Understanding how humans reason -- and how reasoning responses vary across tasks and individuals -- remains a core challenge for modeling and explanation in cognitive science. We investigate the stability of response patterns within reasoners and whether variation in these patterns can be used to predict learning effects. We introduce a formal, geometry-based method to quantify distances between individual reasoning patterns and their internal variability, grounded in heuristic theories. The proposed framework is tested against experimental data via generalized linear mixed-effects models and clustering, where we find that our proposed variation measure interacts with correctness to predict performance gains. Moreover, we find that reasoning patterns are stable over time within the same reasoner. The method is general enough to be applied to other reasoning domains.
Figures & tables
Figure 1: Participant-level parameter ( k ) selection using the elbow and silhouette criteria. The shaded region marks the selected number of clusters k .
Figure 2: Principal component analysis of participant-level feature vectors. Points represent participants projected onto the first two principal components; colors and marker shapes indicate k -means cluster membership. Axis labels show the variance explained by each component.
M1
M0
Intercept
−0.467∗∗(0.152)
−0.360∗(0.141)
Correctness C
1.560∗∗∗(0.139)
1.446∗∗∗(0.133)
Validity V
0.242∗(0.121)
0.227∗(0.109)
Energy E2
0.225∗∗(0.076)
Av. Corr. C
1.307∗∗∗(0.074)
1.281∗∗∗(0.073)
C:V
0.037(0.121)
−0.018(0.111)
Table 1: Fixed effects for models M1 and M0 . N=6400 observations; 100 participants; 64 tasks.
Figure 3: Empirical cumulative distribution functions (cdfs) for test-retest distance.