diff --git a/notebooks/en/fine_tuning_vlm_trl.ipynb b/notebooks/en/fine_tuning_vlm_trl.ipynb
index a6249bcf..797cbd6a 100644
--- a/notebooks/en/fine_tuning_vlm_trl.ipynb
+++ b/notebooks/en/fine_tuning_vlm_trl.ipynb
@@ -20,17 +20,17 @@
         "id": "JATmSI8mcyW2"
       },
       "source": [
-        "🚨 **WARNING**: This notebook is resource-intensive and requires substantial computational power. If you’re running this in Colab, it will utilize an A100 GPU.\n",
+        "\ud83d\udea8 **WARNING**: This notebook is resource-intensive and requires substantial computational power. If you\u2019re running this in Colab, it will utilize an A100 GPU.\n",
         "\n",
-        "In this recipe, we’ll demonstrate how to fine-tune a [Vision Language Model (VLM)](https://huggingface.co/blog/vlms) using the Hugging Face ecosystem, specifically with the [Transformer Reinforcement Learning library (TRL)](https://huggingface.co/docs/trl/index).\n",
+        "In this recipe, we\u2019ll demonstrate how to fine-tune a [Vision Language Model (VLM)](https://huggingface.co/blog/vlms) using the Hugging Face ecosystem, specifically with the [Transformer Reinforcement Learning library (TRL)](https://huggingface.co/docs/trl/index).\n",
         "\n",
-        "**🌟 Model & Dataset Overview**\n",
+        "**\ud83c\udf1f Model & Dataset Overview**\n",
         "\n",
-        "We’ll be fine-tuning the [Qwen2-VL-7B](https://qwenlm.github.io/blog/qwen2-vl/) model on the [ChartQA](https://huggingface.co/datasets/HuggingFaceM4/ChartQA) dataset. This dataset includes images of various chart types paired with question-answer pairs—ideal for enhancing the model's visual question-answering capabilities.\n",
+        "We\u2019ll be fine-tuning the [Qwen2-VL-7B](https://qwenlm.github.io/blog/qwen2-vl/) model on the [ChartQA](https://huggingface.co/datasets/HuggingFaceM4/ChartQA) dataset. This dataset includes images of various chart types paired with question-answer pairs\u2014ideal for enhancing the model's visual question-answering capabilities.\n",
         "\n",
-        "**📖 Additional Resources**\n",
+        "**\ud83d\udcd6 Additional Resources**\n",
         "\n",
-        "If you’re interested in more VLM applications, check out:\n",
+        "If you\u2019re interested in more VLM applications, check out:\n",
         "- [Multimodal Retrieval-Augmented Generation (RAG) Recipe](https://huggingface.co/learn/cookbook/multimodal_rag_using_document_retrieval_and_vlms): where I guide you through building a RAG system using Document Retrieval (ColPali) and Vision Language Models (VLMs).\n",
         "- [Phil Schmid's tutorial](https://www.philschmid.de/fine-tune-multimodal-llms-with-trl): an excellent deep dive into fine-tuning multimodal LLMs with TRL.\n",
         "- [Merve Noyan's **smol-vision** repository](https://github.com/merveenoyan/smol-vision/tree/main): a collection of engaging notebooks on cutting-edge vision and multimodal AI topics.\n"
@@ -53,7 +53,7 @@
       "source": [
         "## 1. Install Dependencies\n",
         "\n",
-        "Let’s start by installing the essential libraries we’ll need for fine-tuning! 🚀\n"
+        "Let\u2019s start by installing the essential libraries we\u2019ll need for fine-tuning! \ud83d\ude80\n"
       ]
     },
     {
@@ -78,7 +78,7 @@
         "id": "J4pAvoQaOJ1M"
       },
       "source": [
-        "We’ll also need to install an earlier version of *PyTorch*, as the latest version has an issue that currently prevents this notebook from running correctly. You can learn more about the issue [here](https://github.com/pytorch/pytorch/issues/138340) and consider updating to the latest version once it’s resolved."
+        "We\u2019ll also need to install an earlier version of *PyTorch*, as the latest version has an issue that currently prevents this notebook from running correctly. You can learn more about the issue [here](https://github.com/pytorch/pytorch/issues/138340) and consider updating to the latest version once it\u2019s resolved."
       ]
     },
     {
@@ -102,9 +102,9 @@
         "id": "V0-2Lso6wkIh"
       },
       "source": [
-        "Log in to Hugging Face to upload your fine-tuned model! 🗝️\n",
+        "Log in to Hugging Face to upload your fine-tuned model! \ud83d\udddd\ufe0f\n",
         "\n",
-        "You’ll need to authenticate with your Hugging Face account to save and share your model directly from this notebook.\n"
+        "You\u2019ll need to authenticate with your Hugging Face account to save and share your model directly from this notebook.\n"
       ]
     },
     {
@@ -161,7 +161,7 @@
               "version_minor": 0
             },
             "text/plain": [
-              "VBox(children=(HTML(value='<center> <img\\nsrc=https://huggingface.co/front/assets/huggingface_logo-noborder.sv…"
+              "VBox(children=(HTML(value='<center> <img\\nsrc=https://huggingface.co/front/assets/huggingface_logo-noborder.sv\u2026"
             ]
           },
           "metadata": {},
@@ -180,9 +180,9 @@
         "id": "g9QXwbJ7ovM5"
       },
       "source": [
-        "## 2. Load Dataset 📁\n",
+        "## 2. Load Dataset \ud83d\udcc1\n",
         "\n",
-        "In this section, we’ll load the [HuggingFaceM4/ChartQA](https://huggingface.co/datasets/HuggingFaceM4/ChartQA) dataset. This dataset contains chart images paired with related questions and answers, making it ideal for training on visual question answering tasks.\n",
+        "In this section, we\u2019ll load the [HuggingFaceM4/ChartQA](https://huggingface.co/datasets/HuggingFaceM4/ChartQA) dataset. This dataset contains chart images paired with related questions and answers, making it ideal for training on visual question answering tasks.\n",
         "\n",
         "\n"
       ]
@@ -193,7 +193,7 @@
         "id": "LBWqnXkcTN-s"
       },
       "source": [
-        "Next, we’ll generate a system message for the VLM. In this case, we want to create a system that acts as an expert in analyzing chart images and providing concise answers to questions based on them."
+        "Next, we\u2019ll generate a system message for the VLM. In this case, we want to create a system that acts as an expert in analyzing chart images and providing concise answers to questions based on them."
       ]
     },
     {
@@ -216,9 +216,9 @@
         "id": "z8UpL5ZxTakm"
       },
       "source": [
-        "We’ll format the dataset into a chatbot structure for interaction. Each interaction will consist of a system message, followed by the image and the user's query, and finally, the answer to the query.\n",
+        "We\u2019ll format the dataset into a chatbot structure for interaction. Each interaction will consist of a system message, followed by the image and the user's query, and finally, the answer to the query.\n",
         "\n",
-        "💡For more usage tips specific to this model, check out the [Model Card](https://huggingface.co/Qwen/Qwen2-VL-7B-Instruct#more-usage-tips)."
+        "\ud83d\udca1For more usage tips specific to this model, check out the [Model Card](https://huggingface.co/Qwen/Qwen2-VL-7B-Instruct#more-usage-tips)."
       ]
     },
     {
@@ -271,7 +271,7 @@
         "id": "IQ2zuDeGThNe"
       },
       "source": [
-        "For educational purposes, we’ll load only 10% of each split in the dataset. However, in a real-world use case, you would typically load the entire set of samples.\n"
+        "For educational purposes, we\u2019ll load only 10% of each split in the dataset. However, in a real-world use case, you would typically load the entire set of samples.\n"
       ]
     },
     {
@@ -294,7 +294,7 @@
         "id": "I0X4ZajcPV10"
       },
       "source": [
-        "Let’s take a look at the structure of the dataset. It includes an image, a query, a label (which is the answer), and a fourth feature that we’ll be discarding.\n"
+        "Let\u2019s take a look at the structure of the dataset. It includes an image, a query, a label (which is the answer), and a fourth feature that we\u2019ll be discarding.\n"
       ]
     },
     {
@@ -332,7 +332,7 @@
         "id": "1edUqNGWTtjA"
       },
       "source": [
-        "Now, let’s format the data using the chatbot structure. This will allow us to set up the interactions appropriately for our model.\n"
+        "Now, let\u2019s format the data using the chatbot structure. This will allow us to set up the interactions appropriately for our model.\n"
       ]
     },
     {
@@ -388,9 +388,9 @@
         "id": "YY1Y_KDtoycB"
       },
       "source": [
-        "## 3. Load Model and Check Performance! 🤔\n",
+        "## 3. Load Model and Check Performance! \ud83e\udd14\n",
         "\n",
-        "Now that we’ve loaded the dataset, let’s start by loading the model and evaluating its performance using a sample from the dataset. We’ll be using [Qwen/Qwen2-VL-7B-Instruct](https://huggingface.co/Qwen/Qwen2-VL-7B-Instruct), a Vision Language Model (VLM) capable of understanding both visual data and text.\n",
+        "Now that we\u2019ve loaded the dataset, let\u2019s start by loading the model and evaluating its performance using a sample from the dataset. We\u2019ll be using [Qwen/Qwen2-VL-7B-Instruct](https://huggingface.co/Qwen/Qwen2-VL-7B-Instruct), a Vision Language Model (VLM) capable of understanding both visual data and text.\n",
         "\n",
         "If you're exploring alternatives, consider these open-source options:\n",
         "- Meta AI's [Llama-3.2-11B-Vision](https://huggingface.co/meta-llama/Llama-3.2-11B-Vision-Instruct)\n",
@@ -462,7 +462,7 @@
         "id": "2HobU2iPUDWL"
       },
       "source": [
-        "Next, we’ll load the model and the tokenizer to prepare for inference."
+        "Next, we\u2019ll load the model and the tokenizer to prepare for inference."
       ]
     },
     {
@@ -903,7 +903,7 @@
         "id": "7JtKcuuXUGUT"
       },
       "source": [
-        "To evaluate the model's performance, we’ll use a sample from the dataset. First, let’s take a look at the internal structure of this sample.\n"
+        "To evaluate the model's performance, we\u2019ll use a sample from the dataset. First, let\u2019s take a look at the internal structure of this sample.\n"
       ]
     },
     {
@@ -945,7 +945,7 @@
         "id": "hLaWWJk_RkVU"
       },
       "source": [
-        "We’ll use the sample without the system message to assess the VLM's raw understanding. Here’s the input we will use:"
+        "We\u2019ll use the sample without the system message to assess the VLM's raw understanding. Here\u2019s the input we will use:"
       ]
     },
     {
@@ -983,7 +983,7 @@
         "id": "3IK2HOMuRtY_"
       },
       "source": [
-        "Now, let’s take a look at the chart corresponding to the sample. Can you answer the query based on the visual information?\n"
+        "Now, let\u2019s take a look at the chart corresponding to the sample. Can you answer the query based on the visual information?\n"
       ]
     },
     {
@@ -1021,7 +1021,7 @@
         "id": "gpLfsCUtUW6I"
       },
       "source": [
-        "Let’s create a method that takes the model, processor, and sample as inputs to generate the model's answer. This will allow us to streamline the inference process and easily evaluate the VLM's performance.\n"
+        "Let\u2019s create a method that takes the model, processor, and sample as inputs to generate the model's answer. This will allow us to streamline the inference process and easily evaluate the VLM's performance.\n"
       ]
     },
     {
@@ -1108,7 +1108,7 @@
         "id": "ysh0e9DRUfF-"
       },
       "source": [
-        "While the model successfully retrieves the correct visual information, it struggles to answer the question accurately. This indicates that fine-tuning might be the key to enhancing its performance. Let’s proceed with the fine-tuning process!\n"
+        "While the model successfully retrieves the correct visual information, it struggles to answer the question accurately. This indicates that fine-tuning might be the key to enhancing its performance. Let\u2019s proceed with the fine-tuning process!\n"
       ]
     },
     {
@@ -1174,9 +1174,9 @@
         "id": "yIrR9gP2z90z"
       },
       "source": [
-        "### 4.1 Load the Quantized Model for Training ⚙️\n",
+        "### 4.1 Load the Quantized Model for Training \u2699\ufe0f\n",
         "\n",
-        "Next, we’ll load the quantized model using [bitsandbytes](https://huggingface.co/docs/bitsandbytes/main/en/index). If you want to learn more about quantization, check out [this blog post](https://huggingface.co/blog/merve/quantization) or [this one](https://www.maartengrootendorst.com/blog/quantization/).\n"
+        "Next, we\u2019ll load the quantized model using [bitsandbytes](https://huggingface.co/docs/bitsandbytes/main/en/index). If you want to learn more about quantization, check out [this blog post](https://huggingface.co/blog/merve/quantization) or [this one](https://www.maartengrootendorst.com/blog/quantization/).\n"
       ]
     },
     {
@@ -1246,7 +1246,7 @@
         "id": "65wfO29isQlX"
       },
       "source": [
-        "### 4.2 Set Up QLoRA and SFTConfig 🚀\n",
+        "### 4.2 Set Up QLoRA and SFTConfig \ud83d\ude80\n",
         "\n",
         "Next, we will configure [QLoRA](https://github.com/artidoro/qlora) for our training setup. QLoRA enables efficient fine-tuning of large language models while significantly reducing the memory footprint compared to traditional methods. Unlike standard LoRA, which reduces memory usage by applying a low-rank approximation, QLoRA takes it a step further by quantizing the weights of the LoRA adapters. This leads to even lower memory requirements and improved training efficiency, making it an excellent choice for optimizing our model's performance without sacrificing quality.\n",
         "\n",
@@ -1298,7 +1298,7 @@
         "id": "K5zzHM2GVtxD"
       },
       "source": [
-        "We will use Supervised Fine-Tuning (SFT) to refine our model’s performance on the task at hand. To do this, we'll define the training arguments using the [SFTConfig](https://huggingface.co/docs/trl/sft_trainer) class from the [TRL library](https://huggingface.co/docs/trl/index). SFT allows us to provide labeled data, helping the model learn to generate more accurate responses based on the input it receives. This approach ensures that the model is tailored to our specific use case, leading to better performance in understanding and responding to visual queries.\n",
+        "We will use Supervised Fine-Tuning (SFT) to refine our model\u2019s performance on the task at hand. To do this, we'll define the training arguments using the [SFTConfig](https://huggingface.co/docs/trl/sft_trainer) class from the [TRL library](https://huggingface.co/docs/trl/index). SFT allows us to provide labeled data, helping the model learn to generate more accurate responses based on the input it receives. This approach ensures that the model is tailored to our specific use case, leading to better performance in understanding and responding to visual queries.\n",
         "\n",
         "\n",
         "\n",
@@ -1361,7 +1361,7 @@
         "id": "pOUrD9P-y-Kf"
       },
       "source": [
-        "### 4.3 Training the Model 🏃"
+        "### 4.3 Training the Model \ud83c\udfc3"
       ]
     },
     {
@@ -1370,7 +1370,7 @@
         "id": "wjQGt-iZVyef"
       },
       "source": [
-        "We will log our training progress using [Weights & Biases (W&B)](https://wandb.ai/). Let’s connect our notebook to W&B to capture essential information during training.\n"
+        "We will log our training progress using [Weights & Biases (W&B)](https://wandb.ai/). Let\u2019s connect our notebook to W&B to capture essential information during training.\n"
       ]
     },
     {
@@ -1403,7 +1403,7 @@
       "source": [
         "We need a collator function to properly retrieve and batch the data during the training procedure. This function will handle the formatting of our dataset inputs, ensuring they are correctly structured for the model. Let's define the collator function below.\n",
         "\n",
-        "👉 Check out the TRL official example [scripts]( https://github.com/huggingface/trl/blob/main/examples/scripts/sft_vlm.py#L87) for more details.\n"
+        "\ud83d\udc49 Check out the TRL official example [scripts]( https://github.com/huggingface/trl/blob/main/examples/scripts/sft_vlm.py#L87) for more details.\n"
       ]
     },
     {
@@ -1483,7 +1483,7 @@
         "id": "NlDsh4WvWCx0"
       },
       "source": [
-        "Time to Train the Model! 🎉"
+        "Time to Train the Model! \ud83c\udf89"
       ]
     },
     {
@@ -1503,7 +1503,7 @@
         "id": "w6CykSCtX-Xa"
       },
       "source": [
-        "Let's save the results 💾"
+        "Let's save the results \ud83d\udcbe"
       ]
     },
     {
@@ -1556,9 +1556,9 @@
         "id": "6yx_sGW42dN3"
       },
       "source": [
-        "## 5. Testing the Fine-Tuned Model 🔍\n",
+        "## 5. Testing the Fine-Tuned Model \ud83d\udd0d\n",
         "\n",
-        "Now that we've successfully fine-tuned our Vision Language Model (VLM), it's time to evaluate its performance! In this section, we will test the model using examples from the ChartQA dataset to see how well it answers questions based on chart images. Let's dive in and explore the results! 🚀\n",
+        "Now that we've successfully fine-tuned our Vision Language Model (VLM), it's time to evaluate its performance! In this section, we will test the model using examples from the ChartQA dataset to see how well it answers questions based on chart images. Let's dive in and explore the results! \ud83d\ude80\n",
         "\n"
       ]
     },
@@ -1568,7 +1568,7 @@
         "id": "i0KEPu6qYKqn"
       },
       "source": [
-        "Let's clean up the GPU memory to ensure optimal performance 🧹"
+        "Let's clean up the GPU memory to ensure optimal performance \ud83e\uddf9"
       ]
     },
     {
@@ -1934,7 +1934,7 @@
         "id": "NUr6jmnAIlh1"
       },
       "source": [
-        "The model has successfully learned to respond to the queries as specified in the dataset. We've achieved our goal! 🎉✨"
+        "The model has successfully learned to respond to the queries as specified in the dataset. We've achieved our goal! \ud83c\udf89\u2728"
       ]
     },
     {
@@ -1943,7 +1943,7 @@
         "id": "Z_Ns3p0Dhjbr"
       },
       "source": [
-        "💻 I’ve developed an example application to test the model, which you can find [here](https://huggingface.co/spaces/sergiopaniego/Qwen2-VL-7B-trl-sft-ChartQA). You can easily compare it with another Space featuring the pre-trained model, available [here](https://huggingface.co/spaces/GanymedeNil/Qwen2-VL-7B)."
+        "\ud83d\udcbb I\u2019ve developed an example application to test the model, which you can find [here](https://huggingface.co/spaces/sergiopaniego/Qwen2-VL-7B-trl-sft-ChartQA). You can easily compare it with another Space featuring the pre-trained model, available [here](https://huggingface.co/spaces/GanymedeNil/Qwen2-VL-7B)."
       ]
     },
     {
@@ -1993,13 +1993,13 @@
         "id": "daUMWw5xxhSc"
       },
       "source": [
-        "## 6. Compare Fine-Tuned Model vs. Base Model + Prompting 📊\n",
+        "## 6. Compare Fine-Tuned Model vs. Base Model + Prompting \ud83d\udcca\n",
         "\n",
         "We have explored how fine-tuning the VLM can be a valuable option for adapting it to our specific needs. Another approach to consider is directly using prompting or implementing a RAG system, which is covered in another [recipe](https://huggingface.co/learn/cookbook/multimodal_rag_using_document_retrieval_and_vlms).\n",
         "\n",
         "Fine-tuning a VLM requires significant amounts of data and computational resources, which can incur costs. In contrast, we can experiment with prompting to see if we can achieve similar results without the overhead of fine-tuning.\n",
         "\n",
-        "Let's again clean up the GPU memory to ensure optimal performance 🧹"
+        "Let's again clean up the GPU memory to ensure optimal performance \ud83e\uddf9"
       ]
     },
     {
@@ -2032,7 +2032,7 @@
         "id": "9NApMx5S4-sh"
       },
       "source": [
-        "🏗️ First, we will load the baseline model following the same pipeline as before.\n"
+        "\ud83c\udfd7\ufe0f First, we will load the baseline model following the same pipeline as before.\n"
       ]
     },
     {
@@ -2091,7 +2091,7 @@
         "id": "1bwatIlf5EDE"
       },
       "source": [
-        "📜 In this case, we will again use the previous sample, but this time we will include the system message as follows. This addition helps to contextualize the input for the model, potentially improving its response accuracy.\n",
+        "\ud83d\udcdc In this case, we will again use the previous sample, but this time we will include the system message as follows. This addition helps to contextualize the input for the model, potentially improving its response accuracy.\n",
         "\n",
         "\n"
       ]
@@ -2196,7 +2196,7 @@
         "id": "o9Id3dzV5Wwy"
       },
       "source": [
-        "💡 As we can see, the model generates the correct answer using the pretrained model along with the additional system message, without any training. This approach may serve as a viable alternative to fine-tuning, depending on the specific use case."
+        "\ud83d\udca1 As we can see, the model generates the correct answer using the pretrained model along with the additional system message, without any training. This approach may serve as a viable alternative to fine-tuning, depending on the specific use case."
       ]
     },
     {
@@ -2205,7 +2205,7 @@
         "id": "Wgv0-sy8TLPE"
       },
       "source": [
-        "## 7. Continuing the Learning Journey 🧑‍🎓️\n",
+        "## 7. Continuing the Learning Journey \ud83e\uddd1\u200d\ud83c\udf93\ufe0f\n",
         "\n",
         "To further enhance your understanding and skills in working with multimodal models, check out the following resources:\n",
         "\n",
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-            "\u001b[2K   \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m13.5/13.5 MB\u001b[0m \u001b[31m96.9 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
-            "\u001b[2K   \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m116.3/116.3 kB\u001b[0m \u001b[31m10.1 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
-            "\u001b[2K   \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m179.3/179.3 kB\u001b[0m \u001b[31m17.1 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
-            "\u001b[2K   \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m143.5/143.5 kB\u001b[0m \u001b[31m13.9 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
-            "\u001b[2K   \u001b[90m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m194.8/194.8 kB\u001b[0m \u001b[31m17.5 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
+            "\u001b[2K     \u001b[90m\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u001b[0m \u001b[32m44.4/44.4 kB\u001b[0m \u001b[31m3.8 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
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+            "\u001b[2K   \u001b[90m\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u001b[0m \u001b[32m179.3/179.3 kB\u001b[0m \u001b[31m17.1 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
+            "\u001b[2K   \u001b[90m\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u001b[0m \u001b[32m143.5/143.5 kB\u001b[0m \u001b[31m13.9 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
+            "\u001b[2K   \u001b[90m\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u001b[0m \u001b[32m194.8/194.8 kB\u001b[0m \u001b[31m17.5 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
             "\u001b[?25h\u001b[31mERROR: pip's dependency resolver does not currently take into account all the packages that are installed. This behaviour is the source of the following dependency conflicts.\n",
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\ No newline at end of file
diff --git a/notebooks/en/search_and_learn.ipynb b/notebooks/en/search_and_learn.ipynb
index 4fc052ed..4cb32640 100644
--- a/notebooks/en/search_and_learn.ipynb
+++ b/notebooks/en/search_and_learn.ipynb
@@ -1,8207 +1,1102 @@
 {
-  "cells": [
-    {
-      "cell_type": "markdown",
-      "metadata": {
-        "id": "xctusmJ6BZ6_"
-      },
-      "source": [
-        "# Scaling Test-Time Compute for Longer Thinking in LLMs\n",
-        "\n",
-        "_Authored by: [Sergio Paniego](https://github.com/sergiopaniego)_"
-      ]
-    },
-    {
-      "cell_type": "markdown",
-      "metadata": {
-        "id": "JmgoppItAO7B"
-      },
-      "source": [
-        "🚨 **WARNING**: This notebook is **resource-intensive** and requires substantial computational power. If you’re running this in **Colab**, it will utilize an **A100 GPU**.\n",
-        "\n",
-        "---\n",
-        "\n",
-        "In this recipe, we'll guide you through extending the inference time for an **Instruct LLM system** using **test-time compute** to solve more challenging problems, such as **complex math problems**. This approach, inspired by [**OpenAI o1-o3 models**](https://openai.com/index/learning-to-reason-with-llms/), demonstrates that **longer reasoning time** during inference can enhance model performance.\n",
-        "\n",
-        "This technique builds on experiments shared in [this **blog post**](https://huggingface.co/spaces/HuggingFaceH4/blogpost-scaling-test-time-compute), which show that smaller models, like the **1B** and **3B Llama Instruct models**, can outperform much larger ones on the **MATH-500 benchmark** when given enough **\"time to think\"**. Recent research from [DeepMind](https://arxiv.org/abs/2408.03314) suggests that **test-time compute** can be scaled optimally through strategies like iterative self-refinement or using a reward model.\n",
-        "\n",
-        "The blog introduces a [**new repository**](https://github.com/huggingface/search-and-learn) for running these experiments. In this recipe, we'll focus on building a **small chatbot** that engages in **longer reasoning** to tackle **harder problems** using small open models.\n",
-        "\n",
-        "![Instruct LLM Methodology](https://huggingface.co/datasets/HuggingFaceH4/blogpost-images/resolve/main/methods-thumbnail.png)"
-      ]
-    },
-    {
-      "cell_type": "markdown",
-      "metadata": {
-        "id": "twKCzVIg71Xa"
-      },
-      "source": [
-        "## 1. Install Dependencies\n",
-        "\n",
-        "Let’s start by installing the [search-and-learn](https://github.com/huggingface/search-and-learn) repository! 🚀  \n",
-        "This repo is designed to replicate the experimental results and is not a Python pip package. However, we can still use it to generate our system. To do so, we’ll need to install it from source with the following steps:"
-      ]
-    },
-    {
-      "cell_type": "code",
-      "execution_count": null,
-      "metadata": {
-        "colab": {
-          "base_uri": "https://localhost:8080/"
-        },
-        "id": "t0YDC2_7XTm8",
-        "outputId": "d804071f-8a3e-4463-9721-d6100ae1d48b"
-      },
-      "outputs": [],
-      "source": [
-        "!git clone https://github.com/huggingface/search-and-learn"
-      ]
-    },
-    {
-      "cell_type": "code",
-      "execution_count": null,
-      "metadata": {
-        "colab": {
-          "base_uri": "https://localhost:8080/",
-          "height": 1000
-        },
-        "id": "kT3jH_d_XcEb",
-        "outputId": "b50f463e-2c9d-4554-cd20-00887acc2114"
-      },
-      "outputs": [],
-      "source": [
-        "%cd search-and-learn\n",
-        "!pip install -e '.[dev]'"
-      ]
-    },
-    {
-      "cell_type": "markdown",
-      "metadata": {
-        "id": "VAQHu9T176zh"
-      },
-      "source": [
-        "Log in to Hugging Face to access [meta-llama/Llama-3.2-1B-Instruct](https://huggingface.co/meta-llama/Llama-3.2-1B-Instruct), as it is a gated model! 🗝️  \n",
-        "If you haven't previously requested access, you'll need to submit a request before proceeding.\n"
-      ]
-    },
-    {
-      "cell_type": "code",
-      "execution_count": null,
-      "metadata": {
-        "colab": {
-          "base_uri": "https://localhost:8080/",
-          "height": 17,
-          "referenced_widgets": [
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-        },
-        "id": "pnEaTlFYZF_H",
-        "outputId": "aa361d8b-23b9-4c21-aa4c-2c0771ea40b7"
-      },
-      "outputs": [],
-      "source": [
-        "from huggingface_hub import notebook_login\n",
-        "\n",
-        "notebook_login()"
-      ]
-    },
-    {
-      "cell_type": "markdown",
-      "metadata": {
-        "id": "wX07zCTA8MWL"
-      },
-      "source": [
-        "## 2. Setup the Large Language Model (LLM) and the Process Reward Model (PRM) 💬\n",
-        "\n",
-        "As illustrated in the diagram, the system consists of an LLM that generates intermediate answers based on user input, a [PRM model](https://huggingface.co/papers/2211.14275) that evaluates and scores these answers, and a search strategy that uses the PRM feedback to guide the subsequent steps in the search process until reaching the final answer.\n",
-        "\n",
-        "Let’s begin by initializing each model. For the LLM, we’ll use the [meta-llama/Llama-3.2-1B-Instruct](https://huggingface.co/meta-llama/Llama-3.2-1B-Instruct) model, and for the PRM, we’ll use the [RLHFlow/Llama3.1-8B-PRM-Deepseek-Data](https://huggingface.co/RLHFlow/Llama3.1-8B-PRM-Deepseek-Data) model.\n",
-        "\n",
-        "\n"
-      ]
-    },
-    {
-      "cell_type": "markdown",
-      "metadata": {
-        "id": "IkJw0x7gDJEY"
-      },
-      "source": [
-        "![system](https://huggingface.co/datasets/HuggingFaceH4/blogpost-images/resolve/main/system.png)"
-      ]
-    },
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-        },
-        "id": "MG1MolfxmZ7M",
-        "outputId": "b8271db3-a092-4ef9-aacb-730ef489a89e"
-      },
-      "outputs": [],
-      "source": [
-        "import torch\n",
-        "from vllm import LLM\n",
-        "from sal.models.reward_models import RLHFFlow\n",
-        "\n",
-        "model_path=\"meta-llama/Llama-3.2-1B-Instruct\"\n",
-        "prm_path=\"RLHFlow/Llama3.1-8B-PRM-Deepseek-Data\"\n",
-        "\n",
-        "llm = LLM(\n",
-        "    model=model_path,\n",
-        "    gpu_memory_utilization=0.5,  # Utilize 50% of GPU memory\n",
-        "    enable_prefix_caching=True,  # Optimize repeated prefix computations\n",
-        "    seed=42,                     # Set seed for reproducibility\n",
-        ")\n",
-        "\n",
-        "prm = RLHFFlow(prm_path)"
-      ]
-    },
-    {
-      "cell_type": "markdown",
-      "metadata": {
-        "id": "xYtPn0_V_YRx"
-      },
-      "source": [
-        "### 2.1 Instantiate the Question, Search Strategy, and Call the Pipeline\n",
-        "\n",
-        "Now that we've set up the LLM and PRM, let's proceed by defining the question, selecting a search strategy to retrieve relevant information, and calling the pipeline to process the question through the models.\n",
-        "\n",
-        "1. **Instantiate the Question**: In this step, we define the input question that the system will answer, considering the given context.\n",
-        "\n",
-        "2. **Search Strategy**: The system currently supports the following search strategies: `best_of_n`, `beam_search`, and `dvts` (see diagram). For this example, we'll use `best_of_n`, but you can easily switch to any of the other strategies based on your needs. We need to define some configuration parameters for the configuration of the search strategy. You can check the full list [here](https://github.com/huggingface/search-and-learn/blob/main/src/sal/config.py).\n",
-        "\n",
-        "3. **Call the Pipeline**: With the question and search strategy in place, we’ll call the inference pipeline, processing the inputs through both the LLM and PRM to generate the final answer."
-      ]
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "id": "xctusmJ6BZ6_"
+   },
+   "source": [
+    "# Scaling Test-Time Compute for Longer Thinking in LLMs\n",
+    "\n",
+    "_Authored by: [Sergio Paniego](https://github.com/sergiopaniego)_"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "id": "JmgoppItAO7B"
+   },
+   "source": [
+    "🚨 **WARNING**: This notebook is **resource-intensive** and requires substantial computational power. If you’re running this in **Colab**, it will utilize an **A100 GPU**.\n",
+    "\n",
+    "---\n",
+    "\n",
+    "In this recipe, we'll guide you through extending the inference time for an **Instruct LLM system** using **test-time compute** to solve more challenging problems, such as **complex math problems**. This approach, inspired by [**OpenAI o1-o3 models**](https://openai.com/index/learning-to-reason-with-llms/), demonstrates that **longer reasoning time** during inference can enhance model performance.\n",
+    "\n",
+    "This technique builds on experiments shared in [this **blog post**](https://huggingface.co/spaces/HuggingFaceH4/blogpost-scaling-test-time-compute), which show that smaller models, like the **1B** and **3B Llama Instruct models**, can outperform much larger ones on the **MATH-500 benchmark** when given enough **\"time to think\"**. Recent research from [DeepMind](https://arxiv.org/abs/2408.03314) suggests that **test-time compute** can be scaled optimally through strategies like iterative self-refinement or using a reward model.\n",
+    "\n",
+    "The blog introduces a [**new repository**](https://github.com/huggingface/search-and-learn) for running these experiments. In this recipe, we'll focus on building a **small chatbot** that engages in **longer reasoning** to tackle **harder problems** using small open models.\n",
+    "\n",
+    "![Instruct LLM Methodology](https://huggingface.co/datasets/HuggingFaceH4/blogpost-images/resolve/main/methods-thumbnail.png)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "id": "twKCzVIg71Xa"
+   },
+   "source": [
+    "## 1. Install Dependencies\n",
+    "\n",
+    "Let’s start by installing the [search-and-learn](https://github.com/huggingface/search-and-learn) repository! 🚀  \n",
+    "This repo is designed to replicate the experimental results and is not a Python pip package. However, we can still use it to generate our system. To do so, we’ll need to install it from source with the following steps:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "colab": {
+     "base_uri": "https://localhost:8080/"
     },
-    {
-      "cell_type": "markdown",
-      "metadata": {
-        "id": "xSWINPerJrhm"
-      },
-      "source": [
-        "![](https://huggingface.co/datasets/HuggingFaceH4/blogpost-images/resolve/main/search-strategies.png)"
-      ]
+    "id": "t0YDC2_7XTm8",
+    "outputId": "d804071f-8a3e-4463-9721-d6100ae1d48b"
+   },
+   "outputs": [],
+   "source": [
+    "!git clone https://github.com/huggingface/search-and-learn"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "colab": {
+     "base_uri": "https://localhost:8080/",
+     "height": 1000
     },
-    {
-      "cell_type": "markdown",
-      "metadata": {
-        "id": "z69xD6i2L5a6"
-      },
-      "source": [
-        "The first step is to clearly define the question that the system will answer. This ensures that we have a precise task for the model to tackle."
-      ]
+    "id": "kT3jH_d_XcEb",
+    "outputId": "b50f463e-2c9d-4554-cd20-00887acc2114"
+   },
+   "outputs": [],
+   "source": [
+    "%cd search-and-learn\n",
+    "!pip install -e '.[dev]'"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "id": "VAQHu9T176zh"
+   },
+   "source": [
+    "Log in to Hugging Face to access [meta-llama/Llama-3.2-1B-Instruct](https://huggingface.co/meta-llama/Llama-3.2-1B-Instruct), as it is a gated model! 🗝️  \n",
+    "If you haven't previously requested access, you'll need to submit a request before proceeding.\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "colab": {
+     "base_uri": "https://localhost:8080/",
+     "height": 17,
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     },
-    {
-      "cell_type": "code",
-      "execution_count": 38,
-      "metadata": {
-        "id": "83puLxhzsOM0"
-      },
-      "outputs": [],
-      "source": [
-        "question_text = 'Convert the point $(0,3)$ in rectangular coordinates to polar coordinates.  Enter your answer in the form $(r,\\theta),$ where $r > 0$ and $0 \\le \\theta < 2 \\pi.$'\n",
-        "input_batch = {\"problem\": [question_text]}"
-      ]
+    "id": "pnEaTlFYZF_H",
+    "outputId": "aa361d8b-23b9-4c21-aa4c-2c0771ea40b7"
+   },
+   "outputs": [],
+   "source": [
+    "from huggingface_hub import notebook_login\n",
+    "\n",
+    "notebook_login()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "id": "wX07zCTA8MWL"
+   },
+   "source": [
+    "## 2. Setup the Large Language Model (LLM) and the Process Reward Model (PRM) 💬\n",
+    "\n",
+    "As illustrated in the diagram, the system consists of an LLM that generates intermediate answers based on user input, a [PRM model](https://huggingface.co/papers/2211.14275) that evaluates and scores these answers, and a search strategy that uses the PRM feedback to guide the subsequent steps in the search process until reaching the final answer.\n",
+    "\n",
+    "Let’s begin by initializing each model. For the LLM, we’ll use the [meta-llama/Llama-3.2-1B-Instruct](https://huggingface.co/meta-llama/Llama-3.2-1B-Instruct) model, and for the PRM, we’ll use the [RLHFlow/Llama3.1-8B-PRM-Deepseek-Data](https://huggingface.co/RLHFlow/Llama3.1-8B-PRM-Deepseek-Data) model.\n",
+    "\n",
+    "\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "id": "IkJw0x7gDJEY"
+   },
+   "source": [
+    "![system](https://huggingface.co/datasets/HuggingFaceH4/blogpost-images/resolve/main/system.png)"
+   ]
+  },
+  {
+   "cell_type": "code",
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-    {
-      "cell_type": "markdown",
-      "metadata": {
-        "id": "yGpyzMNkAO7H"
-      },
-      "source": [
-        "Next, we define the configuration, including parameters like the number of candidate answers `(N)`, and choose the search strategy that will be used. The search strategy dictates how we explore the potential answers. In this case, we'll use `best_of_n`.\n",
-        "\n",
-        "With the question and configuration in place, we use the selected search strategy to generate multiple candidate answers. These candidates are evaluated based on their relevance and quality and the final answer is returned.\n"
-      ]
+    "id": "MG1MolfxmZ7M",
+    "outputId": "b8271db3-a092-4ef9-aacb-730ef489a89e"
+   },
+   "outputs": [],
+   "source": [
+    "import torch\n",
+    "from vllm import LLM\n",
+    "from sal.models.reward_models import RLHFFlow\n",
+    "\n",
+    "model_path=\"meta-llama/Llama-3.2-1B-Instruct\"\n",
+    "prm_path=\"RLHFlow/Llama3.1-8B-PRM-Deepseek-Data\"\n",
+    "\n",
+    "llm = LLM(\n",
+    "    model=model_path,\n",
+    "    gpu_memory_utilization=0.5,  # Utilize 50% of GPU memory\n",
+    "    enable_prefix_caching=True,  # Optimize repeated prefix computations\n",
+    "    seed=42,                     # Set seed for reproducibility\n",
+    ")\n",
+    "\n",
+    "prm = RLHFFlow(prm_path)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "id": "xYtPn0_V_YRx"
+   },
+   "source": [
+    "### 2.1 Instantiate the Question, Search Strategy, and Call the Pipeline\n",
+    "\n",
+    "Now that we've set up the LLM and PRM, let's proceed by defining the question, selecting a search strategy to retrieve relevant information, and calling the pipeline to process the question through the models.\n",
+    "\n",
+    "1. **Instantiate the Question**: In this step, we define the input question that the system will answer, considering the given context.\n",
+    "\n",
+    "2. **Search Strategy**: The system currently supports the following search strategies: `best_of_n`, `beam_search`, and `dvts` (see diagram). For this example, we'll use `best_of_n`, but you can easily switch to any of the other strategies based on your needs. We need to define some configuration parameters for the configuration of the search strategy. You can check the full list [here](https://github.com/huggingface/search-and-learn/blob/main/src/sal/config.py).\n",
+    "\n",
+    "3. **Call the Pipeline**: With the question and search strategy in place, we’ll call the inference pipeline, processing the inputs through both the LLM and PRM to generate the final answer."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "id": "xSWINPerJrhm"
+   },
+   "source": [
+    "![](https://huggingface.co/datasets/HuggingFaceH4/blogpost-images/resolve/main/search-strategies.png)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "id": "z69xD6i2L5a6"
+   },
+   "source": [
+    "The first step is to clearly define the question that the system will answer. This ensures that we have a precise task for the model to tackle."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 38,
+   "metadata": {
+    "id": "83puLxhzsOM0"
+   },
+   "outputs": [],
+   "source": [
+    "question_text = 'Convert the point $(0,3)$ in rectangular coordinates to polar coordinates.  Enter your answer in the form $(r,\\theta),$ where $r > 0$ and $0 \\le \\theta < 2 \\pi.$'\n",
+    "input_batch = {\"problem\": [question_text]}"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "id": "yGpyzMNkAO7H"
+   },
+   "source": [
+    "Next, we define the configuration, including parameters like the number of candidate answers `(N)`, and choose the search strategy that will be used. The search strategy dictates how we explore the potential answers. In this case, we'll use `best_of_n`.\n",
+    "\n",
+    "With the question and configuration in place, we use the selected search strategy to generate multiple candidate answers. These candidates are evaluated based on their relevance and quality and the final answer is returned.\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 39,
+   "metadata": {
+    "id": "C6s6GS16QZLV"
+   },
+   "outputs": [],
+   "source": [
+    "from sal.config import Config\n",
+    "from sal.search import beam_search, best_of_n, dvts\n",
+    "\n",
+    "config = Config()\n",
+    "config.n=32 # Number of answers to generate during the search\n",
+    "\n",
+    "search_result = best_of_n(x=input_batch, config=config, llm=llm, prm=prm)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "id": "lsLHD_6C_15p"
+   },
+   "source": [
+    "### 2.2 Display the Final Result\n",
+    "\n",
+    "Once the pipeline has processed the question through the LLM and PRM, we can display the final result. This result will be the model's output after considering the intermediate answers and scoring them using the PRM.\n",
+    "\n",
+    "Here's how to display the final answer:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 40,
+   "metadata": {
+    "colab": {
+     "base_uri": "https://localhost:8080/",
+     "height": 105
     },
+    "id": "v8medbURbgdI",
+    "outputId": "3620f3e6-a25d-4bec-f41c-c4f03a6ed770"
+   },
+   "outputs": [
     {
-      "cell_type": "code",
-      "execution_count": 39,
-      "metadata": {
-        "id": "C6s6GS16QZLV"
+     "data": {
+      "application/vnd.google.colaboratory.intrinsic+json": {
+       "type": "string"
       },
-      "outputs": [],
-      "source": [
-        "from sal.config import Config\n",
-        "from sal.search import beam_search, best_of_n, dvts\n",
-        "\n",
-        "config = Config()\n",
-        "config.n=32 # Number of answers to generate during the search\n",
-        "\n",
-        "search_result = best_of_n(x=input_batch, config=config, llm=llm, prm=prm)"
+      "text/plain": [
+       "'## Step 1: Recall the conversion formulas\\nTo convert from rectangular coordinates $(x, y)$ to polar coordinates $(r, \\\\theta)$, we use the following formulas:\\n- $r = \\\\sqrt{x^2 + y^2}$\\n- $\\\\theta = \\\\tan^{-1}\\\\left(\\\\frac{y}{x}\\\\right)$\\n\\n## Step 2: Substitute the given values into the formulas\\nGiven $(x, y) = (0, 3)$, we substitute these values into the formulas:\\n- $r = \\\\sqrt{0^2 + 3^2} = \\\\sqrt{0 + 9} = \\\\sqrt{9} = 3$\\n- $\\\\theta = \\\\tan^{-1}\\\\left(\\\\frac{3}{0}\\\\right)$. However, since division by zero is undefined, we recognize that the point $(0, 3)$ is on the positive y-axis, meaning $\\\\theta = \\\\frac{\\\\pi}{2}$.\\n\\n## Step 3: Combine the results for the polar coordinates\\nTherefore, the polar coordinates of the point $(0, 3)$ are $\\\\left(3, \\\\frac{\\\\pi}{2}\\\\right)$.\\n\\nThe final answer is: $\\\\boxed{\\\\left(3, \\\\frac{\\\\pi}{2}\\\\right)}$'"
       ]
+     },
+     "execution_count": 40,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "search_result['pred'][0]"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "id": "F-8hIu05AO7J"
+   },
+   "source": [
+    "The model’s output might include special tokens, such as `<|start_header_id|>` or `<|end_header_id|>`. To make the answer more readable, we can safely remove them before displaying it to the end user."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 41,
+   "metadata": {
+    "colab": {
+     "base_uri": "https://localhost:8080/",
+     "height": 105
     },
+    "id": "flbIu6-rDapM",
+    "outputId": "fcb197d5-0f21-4953-8a21-869c92a1f957"
+   },
+   "outputs": [
     {
-      "cell_type": "markdown",
-      "metadata": {
-        "id": "lsLHD_6C_15p"
+     "data": {
+      "application/vnd.google.colaboratory.intrinsic+json": {
+       "type": "string"
       },
-      "source": [
-        "### 2.2 Display the Final Result\n",
-        "\n",
-        "Once the pipeline has processed the question through the LLM and PRM, we can display the final result. This result will be the model's output after considering the intermediate answers and scoring them using the PRM.\n",
-        "\n",
-        "Here's how to display the final answer:"
+      "text/plain": [
+       "'## Step 1: Recall the conversion formulas\\nTo convert from rectangular coordinates $(x, y)$ to polar coordinates $(r, \\\\theta)$, we use the following formulas:\\n- $r = \\\\sqrt{x^2 + y^2}$\\n- $\\\\theta = \\\\tan^{-1}\\\\left(\\\\frac{y}{x}\\\\right)$\\n\\n## Step 2: Substitute the given values into the formulas\\nGiven $(x, y) = (0, 3)$, we substitute these values into the formulas:\\n- $r = \\\\sqrt{0^2 + 3^2} = \\\\sqrt{0 + 9} = \\\\sqrt{9} = 3$\\n- $\\\\theta = \\\\tan^{-1}\\\\left(\\\\frac{3}{0}\\\\right)$. However, since division by zero is undefined, we recognize that the point $(0, 3)$ is on the positive y-axis, meaning $\\\\theta = \\\\frac{\\\\pi}{2}$.\\n\\n## Step 3: Combine the results for the polar coordinates\\nTherefore, the polar coordinates of the point $(0, 3)$ are $\\\\left(3, \\\\frac{\\\\pi}{2}\\\\right)$.\\n\\nThe final answer is: $\\\\boxed{\\\\left(3, \\\\frac{\\\\pi}{2}\\\\right)}$'"
       ]
+     },
+     "execution_count": 41,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "formatted_output = search_result['pred'][0].replace(\"<|start_header_id|>assistant<|end_header_id|>\\n\\n\", \"\").strip()\n",
+    "formatted_output"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "id": "7ZuLZNirAO7J"
+   },
+   "source": [
+    "After removing any special tokens, we can display the final answer to the user. Since the answer is based on markdown, it can be rendered properly by displaying it as markdown."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 42,
+   "metadata": {
+    "colab": {
+     "base_uri": "https://localhost:8080/",
+     "height": 385
     },
+    "id": "P4En0qJRD0cl",
+    "outputId": "56400fea-e304-4f16-d255-909f42f636e0"
+   },
+   "outputs": [
     {
-      "cell_type": "code",
-      "execution_count": 40,
-      "metadata": {
-        "colab": {
-          "base_uri": "https://localhost:8080/",
-          "height": 105
-        },
-        "id": "v8medbURbgdI",
-        "outputId": "3620f3e6-a25d-4bec-f41c-c4f03a6ed770"
-      },
-      "outputs": [
-        {
-          "data": {
-            "application/vnd.google.colaboratory.intrinsic+json": {
-              "type": "string"
-            },
-            "text/plain": [
-              "'## Step 1: Recall the conversion formulas\\nTo convert from rectangular coordinates $(x, y)$ to polar coordinates $(r, \\\\theta)$, we use the following formulas:\\n- $r = \\\\sqrt{x^2 + y^2}$\\n- $\\\\theta = \\\\tan^{-1}\\\\left(\\\\frac{y}{x}\\\\right)$\\n\\n## Step 2: Substitute the given values into the formulas\\nGiven $(x, y) = (0, 3)$, we substitute these values into the formulas:\\n- $r = \\\\sqrt{0^2 + 3^2} = \\\\sqrt{0 + 9} = \\\\sqrt{9} = 3$\\n- $\\\\theta = \\\\tan^{-1}\\\\left(\\\\frac{3}{0}\\\\right)$. However, since division by zero is undefined, we recognize that the point $(0, 3)$ is on the positive y-axis, meaning $\\\\theta = \\\\frac{\\\\pi}{2}$.\\n\\n## Step 3: Combine the results for the polar coordinates\\nTherefore, the polar coordinates of the point $(0, 3)$ are $\\\\left(3, \\\\frac{\\\\pi}{2}\\\\right)$.\\n\\nThe final answer is: $\\\\boxed{\\\\left(3, \\\\frac{\\\\pi}{2}\\\\right)}$'"
-            ]
-          },
-          "execution_count": 40,
-          "metadata": {},
-          "output_type": "execute_result"
-        }
+     "data": {
+      "text/markdown": [
+       "## Step 1: Recall the conversion formulas\n",
+       "To convert from rectangular coordinates $(x, y)$ to polar coordinates $(r, \\theta)$, we use the following formulas:\n",
+       "- $r = \\sqrt{x^2 + y^2}$\n",
+       "- $\\theta = \\tan^{-1}\\left(\\frac{y}{x}\\right)$\n",
+       "\n",
+       "## Step 2: Substitute the given values into the formulas\n",
+       "Given $(x, y) = (0, 3)$, we substitute these values into the formulas:\n",
+       "- $r = \\sqrt{0^2 + 3^2} = \\sqrt{0 + 9} = \\sqrt{9} = 3$\n",
+       "- $\\theta = \\tan^{-1}\\left(\\frac{3}{0}\\right)$. However, since division by zero is undefined, we recognize that the point $(0, 3)$ is on the positive y-axis, meaning $\\theta = \\frac{\\pi}{2}$.\n",
+       "\n",
+       "## Step 3: Combine the results for the polar coordinates\n",
+       "Therefore, the polar coordinates of the point $(0, 3)$ are $\\left(3, \\frac{\\pi}{2}\\right)$.\n",
+       "\n",
+       "The final answer is: $\\boxed{\\left(3, \\frac{\\pi}{2}\\right)}$"
       ],
-      "source": [
-        "search_result['pred'][0]"
-      ]
-    },
-    {
-      "cell_type": "markdown",
-      "metadata": {
-        "id": "F-8hIu05AO7J"
-      },
-      "source": [
-        "The model’s output might include special tokens, such as `<|start_header_id|>` or `<|end_header_id|>`. To make the answer more readable, we can safely remove them before displaying it to the end user."
-      ]
-    },
-    {
-      "cell_type": "code",
-      "execution_count": 41,
-      "metadata": {
-        "colab": {
-          "base_uri": "https://localhost:8080/",
-          "height": 105
-        },
-        "id": "flbIu6-rDapM",
-        "outputId": "fcb197d5-0f21-4953-8a21-869c92a1f957"
-      },
-      "outputs": [
-        {
-          "data": {
-            "application/vnd.google.colaboratory.intrinsic+json": {
-              "type": "string"
-            },
-            "text/plain": [
-              "'## Step 1: Recall the conversion formulas\\nTo convert from rectangular coordinates $(x, y)$ to polar coordinates $(r, \\\\theta)$, we use the following formulas:\\n- $r = \\\\sqrt{x^2 + y^2}$\\n- $\\\\theta = \\\\tan^{-1}\\\\left(\\\\frac{y}{x}\\\\right)$\\n\\n## Step 2: Substitute the given values into the formulas\\nGiven $(x, y) = (0, 3)$, we substitute these values into the formulas:\\n- $r = \\\\sqrt{0^2 + 3^2} = \\\\sqrt{0 + 9} = \\\\sqrt{9} = 3$\\n- $\\\\theta = \\\\tan^{-1}\\\\left(\\\\frac{3}{0}\\\\right)$. However, since division by zero is undefined, we recognize that the point $(0, 3)$ is on the positive y-axis, meaning $\\\\theta = \\\\frac{\\\\pi}{2}$.\\n\\n## Step 3: Combine the results for the polar coordinates\\nTherefore, the polar coordinates of the point $(0, 3)$ are $\\\\left(3, \\\\frac{\\\\pi}{2}\\\\right)$.\\n\\nThe final answer is: $\\\\boxed{\\\\left(3, \\\\frac{\\\\pi}{2}\\\\right)}$'"
-            ]
-          },
-          "execution_count": 41,
-          "metadata": {},
-          "output_type": "execute_result"
-        }
-      ],
-      "source": [
-        "formatted_output = search_result['pred'][0].replace(\"<|start_header_id|>assistant<|end_header_id|>\\n\\n\", \"\").strip()\n",
-        "formatted_output"
+      "text/plain": [
+       "<IPython.core.display.Markdown object>"
       ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "from IPython.display import display, Markdown\n",
+    "\n",
+    "display(Markdown(formatted_output))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "id": "4uCpYzAw_4o9"
+   },
+   "source": [
+    "## 3. Assembling It All! 🧑‍🏭️\n",
+    "\n",
+    "Now, let's create a method that encapsulates the entire pipeline. This will allow us to easily reuse the process in future applications, making it efficient and modular.\n",
+    "\n",
+    "By combining the LLM, PRM, search strategy, and result display, we can simplify the workflow and ensure that it’s reusable for other tasks or questions.\n",
+    "\n",
+    "We simplify the workflow, ensuring that it’s reusable for different tasks or questions. Additionally, we’ll track the time spent on each method so that we can **understand the practical implications** of using each strategy and configuration.\n",
+    "\n",
+    "Here’s how we can structure the method:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 43,
+   "metadata": {
+    "id": "YpswbcVi37KR"
+   },
+   "outputs": [],
+   "source": [
+    "import time\n",
+    "\n",
+    "def generate_with_search_and_learn(question, config, llm, prm, method='best_of_n'):\n",
+    "    \"\"\"\n",
+    "    Generate an answer for a given question using the search-and-learn pipeline.\n",
+    "\n",
+    "    Args:\n",
+    "    - question (str): The input question to generate an answer for.\n",
+    "    - config (Config): Configuration object containing parameters for search strategy.\n",
+    "    - llm (LLM): Pretrained large language model used for generating answers.\n",
+    "    - prm (RLHFFlow): Process reward model used for evaluating answers.\n",
+    "    - method (str): Search strategy to use. Options are 'best_of_n', 'beam_search', 'dvts'. Default is 'best_of_n'.\n",
+    "\n",
+    "    Returns:\n",
+    "    - str: The formatted output after processing the question.\n",
+    "    \"\"\"\n",
+    "    batch = {\"problem\": [question]}\n",
+    "\n",
+    "    start_time = time.time()\n",
+    "    if method == 'best_of_n':\n",
+    "      result = best_of_n(x=batch, config=config, llm=llm, prm=prm)\n",
+    "    elif method == 'beam_search':\n",
+    "      result = beam_search(examples=batch, config=config, llm=llm, prm=prm)\n",
+    "    elif method == 'dvts':\n",
+    "      result = dvts(examples=batch, config=config, llm=llm, prm=prm)\n",
+    "\n",
+    "    elapsed_time = time.time() - start_time\n",
+    "    print(f\"\\nFinished in {elapsed_time:.2f} seconds\\n\")\n",
+    "\n",
+    "    tokenizer = llm.get_tokenizer()\n",
+    "    total_tokens = 0\n",
+    "    for completion in result['completions']:\n",
+    "        for comp in  completion:\n",
+    "            output_tokens = tokenizer.encode(comp)\n",
+    "            total_tokens += len(output_tokens)\n",
+    "\n",
+    "    print(f\"Total tokens in all completions: {total_tokens}\")\n",
+    "\n",
+    "    formatted_output = result['pred'][0].replace(\"<|start_header_id|>assistant<|end_header_id|>\\n\\n\", \"\").strip()\n",
+    "    return formatted_output"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "id": "RWbOqkiKPVd2"
+   },
+   "source": [
+    "### ⏳  3.1 Comparing Thinking Time for Each Strategy\n",
+    "\n",
+    "Let’s compare the **thinking time** of three methods: `best_of_n`, `beam_search`, and `dvts`. Each method is evaluated using the same number of answers during the search process, measuring the time spent thinking in seconds and the number of generated tokens.\n",
+    "\n",
+    "In the results below, the `best_of_n` method shows the least thinking time, while the `dvts` method takes the most time. However, `best_of_n` generates more tokens due to its simpler search strategy.\n",
+    "\n",
+    "| **Method**      | **Number of Answers During Search** | **Thinking Time (Seconds)** | **Generated Tokens** |\n",
+    "|------------------|-------------------------------------|-----------------------------|-----------------------|\n",
+    "| **best_of_n**    | 8                                   | 3.54                        | 3087                  |\n",
+    "| **beam_search**  | 8                                   | 10.06                       | 2049                  |\n",
+    "| **dvts**         | 8                                   | 8.46                        | 2544                  |\n",
+    "\n",
+    "This comparison illustrates the trade-offs between the strategies, balancing time spent thinking and the complexity of the search process.\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "id": "2ROJwROGX8q-"
+   },
+   "source": [
+    "#### 1. **Best of n**\n",
+    "\n",
+    "We’ll begin by using the `best_of_n` strategy. Here’s how to track the thinking time for this method:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 44,
+   "metadata": {
+    "colab": {
+     "base_uri": "https://localhost:8080/"
     },
+    "id": "c_fWKy5CCTLV",
+    "outputId": "8d77eea3-b23e-4eba-cfe3-5935fae1405d"
+   },
+   "outputs": [
     {
-      "cell_type": "markdown",
-      "metadata": {
-        "id": "7ZuLZNirAO7J"
-      },
-      "source": [
-        "After removing any special tokens, we can display the final answer to the user. Since the answer is based on markdown, it can be rendered properly by displaying it as markdown."
-      ]
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "Finished in 3.54 seconds\n",
+      "\n",
+      "Total tokens in all completions: 3087\n"
+     ]
+    }
+   ],
+   "source": [
+    "question = 'Convert the point $(0,3)$ in rectangular coordinates to polar coordinates.  Enter your answer in the form $(r,\\theta),$ where $r > 0$ and $0 \\le \\theta < 2 \\pi.$'\n",
+    "\n",
+    "config.n=8\n",
+    "\n",
+    "formatted_output = generate_with_search_and_learn(question=question, config=config, llm=llm, prm=prm, method='best_of_n')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 45,
+   "metadata": {
+    "colab": {
+     "base_uri": "https://localhost:8080/",
+     "height": 428
     },
+    "id": "uzKfFoKG9ejC",
+    "outputId": "38326907-685e-4a9c-ca8b-32a7c40f1d3e"
+   },
+   "outputs": [
     {
-      "cell_type": "code",
-      "execution_count": 42,
-      "metadata": {
-        "colab": {
-          "base_uri": "https://localhost:8080/",
-          "height": 385
-        },
-        "id": "P4En0qJRD0cl",
-        "outputId": "56400fea-e304-4f16-d255-909f42f636e0"
-      },
-      "outputs": [
-        {
-          "data": {
-            "text/markdown": [
-              "## Step 1: Recall the conversion formulas\n",
-              "To convert from rectangular coordinates $(x, y)$ to polar coordinates $(r, \\theta)$, we use the following formulas:\n",
-              "- $r = \\sqrt{x^2 + y^2}$\n",
-              "- $\\theta = \\tan^{-1}\\left(\\frac{y}{x}\\right)$\n",
-              "\n",
-              "## Step 2: Substitute the given values into the formulas\n",
-              "Given $(x, y) = (0, 3)$, we substitute these values into the formulas:\n",
-              "- $r = \\sqrt{0^2 + 3^2} = \\sqrt{0 + 9} = \\sqrt{9} = 3$\n",
-              "- $\\theta = \\tan^{-1}\\left(\\frac{3}{0}\\right)$. However, since division by zero is undefined, we recognize that the point $(0, 3)$ is on the positive y-axis, meaning $\\theta = \\frac{\\pi}{2}$.\n",
-              "\n",
-              "## Step 3: Combine the results for the polar coordinates\n",
-              "Therefore, the polar coordinates of the point $(0, 3)$ are $\\left(3, \\frac{\\pi}{2}\\right)$.\n",
-              "\n",
-              "The final answer is: $\\boxed{\\left(3, \\frac{\\pi}{2}\\right)}$"
-            ],
-            "text/plain": [
-              "<IPython.core.display.Markdown object>"
-            ]
-          },
-          "metadata": {},
-          "output_type": "display_data"
-        }
+     "data": {
+      "text/markdown": [
+       "## Step 1: Recall the conversion formulas from rectangular to polar coordinates\n",
+       "The conversion formulas are $r = \\sqrt{x^2 + y^2}$ for the radial coordinate and $\\theta = \\tan^{-1}\\left(\\frac{y}{x}\\right)$ for the angular coordinate.\n",
+       "\n",
+       "## Step 2: Substitute the given rectangular coordinates into the formulas\n",
+       "Given the point $(0, 3)$, we substitute $x = 0$ and $y = 3$ into the formulas.\n",
+       "\n",
+       "## Step 3: Calculate the radial coordinate\n",
+       "$r = \\sqrt{0^2 + 3^2} = \\sqrt{0 + 9} = \\sqrt{9} = 3$\n",
+       "\n",
+       "## Step 4: Calculate the angular coordinate\n",
+       "$\\theta = \\tan^{-1}\\left(\\frac{3}{0}\\right) = \\tan^{-1}(\\infty) = \\frac{\\pi}{2}$\n",
+       "\n",
+       "## Step 5: Combine the results\n",
+       "The polar coordinates of the point $(0, 3)$ are $\\left(3, \\frac{\\pi}{2}\\right)$.\n",
+       "\n",
+       "The final answer is: $\\boxed{\\left(3, \\frac{\\pi}{2}\\right)}$"
       ],
-      "source": [
-        "from IPython.display import display, Markdown\n",
-        "\n",
-        "display(Markdown(formatted_output))"
-      ]
-    },
-    {
-      "cell_type": "markdown",
-      "metadata": {
-        "id": "4uCpYzAw_4o9"
-      },
-      "source": [
-        "## 3. Assembling It All! 🧑‍🏭️\n",
-        "\n",
-        "Now, let's create a method that encapsulates the entire pipeline. This will allow us to easily reuse the process in future applications, making it efficient and modular.\n",
-        "\n",
-        "By combining the LLM, PRM, search strategy, and result display, we can simplify the workflow and ensure that it’s reusable for other tasks or questions.\n",
-        "\n",
-        "We simplify the workflow, ensuring that it’s reusable for different tasks or questions. Additionally, we’ll track the time spent on each method so that we can **understand the practical implications** of using each strategy and configuration.\n",
-        "\n",
-        "Here’s how we can structure the method:"
-      ]
-    },
-    {
-      "cell_type": "code",
-      "execution_count": 43,
-      "metadata": {
-        "id": "YpswbcVi37KR"
-      },
-      "outputs": [],
-      "source": [
-        "import time\n",
-        "\n",
-        "def generate_with_search_and_learn(question, config, llm, prm, method='best_of_n'):\n",
-        "    \"\"\"\n",
-        "    Generate an answer for a given question using the search-and-learn pipeline.\n",
-        "\n",
-        "    Args:\n",
-        "    - question (str): The input question to generate an answer for.\n",
-        "    - config (Config): Configuration object containing parameters for search strategy.\n",
-        "    - llm (LLM): Pretrained large language model used for generating answers.\n",
-        "    - prm (RLHFFlow): Process reward model used for evaluating answers.\n",
-        "    - method (str): Search strategy to use. Options are 'best_of_n', 'beam_search', 'dvts'. Default is 'best_of_n'.\n",
-        "\n",
-        "    Returns:\n",
-        "    - str: The formatted output after processing the question.\n",
-        "    \"\"\"\n",
-        "    batch = {\"problem\": [question]}\n",
-        "\n",
-        "    start_time = time.time()\n",
-        "    if method == 'best_of_n':\n",
-        "      result = best_of_n(x=batch, config=config, llm=llm, prm=prm)\n",
-        "    elif method == 'beam_search':\n",
-        "      result = beam_search(examples=batch, config=config, llm=llm, prm=prm)\n",
-        "    elif method == 'dvts':\n",
-        "      result = dvts(examples=batch, config=config, llm=llm, prm=prm)\n",
-        "\n",
-        "    elapsed_time = time.time() - start_time\n",
-        "    print(f\"\\nFinished in {elapsed_time:.2f} seconds\\n\")\n",
-        "\n",
-        "    tokenizer = llm.get_tokenizer()\n",
-        "    total_tokens = 0\n",
-        "    for completion in result['completions']:\n",
-        "        for comp in  completion:\n",
-        "            output_tokens = tokenizer.encode(comp)\n",
-        "            total_tokens += len(output_tokens)\n",
-        "\n",
-        "    print(f\"Total tokens in all completions: {total_tokens}\")\n",
-        "\n",
-        "    formatted_output = result['pred'][0].replace(\"<|start_header_id|>assistant<|end_header_id|>\\n\\n\", \"\").strip()\n",
-        "    return formatted_output"
-      ]
-    },
-    {
-      "cell_type": "markdown",
-      "metadata": {
-        "id": "RWbOqkiKPVd2"
-      },
-      "source": [
-        "### ⏳  3.1 Comparing Thinking Time for Each Strategy\n",
-        "\n",
-        "Let’s compare the **thinking time** of three methods: `best_of_n`, `beam_search`, and `dvts`. Each method is evaluated using the same number of answers during the search process, measuring the time spent thinking in seconds and the number of generated tokens.\n",
-        "\n",
-        "In the results below, the `best_of_n` method shows the least thinking time, while the `dvts` method takes the most time. However, `best_of_n` generates more tokens due to its simpler search strategy.\n",
-        "\n",
-        "| **Method**      | **Number of Answers During Search** | **Thinking Time (Seconds)** | **Generated Tokens** |\n",
-        "|------------------|-------------------------------------|-----------------------------|-----------------------|\n",
-        "| **best_of_n**    | 8                                   | 3.54                        | 3087                  |\n",
-        "| **beam_search**  | 8                                   | 10.06                       | 2049                  |\n",
-        "| **dvts**         | 8                                   | 8.46                        | 2544                  |\n",
-        "\n",
-        "This comparison illustrates the trade-offs between the strategies, balancing time spent thinking and the complexity of the search process.\n"
+      "text/plain": [
+       "<IPython.core.display.Markdown object>"
       ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "display(Markdown(formatted_output))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "id": "7S9AwP5lQvUN"
+   },
+   "source": [
+    "#### 2. **Beam Search**\n",
+    "\n",
+    "Now, let's try using the `beam_search` strategy."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 46,
+   "metadata": {
+    "colab": {
+     "base_uri": "https://localhost:8080/"
     },
+    "id": "F7CH6KN8Izp9",
+    "outputId": "adef4782-3278-4994-9520-43e23ea047a6"
+   },
+   "outputs": [
     {
-      "cell_type": "markdown",
-      "metadata": {
-        "id": "2ROJwROGX8q-"
-      },
-      "source": [
-        "#### 1. **Best of n**\n",
-        "\n",
-        "We’ll begin by using the `best_of_n` strategy. Here’s how to track the thinking time for this method:"
-      ]
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "Beam search iterations:  20%|██        | 8/40 [00:10<00:40,  1.26s/it]"
+     ]
     },
     {
-      "cell_type": "code",
-      "execution_count": 44,
-      "metadata": {
-        "colab": {
-          "base_uri": "https://localhost:8080/"
-        },
-        "id": "c_fWKy5CCTLV",
-        "outputId": "8d77eea3-b23e-4eba-cfe3-5935fae1405d"
-      },
-      "outputs": [
-        {
-          "name": "stdout",
-          "output_type": "stream",
-          "text": [
-            "\n",
-            "Finished in 3.54 seconds\n",
-            "\n",
-            "Total tokens in all completions: 3087\n"
-          ]
-        }
-      ],
-      "source": [
-        "question = 'Convert the point $(0,3)$ in rectangular coordinates to polar coordinates.  Enter your answer in the form $(r,\\theta),$ where $r > 0$ and $0 \\le \\theta < 2 \\pi.$'\n",
-        "\n",
-        "config.n=8\n",
-        "\n",
-        "formatted_output = generate_with_search_and_learn(question=question, config=config, llm=llm, prm=prm, method='best_of_n')"
-      ]
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "Finished in 10.06 seconds\n",
+      "\n",
+      "Total tokens in all completions: 2049\n"
+     ]
     },
     {
-      "cell_type": "code",
-      "execution_count": 45,
-      "metadata": {
-        "colab": {
-          "base_uri": "https://localhost:8080/",
-          "height": 428
-        },
-        "id": "uzKfFoKG9ejC",
-        "outputId": "38326907-685e-4a9c-ca8b-32a7c40f1d3e"
-      },
-      "outputs": [
-        {
-          "data": {
-            "text/markdown": [
-              "## Step 1: Recall the conversion formulas from rectangular to polar coordinates\n",
-              "The conversion formulas are $r = \\sqrt{x^2 + y^2}$ for the radial coordinate and $\\theta = \\tan^{-1}\\left(\\frac{y}{x}\\right)$ for the angular coordinate.\n",
-              "\n",
-              "## Step 2: Substitute the given rectangular coordinates into the formulas\n",
-              "Given the point $(0, 3)$, we substitute $x = 0$ and $y = 3$ into the formulas.\n",
-              "\n",
-              "## Step 3: Calculate the radial coordinate\n",
-              "$r = \\sqrt{0^2 + 3^2} = \\sqrt{0 + 9} = \\sqrt{9} = 3$\n",
-              "\n",
-              "## Step 4: Calculate the angular coordinate\n",
-              "$\\theta = \\tan^{-1}\\left(\\frac{3}{0}\\right) = \\tan^{-1}(\\infty) = \\frac{\\pi}{2}$\n",
-              "\n",
-              "## Step 5: Combine the results\n",
-              "The polar coordinates of the point $(0, 3)$ are $\\left(3, \\frac{\\pi}{2}\\right)$.\n",
-              "\n",
-              "The final answer is: $\\boxed{\\left(3, \\frac{\\pi}{2}\\right)}$"
-            ],
-            "text/plain": [
-              "<IPython.core.display.Markdown object>"
-            ]
-          },
-          "metadata": {},
-          "output_type": "display_data"
-        }
-      ],
-      "source": [
-        "display(Markdown(formatted_output))"
-      ]
-    },
-    {
-      "cell_type": "markdown",
-      "metadata": {
-        "id": "7S9AwP5lQvUN"
-      },
-      "source": [
-        "#### 2. **Beam Search**\n",
-        "\n",
-        "Now, let's try using the `beam_search` strategy."
-      ]
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n"
+     ]
+    }
+   ],
+   "source": [
+    "config.n=8\n",
+    "# beam search specific\n",
+    "config.sort_completed=True\n",
+    "config.filter_duplicates=True\n",
+    "\n",
+    "formatted_output = generate_with_search_and_learn(question=question, config=config, llm=llm, prm=prm, method='beam_search')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 47,
+   "metadata": {
+    "colab": {
+     "base_uri": "https://localhost:8080/",
+     "height": 364
     },
+    "id": "Hw6tQD_dMwXZ",
+    "outputId": "0f66c7ed-2071-45a4-e562-3967deb0bc9d"
+   },
+   "outputs": [
     {
-      "cell_type": "code",
-      "execution_count": 46,
-      "metadata": {
-        "colab": {
-          "base_uri": "https://localhost:8080/"
-        },
-        "id": "F7CH6KN8Izp9",
-        "outputId": "adef4782-3278-4994-9520-43e23ea047a6"
-      },
-      "outputs": [
-        {
-          "name": "stderr",
-          "output_type": "stream",
-          "text": [
-            "Beam search iterations:  20%|██        | 8/40 [00:10<00:40,  1.26s/it]"
-          ]
-        },
-        {
-          "name": "stdout",
-          "output_type": "stream",
-          "text": [
-            "\n",
-            "Finished in 10.06 seconds\n",
-            "\n",
-            "Total tokens in all completions: 2049\n"
-          ]
-        },
-        {
-          "name": "stderr",
-          "output_type": "stream",
-          "text": [
-            "\n"
-          ]
-        }
+     "data": {
+      "text/markdown": [
+       "## Step 1: To convert the point (0,3) from rectangular coordinates to polar coordinates, we need to find the radius (r) and the angle (heta).\n",
+       "\n",
+       "The formula to convert from rectangular coordinates (x, y) to polar coordinates (r, heta) is given by:\n",
+       "r = sqrt(x^2 + y^2)\n",
+       "heta = atan2(y, x)\n",
+       "\n",
+       "## Step 2: Plug in the values (0,3) into the formula to find the radius (r).\n",
+       "\n",
+       "r = sqrt(0^2 + 3^2)\n",
+       "r = sqrt(0 + 9)\n",
+       "r = sqrt(9)\n",
+       "r = 3\n",
+       "\n",
+       "## Step 3: Plug in the values (0,3) into the formula to find the angle (heta).\n",
+       "\n",
+       "heta = atan2(3, 0)\n",
+       "Since the point (0,3) is in the first quadrant and lies on the positive y-axis, heta = pi/2 (or 90 degrees).\n",
+       "\n",
+       "## Step 4: Combine r and heta to get the polar coordinates.\n",
+       "\n",
+       "The polar coordinates are (3, pi/2).\n",
+       "\n",
+       "The final answer is: $\\boxed{(3, \\frac{\\pi}{2})}$"
       ],
-      "source": [
-        "config.n=8\n",
-        "# beam search specific\n",
-        "config.sort_completed=True\n",
-        "config.filter_duplicates=True\n",
-        "\n",
-        "formatted_output = generate_with_search_and_learn(question=question, config=config, llm=llm, prm=prm, method='beam_search')"
+      "text/plain": [
+       "<IPython.core.display.Markdown object>"
       ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "display(Markdown(formatted_output))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "id": "GxBBUd7HQzhd"
+   },
+   "source": [
+    "#### 3. **Diverse Verifier Tree Search (DVTS)**\n",
+    "\n",
+    "Finally, let's try the `dvts` strategy."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 48,
+   "metadata": {
+    "colab": {
+     "base_uri": "https://localhost:8080/"
     },
+    "id": "HzXW1g-dI5wN",
+    "outputId": "86979d67-7dfa-4346-9adb-c386a52af58c"
+   },
+   "outputs": [
     {
-      "cell_type": "code",
-      "execution_count": 47,
-      "metadata": {
-        "colab": {
-          "base_uri": "https://localhost:8080/",
-          "height": 364
-        },
-        "id": "Hw6tQD_dMwXZ",
-        "outputId": "0f66c7ed-2071-45a4-e562-3967deb0bc9d"
-      },
-      "outputs": [
-        {
-          "data": {
-            "text/markdown": [
-              "## Step 1: To convert the point (0,3) from rectangular coordinates to polar coordinates, we need to find the radius (r) and the angle (heta).\n",
-              "\n",
-              "The formula to convert from rectangular coordinates (x, y) to polar coordinates (r, heta) is given by:\n",
-              "r = sqrt(x^2 + y^2)\n",
-              "heta = atan2(y, x)\n",
-              "\n",
-              "## Step 2: Plug in the values (0,3) into the formula to find the radius (r).\n",
-              "\n",
-              "r = sqrt(0^2 + 3^2)\n",
-              "r = sqrt(0 + 9)\n",
-              "r = sqrt(9)\n",
-              "r = 3\n",
-              "\n",
-              "## Step 3: Plug in the values (0,3) into the formula to find the angle (heta).\n",
-              "\n",
-              "heta = atan2(3, 0)\n",
-              "Since the point (0,3) is in the first quadrant and lies on the positive y-axis, heta = pi/2 (or 90 degrees).\n",
-              "\n",
-              "## Step 4: Combine r and heta to get the polar coordinates.\n",
-              "\n",
-              "The polar coordinates are (3, pi/2).\n",
-              "\n",
-              "The final answer is: $\\boxed{(3, \\frac{\\pi}{2})}$"
-            ],
-            "text/plain": [
-              "<IPython.core.display.Markdown object>"
-            ]
-          },
-          "metadata": {},
-          "output_type": "display_data"
-        }
-      ],
-      "source": [
-        "display(Markdown(formatted_output))"
-      ]
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "Beam search iterations:  22%|██▎       | 9/40 [00:08<00:29,  1.06it/s]"
+     ]
     },
     {
-      "cell_type": "markdown",
-      "metadata": {
-        "id": "GxBBUd7HQzhd"
-      },
-      "source": [
-        "#### 3. **Diverse Verifier Tree Search (DVTS)**\n",
-        "\n",
-        "Finally, let's try the `dvts` strategy."
-      ]
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "Finished in 8.46 seconds\n",
+      "\n",
+      "Total tokens in all completions: 2544\n"
+     ]
     },
     {
-      "cell_type": "code",
-      "execution_count": 48,
-      "metadata": {
-        "colab": {
-          "base_uri": "https://localhost:8080/"
-        },
-        "id": "HzXW1g-dI5wN",
-        "outputId": "86979d67-7dfa-4346-9adb-c386a52af58c"
-      },
-      "outputs": [
-        {
-          "name": "stderr",
-          "output_type": "stream",
-          "text": [
-            "Beam search iterations:  22%|██▎       | 9/40 [00:08<00:29,  1.06it/s]"
-          ]
-        },
-        {
-          "name": "stdout",
-          "output_type": "stream",
-          "text": [
-            "\n",
-            "Finished in 8.46 seconds\n",
-            "\n",
-            "Total tokens in all completions: 2544\n"
-          ]
-        },
-        {
-          "name": "stderr",
-          "output_type": "stream",
-          "text": [
-            "\n"
-          ]
-        }
-      ],
-      "source": [
-        "config.n=8\n",
-        "# dvts specific\n",
-        "config.n_beams = config.n // config.beam_width\n",
-        "\n",
-        "formatted_output = generate_with_search_and_learn(question=question, config=config, llm=llm, prm=prm, method='dvts')"
-      ]
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "\n"
+     ]
+    }
+   ],
+   "source": [
+    "config.n=8\n",
+    "# dvts specific\n",
+    "config.n_beams = config.n // config.beam_width\n",
+    "\n",
+    "formatted_output = generate_with_search_and_learn(question=question, config=config, llm=llm, prm=prm, method='dvts')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 49,
+   "metadata": {
+    "colab": {
+     "base_uri": "https://localhost:8080/",
+     "height": 416
     },
+    "id": "RGkG9MPXMvN0",
+    "outputId": "18a333ae-7b3a-455e-df2c-bb497b1381a5"
+   },
+   "outputs": [
     {
-      "cell_type": "code",
-      "execution_count": 49,
-      "metadata": {
-        "colab": {
-          "base_uri": "https://localhost:8080/",
-          "height": 416
-        },
-        "id": "RGkG9MPXMvN0",
-        "outputId": "18a333ae-7b3a-455e-df2c-bb497b1381a5"
-      },
-      "outputs": [
-        {
-          "data": {
-            "text/markdown": [
-              "## Step 1: To convert the point (0,3) from rectangular coordinates to polar coordinates, we need to find the radius r and the angle theta.\n",
-              "\n",
-              "The radius r can be calculated using the formula $r = \\sqrt{x^2 + y^2}$, where x is the x-coordinate and y is the y-coordinate.\n",
-              "\n",
-              "## Step 2: Substitute the values of x and y into the formula to find the radius r.\n",
-              "\n",
-              "$r = \\sqrt{0^2 + 3^2}$\n",
-              "$r = \\sqrt{9}$\n",
-              "$r = 3$\n",
-              "\n",
-              "## Step 3: Now that we have the radius r, we can find the angle theta using the formula $\\theta = \\tan^{-1}\\left(\\frac{y}{x}\\right)$.\n",
-              "\n",
-              "Since x = 0 and y = 3, the angle theta is 90 degrees or $\\frac{\\pi}{2}$ radians.\n",
-              "\n",
-              "## Step 4: Now that we have the radius r and the angle theta, we can write the polar coordinates as (r, theta).\n",
-              "\n",
-              "Therefore, the polar coordinates for the point (0, 3) are $\\left(3, \\frac{\\pi}{2}\\right).$\n",
-              "\n",
-              "The final answer is: $\\boxed{\\left(3, \\frac{\\pi}{2}\\right)}$"
-            ],
-            "text/plain": [
-              "<IPython.core.display.Markdown object>"
-            ]
-          },
-          "metadata": {},
-          "output_type": "display_data"
-        }
+     "data": {
+      "text/markdown": [
+       "## Step 1: To convert the point (0,3) from rectangular coordinates to polar coordinates, we need to find the radius r and the angle theta.\n",
+       "\n",
+       "The radius r can be calculated using the formula $r = \\sqrt{x^2 + y^2}$, where x is the x-coordinate and y is the y-coordinate.\n",
+       "\n",
+       "## Step 2: Substitute the values of x and y into the formula to find the radius r.\n",
+       "\n",
+       "$r = \\sqrt{0^2 + 3^2}$\n",
+       "$r = \\sqrt{9}$\n",
+       "$r = 3$\n",
+       "\n",
+       "## Step 3: Now that we have the radius r, we can find the angle theta using the formula $\\theta = \\tan^{-1}\\left(\\frac{y}{x}\\right)$.\n",
+       "\n",
+       "Since x = 0 and y = 3, the angle theta is 90 degrees or $\\frac{\\pi}{2}$ radians.\n",
+       "\n",
+       "## Step 4: Now that we have the radius r and the angle theta, we can write the polar coordinates as (r, theta).\n",
+       "\n",
+       "Therefore, the polar coordinates for the point (0, 3) are $\\left(3, \\frac{\\pi}{2}\\right).$\n",
+       "\n",
+       "The final answer is: $\\boxed{\\left(3, \\frac{\\pi}{2}\\right)}$"
       ],
-      "source": [
-        "display(Markdown(formatted_output))"
-      ]
-    },
-    {
-      "cell_type": "markdown",
-      "metadata": {
-        "id": "5PM9HHwBSYWk"
-      },
-      "source": [
-        "### 🙋 3.2 Testing the System with a Simple Question\n",
-        "\n",
-        "In this final example, we’ll test the system using a straightforward question to observe how it performs in simpler cases. This allows us to verify that the system works as expected even for basic queries.\n",
-        "\n",
-        "Let's try the following question:"
+      "text/plain": [
+       "<IPython.core.display.Markdown object>"
       ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "display(Markdown(formatted_output))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "id": "5PM9HHwBSYWk"
+   },
+   "source": [
+    "### 🙋 3.2 Testing the System with a Simple Question\n",
+    "\n",
+    "In this final example, we’ll test the system using a straightforward question to observe how it performs in simpler cases. This allows us to verify that the system works as expected even for basic queries.\n",
+    "\n",
+    "Let's try the following question:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 50,
+   "metadata": {
+    "colab": {
+     "base_uri": "https://localhost:8080/"
     },
+    "id": "bq9vM1uRM7A8",
+    "outputId": "65ef318d-2b89-4d46-b660-293195c2b8e1"
+   },
+   "outputs": [
     {
-      "cell_type": "code",
-      "execution_count": 50,
-      "metadata": {
-        "colab": {
-          "base_uri": "https://localhost:8080/"
-        },
-        "id": "bq9vM1uRM7A8",
-        "outputId": "65ef318d-2b89-4d46-b660-293195c2b8e1"
-      },
-      "outputs": [
-        {
-          "name": "stdout",
-          "output_type": "stream",
-          "text": [
-            "\n",
-            "Finished in 1.03 seconds\n",
-            "\n",
-            "Total tokens in all completions: 544\n"
-          ]
-        }
-      ],
-      "source": [
-        "question = 'What\\'s the capital of Spain?'\n",
-        "\n",
-        "config.n=32\n",
-        "\n",
-        "formatted_output = generate_with_search_and_learn(question=question, config=config, llm=llm, prm=prm, method='best_of_n')"
-      ]
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "Finished in 1.03 seconds\n",
+      "\n",
+      "Total tokens in all completions: 544\n"
+     ]
+    }
+   ],
+   "source": [
+    "question = 'What\\'s the capital of Spain?'\n",
+    "\n",
+    "config.n=32\n",
+    "\n",
+    "formatted_output = generate_with_search_and_learn(question=question, config=config, llm=llm, prm=prm, method='best_of_n')"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 51,
+   "metadata": {
+    "colab": {
+     "base_uri": "https://localhost:8080/",
+     "height": 46
     },
+    "id": "ysfR0nPfM-Ub",
+    "outputId": "b474aeb6-6cb7-4f15-ba48-fa59022f31ef"
+   },
+   "outputs": [
     {
-      "cell_type": "code",
-      "execution_count": 51,
-      "metadata": {
-        "colab": {
-          "base_uri": "https://localhost:8080/",
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-        "id": "ysfR0nPfM-Ub",
-        "outputId": "b474aeb6-6cb7-4f15-ba48-fa59022f31ef"
-      },
-      "outputs": [
-        {
-          "data": {
-            "text/markdown": [
-              "The capital of Spain is Madrid."
-            ],
-            "text/plain": [
-              "<IPython.core.display.Markdown object>"
-            ]
-          },
-          "metadata": {},
-          "output_type": "display_data"
-        }
+     "data": {
+      "text/markdown": [
+       "The capital of Spain is Madrid."
       ],
-      "source": [
-        "display(Markdown(formatted_output))"
-      ]
-    },
-    {
-      "cell_type": "markdown",
-      "metadata": {
-        "id": "NgdeSegeANoT"
-      },
-      "source": [
-        "Even though we set a larger number of candidate answers (`N`), the time spent thinking remains relatively small (1.03 seconds and 544 generated tokens). This demonstrates the system’s ability to efficiently handle easier problems, spending less time on them, while leveraging its enhanced capabilities for more complex questions.\n",
-        "\n",
-        "🏆 **We now have a fully operational pipeline** that leverages test-time compute, enabling the system to \"think longer\" for more complicated queries, while also maintaining fast response times for straightforward questions.\n",
-        "\n",
-        "This approach ensures the system can scale its thinking time based on the task's complexity, offering an efficient and responsive solution for both simple and challenging problems.\n"
-      ]
-    },
-    {
-      "cell_type": "markdown",
-      "metadata": {
-        "id": "92znAyJ0AOPY"
-      },
-      "source": [
-        "## 4. Continuing the Journey and Resources 🧑‍🎓️\n",
-        "\n",
-        "If you're eager to continue exploring, be sure to check out the original experimental [blog](https://huggingface.co/spaces/HuggingFaceH4/blogpost-scaling-test-time-compute) and all the references mentioned within it. These resources will deepen your understanding of test-time compute, its benefits, and its applications in LLMs.\n",
-        "\n",
-        "\n",
-        "Happy learning and experimenting! 🚀"
+      "text/plain": [
+       "<IPython.core.display.Markdown object>"
       ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
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+    "display(Markdown(formatted_output))"
+   ]
+  },
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+   "metadata": {
+    "id": "NgdeSegeANoT"
+   },
+   "source": [
+    "Even though we set a larger number of candidate answers (`N`), the time spent thinking remains relatively small (1.03 seconds and 544 generated tokens). This demonstrates the system’s ability to efficiently handle easier problems, spending less time on them, while leveraging its enhanced capabilities for more complex questions.\n",
+    "\n",
+    "🏆 **We now have a fully operational pipeline** that leverages test-time compute, enabling the system to \"think longer\" for more complicated queries, while also maintaining fast response times for straightforward questions.\n",
+    "\n",
+    "This approach ensures the system can scale its thinking time based on the task's complexity, offering an efficient and responsive solution for both simple and challenging problems.\n"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {
+    "id": "92znAyJ0AOPY"
+   },
+   "source": [
+    "## 4. Continuing the Journey and Resources 🧑‍🎓️\n",
+    "\n",
+    "If you're eager to continue exploring, be sure to check out the original experimental [blog](https://huggingface.co/spaces/HuggingFaceH4/blogpost-scaling-test-time-compute) and all the references mentioned within it. These resources will deepen your understanding of test-time compute, its benefits, and its applications in LLMs.\n",
+    "\n",
+    "\n",
+    "Happy learning and experimenting! 🚀"
+   ]
+  }
+ ],
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