finding

active

finding:ei-of-er-random-networks-converges-to-log2-p-with-increasing-size-with-a-phase-transition-at-average-degree-log2-n

EI of ER random networks converges to -log2(p) with increasing size, with a phase transition at average degree ≈ log2(N).

From Klein & Hoel (2020) analysis of artificial complex networks.

Source paper

extracted_from

Emergence and Causality in Complex Systems: A Survey on Causal Emergence and Related Quantitative Studies

(2023) · Bing Yuan · Jiang Zhang · Aobo Lyu · Jiayun Wu +5

Neighborhood — ranked by edge-count

Communities (3)

community

Causal emergence in biological systems
members_of
Examines how macro-scale causal power exceeds micro-scale in living and learning systems.
Causal emergence in learning agents
members_of
Uses effective information (EI) and coarse-graining to link causal emergence with RL and biological learning.
Causal emergence via information-geometric coarse-graining
members_of
Framework using effective information (EI) and NIS+ to automatically discover macro-scale dynamics from micro-level data, validated on fMRI, Conway's Game of Life, and SIR models.

Concepts (1)

concept

Effective Information (EI)
supports
Core measure of causal effect in Hoel's theory; mutual information between uniform input and output distributions.

Related by similarity (8)

cosine ≥ 0.65 · no typed edge

Entities in the same semantic neighborhood but without a typed relation to this one — candidates for new edges or unrecognized duplicates.

Biological networks exhibit the lowest EI among real networks and show the most significant causal emergence after coarse-graining.finding0.790
Finding from Klein & Hoel (2020) on real network analysis.
Causal emergence depends on the coarse-graining strategy: different partitions of the same boolean network yield EI values 1.55 (emergence) vs 0.18 (degradation).finding0.772
Example from Hoel et al. (2013) replicated in the survey.
DAS on oversized randomly initialized network (|N|=4096 for 16-dim input) achieves 0.64 IIA by searching random structurefinding0.768
Shows that overly large hidden dimensions allow DAS to find random causal structures; calibration check.
DAS on randomly initialized small networks (|N|=16) achieves only 0.50 IIA (chance), cannot construct new behaviorsfinding0.757
Demonstrates DAS cannot manufacture behaviors from random structure in appropriately sized networks.
EI and normalized EI could serve as a unified metric for out-of-distribution generalization.claim0.734
Conjecture that maximizing EI yields causal representations invariant to distribution shifts.
Random latent ablation produces slight increase in ESR rate (3.8% to 4.2%), not statistically significantfinding0.728
Control result confirming OTD ablation effect is specific to those latents, not a general ablation artifact
Free-energy scaling under domain-wall formation in Potts, autoregressive, and hierarchical networks shows that combinatorics of interactions on a graph prevent or allow spontaneous ordering.finding0.720
Core result demonstrating topological constraints on self-organization
Most independent dimension pair is aesthetic_response and boundary_awareness (rho=0.553); most correlated is prediction_error and conceptual_crystallization (rho=0.886)finding0.717
Characterizes internal structure of the six scoring dimensions