diff --git a/.idea/workspace.xml b/.idea/workspace.xml
index 038f707..91accaa 100644
--- a/.idea/workspace.xml
+++ b/.idea/workspace.xml
@@ -2,9 +2,7 @@
 <project version="4">
   <component name="ChangeListManager">
     <list default="true" id="be5bf74e-ad1c-4197-8a1f-ac93566d8aa7" name="Default" comment="init">
-      <change type="NEW" beforePath="" afterPath="$PROJECT_DIR$/机器学习/聚类/kmeans.md" />
-      <change type="NEW" beforePath="" afterPath="$PROJECT_DIR$/自然语言处理/GloVe.md" />
-      <change type="NEW" beforePath="" afterPath="$PROJECT_DIR$/自然语言处理/Word2Vec.md" />
+      <change type="NEW" beforePath="" afterPath="$PROJECT_DIR$/自然语言处理/CRF.md" />
       <change type="MODIFICATION" beforePath="$PROJECT_DIR$/.idea/workspace.xml" afterPath="$PROJECT_DIR$/.idea/workspace.xml" />
       <change type="MODIFICATION" beforePath="$PROJECT_DIR$/README.md" afterPath="$PROJECT_DIR$/README.md" />
     </list>
@@ -27,7 +25,7 @@
   </component>
   <component name="FileEditorManager">
     <leaf SIDE_TABS_SIZE_LIMIT_KEY="300">
-      <file leaf-file-name="README.md" pinned="false" current-in-tab="true">
+      <file leaf-file-name="README.md" pinned="false" current-in-tab="false">
         <entry file="file://$PROJECT_DIR$/README.md">
           <provider editor-type-id="split-provider[text-editor;MarkdownPreviewEditor]">
             <state split_layout="SPLIT">
@@ -42,8 +40,8 @@
           </provider>
           <provider selected="true" editor-type-id="split-provider[text-editor;markdown-preview-editor]">
             <state split_layout="SPLIT">
-              <first_editor relative-caret-position="519">
-                <caret line="306" column="23" selection-start-line="306" selection-start-column="23" selection-end-line="306" selection-end-column="23" />
+              <first_editor relative-caret-position="384">
+                <caret line="307" column="5" selection-start-line="307" selection-start-column="2" selection-end-line="307" selection-end-column="5" />
                 <folding />
               </first_editor>
               <second_editor />
@@ -51,8 +49,8 @@
           </provider>
         </entry>
       </file>
-      <file leaf-file-name="Word2Vec.md" pinned="false" current-in-tab="false">
-        <entry file="file://$PROJECT_DIR$/自然语言处理/Word2Vec.md">
+      <file leaf-file-name="CRF.md" pinned="false" current-in-tab="true">
+        <entry file="file://$PROJECT_DIR$/自然语言处理/CRF.md">
           <provider editor-type-id="split-provider[text-editor;MarkdownPreviewEditor]">
             <state split_layout="SPLIT">
               <first_editor relative-caret-position="0">
@@ -66,8 +64,8 @@
           </provider>
           <provider selected="true" editor-type-id="split-provider[text-editor;markdown-preview-editor]">
             <state split_layout="SPLIT">
-              <first_editor relative-caret-position="390">
-                <caret line="26" column="18" selection-start-line="26" selection-start-column="2" selection-end-line="26" selection-end-column="18" />
+              <first_editor relative-caret-position="285">
+                <caret line="19" column="51" selection-start-line="19" selection-start-column="51" selection-end-line="19" selection-end-column="51" />
                 <folding />
               </first_editor>
               <second_editor />
@@ -122,6 +120,7 @@
         <option value="$PROJECT_DIR$/自然语言处理/GloVe.md" />
         <option value="$PROJECT_DIR$/自然语言处理/Word2Vec.md" />
         <option value="$PROJECT_DIR$/README.md" />
+        <option value="$PROJECT_DIR$/自然语言处理/CRF.md" />
       </list>
     </option>
   </component>
@@ -231,20 +230,6 @@
               <option name="myItemType" value="com.intellij.ide.projectView.impl.nodes.PsiDirectoryNode" />
             </PATH_ELEMENT>
           </PATH>
-          <PATH>
-            <PATH_ELEMENT>
-              <option name="myItemId" value="Reflection_Summary" />
-              <option name="myItemType" value="com.intellij.ide.projectView.impl.nodes.ProjectViewProjectNode" />
-            </PATH_ELEMENT>
-            <PATH_ELEMENT>
-              <option name="myItemId" value="Reflection_Summary" />
-              <option name="myItemType" value="com.intellij.ide.projectView.impl.nodes.PsiDirectoryNode" />
-            </PATH_ELEMENT>
-            <PATH_ELEMENT>
-              <option name="myItemId" value="机器学习" />
-              <option name="myItemType" value="com.intellij.ide.projectView.impl.nodes.PsiDirectoryNode" />
-            </PATH_ELEMENT>
-          </PATH>
         </subPane>
       </pane>
       <pane id="Scope" />
@@ -549,9 +534,9 @@
   </component>
   <component name="ToolWindowManager">
     <frame x="0" y="23" width="1440" height="823" extended-state="6" />
-    <editor active="false" />
+    <editor active="true" />
     <layout>
-      <window_info id="Project" active="true" anchor="left" auto_hide="false" internal_type="DOCKED" type="DOCKED" visible="true" show_stripe_button="true" weight="0.119456366" sideWeight="0.5" order="0" side_tool="false" content_ui="combo" />
+      <window_info id="Project" active="false" anchor="left" auto_hide="false" internal_type="DOCKED" type="DOCKED" visible="true" show_stripe_button="true" weight="0.119456366" sideWeight="0.5" order="0" side_tool="false" content_ui="combo" />
       <window_info id="TODO" active="false" anchor="bottom" auto_hide="false" internal_type="DOCKED" type="DOCKED" visible="false" show_stripe_button="true" weight="0.33" sideWeight="0.5" order="6" side_tool="false" content_ui="tabs" />
       <window_info id="Event Log" active="false" anchor="bottom" auto_hide="false" internal_type="DOCKED" type="DOCKED" visible="false" show_stripe_button="true" weight="0.33" sideWeight="0.5" order="7" side_tool="true" content_ui="tabs" />
       <window_info id="Database" active="false" anchor="right" auto_hide="false" internal_type="DOCKED" type="DOCKED" visible="false" show_stripe_button="true" weight="0.33" sideWeight="0.5" order="3" side_tool="false" content_ui="tabs" />
@@ -615,16 +600,6 @@
     <watches-manager />
   </component>
   <component name="editorHistoryManager">
-    <entry file="file://$PROJECT_DIR$/数学/微分中值定理/微分中值定理.md">
-      <provider selected="true" editor-type-id="split-provider[text-editor;markdown-preview-editor]">
-        <state split_layout="SPLIT">
-          <first_editor relative-caret-position="195">
-            <caret line="13" column="35" selection-start-line="13" selection-start-column="35" selection-end-line="13" selection-end-column="36" />
-          </first_editor>
-          <second_editor />
-        </state>
-      </provider>
-    </entry>
     <entry file="file://$PROJECT_DIR$/数学/泰勒公式/泰勒公式.md">
       <provider selected="true" editor-type-id="split-provider[text-editor;markdown-preview-editor]">
         <state split_layout="SPLIT">
@@ -1200,8 +1175,8 @@
       </provider>
       <provider selected="true" editor-type-id="split-provider[text-editor;markdown-preview-editor]">
         <state split_layout="SPLIT">
-          <first_editor relative-caret-position="390">
-            <caret line="26" column="18" selection-start-line="26" selection-start-column="2" selection-end-line="26" selection-end-column="18" />
+          <first_editor relative-caret-position="450">
+            <caret line="30" column="50" selection-start-line="30" selection-start-column="50" selection-end-line="30" selection-end-column="50" />
             <folding />
           </first_editor>
           <second_editor />
@@ -1222,8 +1197,30 @@
       </provider>
       <provider selected="true" editor-type-id="split-provider[text-editor;markdown-preview-editor]">
         <state split_layout="SPLIT">
-          <first_editor relative-caret-position="519">
-            <caret line="306" column="23" selection-start-line="306" selection-start-column="23" selection-end-line="306" selection-end-column="23" />
+          <first_editor relative-caret-position="384">
+            <caret line="307" column="5" selection-start-line="307" selection-start-column="2" selection-end-line="307" selection-end-column="5" />
+            <folding />
+          </first_editor>
+          <second_editor />
+        </state>
+      </provider>
+    </entry>
+    <entry file="file://$PROJECT_DIR$/自然语言处理/CRF.md">
+      <provider editor-type-id="split-provider[text-editor;MarkdownPreviewEditor]">
+        <state split_layout="SPLIT">
+          <first_editor relative-caret-position="0">
+            <caret line="0" column="0" selection-start-line="0" selection-start-column="0" selection-end-line="0" selection-end-column="0" />
+            <folding />
+          </first_editor>
+          <second_editor>
+            <js_state />
+          </second_editor>
+        </state>
+      </provider>
+      <provider selected="true" editor-type-id="split-provider[text-editor;markdown-preview-editor]">
+        <state split_layout="SPLIT">
+          <first_editor relative-caret-position="285">
+            <caret line="19" column="51" selection-start-line="19" selection-start-column="51" selection-end-line="19" selection-end-column="51" />
             <folding />
           </first_editor>
           <second_editor />
diff --git a/README.md b/README.md
index b61fee5..eee1a20 100644
--- a/README.md
+++ b/README.md
@@ -281,7 +281,7 @@
     - [Linear SVM 和 LR 有什么异同](机器学习/支持向量机/支持向量机.md#L164)
 # 深度学习
 - dropout
-- batchnormalization
+- batch_normalization
 - bp过程
 - embedding
 - softmax
@@ -305,6 +305,7 @@
     - [word2vec两种方法各自的优势](自然语言处理/Word2Vec.md#L164)
     - [怎么衡量学到的embedding的好坏](自然语言处理/Word2Vec.md#L164)
     - [word2vec和glove区别](自然语言处理/Word2Vec.md#L164)
+- CRF
 - LDA
 - LSTM
 - GRU
diff --git "a/\350\207\252\347\204\266\350\257\255\350\250\200\345\244\204\347\220\206/CRF.md" "b/\350\207\252\347\204\266\350\257\255\350\250\200\345\244\204\347\220\206/CRF.md"
new file mode 100644
index 0000000..e3669d2
--- /dev/null
+++ "b/\350\207\252\347\204\266\350\257\255\350\250\200\345\244\204\347\220\206/CRF.md"
@@ -0,0 +1,20 @@
+# 阐述CRF原理？
+- 首先X,Y是随机变量，P(Y/X)是给定X条件下Y的条件概率分布
+- 如果Y满足马尔可夫满足马尔科夫性，及不相邻则条件独立
+- 则条件概率分布P(Y|X)为条件随机场CRF
+
+# 线性链条件随机场的公式是？
+- ![](https://tva1.sinaimg.cn/large/006y8mN6gy1g9ah66y1nxj30cr015747.jpg)
+
+# CRF与HMM区别?
+- CRF是判别模型求的是p(Y/X),HMM是生成模型求的是P(X,Y)
+- CRF是无向图，HMM是有向图
+- CRF全局最优输出节点的条件概率，HMM对转移概率和表现概率直接建模，统计共现概率
+
+# Bert+crf中的各部分作用详解？
+- Bert把中文文本进行了embedding，得到每个字的表征向量
+- dense操作得到了每个文本文本对应的未归一化的tag概率
+- CRF在选择每个词的tag的过程其实就是一个最优Tag路径的选择过程
+    - CRF层能从训练数据中获得约束性的规则
+        - 比如开始都是以xxx-B，中间都是以xxx-I，结尾都是以xxx-E
+        - 比如在只有label1-I，label2-I..的情况下，不会出现label1-B
\ No newline at end of file