diff --git a/backend/app/controllers/posts_controller.rb b/backend/app/controllers/posts_controller.rb
index ce555ed..a3a4538 100644
--- a/backend/app/controllers/posts_controller.rb
+++ b/backend/app/controllers/posts_controller.rb
@@ -88,7 +88,7 @@ class PostsController < ApplicationController
     original_created_from = params[:original_created_from]
     original_created_before = params[:original_created_before]
 
-    post = Post.new(title:, url:, thumbnail_base: '', uploaded_user: current_user,
+    post = Post.new(title:, url:, thumbnail_base: nil, uploaded_user: current_user,
                     original_created_from:, original_created_before:)
     post.thumbnail.attach(thumbnail)
     if post.save
diff --git a/backend/app/models/tag_similarity.rb b/backend/app/models/tag_similarity.rb
new file mode 100644
index 0000000..d983409
--- /dev/null
+++ b/backend/app/models/tag_similarity.rb
@@ -0,0 +1,4 @@
+class TagSimilarity < ApplicationRecord
+  belongs_to :tag, class_name: 'Tag', foreign_key: 'tag_id'
+  belongs_to :target_tag, class_name: 'Tag', foreign_key: 'target_tag_id'
+end
diff --git a/backend/db/migrate/20251230143400_make_thumbnail_base_nullable_in_posts.rb b/backend/db/migrate/20251230143400_make_thumbnail_base_nullable_in_posts.rb
new file mode 100644
index 0000000..f9da7c0
--- /dev/null
+++ b/backend/db/migrate/20251230143400_make_thumbnail_base_nullable_in_posts.rb
@@ -0,0 +1,27 @@
+class MakeThumbnailBaseNullableInPosts < ActiveRecord::Migration[7.0]
+  def up
+    change_column_null :posts, :thumbnail_base, true
+
+    execute <<~SQL
+      UPDATE
+        posts
+      SET
+        thumbnail_base = NULL
+      WHERE
+        thumbnail_base = ''
+    SQL
+  end
+
+  def down
+    execute <<~SQL
+      UPDATE
+        posts
+      SET
+        thumbnail_base = ''
+      WHERE
+        thumbnail_base IS NULL
+    SQL
+
+    change_column_null :posts, :thumbnail_base, false
+  end
+end
diff --git a/backend/db/schema.rb b/backend/db/schema.rb
index 116a1a2..697bd8f 100644
--- a/backend/db/schema.rb
+++ b/backend/db/schema.rb
@@ -10,7 +10,7 @@
 #
 # It's strongly recommended that you check this file into your version control system.
 
-ActiveRecord::Schema[8.0].define(version: 2025_12_29_022100) do
+ActiveRecord::Schema[8.0].define(version: 2025_12_30_143400) do
   create_table "active_storage_attachments", charset: "utf8mb4", collation: "utf8mb4_0900_ai_ci", force: :cascade do |t|
     t.string "name", null: false
     t.string "record_type", null: false
@@ -86,7 +86,7 @@ ActiveRecord::Schema[8.0].define(version: 2025_12_29_022100) do
   create_table "posts", charset: "utf8mb4", collation: "utf8mb4_0900_ai_ci", force: :cascade do |t|
     t.string "title", null: false
     t.string "url", limit: 2000, null: false
-    t.string "thumbnail_base", limit: 2000, null: false
+    t.string "thumbnail_base", limit: 2000
     t.bigint "parent_id"
     t.bigint "uploaded_user_id"
     t.datetime "created_at", null: false
diff --git a/backend/lib/tasks/calc_tag_similarities.rake b/backend/lib/tasks/calc_tag_similarities.rake
new file mode 100644
index 0000000..9e16977
--- /dev/null
+++ b/backend/lib/tasks/calc_tag_similarities.rake
@@ -0,0 +1,28 @@
+namespace :tag_similarity do
+  desc '関聯タグ・テーブル作成'
+  task calc: :environment do
+    dot = -> a, b { (a.keys & b.keys).sum { |k| a[k] * b[k] } }
+    norm = -> v { Math.sqrt(v.values.sum { |e| e * e }) }
+    cos = -> a, b do
+      na = norm.(a)
+      nb = norm.(b)
+      if na.zero? || nb.zero?
+        0.0
+      else
+        dot.(a, b) / na / nb
+      end
+    end
+
+    tags = Tag.includes(:posts).to_a
+    tags.each_with_index do |tag, i|
+      existence_of_posts = tag.posts.index_with(1)
+      ((i + 1)...tags.size).each do |j|
+        target_tag = tags[j]
+        existence_of_target_posts = target_tag.posts.index_with(1)
+        TagSimilarity.find_or_initialize_by(tag:, target_tag:).tap { |ts|
+          ts.cos = cos.(existence_of_posts, existence_of_target_posts)
+        }.save!
+      end
+    end
+  end
+end
diff --git a/backend/lib/tasks/sync_nico.rake b/backend/lib/tasks/sync_nico.rake
index d20150c..d09a424 100644
--- a/backend/lib/tasks/sync_nico.rake
+++ b/backend/lib/tasks/sync_nico.rake
@@ -49,7 +49,7 @@ namespace :nico do
       unless post
         title = datum['title']
         url = "https://www.nicovideo.jp/watch/#{ datum['code'] }"
-        thumbnail_base = fetch_thumbnail.(url) || '' rescue ''
+        thumbnail_base = fetch_thumbnail.(url) rescue nil
         post = Post.new(title:, url:, thumbnail_base:, uploaded_user: nil)
         if thumbnail_base.present?
           post.thumbnail.attach(