train: --bf16 flag (fp32-master AMP) + bf16 correctness test

- TinyTransformer::with_compute_dtype(BF16): embedding stays fp32
  master then casts to bf16; each linear casts its fp32 weight to bf16
  on the fly; logits cast back to fp32 for cross-entropy. Default F32
  reproduces the v0-v4 forward graph bit-for-bit.
- --bf16 flag on bin/train and bin/train_ddp (off by default).
- tests/bf16.rs: same fp32 master weights run fp32 vs bf16; assert
  loss/logits/grads within a loose bf16 tol, no NaN, and grads are
  fp32 (master untouched).

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

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

@@ -82,6 +82,9 @@ fn main() {
     let val_tokens: usize = flag(&args, "--val-tokens", 0);
     let eval_every: usize = flag(&args, "--eval-every", 0);
     let eval_batches: usize = flag(&args, "--eval-batches", 64);
+    // bf16 mixed precision (Phase T12): fp32 master weights, bf16 linears +
+    // activations. Opt-in; default fp32 reproduces v0–v4 numerics.
+    let bf16 = args.iter().any(|a| a == "--bf16");
     let ckpt: Option<PathBuf> = args
         .iter()
         .position(|a| a == "--ckpt")
@@ -161,12 +164,22 @@ fn main() {
          eval every {eval_every}"
     );
 
+    if bf16 {
+        println!("bf16 mixed precision: ON (fp32 master weights)");
+    }
     let results = launch(
         &devices,
         &train_corpus,
         valid.as_ref(),
         &dcfg,
-        move |device| build_model(cfg, device),
+        move |device| {
+            let m = build_model(cfg, device);
+            if bf16 {
+                m.with_compute_dtype(xtrain_tensor::DType::BF16)
+            } else {
+                m
+            }
+        },
     );
     let r0 = &results[0];
     let start = r0.losses.first().copied().unwrap_or(0.0);