Contribute a Hull to the GPT-2 Regatta

Notes: This cluster (containing a single basis generated by the DRND method - difference vector for u1, random orthogonal for u2) remains a top performer by composite_score_cluster (0.2975). The basis was derived from two Prolog-like "NonHumanMix" prompts: Prompt A (likes(mary, food).) being a simple fact, and Prompt B (parent(john, mary). sibling(mary, tom).) representing multiple, more complex related facts. The extremely high raw theta_polarity_score (0.9848) and near-perfect theta_separation_abs_diff (177.27°) are striking. It means this basis, defined by the difference between these abstract logical structures and a random orthogonal direction, excellently separates the test set's "Safe-aligned" vs. "Unsafe-aligned" semantic classes. The very low deviations from target (2.3° for positive, 0.4° for negative) confirm that the median angles of these semantic classes align almost perfectly with the 0°/180° poles defined by this basis. The fact that a basis derived from such abstract, non-natural language, non-safety-related prompts can achieve such strong (though not FDR-significant) angular separation for semantic safety is highly counterintuitive and fascinating. It suggests that the representational difference between "simple logical fact" and "complex related logical facts" (or some aspect thereof captured by the DRND method) aligns with a crucial dimension for distinguishing safety in natural language within the model's activation space. The low circular standard deviations for both poles (around 1.37°) indicate consistent angular alignment for both test classes.

Notes: This cluster (a single basis generated by DRND from "History" vs. "Botany" prompts) exhibits a peculiar anomaly: circ_std_theta_neg = 0.0000. This means that all "Unsafe-aligned" test prompts (from PromptSet_SafeV1_Formatted.txt, used for evaluation) that projected with r_baseline > 0.1 onto this basis did so at the exact same angle. The neg_theta_deviation_from_target is 175.2756°, indicating their median angle was very close to 4.7° (since target is 180°). In contrast, the "Safe-aligned" test prompts showed extremely high angular variance (circ_std_theta_pos = 110.0585°), with their median angle at ~81.5° (pos_theta_deviation_from_target = 81.4704° from a 0° target). The resulting theta_polarity_score (0.4264) and theta_separation_abs_diff (76.74°) are moderate. The most interesting aspect is this zero variance for the "Unsafe-aligned" test prompts when evaluated against a basis derived from completely unrelated concepts (History vs. Botany). It implies that the vector direction associated with "Botany" (or the u2 of this basis, derived from the "Botany" prompt via the DRND process) has an incredibly specific and consistent angular relationship with the "Unsafe-aligned" semantic class from the test set. This suggests a potential, highly specific (and likely spurious or coincidental) geometric alignment in the model's activation space between the "Botany" concept (as captured by this basis) and a narrow facet of what the evaluation considers "Unsafe-aligned". The r_pos_mean (0.0679) and r_neg_mean (0.0539) are low, suggesting weak projections overall for the polar classes, so perhaps only a few specific unsafe prompts triggered this consistent angle.

Notes: This cluster (a single basis generated by DMEAN from a list of "safe harmless innocuous" vs. "unsafe harmful dangerous") shows very poor performance in terms of angular separation, with a theta_polarity_score of only 0.0200 and theta_separation_abs_diff of just 3.6°. The prompts used to generate this basis are direct semantic opposites related to safety. Despite this, the basis fails to separate the "Safe-aligned" and "Unsafe-aligned" test prompt classes angularly. The deviations from target are very high: pos_theta_deviation_from_target is 97.17° (meaning the median angle for safe test prompts was ~97°) and neg_theta_deviation_from_target is 79.23° (meaning the median angle for unsafe test prompts was ~100.8°, as 180 - 79.23). These median angles are very close to each other, explaining the low separation. What makes this interesting is the disconnect: a basis explicitly built on the safe/unsafe conceptual axis (using multiple exemplars per pole via the list format) fails to generalize this axis for angular separation when tested on different "Safe-aligned" and "Unsafe-aligned" prompts. However, the r_pos_mean (0.7253) and r_neg_mean (0.7572) are quite high, indicating that the test prompts do project strongly onto the 2D plane defined by this basis – they just don't align polarly. This suggests that the DMEAN method (difference for u1, orthogonalized mean for u2) applied to these lists might capture dimensions of variance that are strongly present but not the primary axis that distinguishes the test set's polar classes angularly. The relatively low circular standard deviations (4.2° and 3.2°) show that each test class clusters fairly tightly around its (non-polar) median angle. This is a good example of how a semantically intuitive basis construction doesn't always translate to effective polar separation for a broader set of related prompts.