+    let (lmin, lmax) = (*toklens.iter().min().unwrap(), *toklens.iter().max().unwrap());
+    println!("samples N={n}, seq len {lmin}..{lmax} (ragged), micro={micro}, β={beta}\n");
+
+    // Replace random completion targets with the model's own argmax (teacher forcing):
+    // well-conditioned logp (top-1, not the ~−20 of a random token where bf16 noise
+    // blows up via −log p). The completion target positions are where the skeleton is
+    // ≥0; prompt positions stay masked (−100).
+    let inputs: Vec<Vec<i32>> = io.iter().map(|(i, _)| i.clone()).collect();
+    let preds = model_argmax(&policy, device, &inputs, vocab, micro);
+    for (s, (_, target)) in io.iter_mut().enumerate() {
+        for j in 0..target.len() {
+            if target[j] >= 0 {
+                target[j] = preds[s][j];
+            }
+        }
+    }
+
+    // ---------------- Phase 1: capture (per_token_logp) ----------------
+    let logp_loop: Vec<Vec<f32>> = io.iter().map(|(i, t)| per_token_logp(&policy, device, i, t)).collect();
+    let logp_batch = per_token_logp_batched(&policy, device, &io, micro);
+    let cap_dmax = logp_loop
+        .iter()
+        .zip(&logp_batch)
+        .flat_map(|(a, b)| a.iter().zip(b).map(|(x, y)| (x - y).abs()))
+        .fold(0.0f32, f32::max);
+    let t_cap_loop = elapsed_ms(reps, || {
+        let _: Vec<Vec<f32>> = io.iter().map(|(i, t)| per_token_logp(&policy, device, i, t)).collect();
+    });
+    let t_cap_batch = elapsed_ms(reps, || {
+        let _ = per_token_logp_batched(&policy, device, &io, micro);
+    });
+
+    // Build PgSamples from the (matching) capture; ref = old − 0.3 to exercise KL.
+    let batch: Vec<PgSample> = io
+        .iter()
+        .zip(&advs)
+        .zip(&logp_batch)
+        .map(|(((input, target), &adv), lp)| PgSample {
+            input: input.clone(),
+            target: target.clone(),
+            adv,
+            logp_old: lp.clone(),
+            logp_ref: lp.iter().map(|v| v - 0.3).collect(),
+        })
+        .collect();
+
+    // ---------------- Phase 2: inner clipped-PG (forward + backward) ----------------
+    // Representative grad snapshots: layer-0 wq (params[2]) + final_norm.
+    let wq0 = &params[2];
+    let fnorm = &params[1 + n_layers * 11];
+    let snap = |v: &xtrain_autodiff::Var| -> Vec<f32> {
+        v.grad().map(|g| g.to_device(Device::Cpu).as_slice::<f32>().to_vec()).unwrap_or_default()
+    };
+    let zero = |ps: &[xtrain_autodiff::Var]| ps.iter().for_each(|p| p.zero_grad());
+
+    zero(&params);
+    inner_pg_step_looped(&policy, device, &batch, eps, beta);
+    let (gq_loop, gn_loop) = (snap(wq0), snap(fnorm));
+    zero(&params);
+    inner_pg_step_batched(&policy, device, &batch, eps, beta, micro);
+    let (gq_batch, gn_batch) = (snap(wq0), snap(fnorm));
+    zero(&params);
+
+    let reldiff = |a: &[f32], b: &[f32]| -> f32 {
+        let num = a.iter().zip(b).map(|(x, y)| (x - y).abs()).fold(0.0f32, f32::max);
+        let den = a.iter().map(|x| x.abs()).fold(0.0f32, f32::max).max(1e-12);
+        num / den
+    };
+    let gq_rel = reldiff(&gq_loop, &gq_batch);
+    let gn_rel = reldiff(&gn_loop, &gn_batch);
+
+    // Time only forward+backward — the lever. opt.step + grad-clip are identical in
+    // both paths (one call over `params` after the per-sample loop), so they would
+    // only add a constant; excluding them also dodges the unrelated 1B-Adam-state
+    // memory wall (the M4 finding) that this diagnostic doesn't need to reproduce.
+    let t_inner_loop = elapsed_ms(reps, || {
+        inner_pg_step_looped(&policy, device, &batch, eps, beta);
+        zero(&params);
+    });
+    let t_inner_batch = elapsed_ms(reps, || {
+        inner_pg_step_batched(&policy, device, &batch, eps, beta, micro);
+        zero(&params);
+    });
+
+    // ---------------- Report ----------------
+    let spd = |a: f32, b: f32| if b > 0.0 { a / b } else { 0.0 };
+    println!("=== closeness gate (looped vs batched) ===");
+    println!("  capture per_token_logp : max|Δ| = {cap_dmax:.3e}");
+    println!("  inner grad wq[0]       : rel|Δ| = {gq_rel:.3e}");
+    println!("  inner grad final_norm  : rel|Δ| = {gn_rel:.3e}");
+    println!("\n=== timing (mean of {reps} reps, ms/phase) ===");
+    println!("  capture : looped {t_cap_loop:8.1}  batched {t_cap_batch:8.1}  ({:.2}× )", spd(t_cap_loop, t_cap_batch));
+    println!("  inner   : looped {t_inner_loop:8.1}  batched {t_inner_batch:8.1}  ({:.2}× )", spd(t_inner_loop, t_inner_batch));
+    let (step_loop, step_batch) = (t_cap_loop + t_inner_loop, t_cap_batch + t_inner_batch);
+    println!("  STEP    : looped {step_loop:8.1}  batched {step_batch:8.1}  ({:.2}× )", spd(step_loop, step_batch));
+
+    // The RIGOROUS correctness gates live in the test suite (exact, not bf16-noisy):
+    //   - xtrain-model  forward_batched_ragged_matches_looped  (forward+pad == looped)
+    //   - xtrain-autodiff clipped_pg_loss_batched_matches_looped (op == looped, f32)
+    // This is a smoke check at the 1B/bf16 scale: single-seq vs batched GEMM differ in
+    // batch-reduction order, so a loose band, with well-conditioned (argmax) targets.
+    assert!(cap_dmax < 0.2, "capture closeness smoke FAILED: max|Δlogp| = {cap_dmax}");
+    assert!(gq_rel < 0.2 && gn_rel < 0.2, "inner grad closeness smoke FAILED: wq {gq_rel}, fn {gn_rel}");
+    println!("\nSMOKE PASS (bf16 band): batched ≈ looped; rigorous gates are the two tests above.");
+}