model: batched forward [B,S]

forward_batched(ids[B*S], batch)/loss_batched: run B equal-length sequences as
ONE forward over flattened [B*S] ids, so every linear is one big [B*S,dim] GEMM.
Attention reshapes to [B*nh,S,hd], runs the fused batched causal SDPA (per-seq
mask + RoPE period=S, no cross-sequence attention), writes back [B*S,dim]. The
old per-(batch,head) loop + host-round-tripping split/merge_heads + the additive
causal_mask leaf are gone. forward(ids[seq]) is now forward_batched(ids,1), so
the sampler / inference path (batch=1) is unchanged.

+batched_ids_tensor helper. New batched.rs test: batched forward == looped
single-sequence (logits identical 0.0, grads 6.4e-4, loss identical). PyTorch
parity now exercises B>1 (B=2,S=4): loss 5e-8, logits 6.9e-6, all 25 param
grads within rtol — verifying per-seq RoPE position + per-seq causal masking.

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

crates/xtrain-model/tests/batched.rs

@@ -0,0 +1,142 @@
+// T10 batched-forward equivalence: a batched forward over B sequences must equal
+// the old single-sequence path (run each sequence on its own, concatenate the
+// logits) — both for the forward logits AND every parameter's gradient.
+//
+// This is THE on-GPU correctness gate for batching (no PyTorch needed): if the
+// per-sequence RoPE position, per-sequence causal masking, or any flattened op
+// were wrong, the batched logits/grads would drift from the looped reference.
+//
+// Forward equivalence: batched logits[b*S+i] == single-seq-b logits[i].
+// Gradient equivalence: the batched loss is the mean over all B*S rows, i.e.
+// (1/B)·Σ_b mean_i(loss_b); summing the B single-sequence losses and scaling by
+// 1/B gives the SAME scalar, so their summed grads (tape fan-out) ×1/B match the
+// batched grads. We check that.
+#![cfg(not(no_cuda))]
+
+use xtrain_cuda::device;
+use xtrain_model::{Config, TinyTransformer, batched_ids_tensor, ids_tensor};
+use xtrain_tensor::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) -> TinyTransformer {
+    let mut seed = 1u64;
+    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)
+        }
+    })
+}
+
+fn host(t: &xtrain_tensor::Tensor) -> Vec<f32> {
+    t.to_device(Device::Cpu).as_slice::<f32>().to_vec()
+}
+
+#[test]
+fn batched_matches_looped_single_sequence() {
+    assert!(device::device_count().unwrap() > 0, "no CUDA device");
+    device::set_device(0).unwrap();
+    let device = Device::Cuda(0);
+
+    let mut cfg = Config::tiny();
+    cfg.vocab = 16;
+    let batch = 3usize;
+    let seq = 5usize;
+    // B distinct sequences (sequence-major), within vocab.
+    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();
+
+    // --- Batched forward: ONE pass over [B*S]. ---
+    let bmodel = build(cfg, device);
+    let bids = batched_ids_tensor(&seqs, device);
+    let blogits = host(&bmodel.forward_batched(&bids, batch).value());
+
+    // --- Looped reference: each sequence on its own, concatenate logits. ---
+    let smodel = build(cfg, device);
+    let mut slogits = Vec::with_capacity(batch * seq * cfg.vocab);
+    for s in &seqs {
+        let ids = ids_tensor(s, device);
+        slogits.extend(host(&smodel.forward(&ids).value()));
+    }
+
+    // Forward equivalence (fp GEMM rounding only differs in summation order).
+    let max_rel = blogits
+        .iter()
+        .zip(&slogits)
+        .map(|(b, s)| (b - s).abs() / s.abs().max(1e-4))
+        .fold(0.0f32, f32::max);
+    println!("batched vs looped: logits max rel err = {max_rel:.3e}");
+    assert!(max_rel < 1e-3, "batched logits diverged: {max_rel:.3e}");
+
+    // --- Gradient equivalence. ---
+    // Batched: loss = mean over B*S rows; one backward.
+    let bparams = bmodel.params();
+    let btgt = batched_ids_tensor(&tgts, device);
+    let bloss = bmodel.loss_batched(&bids, &btgt, batch);
+    let bloss_val = host(&bloss.value())[0];
+    bloss.backward();
+
+    // Looped: Σ_b loss_b (each a per-sequence mean), then grad ×(1/B) == batched.
+    let sparams = smodel.params();
+    let mut sloss_sum = 0.0f32;
+    for (s, t) in seqs.iter().zip(&tgts) {
+        let ids = ids_tensor(s, device);
+        let tg = ids_tensor(t, device);
+        let l = smodel.loss(&ids, &tg);
+        sloss_sum += host(&l.value())[0];
+        l.backward();
+    }
+    println!(
+        "batched loss = {bloss_val:.6}  looped mean = {:.6}",
+        sloss_sum / batch as f32
+    );
+    assert!(
+        (bloss_val - sloss_sum / batch as f32).abs() < 1e-4,
+        "batched loss != looped mean"
+    );
+
+    let mut max_grad_rel = 0.0f32;
+    for (bp, sp) in bparams.iter().zip(&sparams) {
+        let bg = host(&bp.grad().expect("batched grad"));
+        let sg = host(&sp.grad().expect("looped grad"));
+        for (g_b, g_s) in bg.iter().zip(&sg) {
+            // looped grad is the SUM over B sequences; ×(1/B) recovers the mean.
+            let g_s = g_s / batch as f32;
+            let rel = (g_b - g_s).abs() / g_s.abs().max(1e-4);
+            max_grad_rel = max_grad_rel.max(rel);
+        }
+    }
+    println!("batched vs looped: grad max rel err = {max_grad_rel:.3e}");
+    assert!(
+        max_grad_rel < 5e-3,
+        "batched grads diverged: {max_grad_rel:.3e}"
+    );
+}