PRefLexOR: Preference-based Recursive Language Modeling for Exploratory Optimization of Reasoning and Agentic Thinking

We introduce PRefLexOR (Preference-based Recursive Language Modeling for Exploratory Optimization of Reasoning), a framework that combines preference optimization with concepts from Reinforcement Learning (RL) to enable models to self-teach through iterative reasoning improvements. Central to PRefLexOR are thinking tokens, which explicitly mark reflective reasoning phases within model outputs, allowing the model to recursively engage in multi-step reasoning, revisiting, and refining intermediate steps before producing a final output. The foundation of PRefLexOR lies in Odds Ratio Preference Optimization (ORPO), where the model learns to align its reasoning with human-preferred decision paths by optimizing the log odds between preferred and non-preferred responses. The integration of Direct Preference Optimization (DPO) further enhances model performance by using rejection sampling to fine-tune reasoning quality, ensuring nuanced preference alignment. This hybrid approach between ORPO and DPO mirrors key aspects of RL, where the model is continuously guided by feedback to improve decision-making and reasoning. Active learning mechanisms allow PRefLexOR to dynamically generate new tasks, reasoning steps, and rejected answers on-the-fly during training. This adaptive process enables the model to self-teach as it continually improves through real-time feedback and recursive processing.

Our method diverges from traditional approaches by not relying on pre-generated datasets; instead, it dynamically generates new tasks, reasoning steps, and feedback on the fly, allowing the model to continuously adapt and improve in real time. Recursive optimization within the thinking token framework introduces iterative feedback loops, where the model refines its reasoning, much like policy refinement in RL, achieving deeper coherence, consistency, and adaptability. By recursively optimizing reasoning through feedback-driven learning, PRefLexOR achieves significant flexibility in its ability to handle complex tasks, learning and evolving its cognitive abilities autonomously. This framework advances the field of cognitive alignment by demonstrating that models can iteratively teach themselves to reason with greater depth and reflectivity, akin to an RL-based self-improving system capable of solving open-domain problems with superior reasoning depth and logic. Our implementation is straightforward and can be Incorporated into any existing pretrained LLM. The approach is demonstrated in use cases of materials design applications, where a small language model is trained to develop sophisticated reasoning capabilities. Thereby, PRefLexOR builds a dynamic knowledge graph by generating questions from random text and using Retrieval-Augmented Generation (RAG) to retrieve contextually relevant data from the entire corpus, facilitating recursive reasoning through complex interactions between similar nodes in the embedding space.

Figure 1: Illustration of the workflow and design principles behind generative materials informatics. Panel a: The process of transforming information into knowledge and actionable outcomes. Each individual piece of information (left) is synthesized into a network of interconnected knowledge, leading to informed decisions and innovative designs (right). Panel b: Conventional approaches in materials science rely on data-driven models, partial differential equations (PDEs), and experimental results, focusing on single-step predictions. Panel c: In contrast, generative materials informatics models built on the PRefLexOR framework proposed in this paper use 'thinking' and 'reflection' explicitly by incorporating iterative reasoning and contextual understanding, allowing for more complex, multi-step predictions. This approach expands from single inference steps, includes multiple modalities of data and responses, integrates real-world feedback and physics, and leverages self-assessment and self-learning. Using using reinforcement learning (RL) principles, the discovery of principles or the solution of specific tasks is further inspired by biological paradigms, using bio-inspired neural network designs. These advanced methods support continuous improvement in material predictions, enabling more adaptable and intelligent designs

Figure 2: PRefLexOR Recursive Reasoning Algorithm: An iterative approach leveraging a fine-tuned Reasoning Model and a general-purpose Critic Model to generate, refine, and optionally integrate responses. The process involves generating initial responses, extracting reflections, improving thinking processes, and creating new responses based on refined thinking, with an optional final integration step. The algorithm relies on extracting thinking processes (indicated via <|thinking|>...<|/thinking|>) and reflection processes (indicated via <|reflect|>...<|/reflect|>). The use of special tokens allows us to easily construct such agentic modeling as it facilitates pausing inference, improving the strategy, and re-generating improved answers. The sampled responses can either be used in their final state or integrated into an amalgamated response that shows very rich facets in the scientific process.

Installation

Install:

pip install git+https://github.com/lamm-mit/PRefLexOR.git

If you want to create an editable installation, clone the repository using git:

git clone https://github.com/lamm-mit/PRefLexOR.git
cd PRefLexOR

Then, install:

pip install -r requirements.txt
pip install -e .

Flash Attention

Install flash attention (https://github.com/Dao-AILab/flash-attention) if you want to use that option:

MAX_JOBS=4 pip install flash-attn --no-build-isolation

Directory structure

PRefLexOR/
│
├── PRefLexOR/ # Source code directory
│ ├── active_trainer.py
│ ├── inference.py
│ └── utils.py
│
├── setup.py # The setup file for packaging
├── requirements.txt # List of dependencies
├── README.md # Documentation
└── ...

Example codes

More will be added shortly, including full notebooks. Here are code snippets that show how the trainers are initialized and used.

Figure 3: Overview of the PRefLexOR algorithm, consisting of Base Model Pre-training/Incipient Fine-tuning, Structured Thought Integration Training, Independent Reasoning Development, and the Recursive Reasoning Algorithm. Each phase can be scaled independently with additional compute to improve performance.

Model weights

Model weightsare available via Hugging Face. For example:

fromtransformersimportAutoModelForCausalLM, AutoTokenizermodel_name='lamm-mit/PRefLexOR_ORPO_DPO_EXO_10242024'model=AutoModelForCausalLM.from_pretrained(model_name, torch_dtype=torch.bfloat16,
attn_implementation="flash_attention_2",device_map="auto",trust_remote_code=True,
)
tokenizer=AutoTokenizer.from_pretrained(model_name, trust_remote_code=True,
use_fast=False,
)

PRefLexOR Structured Thought Integration Training via Odds Ratio Preference Optimization (ORPO) phase

fromtrlimportORPOConfigfromtransformersimportTrainingArgumentsfromdatasetsimportload_dataset, concatenate_datasets# Import PRefLexOR trainer classes and utilsfromPRefLexORimport*fromutilsimport*# ConfigurationFT_model_name='PRefLexOR_ORPO_Model'repo_ID='lamm-mit'max_prompt_length=512max_length=2048private=True#whether or not HF repos are privatethink_start='<|thinking|>'think_end='<|/thinking|>'# Adjust learning rate based on LoRA usagelearning_rate=5e-5ifuse_LoRAelse5e-6# ORPO Configurationcfg=ORPOConfig(
output_dir=FT_model_name, # Output directorynum_train_epochs=1, # Number of training epochsper_device_train_batch_size=1, # Batch size per device during traininggradient_accumulation_steps=2, # Steps before a backward/update passgradient_checkpointing=False, # Use gradient checkpointing to save memoryoptim="adamw_torch_fused", # Fused adamw optimizerlogging_steps=10, # Log every X stepsbf16=True, # Use bfloat16 precisionlearning_rate=learning_rate, # Learning ratewarmup_ratio=0, # Warmup ratiowarmup_steps=0, # Warmup stepslr_scheduler_type="constant", # Learning rate scheduler typemax_prompt_length=max_prompt_length, # Max length for promptsremove_unused_columns=False,
max_length=max_length, # Max length for outputsbeta=0.1, # ORPO betasave_total_limit=3, # Limit on total saved modelssave_strategy="no", # Save strategyreport_to=['none'], # Reporting#hub_private_repo=private, # Use a private hub repo#hub_model_id=f'{repo_ID}/{FT_model_name}' # Hub model ID
)
# Dataset and training parameterstopics=50num_questions_per_topic=1num_epochs_per_dataset_generation=2# Calculate number of stepsifisinstance(topics, list) andall(isinstance(t, str) fortintopics):
n_steps=len(topics) *num_questions_per_topic*num_epochs_per_dataset_generationelse:
n_steps=topics*num_questions_per_topic*num_epochs_per_dataset_generation# Trainer setuptrainer=PRefLexORORPOTrainer(
model=model,
args=cfg,
train_dataset=temp,
tokenizer=tokenizer,
n_steps=n_steps, # Train for n_steps before updating datasettopics=topics,
number_nodes_to_get=3,
n_questions_for_each=num_questions_per_topic,
only_include_wrong_answers=False,
process=process,
generate_dataset=generate_dataset,
generate=generate_GPT_MistralRS, # Function for generating datasetsindex=index,
get_rejected_from_trained_model=True,
)

Training loop:

# Configurationsystem_prompt='You are a materials scientist.'num_iterations=50# Number of iterations for the training loop# Training Loopforiterationinrange(num_iterations):
print(f"Starting iteration {iteration+1}/{num_iterations}")
# Train for N steps (no specific steps defined here, but you can update it if needed to train for different steps in different iterations)n_steps=Nonetrainer.train(n_steps=n_steps)
print("#"*64)
# Prompts and text generation examplesprompts= [
f'Tell me why hierarchical structures work so well. Use {think_start}.',
f'What is the relationship between materials and music? Use {think_start}.',
]
fortxtinprompts:
output_text, _=generate_local_model(
model=model,
tokenizer=tokenizer,
prompt=txt,
system_prompt=system_prompt,
prepend_response=f'{think_start}'if"Use"intxtelse'',
num_return_sequences=1,
repetition_penalty=1.0,
temperature=0.1,
max_new_tokens=1024,
messages=[],
do_sample=True,
)
print(output_text)
print("-"*64)
# Save the modeltrainer.save_model(f"./{FT_model_name}")
model.push_to_hub(f"lamm-mit/{FT_model_name}", private=private)
tokenizer.push_to_hub(f"lamm-mit/{FT_model_name}", private=private)
# Update the datasettrainer.update_dataset()
print(f"Completed iteration {iteration+1}/{num_iterations}")
print("#"*64)

PRefLexOR Independent Reasoning Development Phase via Efficient Exact Optimization (EXO)

importjsonfromtrlimportDPOConfig, DPOTrainerfromtransformersimportTrainingArgumentsfromdatasetsimportload_dataset, concatenate_datasetsfromPRefLexORimport*# Reward Logging CallbackclassRewardLoggingCallback(TrainerCallback):
defon_log(self, args, state, control, logs=None, **kwargs):
# Safely access and print the last log entryifstate.log_history:
try:
print(f"Step={state.log_history[-1]['step']}",
"rewards/margins=", state.log_history[-1]['rewards/margins'],
"loss=", state.log_history[-1]['loss'],
"rewards/accuracy=", state.log_history[-1]['rewards/accuracies'])
exceptKeyError:
print(end='')
# Model and configuration settingsFT_model_name='PRefLexOR_EXO_Model'repo_id='lamm-mit'think_start='<|thinking|>'think_end='<|/thinking|>'cfg=DPOConfig(
output_dir=FT_model_name, # Output directorynum_train_epochs=1, # Number of training epochsper_device_train_batch_size=1, # Batch size per device during traininggradient_accumulation_steps=2, # Steps before a backward/update passgradient_checkpointing=False, # Gradient checkpointingoptim="adamw_torch_fused", # Optimizer typelogging_steps=10, # Log every X stepsbf16=True, # Use bfloat16 precisionmax_grad_norm=0.3, # Max gradient normlearning_rate=5e-7, # Learning ratewarmup_ratio=0,
warmup_steps=0,
lr_scheduler_type="constant", # LR scheduler typemax_prompt_length=512,
max_length=2000,
remove_unused_columns=False,
beta=0.1, # DPO betasave_total_limit=50, # Save limitsave_strategy="epoch",
report_to=['none'], # Reporting#hub_private_repo=True, # Private hub repo#hub_model_id=f'lamm-mit/{FT_model_name}',loss_type="exo_pair", # Loss type for DPOlabel_smoothing=5e-3,
)
# Dataset and training parameterstopics=50num_questions_per_topic=1num_epochs_per_dataset_generation=2private=True#whether or not HF repos are private# Calculate number of stepsifisinstance(topics, list) andall(isinstance(t, str) fortintopics):
n_steps=len(topics) *num_questions_per_topic*num_epochs_per_dataset_generationelse:
n_steps=topics*num_questions_per_topic*num_epochs_per_dataset_generation# Trainer setuptrainer=PRefLexORDPOTrainer(
model=model,
ref_model=ref_model, # Set to None if using PEFTargs=cfg,
train_dataset=temp, # Temporary training datasettokenizer=tokenizer,
n_steps=n_steps, # Train for n_steps before updating datasettopics=topics,
number_nodes_to_get=3,
n_questions_for_each=num_questions_per_topic,
only_include_wrong_answers=False,
process=process,
generate_dataset=generate_dataset,
generate=generate_GPT_MistralRS, # Function for generating datasetsget_rejected_from_trained_model=True,
index=index,
# Dynamic Answer Comparisondynamic_answer_comparison=True, # Option for dynamic comparison# Mask Thinking Tokens Optionsmask_thinking_tokens=False, # Whether to mask thinking tokensthinking_token_mask_percentage=0.2, # Percentage of thinking tokens to mask in thinking sections# Thinking Tokensthink_start_token=think_start,
think_end_token=think_end,
include_thinking_token_in_labels=True,
# Callbackscallbacks=[RewardLoggingCallback()],
)

Training loop:

importjson# Configurationnum_iterations=50# Training Loopforiterationinrange(num_iterations):
print(f"Starting iteration {iteration+1}/{num_iterations}")
# Train for the current iterationtrainer.train()
print("#"*64)
# Prompts and text generationprompts= [
f'Tell me why hierarchical structures work so well. Use {think_start}.',
f'Explain the relationship between materials and music. Use {think_start}.'
]
fortxtinprompts:
output_text, _=generate_local_model(
model=model,
tokenizer=tokenizer,
prompt=txt,
system_prompt=system_prompt,
prepend_response=f'{think_start}'if"Use"intxtelse'',
num_return_sequences=1,
repetition_penalty=1.0,
temperature=0.1,
max_new_tokens=1024,
messages=[],
do_sample=True,
)
print(output_text)
print("-"*64)
# Save the modeltrainer.save_model(f"./{FT_model_name}")
model.push_to_hub(f"{repo_id}/{FT_model_name}", private=private, commit_message=f'iteration_{iteration+1}')
tokenizer.push_to_hub(f"{repo_id}/{FT_model_name}", private=private, commit_message=f'iteration_{iteration+1}')
# Save training logstry:
withopen("trainer_log_history.txt", "w") asf:
json.dump(trainer.log_history, f)
# Path to the file and repository IDfile_path="trainer_log_history.txt"repo_id=f"lamm-mit/{model_current}"# Upload the fileapi.upload_file(
path_or_fileobj=file_path,
path_in_repo="trainer_log_history.txt",
repo_id=repo_id,
repo_type="model",
commit_message="Upload trainer log history"
)
exceptExceptionase:
print("Could not push training logs:", e)
# Save dataset logstry:
temp_data=trainer.concatenated_train_datasettemp_data.push_to_hub(f"lamm-mit/{model_current}_data", private=True)
exceptExceptionase:
print("Could not push dataset logs:", e)
# Update the datasettrainer.update_dataset()
print(f"Completed iteration {iteration+1}/{num_iterations}")
print("#"*64)

Colab example: Inference notebooks

PRefLexOR Inference: Thinking and Agentic Reflection

PRefLexOR Inference: Thinking and Reflection and Agentic Reasoning

Graph-PRefLexOR

Sample graph generated based on autonomous extended reasoning (see: https://arxiv.org/abs/2502.13025).

References

@article{buehler2024PRefLexOR,
title={PRefLexOR: Preference-based Recursive Language Modeling for Exploratory Optimization of Reasoning and Agentic Thinking}, author={Markus J. Buehler},
year={2024},
eprint={2410.12375},
archivePrefix={arXiv},
primaryClass={cs.AI},
url={https://arxiv.org/abs/2410.12375}, }
@misc{buehler2025insitugraphreasoningknowledge,
title={In-situ graph reasoning and knowledge expansion using Graph-PReFLexOR}, author={Markus J. Buehler},
year={2025},
eprint={2501.08120},
archivePrefix={arXiv},
primaryClass={cs.AI},
url={https://arxiv.org/abs/2501.08120}, }
@misc{buehler2025agentic,
title={Agentic Deep Graph Reasoning Yields Self-Organizing Knowledge Networks},
author={Markus J. Buehler},
year={2025},
eprint={2502.13025},
archivePrefix={arXiv},
primaryClass={cs.AI}
}