Geometry of Divergence: Tracking Hidden-State Trajectories for Adaptive Multi-Turn Reasoning
Not assessedPlan blockedFindingclaim-temporal-curvature-differences

Failed episodes exhibit systematically more negative temporal curvature kappa across all six task-LLM pairings, with correct minus incorrect mean differences of: Math (Llama-3.1-8B) +0.047, Code (Qwen3-14B) +0.148, Retail (Qwen3-14B) +0.030, Airline (Qwen3-14B) +0.049, Retail (Qwen3-32B) +0.035, and Airline (Qwen3-32B) +0.088.

Source: paper:Page 4, Section 4.2, Paragraph 'Failed episodes exhibit systematically more negative kappa'

Reported and observed measurements

curvature_difference_correct_minus_incorrect

meas-diff-kappa-math-8b

Reported 0.047 scalar

Observed — scalar

curvature_difference_correct_minus_incorrect

meas-diff-kappa-code-14b

Reported 0.148 scalar

Observed — scalar

curvature_difference_correct_minus_incorrect

meas-diff-kappa-retail-14b

Reported 0.03 scalar

Observed — scalar

curvature_difference_correct_minus_incorrect

meas-diff-kappa-airline-14b

Reported 0.049 scalar

Observed — scalar

curvature_difference_correct_minus_incorrect

meas-diff-kappa-retail-32b

Reported 0.035 scalar

Observed — scalar

curvature_difference_correct_minus_incorrect

meas-diff-kappa-airline-32b

Reported 0.088 scalar

Observed — scalar

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