Geodesic Learning Pathways

Overview

Geodesic Learning Pathways is an innovative framework combining information theory, geometric analysis, and curriculum design to optimize training pathways in AI systems. Inspired by brain responses to stimuli, this methodology uses the Fisher Information Matrix and geometric structures to derive adaptive learning stages that enhance training efficiency and performance.

---

Key Steps

1. Initial Data & Model Fitting

• Objective: Understand brain responses to various stimuli (e.g., noise levels in music).
• Process:
  • Analyze fMRI data showing brain activity under different noise levels.
  • Fit multiple models (linear, quadratic, cubic, exponential) to the data.
  • Select the best-fitting model using criteria such as AIC, BIC, or error minimization.

2. Information Geometric Analysis

• Objective: Derive geometric insights from the best-fitting model.
• Process:
  • Calculate the Fisher Information Matrix to represent the metric tensor.
  • Compute geometric structures:
    • Christoffel symbols for parallel transport.
    • Riemann curvature tensor for understanding intrinsic structure.
    • Sectional curvatures and geodesics to map optimal learning pathways.

3. Geometric Curriculum Design

• Objective: Use geometric insights to create a learning curriculum.
• Process:
  • Identify critical points where processing changes significantly.
  • Determine optimal paths between these points using geodesics.
  • Design curriculum stages with:
    • Specific noise levels.
    • Number of epochs.
    • Transition points and difficulty metrics.

4. Implementation

• Objective: Train models using the designed curriculum.
• Process:
  • Set up a training framework compatible with PyTorch.
  • Implement curriculum-based training.
  • Track metrics such as loss, accuracy, perceptual quality, and information content during training.

5. Validation

• Objective: Evaluate the effectiveness of the curriculum.
• Process:
  • Compare against baselines, including non-curriculum training and simpler strategies.
  • Validate geometric predictions by checking learning paths and difficulty assessments.
  • Evaluate outcomes such as reconstruction quality, training efficiency, and generalization ability.

---

Implementation Details

• Fisher Information Matrix:
  • Captures sensitivity of model outputs to parameter changes.
• Geometric Structures:
  • Christoffel symbols facilitate parallel transport for understanding model dynamics.
  • Riemann tensor uncovers the curvature of the information space.
• Curriculum Design:
  • Adaptive stages are informed by geometric properties and difficulty metrics.

---

How to Use

1. Data Preparation:
   • Provide fMRI data or other relevant datasets.
2. Model Fitting:
   • Fit models using the provided scripts.
3. Geometric Analysis:
   • Run the geometric_analysis.py script to calculate Fisher Information Matrix and geometric structures.
4. Curriculum Creation:
   • Use curriculum_design.py to generate curriculum stages.
5. Training:
   • Train models with curriculum_implementation.py.
6. Validation:
   • Validate results with validation.py.

---

Future Directions

• Apply to real-world datasets beyond fMRI, such as speech, vision, or language processing.
• Extend to multi-modal datasets and more complex geometric analyses.
• Explore non-Euclidean spaces for richer geometric structures.

---

Contact

For questions or collaboration, please contact the development team at ajithksenthil@gmail.com