Initial K3 snapshot: 0.5B KDA/MLA/MoE train path

Standalone tree split from LLMRL/projects/kda. Includes Triton dt_bias
backward fix, train_k3 --preset 0.5b, SFT, Docker runtime, and tests.

tests/correctness/test_recurrent.py

@@ -0,0 +1,34 @@
+"""L1: gradcheck for naive_recurrent_kda.
+
+验证策略: torch.autograd.gradcheck 走 forward+backward 五个梯度.
+强制 dtype=float64; eps=1e-6, atol=1e-4.
+
+shape (small):
+    B=2, T=8, H=2, HV=4, K=4, V=4
+"""
+import torch
+
+from kda.ops.reference.recurrent import naive_kda
+
+
+def test_gradcheck():
+    B, T, H, HV, K, V = 2, 8, 2, 4, 4, 4
+    torch.manual_seed(0)
+
+    # 所有输入都需要 requires_grad=True
+    q = torch.randn(B, T, H, K, dtype=torch.float64, requires_grad=True)
+    k = torch.randn(B, T, H, K, dtype=torch.float64, requires_grad=True)
+    v = torch.randn(B, T, HV, V, dtype=torch.float64, requires_grad=True)
+    g = torch.randn(B, T, HV, K, dtype=torch.float64, requires_grad=True) * 0.1
+    beta = torch.rand(B, T, HV, dtype=torch.float64, requires_grad=True)
+
+    assert torch.autograd.gradcheck(
+        lambda q, k, v, g, b: naive_kda(q, k, v, g, b, output_final_state=True),
+        (q, k, v, g, beta),
+        eps=1e-6, atol=1e-4, rtol=1e-3,
+    ), "L1 gradcheck 失败"
+    print("L1 gradcheck: PASSED")
+
+
+if __name__ == "__main__":
+    test_gradcheck()