Summary
The current Φ (integrated information) computation uses dense transition probability matrices. For large state spaces, sparse representations could reduce memory and computation time significantly.
Background
IIT's Φ requires computing the Minimum Information Partition (MIP) across a system's transition probability matrix (TPM). This is exponential in the number of elements, making it the primary bottleneck for scaling consciousness measurement.
Investigation areas
- CSR/CSC sparse matrix formats — many TPM entries are near-zero for biological-like connectivity
- Threshold-based sparsification — drop entries below ε, measure Φ approximation error
- Block-sparse structure — the 4D hypercube topology (our Φ champion with 35 topologies tested) has natural block structure
- Approximation bounds — what sparsity level keeps Φ within X% of the dense computation?
Key files
symthaea-core/src/hdc/consciousness_equation.rs — Φ computationsymthaea-core/src/hdc/substrate_independence.rs — substrate-dependent Φ analysis- The 4D hypercube achieves highest Φ among all tested topologies
References
- Tononi, G. (2004). IIT theory
- Oizumi et al. (2014). From the phenomenology to the mechanisms of consciousness
- Barrett & Seth (2011). Practical measures of integrated information
Summary
The current Φ (integrated information) computation uses dense transition probability matrices. For large state spaces, sparse representations could reduce memory and computation time significantly.
Background
IIT's Φ requires computing the Minimum Information Partition (MIP) across a system's transition probability matrix (TPM). This is exponential in the number of elements, making it the primary bottleneck for scaling consciousness measurement.
Investigation areas
Key files
symthaea-core/src/hdc/consciousness_equation.rs— Φ computationsymthaea-core/src/hdc/substrate_independence.rs— substrate-dependent Φ analysisReferences