diff --git a/.github/actions/post-slack/action.yml b/.github/actions/post-slack/action.yml
new file mode 100644
index 00000000000..74075a4fedc
--- /dev/null
+++ b/.github/actions/post-slack/action.yml
@@ -0,0 +1,79 @@
+name: Send message to slack
+
+description: 'Send results to slack'
+author: 'Hugging Face'
+inputs:
+  slack_channel:
+    required: true
+    type: string
+  title:
+    required: true
+    type: string
+  status:
+    required: true
+    type: string
+  slack_token:
+    required: true
+    type: string
+
+runs:
+  using: "composite"
+  steps:
+    - name: Create content to post
+      id: create-message
+      run: |
+        if [ "${{ inputs.status }}" == "success" ]; then
+          echo STATUS_MESSAGE='🟢 Tests are passing!' >> $GITHUB_ENV
+        else
+          echo STATUS_MESSAGE='🔴 Tests failed! Please check the GitHub action link below' >> $GITHUB_ENV
+        fi
+      shell: bash
+
+    - name: Post Canceled results Slack channel
+      id: post-slack
+      uses: slackapi/slack-github-action@6c661ce58804a1a20f6dc5fbee7f0381b469e001
+      with:
+        # Slack channel id, channel name, or user id to post message.
+        # See also: https://api.slack.com/methods/chat.postMessage#channels
+        channel-id: ${{ inputs.slack_channel }}
+        # For posting a rich message using Block Kit
+        payload: |
+          {
+            "text": "${{ inputs.title }}",
+            "blocks": [
+              {
+                "type": "header",
+                "text": {
+                    "type": "plain_text",
+                    "text": "${{ inputs.title }}"
+                }
+              },
+              {
+                "type": "section",
+                "text": {
+                  "type": "mrkdwn",
+                  "text": "${{ env.STATUS_MESSAGE }}"
+                }
+              },
+              {
+                "type": "section",
+                "text": {"type": "mrkdwn", "text": "*Click the button for more details about the commit*"},
+                "accessory": {
+                    "type": "button",
+                    "text": {"type": "plain_text", "text": "Check Commit results"},
+                    "url": "${{ github.event.pull_request.html_url || github.event.head_commit.url }}"
+                }
+              },
+              {
+                "type": "section",
+                "text": {"type": "mrkdwn", "text": "*Click here for more details about the action ran*"},
+                "accessory": {
+                    "type": "button",
+                    "text": {"type": "plain_text", "text": "Check Action results"},
+                    "url": "${{ github.server_url }}/${{ github.repository }}/actions/runs/${{ github.run_id }}"
+                }
+              }
+            ]
+          }
+      env:
+        SLACK_BOT_TOKEN: ${{ inputs.slack_token }}
\ No newline at end of file
diff --git a/.github/workflows/push-important-models.yml b/.github/workflows/push-important-models.yml
new file mode 100644
index 00000000000..5eef6f40f87
--- /dev/null
+++ b/.github/workflows/push-important-models.yml
@@ -0,0 +1,136 @@
+name: Slow tests on important models (on Push - A10)
+
+on:
+  push:
+    branches: [ main ]
+
+env:
+  IS_GITHUB_CI: "1"
+  OUTPUT_SLACK_CHANNEL_ID: "C06L2SGMEEA"
+  HF_HUB_READ_TOKEN: ${{ secrets.HF_HUB_READ_TOKEN }}
+  HF_HOME: /mnt/cache 
+  TRANSFORMERS_IS_CI: yes 
+  OMP_NUM_THREADS: 8 
+  MKL_NUM_THREADS: 8 
+  RUN_SLOW: yes # For gated repositories, we still need to agree to share information on the Hub repo. page in order to get access. # This token is created under the bot `hf-transformers-bot`. 
+  SIGOPT_API_TOKEN: ${{ secrets.SIGOPT_API_TOKEN }} 
+  TF_FORCE_GPU_ALLOW_GROWTH: true 
+  RUN_PT_TF_CROSS_TESTS: 1
+
+jobs:
+  get_modified_models:
+    name: "Get all modified files"
+    runs-on: ubuntu-latest
+    outputs:
+      matrix: ${{ steps.set-matrix.outputs.matrix }}
+    steps:
+      - name: Check out code
+        uses: actions/checkout@v3
+      
+      - name: Get changed files
+        id: changed-files
+        uses: tj-actions/changed-files@3f54ebb830831fc121d3263c1857cfbdc310cdb9 #v42
+        with:
+          files: src/transformers/models/**
+      
+      - name: Run step if only the files listed above change
+        if: steps.changed-files.outputs.any_changed == 'true'
+        id: set-matrix
+        env:
+          ALL_CHANGED_FILES: ${{ steps.changed-files.outputs.all_changed_files }}
+        run: |
+            model_arrays=()
+            for file in $ALL_CHANGED_FILES; do
+                model_path="${file#*models/}"
+                model_path="models/${model_path%%/*}"
+                if grep -qFx "$model_path" utils/important_models.txt; then
+                    # Append the file to the matrix string
+                    model_arrays+=("$model_path")
+                fi
+            done
+            matrix_string=$(printf '"%s", ' "${model_arrays[@]}" | sed 's/, $//')
+            echo "matrix=[$matrix_string]" >> $GITHUB_OUTPUT
+  test_modified_files:
+    needs: get_modified_models
+    name: Slow & FA2 tests
+    runs-on: [single-gpu, nvidia-gpu, a10, ci]
+    container:
+      image: huggingface/transformers-all-latest-gpu
+      options: --gpus all --privileged --ipc host -v /mnt/cache/.cache/huggingface:/mnt/cache/
+    if: ${{ needs.get_modified_models.outputs.matrix != '[]' && needs.get_modified_models.outputs.matrix != '' }}
+    strategy:
+      fail-fast: false
+      matrix: 
+        model-name: ${{ fromJson(needs.get_modified_models.outputs.matrix) }}
+
+    steps:
+      - name: Check out code
+        uses: actions/checkout@v3
+      
+      - name: Install locally transformers & other libs
+        run: |
+          apt install sudo
+          sudo -H pip install --upgrade pip
+          sudo -H pip uninstall -y transformers 
+          sudo -H pip install -U -e ".[testing]" 
+          MAX_JOBS=4 pip install flash-attn --no-build-isolation
+          pip install bitsandbytes
+      
+      - name: NVIDIA-SMI
+        run: |
+          nvidia-smi
+      
+      - name: Show installed libraries and their versions
+        run: pip freeze
+      
+      - name: Run FA2 tests
+        id: run_fa2_tests
+        run:
+          pytest -m "flash_attn_test" --make-reports=${{ matrix.model-name }}_fa2_tests/ tests/${{ matrix.model-name }}/test_modeling_*
+      
+      - name: "Test suite reports artifacts: ${{ matrix.model-name }}_fa2_tests"
+        if: ${{ always() }}
+        uses: actions/upload-artifact@v3
+        with:
+          name: ${{ matrix.model-name }}_fa2_tests
+          path: /transformers/reports/${{ matrix.model-name }}_fa2_tests
+      
+      - name: Post to Slack
+        if: always()
+        uses: ./.github/actions/post-slack
+        with:
+          slack_channel: ${{ env.OUTPUT_SLACK_CHANNEL_ID }}
+          title: 🤗 Results of the FA2 tests - ${{ matrix.model-name }}
+          status: ${{ steps.run_fa2_tests.conclusion}}
+          slack_token: ${{ secrets.CI_SLACK_BOT_TOKEN }}
+      
+      - name: Run integration tests
+        id: run_integration_tests
+        if: always()
+        run:
+          pytest -k "IntegrationTest"  --make-reports=tests_integration_${{ matrix.model-name }} tests/${{ matrix.model-name }}/test_modeling_*
+      
+      - name: "Test suite reports artifacts: tests_integration_${{ matrix.model-name }}"
+        if: ${{ always() }}
+        uses: actions/upload-artifact@v3
+        with:
+          name: tests_integration_${{ matrix.model-name }}
+          path: /transformers/reports/tests_integration_${{ matrix.model-name }}
+
+      - name: Post to Slack
+        if: always()
+        uses: ./.github/actions/post-slack
+        with:
+          slack_channel: ${{ env.OUTPUT_SLACK_CHANNEL_ID }}
+          title: 🤗 Results of the Integration tests - ${{ matrix.model-name }}
+          status: ${{ steps.run_integration_tests.conclusion}}
+          slack_token: ${{ secrets.CI_SLACK_BOT_TOKEN }}
+
+      - name: Tailscale # In order to be able to SSH when a test fails
+        if: ${{ failure() || runner.debug == '1'}}
+        uses: huggingface/tailscale-action@ssh-improvments
+        with:
+          authkey: ${{ secrets.TAILSCALE_SSH_AUTHKEY }}
+          slackChannel: ${{ secrets.SLACK_CIFEEDBACK_CHANNEL }}
+          slackToken: ${{ secrets.SLACK_CIFEEDBACK_BOT_TOKEN }}
+          waitForSSH: true
\ No newline at end of file
diff --git a/utils/important_models.txt b/utils/important_models.txt
new file mode 100644
index 00000000000..6dcd5de8d66
--- /dev/null
+++ b/utils/important_models.txt
@@ -0,0 +1,4 @@
+models/llama
+models/mistral
+models/mixtral
+models/gemma
\ No newline at end of file