diff --git a/ostd/src/task/mod.rs b/ostd/src/task/mod.rs
index d857697ec..a8b0293cb 100644
--- a/ostd/src/task/mod.rs
+++ b/ostd/src/task/mod.rs
@@ -210,7 +210,8 @@ impl TaskOptions {
         /// all task will entering this function
         /// this function is mean to executing the task_fn in Task
         extern "C" fn kernel_task_entry() -> ! {
-            // SAFETY: This is called only once when we are switched to a CPU.
+            // SAFETY: The new task is switched on a CPU for the first time, `after_switching_to`
+            // hasn't been called yet.
             unsafe { processor::after_switching_to() };
 
             let current_task = Task::current()
diff --git a/ostd/src/task/processor.rs b/ostd/src/task/processor.rs
index 889cade8e..c74e066d6 100644
--- a/ostd/src/task/processor.rs
+++ b/ostd/src/task/processor.rs
@@ -49,20 +49,22 @@ pub(super) fn switch_to_task(next_task: Arc<Task>) {
     let current_task_ctx_ptr = if !current_task_ptr.is_null() {
         // SAFETY: The pointer is set by `switch_to_task` and is guaranteed to be
         // built with `Arc::into_raw`. It will only be dropped as a previous task,
-        // So reference will be valid across this function.
+        // so its reference will be valid until `after_switching_to`.
         let current_task = unsafe { &*current_task_ptr };
 
         current_task.save_fpu_state();
 
-        // Throughout this method, the task's context is alive and can be exclusively used.
+        // Until `after_switching_to`, the task's context is alive and can be exclusively used.
         current_task.ctx.get()
     } else {
-        // Throughout this method, interrupts are disabled and the context can be exclusively used.
+        // Until `after_switching_to`, IRQs are disabled and the context can be exclusively used.
         BOOTSTRAP_CONTEXT.as_mut_ptr()
     };
 
     before_switching_to(&next_task, &irq_guard);
 
+    // `before_switching_to` guarantees that from now on, and while the next task is running on the
+    // CPU, its context can be used exclusively.
     let next_task_ctx_ptr = next_task.ctx().get().cast_const();
 
     CURRENT_TASK_PTR.store(Arc::into_raw(next_task));
@@ -73,16 +75,16 @@ pub(super) fn switch_to_task(next_task: Arc<Task>) {
     let _ = core::mem::ManuallyDrop::new(irq_guard);
 
     // SAFETY:
-    // 1. `ctx` is only used in `reschedule()`. We have exclusive access to both the current task
-    //    context and the next task context.
-    // 2. The next task context is a valid task context.
+    // 1. We have exclusive access to both the current context and the next context (see above).
+    // 2. The next context is valid (because it is either correctly initialized or written by a
+    //    previous `context_switch`).
     unsafe {
         // This function may not return, for example, when the current task exits. So make sure
         // that all variables on the stack can be forgotten without causing resource leakage.
         context_switch(current_task_ctx_ptr, next_task_ctx_ptr);
     }
 
-    // SAFETY: We would only call once after switching back to this task.
+    // SAFETY: The task is just switched back, `after_switching_to` hasn't been called yet.
     unsafe { after_switching_to() };
 
     if let Some(current) = Task::current() {
diff --git a/ostd/src/task/scheduler/mod.rs b/ostd/src/task/scheduler/mod.rs
index a8e226224..e2faf8698 100644
--- a/ostd/src/task/scheduler/mod.rs
+++ b/ostd/src/task/scheduler/mod.rs
@@ -259,10 +259,12 @@ where
         };
     };
 
-    // FIXME: At this point, we need to prevent the current task from being scheduled on another
-    // CPU core. However, we currently have no way to ensure this. This is a soundness hole and
-    // should be fixed. See <https://github.com/asterinas/asterinas/issues/1471> for details.
-
+    // `switch_to_task` will spin if it finds that the next task is still running on some CPU core,
+    // which guarantees soundness regardless of the scheduler implementation.
+    //
+    // FIXME: The scheduler decision and context switching are not atomic, which can lead to some
+    // strange behavior even if the scheduler is implemented correctly. See "Problem 2" at
+    // <https://github.com/asterinas/asterinas/issues/1633> for details.
     cpu_local::clear_need_preempt();
     processor::switch_to_task(next_task);
 }