IIT-ANN: Quantifying Consciousness Metrics of Neural Networks Using Integrated Information Theory

IIT-ANN is an open-source framework that integrates Integrated Information Theory (IIT) with neural network training, aiming to solve the problems of high computational complexity and difficulty in real-time observation of integrated information changes when traditional IIT is applied to neural networks. This framework combines PyTorch training, PyPhi library for IIT computation, and Three.js for real-time visualization, helping researchers understand consciousness-related properties of neural networks. By calculating and visualizing Φ values (consciousness metric) in real time, it promotes interdisciplinary research between consciousness science and artificial intelligence.

Integrated Information Theory (IIT) is one of the most influential theories in contemporary neuroscience and consciousness research. It proposes that consciousness can be quantified as the degree of information integration within a system, represented by the Φ value (the higher the Φ, the stronger the information integration, theoretically corresponding to a higher level of consciousness). However, traditional IIT computation requires constructing a state transition probability matrix (TPM) and exhaustively enumerating all system partitions, whose complexity grows exponentially with the number of neurons, making it difficult to observe changes in integrated information in real time during neural network training. The IIT-ANN project was born to address this, building an end-to-end framework that integrates PyTorch training, PyPhi computation, and Three.js visualization, supporting real-time observation of dynamic changes in Φ values during training.

The project adopts a front-end and back-end separation architecture: Backend System (Python)：Flask server (providing RESTful API and WebSocket real-time communication), PyTorch training engine (supporting training on datasets like MNIST), PyPhi integration (accurate Φ value computation), state extraction module (extracting hidden layer activation states). Front-end Visualization (Three.js)：3D neural network visualization (dynamically displaying neuron activation and connection strength), TPM matrix heatmap (real-time display of state transition probabilities), Φ value trend chart (plotting Φ change curves during training), interactive control panel (adjusting training parameters and real-time control). Data Flow：After each epoch ends, the backend extracts hidden layer activation states → binarization → constructs TPM → calls PyPhi to compute Φ value → pushes to the front-end via WebSocket to update visualization.

State Extraction and Binarization

During training, the activation values of hidden layer neurons are continuous floating-point numbers, which need to be converted into discrete binary states: if the activation value exceeds the threshold, it is recorded as 1; otherwise, it is 0. n neurons correspond to an n-bit binary state.

TPM Construction

TPM is a 2^n × 2^n matrix, where elements represent state transition probabilities. The project estimates transition probabilities by continuously sampling hidden layer states, and changes in network weights will affect the TPM pattern.

Φ Value Computation Principle

Φ measures the amount of information that a system cannot be decomposed into independent subsystems: 1. Consider all system partitioning methods; 2. Compute the effective information (EI) between subsystems for each partition; 3. Find the Minimum Information Partition (MIP) that minimizes the loss of EI; 4. Φ is the difference between the EI of the original system and the sum of EIs of the subsystems after MIP. The PyPhi library implements the IIT3.0 algorithm to handle complex causal structures.

The Three.js front-end provides an immersive 3D experience: Neural Network Animation：Neurons are presented as nodes, connections as lines. Activated neurons have pulse animations, and the thickness of connections reflects the weight strength, allowing observation of the evolution of network connection patterns. TPM Heatmap：A color heatmap displays state transition probabilities, where the depth of color indicates the probability level, helping to understand the dynamic change rules of states. Φ Value Tracking：A real-time line chart shows the Φ value of each epoch, allowing observation of the change trend of Φ with the training process and exploration of the relationship between network structure and integrated information. Interactive Control：Select model architecture (supports MLP), set training epochs, start/stop training, and manually trigger MIP computation to view partition details.

The application scenarios of the IIT-ANN framework include: Consciousness Science Research：Quantify the integrated information of neural networks, provide empirical data for artificial consciousness theory, and explore the impact of architecture/training strategies on Φ values. Network Interpretability：As a new complexity metric, Φ helps understand why a network architecture performs better on specific tasks (high Φ may correspond to stronger information integration capabilities). Neuromorphic Computing：Guide the design of neural network architectures with high integrated information efficiency, promoting the development of computational models close to biological nervous systems. Educational Demonstration：Intuitive visualization makes the IIT theory easy to understand, suitable for teaching and popular science.

Current Limitations:

1. Computational Complexity：Φ computation for large-scale networks is time-consuming. It is recommended to start with a small number of neurons (e.g., 6) and provide simplified computation options.
2. Binarization Loss：Binarization of continuous activation values loses information, which may affect the accuracy of Φ. More refined state discretization methods are needed in the future.
3. Single Task：Currently supports MNIST classification; more architectures and tasks need to be expanded. Future Directions: Add more model architectures, implement model save/load, develop comparative analysis tools, and optimize Φ computation performance for large-scale networks.

The project provides complete deployment documentation and supports local operation in a Python virtual environment: the backend Flask server runs on port 5000 by default, and the front-end is served via Python http.server on port 8000. The two communicate in real time via WebSocket. For researchers who want to delve into IIT theory or explore consciousness metrics of neural networks, IIT-ANN provides a fully functional and easy-to-use experimental platform, transforming esoteric theories into interactive tools and opening up new possibilities for interdisciplinary research.