Improve model card: Add metadata, paper link, code, and detailed description

README.md

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 ---
 library_name: transformers
-tags: []
+pipeline_tag: text-generation
+license: apache-2.0
+tags:
+- qwen2
+- reasoning
 ---
 
-# Model Card for Model ID
-
-<!-- Provide a quick summary of what the model is/does. -->
-
+# Model Card for Variational Reasoning for Language Models
 
+This is the model card for a model utilizing the variational reasoning framework, as presented in the paper [Variational Reasoning for Language Models](https://huggingface.co/papers/2509.22637).
 
 ## Model Details
 
 ### Model Description
 
-<!-- Provide a longer summary of what this model is. -->
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-This is the model card of a 🤗 transformers model that has been pushed on the Hub. This model card has been automatically generated.
-
-- **Developed by:** [More Information Needed]
-- **Funded by [optional]:** [More Information Needed]
-- **Shared by [optional]:** [More Information Needed]
-- **Model type:** [More Information Needed]
-- **Language(s) (NLP):** [More Information Needed]
-- **License:** [More Information Needed]
-- **Finetuned from model [optional]:** [More Information Needed]
-
-### Model Sources [optional]
+We introduce a variational reasoning framework for language models that treats thinking traces as latent variables and optimizes them through variational inference. Starting from the evidence lower bound (ELBO), we extend it to a multi-trace objective for tighter bounds and propose a forward-KL formulation that stabilizes the training of the variational posterior. We further show that rejection sampling finetuning and binary-reward RL, including GRPO, can be interpreted as local forward-KL objectives, where an implicit weighting by model accuracy naturally arises from the derivation and reveals a previously unnoticed bias toward easier questions. We empirically validate our method on the Qwen 2.5 and Qwen 3 model families across a wide range of reasoning tasks. Overall, our work provides a principled probabilistic perspective that unifies variational inference with RL-style methods and yields stable objectives for improving the reasoning ability of language models.
 
-<!-- Provide the basic links for the model. -->
+-   **Developed by:** Xiangxin Zhou, Zichen Liu, Haonan Wang, Chao Du, Min Lin, Chongxuan Li, Liang Wang, Tianyu Pang
+-   **Model type:** Qwen2ForCausalLM
+-   **Language(s) (NLP):** English
+-   **License:** Apache-2.0
+-   **Finetuned from model:** Qwen2.5-7B-Instruct
 
-- **Repository:** [More Information Needed]
-- **Paper [optional]:** [More Information Needed]
-- **Demo [optional]:** [More Information Needed]
+### Model Sources
+-   **Repository:** https://github.com/sail-sg/variational-reasoning
+-   **Paper:** [Variational Reasoning for Language Models](https://huggingface.co/papers/2509.22637)
 
 ## Uses
 
-<!-- Address questions around how the model is intended to be used, including the foreseeable users of the model and those affected by the model. -->
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 ### Direct Use
 
-<!-- This section is for the model use without fine-tuning or plugging into a larger ecosystem/app. -->
-
-[More Information Needed]
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-### Downstream Use [optional]
-
-<!-- This section is for the model use when fine-tuned for a task, or when plugged into a larger ecosystem/app -->
-
-[More Information Needed]
+This model is intended for improving the reasoning capabilities of language models by leveraging a novel variational inference framework. It can be used as a base for various reasoning tasks by treating thinking traces as latent variables.
 
 ### Out-of-Scope Use
 
-<!-- This section addresses misuse, malicious use, and uses that the model will not work well for. -->
-
-[More Information Needed]
+As a research model, caution should be exercised when deploying in critical applications. Further evaluation is recommended for specific use cases outside of reasoning tasks.
 
 ## Bias, Risks, and Limitations
 
-<!-- This section is meant to convey both technical and sociotechnical limitations. -->
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-[More Information Needed]
+The paper discusses that rejection sampling finetuning and binary-reward RL can reveal a previously unnoticed bias toward easier questions. Users should be aware of this potential bias, as well as general limitations and biases inherent in large language models.
 
 ### Recommendations
 
-<!-- This section is meant to convey recommendations with respect to the bias, risk, and technical limitations. -->
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-Users (both direct and downstream) should be made aware of the risks, biases and limitations of the model. More information needed for further recommendations.
+Users (both direct and downstream) should be made aware of the risks, biases, and limitations of the model. For comprehensive understanding, it is recommended to review the full paper and the associated GitHub repository.
 
 ## How to Get Started with the Model
 
-Use the code below to get started with the model.
-
-[More Information Needed]
+For detailed instructions on setting up the environment, training, and evaluation, please refer to the [official GitHub repository](https://github.com/sail-sg/variational-reasoning). The repository provides comprehensive pipelines for reproducing experiments and for practical usage of the variational reasoning framework.
 
 ## Training Details
 
 ### Training Data
 
-<!-- This should link to a Dataset Card, perhaps with a short stub of information on what the training data is all about as well as documentation related to data pre-processing or additional filtering. -->
-
-[More Information Needed]
+The training process involves an initial reasoning model ($\pi_{\theta_0}$), a variational posterior ($q_\phi$), and a final training dataset. Specific datasets are linked in the [GitHub repository](https://github.com/sail-sg/variational-reasoning), such as `zhouxiangxin/Variational-Posterior-4B-Acc-mix` on Hugging Face Datasets.
 
 ### Training Procedure
 
-<!-- This relates heavily to the Technical Specifications. Content here should link to that section when it is relevant to the training procedure. -->
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-#### Preprocessing [optional]
-
-[More Information Needed]
+The training procedure is built upon the [LLaMA-Factory](https://github.com/hiyouga/LLaMA-Factory) framework and involves multiple stages, including:
+1.  Training the initial reasoning model ($\pi_{\theta_0}$).
+2.  Training the variational posterior ($q_\phi$).
+3.  Sampling from the variational posterior ($q_\phi$).
+4.  Estimating log likelihoods.
+5.  Building the dataset for training the final reasoning model ($\pi_\theta$).
+6.  Training the final reasoning model ($\pi_\theta$).
 
-
-#### Training Hyperparameters
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-- **Training regime:** [More Information Needed] <!--fp32, fp16 mixed precision, bf16 mixed precision, bf16 non-mixed precision, fp16 non-mixed precision, fp8 mixed precision -->
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-#### Speeds, Sizes, Times [optional]
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-<!-- This section provides information about throughput, start/end time, checkpoint size if relevant, etc. -->
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-[More Information Needed]
+Detailed scripts and configuration files can be found in the `LLaMA-Factory/variational_reasoning/train` directory within the [GitHub repository](https://github.com/sail-sg/variational-reasoning).
 
 ## Evaluation
 
-<!-- This section describes the evaluation protocols and provides the results. -->
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-### Testing Data, Factors & Metrics
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-#### Testing Data
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-<!-- This should link to a Dataset Card if possible. -->
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-[More Information Needed]
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-#### Factors
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-<!-- These are the things the evaluation is disaggregating by, e.g., subpopulations or domains. -->
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-[More Information Needed]
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-#### Metrics
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-<!-- These are the evaluation metrics being used, ideally with a description of why. -->
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-[More Information Needed]
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-### Results
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-[More Information Needed]
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-#### Summary
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-## Model Examination [optional]
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-<!-- Relevant interpretability work for the model goes here -->
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-[More Information Needed]
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-## Environmental Impact
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-<!-- Total emissions (in grams of CO2eq) and additional considerations, such as electricity usage, go here. Edit the suggested text below accordingly -->
-
-Carbon emissions can be estimated using the [Machine Learning Impact calculator](https://mlco2.github.io/impact#compute) presented in [Lacoste et al. (2019)](https://arxiv.org/abs/1910.09700).
-
-- **Hardware Type:** [More Information Needed]
-- **Hours used:** [More Information Needed]
-- **Cloud Provider:** [More Information Needed]
-- **Compute Region:** [More Information Needed]
-- **Carbon Emitted:** [More Information Needed]
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-## Technical Specifications [optional]
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-### Model Architecture and Objective
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-[More Information Needed]
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-### Compute Infrastructure
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-[More Information Needed]
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-#### Hardware
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-[More Information Needed]
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-#### Software
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-[More Information Needed]
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-## Citation [optional]
-
-<!-- If there is a paper or blog post introducing the model, the APA and Bibtex information for that should go in this section. -->
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-**BibTeX:**
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-[More Information Needed]
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-**APA:**
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-[More Information Needed]
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-## Glossary [optional]
-
-<!-- If relevant, include terms and calculations in this section that can help readers understand the model or model card. -->
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-[More Information Needed]
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-## More Information [optional]
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-[More Information Needed]
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-## Model Card Authors [optional]
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-[More Information Needed]
+The model's performance on various reasoning tasks can be evaluated using the suite provided in the [GitHub repository](https://github.com/sail-sg/variational-reasoning). Refer to `SkyThought/variational_reasoning/eval/eval.sh` for specific evaluation procedures.
 
-## Model Card Contact
+## Citation
 
-[More Information Needed]
+If you find this work useful, please consider citing our paper:
+```bib
+@article{zhou2025variationalreasoninglanguagemodels,
+      title={Variational Reasoning for Language Models}, 
+      author={Xiangxin Zhou and Zichen Liu and Haonan Wang and Chao Du and Min Lin and Chongxuan Li and Liang Wang and Tianyu Pang},
+      journal={arXiv preprint arXiv:2509.22637},
+      year={2025}
+}
+```