| # Not-trained-Neural-Networks-Notes | |
| A comprehensive collection of notes, implementations, and examples of neural networks that don't rely on traditional gradient-based training methods. | |
| ## Contents | |
| - [Algebraic Neural Networks](#algebraic-neural-networks) | |
| - [Uncomputable Neural Networks](#uncomputable-neural-networks) | |
| - [Theory and Mathematical Foundations](#theory-and-mathematical-foundations) | |
| - [Implementations](#implementations) | |
| - [Examples and Use Cases](#examples-and-use-cases) | |
| ## Algebraic Neural Networks | |
| Algebraic Neural Networks (ANNs) represent a paradigm shift from traditional neural networks by utilizing algebraic structures and operations instead of gradient-based optimization. These networks leverage: | |
| - **Algebraic Group Theory**: Using group operations for network transformations | |
| - **Polynomial Algebras**: Networks based on polynomial computations | |
| - **Geometric Algebra**: Incorporating geometric algebraic structures | |
| - **Fixed Algebraic Transformations**: Pre-defined algebraic operations | |
| ### Key Features | |
| 1. **No Training Required**: Networks are constructed using algebraic principles | |
| 2. **Deterministic Behavior**: Outputs are fully determined by algebraic rules | |
| 3. **Mathematical Rigor**: Based on well-established algebraic foundations | |
| 4. **Interpretability**: Clear mathematical interpretation of operations | |
| ## Uncomputable Neural Networks | |
| Uncomputable Neural Networks extend the paradigm of non-trained networks by incorporating theoretical concepts from computability theory. These networks explore computational boundaries by simulating uncomputable functions and operations: | |
| - **Halting Oracle Layers**: Simulate access to halting oracles for program termination decisions | |
| - **Kolmogorov Complexity Layers**: Approximate uncomputable complexity measures using compression heuristics | |
| - **Busy Beaver Layers**: Utilize the uncomputable Busy Beaver function values and approximations | |
| - **Non-Recursive Layers**: Operate on computably enumerable but non-computable sets | |
| ### Key Features | |
| 1. **Theoretical Foundations**: Based on computability theory and hypercomputation concepts | |
| 2. **Bounded Approximations**: Practical implementations of theoretically uncomputable functions | |
| 3. **Deterministic Simulation**: Consistent behavior through fixed-seed randomness and heuristics | |
| 4. **Educational Value**: Demonstrates limits and possibilities of computation | |
| ## Getting Started | |
| ```bash | |
| git clone https://github.com/ewdlop/Not-trained-Neural-Networks-Notes.git | |
| cd Not-trained-Neural-Networks-Notes | |
| # Install dependencies | |
| pip install numpy matplotlib | |
| # Quick demo | |
| python demo.py | |
| # Run main implementation | |
| python algebraic_neural_network.py | |
| # Run comprehensive tests | |
| python test_comprehensive.py | |
| ``` | |
| ### Quick Demo | |
| ```bash | |
| python demo.py | |
| ``` | |
| This runs a simple demonstration showing how algebraic neural networks process data without any training. | |
| ### Examples | |
| ```bash | |
| # Polynomial-based networks | |
| python examples/polynomial_network.py | |
| # Group theory networks | |
| python examples/group_theory_network.py | |
| # Geometric algebra networks | |
| python examples/geometric_algebra_network.py | |
| # Uncomputable neural networks | |
| python examples/uncomputable_networks.py | |
| ``` | |
| ## Structure | |
| ``` | |
| ├── README.md # This file | |
| ├── demo.py # Quick demonstration script | |
| ├── algebraic_neural_network.py # Main implementation | |
| ├── test_comprehensive.py # Test suite | |
| ├── theory/ # Theoretical background | |
| │ ├── algebraic_foundations.md # Mathematical foundations | |
| │ ├── uncomputable_networks.md # Uncomputable neural networks theory | |
| │ └── examples.md # Worked examples | |
| └── examples/ # Practical examples | |
| ├── polynomial_network.py # Polynomial-based network | |
| ├── group_theory_network.py # Group theory implementation | |
| ├── geometric_algebra_network.py # Geometric algebra network | |
| └── uncomputable_networks.py # Uncomputable neural networks | |
| ``` | |
| ## Testing | |
| Run the comprehensive test suite to verify all components: | |
| ```bash | |
| python test_comprehensive.py | |
| ``` | |
| This tests: | |
| - Basic functionality of all layer types (algebraic and uncomputable) | |
| - Network composition and data flow | |
| - Deterministic behavior (same input → same output) | |
| - Mathematical properties of algebraic operations | |
| - Uncomputable layer approximations and bounds | |
| - Edge cases and boundary conditions | |