diff --git a/engine/ggml/src/ggml.c b/engine/ggml/src/ggml.c
index b43016c8..55d50ad8 100644
--- a/engine/ggml/src/ggml.c
+++ b/engine/ggml/src/ggml.c
@@ -6597,6 +6597,52 @@ static void ggml_compute_backward(
                 ggml_add_or_set(ctx, cgraph, isrc0, tmp);
             }
             if (src1_needs_grads) {
+                // HOT-Step patch: mm-backward — see engine/patches/mm-backward.patch
+                //
+                // The default arm below emits the ACTIVATION gradient as OUT_PROD.
+                // ggml-cuda implements OUT_PROD F32-only (cublasSgemm), so the frozen
+                // weight src0 must be F32, which drags the FORWARD mul_mat onto TF32
+                // tensor cores too. The mul_mat formulation upstream left commented
+                // out here is dtype-agnostic, so a BF16 src0 rides real BF16 tensor
+                // cores with no dequant and no F32 window.
+                //
+                // The two are provably shape-identical:
+                //   out_prod(src0[n,m,q1,r1], transpose(grad)[p,m,qq,rr]) -> [n,p,qq,rr]
+                //   mul_mat(cont(transpose(src0))[m,n,q1,r1], grad[m,p,qq,rr]) -> [n,p,qq,rr]
+                // and their broadcast preconditions are the same pair of
+                // (b->ne[2] % a->ne[2] == 0, b->ne[3] % a->ne[3] == 0) checks.
+                //
+                // Measured on an RTX 5090 (engine/src/train/spike-gemmbench.h): 1.67-1.82x
+                // per layer per step, parity vs the TF32 out_prod arm cosine 0.999996 /
+                // max_rel ~4e-3. Per-use `cont` is free at these shapes, so no
+                // pre-transposed weight cache is needed.
+                //
+                // Env-gated so an unset environment is byte-identical to upstream.
+                // Set GGML_BACKWARD_MM=1 (ace-train's `--bwd mm`) to take it. Read once:
+                // this runs once per mul_mat per graph build, and getenv is not free.
+                //
+                // CONTIGUITY GUARD (measured, not theoretical): `grad` becomes
+                // mul_mat's src1, and the CUDA mul_mat kernels require src1 to be
+                // row-contiguous — ggml-cuda/mmf.cu:28 asserts `nb10 == ts_src1`
+                // and ABORTS otherwise. out_prod has no such requirement, which is
+                // why upstream can hand it an arbitrary transposed view. A
+                // non-contiguous grad therefore keeps the out_prod arm rather than
+                // crashing (ggml_cont on grad is not the answer: grad is an
+                // ACTIVATION-sized tensor, so copying it would cost more than the
+                // GEMM saves). Found by ace-train train-dit --self-test under
+                // GGML_BACKWARD_MM=1: the LoKR rung SC3 aborted here.
+                static int hs_bwd_mm = -1;
+                if (hs_bwd_mm < 0) {
+                    const char * hs_e = getenv("GGML_BACKWARD_MM");
+                    hs_bwd_mm = (hs_e && hs_e[0] && strcmp(hs_e, "0") != 0) ? 1 : 0;
+                }
+                if (hs_bwd_mm && ggml_is_contiguous(grad)) {
+                    ggml_add_or_set(ctx, cgraph, isrc1,
+                            ggml_mul_mat(ctx,                   // [n,p,qq,rr]
+                                ggml_cont(ctx,                  // [m,n,q1,r1]
+                                    ggml_transpose(ctx, src0)), // [m,n,q1,r1]
+                                grad));                         // [m,p,qq,rr]
+                } else {
                 ggml_add_or_set(ctx, cgraph, isrc1,
                         // ggml_mul_mat(ctx,                   // [n,p,qq,rr]
                         //     ggml_cont(ctx,                  // [m,n,q1,r1]
@@ -6610,6 +6656,7 @@ static void ggml_compute_backward(
                             src0,               // [n,m,q1,r1]
                             ggml_transpose(ctx, // [p,m,qq,rr]
                                 grad)));        // [m,p,qq,rr]
+                }
             }
         } break;
         case GGML_OP_SCALE: {