diff --git a/taichi/analysis/gather_immutable_local_vars.cpp b/taichi/analysis/gather_immutable_local_vars.cpp
new file mode 100644
index 0000000000000..82234a87999af
--- /dev/null
+++ b/taichi/analysis/gather_immutable_local_vars.cpp
@@ -0,0 +1,92 @@
+#include "taichi/ir/ir.h"
+#include "taichi/ir/statements.h"
+#include "taichi/ir/transforms.h"
+#include "taichi/ir/visitors.h"
+
+namespace taichi::lang {
+
+// The GatherImmutableLocalVars pass gathers all immutable local vars as input
+// to the EliminateImmutableLocalVars pass. An immutable local var is an alloca
+// which is stored only once (in the same block) and only loaded after that
+// store.
+class GatherImmutableLocalVars : public BasicStmtVisitor {
+ private:
+  using BasicStmtVisitor::visit;
+
+  enum class AllocaStatus { kCreated = 0, kStoredOnce = 1, kInvalid = 2 };
+  std::unordered_map<Stmt *, AllocaStatus> alloca_status_;
+
+ public:
+  explicit GatherImmutableLocalVars() {
+    invoke_default_visitor = true;
+  }
+
+  void visit(AllocaStmt *stmt) override {
+    TI_ASSERT(alloca_status_.find(stmt) == alloca_status_.end());
+    alloca_status_[stmt] = AllocaStatus::kCreated;
+  }
+
+  void visit(LocalLoadStmt *stmt) override {
+    if (stmt->src->is<AllocaStmt>()) {
+      auto status_iter = alloca_status_.find(stmt->src);
+      TI_ASSERT(status_iter != alloca_status_.end());
+      if (status_iter->second == AllocaStatus::kCreated) {
+        status_iter->second = AllocaStatus::kInvalid;
+      }
+    }
+  }
+
+  void visit(LocalStoreStmt *stmt) override {
+    if (stmt->dest->is<AllocaStmt>()) {
+      auto status_iter = alloca_status_.find(stmt->dest);
+      TI_ASSERT(status_iter != alloca_status_.end());
+      if (stmt->parent != stmt->dest->parent ||
+          status_iter->second == AllocaStatus::kStoredOnce ||
+          stmt->val->ret_type != stmt->dest->ret_type.ptr_removed()) {
+        status_iter->second = AllocaStatus::kInvalid;
+      } else if (status_iter->second == AllocaStatus::kCreated) {
+        status_iter->second = AllocaStatus::kStoredOnce;
+      }
+    }
+  }
+
+  void default_visit(Stmt *stmt) {
+    for (auto &op : stmt->get_operands()) {
+      if (op != nullptr && op->is<AllocaStmt>()) {
+        auto status_iter = alloca_status_.find(op);
+        TI_ASSERT(status_iter != alloca_status_.end());
+        status_iter->second = AllocaStatus::kInvalid;
+      }
+    }
+  }
+
+  void visit(Stmt *stmt) override {
+    default_visit(stmt);
+  }
+
+  void preprocess_container_stmt(Stmt *stmt) override {
+    default_visit(stmt);
+  }
+
+  static std::unordered_set<Stmt *> run(IRNode *node) {
+    GatherImmutableLocalVars pass;
+    node->accept(&pass);
+    std::unordered_set<Stmt *> result;
+    for (auto &[k, v] : pass.alloca_status_) {
+      if (v == AllocaStatus::kStoredOnce) {
+        result.insert(k);
+      }
+    }
+    return result;
+  }
+};
+
+namespace irpass::analysis {
+
+std::unordered_set<Stmt *> gather_immutable_local_vars(IRNode *root) {
+  return GatherImmutableLocalVars::run(root);
+}
+
+}  // namespace irpass::analysis
+
+}  // namespace taichi::lang
diff --git a/taichi/ir/analysis.h b/taichi/ir/analysis.h
index dc2159d453316..69d68ee4a32d1 100644
--- a/taichi/ir/analysis.h
+++ b/taichi/ir/analysis.h
@@ -95,6 +95,7 @@ bool definitely_same_address(Stmt *var1, Stmt *var2);
 
 std::unordered_set<Stmt *> detect_fors_with_break(IRNode *root);
 std::unordered_set<Stmt *> detect_loops_with_continue(IRNode *root);
+std::unordered_set<Stmt *> gather_immutable_local_vars(IRNode *root);
 std::unordered_set<SNode *> gather_deactivations(IRNode *root);
 std::pair<std::unordered_set<SNode *>, std::unordered_set<SNode *>>
 gather_snode_read_writes(IRNode *root);
diff --git a/taichi/ir/frontend_ir.cpp b/taichi/ir/frontend_ir.cpp
index 630bef729602f..97ecf385604de 100644
--- a/taichi/ir/frontend_ir.cpp
+++ b/taichi/ir/frontend_ir.cpp
@@ -670,9 +670,12 @@ Stmt *make_tensor_access(Expression::FlattenContext *ctx,
 }
 
 void MatrixExpression::type_check(CompileConfig *config) {
-  // TODO: typecheck matrix
   for (auto &arg : elements) {
     TI_ASSERT_TYPE_CHECKED(arg);
+    if (arg->ret_type != dt.get_element_type()) {
+      arg = cast(arg, dt.get_element_type());
+      arg->type_check(config);
+    }
   }
   ret_type = dt;
 }
@@ -1569,8 +1572,9 @@ Stmt *flatten_global_load(Stmt *ptr_stmt, Expression::FlattenContext *ctx) {
 }
 
 Stmt *flatten_local_load(Stmt *ptr_stmt, Expression::FlattenContext *ctx) {
-  ctx->push_back<LocalLoadStmt>(ptr_stmt);
-  return ctx->back_stmt();
+  auto local_load = ctx->push_back<LocalLoadStmt>(ptr_stmt);
+  local_load->ret_type = local_load->src->ret_type.ptr_removed();
+  return local_load;
 }
 
 Stmt *flatten_rvalue(Expr ptr, Expression::FlattenContext *ctx) {
diff --git a/taichi/ir/transforms.h b/taichi/ir/transforms.h
index ed8571fe02825..20bbb0533c841 100644
--- a/taichi/ir/transforms.h
+++ b/taichi/ir/transforms.h
@@ -29,6 +29,7 @@ namespace irpass {
 
 void re_id(IRNode *root);
 void flag_access(IRNode *root);
+void eliminate_immutable_local_vars(IRNode *root);
 void scalarize(IRNode *root, const CompileConfig &config);
 void lower_matrix_ptr(IRNode *root);
 bool die(IRNode *root);
diff --git a/taichi/transforms/compile_to_offloads.cpp b/taichi/transforms/compile_to_offloads.cpp
index 847b376801dbe..cf3a31e13a61d 100644
--- a/taichi/transforms/compile_to_offloads.cpp
+++ b/taichi/transforms/compile_to_offloads.cpp
@@ -52,6 +52,9 @@ void compile_to_offloads(IRNode *ir,
     print("Lowered");
   }
 
+  irpass::eliminate_immutable_local_vars(ir);
+  print("Immutable local vars eliminated");
+
   if (config.real_matrix_scalarize) {
     irpass::scalarize(ir, config);
 
diff --git a/taichi/transforms/eliminate_immutable_local_vars.cpp b/taichi/transforms/eliminate_immutable_local_vars.cpp
new file mode 100644
index 0000000000000..036e96459f574
--- /dev/null
+++ b/taichi/transforms/eliminate_immutable_local_vars.cpp
@@ -0,0 +1,67 @@
+#include "taichi/ir/ir.h"
+#include "taichi/ir/statements.h"
+#include "taichi/ir/analysis.h"
+#include "taichi/ir/visitors.h"
+#include "taichi/system/profiler.h"
+
+namespace taichi::lang {
+
+// The EliminateImmutableLocalVars pass eliminates all immutable local vars
+// calculated from the GatherImmutableLocalVars pass. An immutable local var
+// can be eliminated by forwarding the value of its only store to all loads
+// after that store. See https://github.com/taichi-dev/taichi/pull/6926 for the
+// background of this optimization.
+class EliminateImmutableLocalVars : public BasicStmtVisitor {
+ private:
+  using BasicStmtVisitor::visit;
+
+  DelayedIRModifier modifier_;
+  std::unordered_set<Stmt *> immutable_local_vars_;
+  std::unordered_map<Stmt *, Stmt *> immutable_local_var_to_value_;
+
+ public:
+  explicit EliminateImmutableLocalVars(
+      const std::unordered_set<Stmt *> &immutable_local_vars)
+      : immutable_local_vars_(immutable_local_vars) {
+  }
+
+  void visit(AllocaStmt *stmt) override {
+    if (immutable_local_vars_.find(stmt) != immutable_local_vars_.end()) {
+      modifier_.erase(stmt);
+    }
+  }
+
+  void visit(LocalLoadStmt *stmt) override {
+    if (immutable_local_vars_.find(stmt->src) != immutable_local_vars_.end()) {
+      stmt->replace_usages_with(immutable_local_var_to_value_[stmt->src]);
+      modifier_.erase(stmt);
+    }
+  }
+
+  void visit(LocalStoreStmt *stmt) override {
+    if (immutable_local_vars_.find(stmt->dest) != immutable_local_vars_.end()) {
+      TI_ASSERT(immutable_local_var_to_value_.find(stmt->dest) ==
+                immutable_local_var_to_value_.end());
+      immutable_local_var_to_value_[stmt->dest] = stmt->val;
+      modifier_.erase(stmt);
+    }
+  }
+
+  static void run(IRNode *node) {
+    EliminateImmutableLocalVars pass(
+        irpass::analysis::gather_immutable_local_vars(node));
+    node->accept(&pass);
+    pass.modifier_.modify_ir();
+  }
+};
+
+namespace irpass {
+
+void eliminate_immutable_local_vars(IRNode *root) {
+  TI_AUTO_PROF;
+  EliminateImmutableLocalVars::run(root);
+}
+
+}  // namespace irpass
+
+}  // namespace taichi::lang