diff --git a/.github/workflows/lint.yml b/.github/workflows/lint.yml
index 8b527922c4d39..fb919989738fb 100644
--- a/.github/workflows/lint.yml
+++ b/.github/workflows/lint.yml
@@ -6,6 +6,10 @@ name: linter
 on:
   - pull_request_target
 
+concurrency:
+  group: ${{ github.workflow }}-${{ github.ref }}
+  cancel-in-progress: true
+
 jobs:
   lint:
     runs-on: ubuntu-latest
@@ -32,7 +36,11 @@ jobs:
           pip install pytest ruff $(get_dep mypy min) $(get_dep black min) cython-lint
 
       - name: Run linting
-        run: ./build_tools/linting.sh &> /tmp/linting_output.txt
+        # We download the linting script from main, since this workflow is run
+        # from main itself.
+        run: |
+          curl https://raw.githubusercontent.com/scikit-learn/scikit-learn/main/build_tools/linting.sh -o ./build_tools/linting.sh
+          ./build_tools/linting.sh &> /tmp/linting_output.txt
 
       - name: Upload Artifact
         if: always()
@@ -78,6 +86,7 @@ jobs:
         env:
           GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }}
           PR_NUMBER: ${{ github.event.pull_request.number }}
+          BRANCH_SHA: ${{ github.event.pull_request.head.sha }}
           RUN_ID: ${{ github.run_id }}
           LOG_FILE: linting_output.txt
         run: python ./build_tools/get_comment.py
diff --git a/build_tools/get_comment.py b/build_tools/get_comment.py
index d414fe92975a0..d67492957510e 100644
--- a/build_tools/get_comment.py
+++ b/build_tools/get_comment.py
@@ -52,7 +52,7 @@ def get_step_message(log, start, end, title, message, details):
     return res
 
 
-def get_message(log_file, repo, run_id, details):
+def get_message(log_file, repo, pr_number, sha, run_id, details):
     with open(log_file, "r") as f:
         log = f.read()
 
@@ -152,15 +152,21 @@ def get_message(log_file, repo, run_id, details):
         details=details,
     )
 
+    commit_link = (
+        "\n\n_Generated for commit:"
+        f" [{sha[:7]}](https://github.com/{repo}/pull/{pr_number}/commits/{sha})_"
+    )
+
     if not message:
         # no issues detected, so this script "fails"
         return (
-            "## Linting Passed\n"
+            "## ✔️ Linting Passed\n"
             "All linting checks passed. Your pull request is in excellent shape! ☀️"
+            + commit_link
         )
 
     message = (
-        "## Linting issues\n\n"
+        "## ❌ Linting issues\n\n"
         "This PR is introducing linting issues. Here's a summary of the issues. "
         "Note that you can avoid having linting issues by enabling `pre-commit` "
         "hooks. Instructions to enable them can be found [here]("
@@ -169,6 +175,7 @@ def get_message(log_file, repo, run_id, details):
         "You can see the details of the linting issues under the `lint` job [here]"
         f"(https://github.com/{repo}/actions/runs/{run_id})\n\n"
         + message
+        + commit_link
     )
 
     return message
@@ -245,6 +252,7 @@ def create_or_update_comment(comment, message, repo, pr_number, token):
     repo = os.environ["GITHUB_REPOSITORY"]
     token = os.environ["GITHUB_TOKEN"]
     pr_number = os.environ["PR_NUMBER"]
+    sha = os.environ["BRANCH_SHA"]
     log_file = os.environ["LOG_FILE"]
     run_id = os.environ["RUN_ID"]
 
@@ -261,7 +269,14 @@ def create_or_update_comment(comment, message, repo, pr_number, token):
         exit(0)
 
     try:
-        message = get_message(log_file, repo=repo, run_id=run_id, details=True)
+        message = get_message(
+            log_file,
+            repo=repo,
+            pr_number=pr_number,
+            sha=sha,
+            run_id=run_id,
+            details=True,
+        )
         create_or_update_comment(
             comment=comment,
             message=message,
@@ -273,7 +288,14 @@ def create_or_update_comment(comment, message, repo, pr_number, token):
     except requests.HTTPError:
         # The above fails if the message is too long. In that case, we
         # try again without the details.
-        message = get_message(log_file, repo=repo, run_id=run_id, details=False)
+        message = get_message(
+            log_file,
+            repo=repo,
+            pr_number=pr_number,
+            sha=sha,
+            run_id=run_id,
+            details=False,
+        )
         create_or_update_comment(
             comment=comment,
             message=message,