I wrote another thing, re: @OpenAI  #o3 launch, Unraveling Patterns & Deconstructing Complexity: Insights into o3’s Limitations Across Complexity Dimensions (via o3 ARC-AGI Performance), based on additional helpful feedback from @GregKamradt at @arcprize. (Many thanks to Greg for his graciousness in offering thoughts on new avenues for research and analysis and his unique insights.)

Read here:The Correlation Matrix visualization shows the relationships between different complexity metrics (i.e., rules) calculated for o3’s 34 “failed” tasks.

There are strong positive correlations (0.84-0.95) between spatial metrics (spatial_entropy, pattern_diversity) and their spectrum components (spectrum_spatial, spectrum_pattern), showing consistent measurement of spatial complexity across different methods. There’s a cluster of strong positive correlations (0.88-1.00) between contextual_dependency_index and spectrum_context, showing alignment between different measures of contextual complexity. Rule confidence shows moderate to strong negative correlations (-0.55) with rule_overlap_score and spectrum_transform, showing that tasks with higher rule confidence tend to have simpler transformation patterns. The partial transformation error shows a strong positive correlation (0.71) with context_variability and moderate positive correlation (0.55) with rule_confidence, showing that more complex contextual patterns and higher rule confidence are associated with increased transformation errors. The hierarchical clustering (dendrogram) reveals distinct groups of related metrics, with spatial / pattern metrics clustering together separately from rule-based and transformation metrics.

The dendogram shows shows two main clusters: one containing rule-based metrics (rule_confidence, partial_transformation_error, contextual_dependency_index) and another containing spatial / pattern metrics (spatial_entropy, pattern_diversity, interaction_score).

The colors range from dark red (strong positive correlation, +1.0) to dark blue (strong negative correlation, -1.0), with white representing no correlation (0.0).

Moreover, these three scatter plot visualizations below (Spatial Entropy, Transformation Chain Depth, and Rule Confidence) show relationships between different complexity metrics in the “failed” tasks analysis.

The first plot shows a strong positive correlation between spatial entropy and pattern diversity, with most points clustering in two distinct regions: a dense group at lower values (0.2-0.6 spatial entropy, 0.1-0.4 pattern diversity) and another cluster at higher values (0.8-1.4 spatial entropy, 0.8-1.0 pattern diversity). The transform spectrum values (shown by color) appear mixed across both clusters, suggesting that spatial complexity isn’t strictly tied to transformation complexity.

The second plot examining transformation chain depth versus rule confidence shows a distribution where rule confidence values are generally high (0.8-1.0) across different transformation chain depths (0.0-0.4). There’s a spread in rule confidence at lower transformation chain depths, with some tasks showing significantly lower confidence (0.6-0.7). The transform spectrum values appear higher (greener points) in tasks with moderate transformation chain depths.

The third plot comparing rule confidence to partial transformation error reveals a pattern where most points cluster at either very low (near 0) or very high (0.7-1.6) partial transformation errors, with few points in between. This shows a binary nature to transformation errors — tasks either succeed almost completely or “fail” significantly.

The transform spectrum values (shown by color) show that higher transformation errors tend to occur with moderate transform spectrum values (blue-green points), while the lowest errors are associated with both very high and very low transform spectrum values.
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