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            # Epsilon-Transformers Belief Analysis Dataset
         
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            This dataset contains trained neural network models and their corresponding belief state regression analysis from the Epsilon-Transformers project. The models were trained on four different stochastic processes and analyzed for their ability to learn and represent belief states.
         
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            ## Dataset Structure
         
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            | 20250421221507 | 0 | Transformer | Moon Process | Transformer trained on Moon Process |
         
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            | 20250422023003 | 1 | Transformer | FRDN | Transformer trained on FRDN |
         
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            ## Process Descriptions
         
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            ### Mess3 (Classical Process)
         
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            A classical stochastic process used as a baseline for comparison with quantum processes.
         
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            ### FRDN (Finite Random Dynamics Networks)
         
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            A quantum process representing finite random dynamics networks, modeling quantum systems with specific structural properties.
         
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            ### Bloch Walk
         
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            A quantum random walk process on the Bloch sphere, representing quantum state evolution in a geometric framework.
         
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            ### Moon Process
         
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            A post-quantum stochastic process that explores computational mechanics beyond standard quantum frameworks.
         
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            ## Model Architectures
         
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            ### RNN Models (LSTM, GRU, RNN)
         
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            - **Layers**: 4
         
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            - **Hidden Units**: 64
         
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            - **Direction**: Unidirectional
         
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            - **Configuration**: L4_H64_uni
         
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            ### Transformer Models
         
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            - **Layers**: 4
         
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            - **Attention Heads**: 4
         
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            - **Head Dimension**: 16
         
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            - **Model Dimension**: 64
         
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            - **Configuration**: L4_H4_DH16_DM64
         
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            ## File Formats
         
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            ### Model Files (.pt)
         
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            ### Analysis Files (.joblib)
         
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            Joblib-serialized files containing:
         
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            - **checkpoint_*.joblib**: Regression analysis results mapping activations to belief states
         
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            - **ground_truth_data.joblib**: True belief states and probabilities for the neural network data
         
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            - **markov3_*.joblib**: Classical Markov model comparisons and baselines
         
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            ## Usage
         
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            ### Loading Models
         
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            ```python
         
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            import torch
         
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            from pathlib import Path
         
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            # Load a model checkpoint
         
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            model_path = Path("models/20241121152808_57/4075724800.pt")
         
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            checkpoint = torch.load(model_path, map_location='cpu')
         
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            ```
         
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            ### Loading Analysis Data
         
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            ```python
         
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            import joblib
         
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            from pathlib import Path
         
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            # Load regression analysis results
         
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            analysis_path = Path("analysis/20241121152808_57/checkpoint_4075724800.joblib")
         
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            analysis_data = joblib.load(analysis_path)
         
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            # Access layer-wise regression metrics
         
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            for layer, metrics in analysis_data.items():
         
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                print(f"Layer {layer} RMSE: {metrics['rmse']}")
         
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            ```
         
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            ## Citation
         
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            If you use this dataset in your research, please cite:
         
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            ```bibtex
         
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            @misc{epsilon-transformers-belief-analysis,
         
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              title={Epsilon-Transformers Belief Analysis Dataset},
         
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              author={[Your Name]},
         
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              year={2024},
         
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              howpublished={Hugging Face Datasets},
         
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              url={https://huggingface.co/datasets/[your-username]/epsilon-transformers-belief-analysis}
         
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            }
         
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            ```
         
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            ## License
         
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            [Specify your license here]
         
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            ## Contact
         
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            [Your contact information]
         
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            # Epsilon-Transformers Belief Analysis Dataset
         
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            This dataset contains trained neural network models and their corresponding belief state regression analysis from the Epsilon-Transformers project. The models were trained on four different stochastic processes and analyzed for their ability to learn and represent belief states.
         
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            See https://github.com/adamimos/epsilon-transformers/tree/quantum-public for codebase which generated this data.
         
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            ## Dataset Structure
         
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            | 20250421221507 | 0 | Transformer | Moon Process | Transformer trained on Moon Process |
         
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            | 20250422023003 | 1 | Transformer | FRDN | Transformer trained on FRDN |
         
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            ## File Formats
         
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            ### Model Files (.pt)
         
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            Transformerlens (for transformers) or Pytorch (for RNNs) model checkpoints containing trained model weights and optimizer states.
         
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            ### Analysis Files (.joblib)
         
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            Joblib-serialized files containing:
         
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            - **checkpoint_*.joblib**: Regression analysis results mapping activations to belief states
         
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            - **ground_truth_data.joblib**: True belief states and probabilities for the neural network data
         
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            - **markov3_*.joblib**: Classical Markov model comparisons and baselines
         
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