diff --git a/packages/r-store/index.d.ts b/packages/r-store/index.d.ts
index f07b32c..bd6f8df 100644
--- a/packages/r-store/index.d.ts
+++ b/packages/r-store/index.d.ts
@@ -205,7 +205,7 @@ export declare const useReactiveState: <T extends Record<string, unknown>>(initi
  */
 export declare type UseSelectorWithState<T, C> = {
     (): DeepReadonly<UnwrapNestedRefs<T>> & C;
-    <P>(selector: (state: DeepReadonly<UnwrapNestedRefs<T>> & C) => P, compare?: (prev: P, next: P) => boolean): P;
+    <P>(selector: (state: DeepReadonly<UnwrapNestedRefs<T>> & C) => P, compare?: <Q extends P = P>(prev: Q, next: Q) => boolean): P;
     /**
      * @deprecated
      * use `getReactiveState` / `getReadonlyState` instead
@@ -215,22 +215,28 @@ export declare type UseSelectorWithState<T, C> = {
     getLifeCycle: () => LifeCycle;
     getReactiveState: () => UnwrapNestedRefs<T>;
     getReadonlyState: () => DeepReadonly<UnwrapNestedRefs<T>>;
+    /**
+     *
+     * @param selector - a method to select the state, when the state change, the `cb` will be called
+     * @param cb - a callback function
+     * @returns a unsubscribe function
+     */
     subscribe: <P>(selector: (state: DeepReadonly<UnwrapNestedRefs<T>>) => P, cb?: () => void, shallow?: boolean) => () => void;
     useDeepSelector: {
         (): DeepReadonly<UnwrapNestedRefs<T>> & C;
-        <P>(selector: (state: DeepReadonly<UnwrapNestedRefs<T>> & C) => P, compare?: (prev: P, next: P) => boolean): P;
+        <P>(selector: (state: DeepReadonly<UnwrapNestedRefs<T>> & C) => P, compare?: <Q extends P = P>(prev: Q, next: Q) => boolean): P;
     };
     useDeepStableSelector: {
         (): DeepReadonly<UnwrapNestedRefs<T>> & C;
-        <P>(selector: (state: DeepReadonly<UnwrapNestedRefs<T>> & C) => P, compare?: (prev: P, next: P) => boolean): P;
+        <P>(selector: (state: DeepReadonly<UnwrapNestedRefs<T>> & C) => P, compare?: <Q extends P = P>(prev: Q, next: Q) => boolean): P;
     };
     useShallowSelector: {
         (): DeepReadonly<UnwrapNestedRefs<T>> & C;
-        <P>(selector: (state: DeepReadonly<UnwrapNestedRefs<T>> & C) => P, compare?: (prev: P, next: P) => boolean): P;
+        <P>(selector: (state: DeepReadonly<UnwrapNestedRefs<T>> & C) => P, compare?: <Q extends P = P>(prev: Q, next: Q) => boolean): P;
     };
     useShallowStableSelector: {
         (): DeepReadonly<UnwrapNestedRefs<T>> & C;
-        <P>(selector: (state: DeepReadonly<UnwrapNestedRefs<T>> & C) => P, compare?: (prev: P, next: P) => boolean): P;
+        <P>(selector: (state: DeepReadonly<UnwrapNestedRefs<T>> & C) => P, compare?: <Q extends P = P>(prev: Q, next: Q) => boolean): P;
     };
 };
 
@@ -239,7 +245,7 @@ export declare type UseSelectorWithState<T, C> = {
  */
 export declare type UseSelectorWithStore<T> = {
     (): DeepReadonly<UnwrapNestedRefs<T>>;
-    <P>(selector: (state: DeepReadonly<UnwrapNestedRefs<T>>) => P): P;
+    <P>(selector: (state: DeepReadonly<UnwrapNestedRefs<T>>) => P, compare?: <Q extends P = P>(prev: Q, next: Q) => boolean): P;
     /**
      * @deprecated
      * use `getReactiveState` / `getReadonlyState` instead
@@ -248,22 +254,28 @@ export declare type UseSelectorWithStore<T> = {
     getLifeCycle: () => LifeCycle;
     getReactiveState: () => UnwrapNestedRefs<T>;
     getReadonlyState: () => DeepReadonly<UnwrapNestedRefs<T>>;
+    /**
+     *
+     * @param selector - a method to select the state, when the state change, the `cb` will be called
+     * @param cb - a callback function
+     * @returns a unsubscribe function
+     */
     subscribe: <P>(selector: (state: DeepReadonly<UnwrapNestedRefs<T>>) => P, cb?: () => void, shallow?: boolean) => () => void;
     useShallowSelector: {
         (): DeepReadonly<UnwrapNestedRefs<T>>;
-        <P>(selector: (state: DeepReadonly<UnwrapNestedRefs<T>>) => P): P;
+        <P>(selector: (state: DeepReadonly<UnwrapNestedRefs<T>>) => P, compare?: <Q extends P = P>(prev: Q, next: Q) => boolean): P;
     };
     useShallowStableSelector: {
         (): DeepReadonly<UnwrapNestedRefs<T>>;
-        <P>(selector: (state: DeepReadonly<UnwrapNestedRefs<T>>) => P): P;
+        <P>(selector: (state: DeepReadonly<UnwrapNestedRefs<T>>) => P, compare?: <Q extends P = P>(prev: Q, next: Q) => boolean): P;
     };
     useDeepSelector: {
         (): DeepReadonly<UnwrapNestedRefs<T>>;
-        <P>(selector: (state: DeepReadonly<UnwrapNestedRefs<T>>) => P): P;
+        <P>(selector: (state: DeepReadonly<UnwrapNestedRefs<T>>) => P, compare?: <Q extends P = P>(prev: Q, next: Q) => boolean): P;
     };
     useDeepStableSelector: {
         (): DeepReadonly<UnwrapNestedRefs<T>>;
-        <P>(selector: (state: DeepReadonly<UnwrapNestedRefs<T>>) => P): P;
+        <P>(selector: (state: DeepReadonly<UnwrapNestedRefs<T>>) => P, compare?: <Q extends P = P>(prev: Q, next: Q) => boolean): P;
     };
 };
 
diff --git a/packages/r-store/src/__test__/type.tsx b/packages/r-store/src/__test__/type.tsx
index ef5cbfe..a2272ba 100644
--- a/packages/r-store/src/__test__/type.tsx
+++ b/packages/r-store/src/__test__/type.tsx
@@ -43,9 +43,9 @@ const useFf = createStore(() => {
   return { vvv };
 });
 
-const h = useFf((s) => s);
+const h = useFf((s) => s.vvv, (p, c) => p === c);
 
-const i = useCount((s) => s);
+const i = useCount((s) => s, Object.is);
 
 const useCount_v2 = createState(
   withActions(
diff --git a/packages/r-store/src/shared/hook.ts b/packages/r-store/src/shared/hook.ts
index bdc30ab..63ee169 100644
--- a/packages/r-store/src/shared/hook.ts
+++ b/packages/r-store/src/shared/hook.ts
@@ -201,8 +201,8 @@ export const createHook = <T extends Record<string, unknown>, C extends Record<s
   const shallowStableHook = generateUseHook("shallow-stable");
 
   function useSelector(): DeepReadonly<UnwrapNestedRefs<T>> & C;
-  function useSelector<P>(selector: (state: DeepReadonly<UnwrapNestedRefs<T>> & C) => P, compare?: (prev: P, next: P) => boolean): P;
-  function useSelector<P>(selector?: (state: DeepReadonly<UnwrapNestedRefs<T>> & C) => P, compare?: (prev: P, next: P) => boolean) {
+  function useSelector<P>(selector: (state: DeepReadonly<UnwrapNestedRefs<T>> & C) => P, compare?: <Q extends P = P>(prev: Q, next: Q) => boolean): P;
+  function useSelector<P>(selector?: (state: DeepReadonly<UnwrapNestedRefs<T>> & C) => P, compare?: <Q extends P = P>(prev: Q, next: Q) => boolean) {
     return defaultHook(selector, compare);
   }
 
diff --git a/packages/r-store/src/state/createState.ts b/packages/r-store/src/state/createState.ts
index 49a41eb..67e4c9b 100644
--- a/packages/r-store/src/state/createState.ts
+++ b/packages/r-store/src/state/createState.ts
@@ -19,7 +19,7 @@ export type Setup<T> = () => T;
  */
 export type UseSelectorWithState<T, C> = {
   (): DeepReadonly<UnwrapNestedRefs<T>> & C;
-  <P>(selector: (state: DeepReadonly<UnwrapNestedRefs<T>> & C) => P, compare?: (prev: P, next: P) => boolean): P;
+  <P>(selector: (state: DeepReadonly<UnwrapNestedRefs<T>> & C) => P, compare?: <Q extends P = P>(prev: Q, next: Q) => boolean): P;
   /**
    * @deprecated
    * use `getReactiveState` / `getReadonlyState` instead
@@ -29,22 +29,28 @@ export type UseSelectorWithState<T, C> = {
   getLifeCycle: () => LifeCycle;
   getReactiveState: () => UnwrapNestedRefs<T>;
   getReadonlyState: () => DeepReadonly<UnwrapNestedRefs<T>>;
+  /**
+   *
+   * @param selector - a method to select the state, when the state change, the `cb` will be called
+   * @param cb - a callback function
+   * @returns a unsubscribe function
+   */
   subscribe: <P>(selector: (state: DeepReadonly<UnwrapNestedRefs<T>>) => P, cb?: () => void, shallow?: boolean) => () => void;
   useDeepSelector: {
     (): DeepReadonly<UnwrapNestedRefs<T>> & C;
-    <P>(selector: (state: DeepReadonly<UnwrapNestedRefs<T>> & C) => P, compare?: (prev: P, next: P) => boolean): P;
+    <P>(selector: (state: DeepReadonly<UnwrapNestedRefs<T>> & C) => P, compare?: <Q extends P = P>(prev: Q, next: Q) => boolean): P;
   };
   useDeepStableSelector: {
     (): DeepReadonly<UnwrapNestedRefs<T>> & C;
-    <P>(selector: (state: DeepReadonly<UnwrapNestedRefs<T>> & C) => P, compare?: (prev: P, next: P) => boolean): P;
+    <P>(selector: (state: DeepReadonly<UnwrapNestedRefs<T>> & C) => P, compare?: <Q extends P = P>(prev: Q, next: Q) => boolean): P;
   };
   useShallowSelector: {
     (): DeepReadonly<UnwrapNestedRefs<T>> & C;
-    <P>(selector: (state: DeepReadonly<UnwrapNestedRefs<T>> & C) => P, compare?: (prev: P, next: P) => boolean): P;
+    <P>(selector: (state: DeepReadonly<UnwrapNestedRefs<T>> & C) => P, compare?: <Q extends P = P>(prev: Q, next: Q) => boolean): P;
   };
   useShallowStableSelector: {
     (): DeepReadonly<UnwrapNestedRefs<T>> & C;
-    <P>(selector: (state: DeepReadonly<UnwrapNestedRefs<T>> & C) => P, compare?: (prev: P, next: P) => boolean): P;
+    <P>(selector: (state: DeepReadonly<UnwrapNestedRefs<T>> & C) => P, compare?: <Q extends P = P>(prev: Q, next: Q) => boolean): P;
   };
 };
 
diff --git a/packages/r-store/src/store/createStore.ts b/packages/r-store/src/store/createStore.ts
index be03900..f8be16b 100644
--- a/packages/r-store/src/store/createStore.ts
+++ b/packages/r-store/src/store/createStore.ts
@@ -11,7 +11,7 @@ export type { Creator } from "./_internal";
  */
 export type UseSelectorWithStore<T> = {
   (): DeepReadonly<UnwrapNestedRefs<T>>;
-  <P>(selector: (state: DeepReadonly<UnwrapNestedRefs<T>>) => P): P;
+  <P>(selector: (state: DeepReadonly<UnwrapNestedRefs<T>>) => P, compare?: <Q extends P = P>(prev: Q, next: Q) => boolean): P;
   /**
    * @deprecated
    * use `getReactiveState` / `getReadonlyState` instead
@@ -20,23 +20,29 @@ export type UseSelectorWithStore<T> = {
   getLifeCycle: () => LifeCycle;
   getReactiveState: () => UnwrapNestedRefs<T>;
   getReadonlyState: () => DeepReadonly<UnwrapNestedRefs<T>>;
+  /**
+   * 
+   * @param selector - a method to select the state, when the state change, the `cb` will be called
+   * @param cb - a callback function
+   * @returns a unsubscribe function
+   */
   subscribe: <P>(selector: (state: DeepReadonly<UnwrapNestedRefs<T>>) => P, cb?: () => void, shallow?: boolean) => () => void;
   useShallowSelector: {
     (): DeepReadonly<UnwrapNestedRefs<T>>;
-    <P>(selector: (state: DeepReadonly<UnwrapNestedRefs<T>>) => P): P;
+    <P>(selector: (state: DeepReadonly<UnwrapNestedRefs<T>>) => P, compare?: <Q extends P = P>(prev: Q, next: Q) => boolean): P;
   };
   useShallowStableSelector: {
     (): DeepReadonly<UnwrapNestedRefs<T>>;
-    <P>(selector: (state: DeepReadonly<UnwrapNestedRefs<T>>) => P): P;
+    <P>(selector: (state: DeepReadonly<UnwrapNestedRefs<T>>) => P, compare?: <Q extends P = P>(prev: Q, next: Q) => boolean): P;
   };
   useDeepSelector: {
     (): DeepReadonly<UnwrapNestedRefs<T>>;
-    <P>(selector: (state: DeepReadonly<UnwrapNestedRefs<T>>) => P): P;
+    <P>(selector: (state: DeepReadonly<UnwrapNestedRefs<T>>) => P, compare?: <Q extends P = P>(prev: Q, next: Q) => boolean): P;
   };
   useDeepStableSelector: {
     (): DeepReadonly<UnwrapNestedRefs<T>>;
-    <P>(selector: (state: DeepReadonly<UnwrapNestedRefs<T>>) => P): P;
-  }
+    <P>(selector: (state: DeepReadonly<UnwrapNestedRefs<T>>) => P, compare?: <Q extends P = P>(prev: Q, next: Q) => boolean): P;
+  };
 };
 
 /**