diff --git a/KLR/NKI/Simplify.lean b/KLR/NKI/Simplify.lean
index c473fc4f..9aec2128 100644
--- a/KLR/NKI/Simplify.lean
+++ b/KLR/NKI/Simplify.lean
@@ -509,7 +509,7 @@ private def edgeName (e : Expr) : Simplify String :=
   | .value (.string s) => return s
   | _ => throw "Schedule edge name must be a string"
 
-private def edge (py : Python.Expr) : Simplify Edges := do
+private def edge (py : Python.Expr) : Simplify (List Edges) := do
   let e <- expr py
   match e.expr with
   | .tuple [e1, e2] =>
@@ -517,7 +517,11 @@ private def edge (py : Python.Expr) : Simplify Edges := do
     let e2 <- match e2.expr with
       | .list es => es.mapM edgeName
       | _ => pure [<- edgeName e2]
-    return .mk e1 e2
+    -- Edges are represented in Python like (x, [y1, y2, ...]).
+    -- This means that x depends on y1, y2, ... and must be scheduled after each of them.
+    -- However components consuming KLIR expect the reverse: y1, y2, ... each depend on x.
+    -- Reverse user-provided scheduling edges to address this.
+    return e2.map (.mk · [e1])
   | _ => throw "Schedule edge must be a pair"
 
 private def flags (py : Python.Expr) : Simplify (String × Value) := do
@@ -549,6 +553,6 @@ def simplify (py : Python.Kernel) : Simplify Kernel := do
     globals := <- kwargs py.globals
     arch    := py.arch
     grid    := py.grid
-    edges   := <- py.scheduleEdges.mapM edge
+    edges   := <- py.scheduleEdges.foldlM (fun acc e => return (<- edge e) ++ acc) []
     flags   := <- py.flags.mapM flags
   }
diff --git a/KLR/Trace/Types.lean b/KLR/Trace/Types.lean
index 294d95a0..9719b270 100644
--- a/KLR/Trace/Types.lean
+++ b/KLR/Trace/Types.lean
@@ -355,7 +355,7 @@ private def swapLast (engine : Engine) (name : String) (last : LastInst) : LastI
 private def updateLast (engine : Engine) (name : String) (state : State) : State :=
   if state.noReorderDepth == 0 then state else
     let (last, names) := swapLast engine name state.lastInst
-    let edges := names.map (name, ·)
+    let edges := names.map (·, name)
     { state with lastInst := last, edges := edges ++ state.edges }
 
 def add_stmt (stmt : Pos -> Stmt) : Trace Unit := do