diff --git a/tao_compiler/mlir/disc/transforms/disc_op_schedule.cc b/tao_compiler/mlir/disc/transforms/disc_op_schedule.cc
index 36461586229..726af7ed2bd 100644
--- a/tao_compiler/mlir/disc/transforms/disc_op_schedule.cc
+++ b/tao_compiler/mlir/disc/transforms/disc_op_schedule.cc
@@ -354,7 +354,7 @@ class ScheduleGraph {
   explicit ScheduleGraph(std::vector<Operation*>& post_order_instructions,
                          LatencyEstimator* latency_estimator,
                          AsyncTracker* async_tracker) {
-    InitilizeGrpahTopology(post_order_instructions, latency_estimator,
+    InitilizeGraphTopology(post_order_instructions, latency_estimator,
                            async_tracker);
     InitializeGraphAnalysis(latency_estimator, async_tracker);
   }
@@ -497,7 +497,7 @@ class ScheduleGraph {
     }
   }
 
-  void InitilizeGrpahTopology(std::vector<Operation*>& post_order_instructions,
+  void InitilizeGraphTopology(std::vector<Operation*>& post_order_instructions,
                               LatencyEstimator* latency_estimator,
                               AsyncTracker* async_tracker) {
     original_order_ = post_order_instructions;
diff --git a/tao_compiler/mlir/disc/transforms/lhlo_legalize_roots_to_loops.cc b/tao_compiler/mlir/disc/transforms/lhlo_legalize_roots_to_loops.cc
old mode 100644
new mode 100755
index 73b1feaaa68..93789480e5c
--- a/tao_compiler/mlir/disc/transforms/lhlo_legalize_roots_to_loops.cc
+++ b/tao_compiler/mlir/disc/transforms/lhlo_legalize_roots_to_loops.cc
@@ -5712,9 +5712,11 @@ struct DiscLhloLegalizeRootsToParallelLoops
     // TODO: We should put even single nodes into a fusion by fusion pass
     // Revisit this and walk lmhlo::FusionOp only after the revision done.
     func.walk([&](lmhlo::LmhloOp op) {
-      // Skip the embedded ops in lmhlo.fusion or lmhlo.reduce/scatter
+      // Skip the embedded ops in lmhlo.fusion or lmhlo.reduce/scatter or
+      // lmhlo_disc.args_mutation
       lmhlo::LmhloOp parent = op->getParentOfType<lmhlo::LmhloOp>();
-      if (parent && !isa<lmhlo::FusionOp>(op)) {
+      if (isa<lmhlo_disc::ArgsMutationOp>(op) ||
+          parent && !isa<lmhlo::FusionOp>(op)) {
         return;
       }
       if (isFusionType<FusionType::kStitch>(op) &&