Concept Direction Reliability Across Languages with Different Tokenizer Fertility
Authors: Muhammad Abdullahi Said, Abass Oguntade, Elisha Komolafe, Babangida Sani, Fatima Muhammad Adam, Muhammad Sammani Sani
Organizations: African Institute for Mathematical Sciences · University of Cape Town · Bayero University Kano · Federal University Dutse · University of Vienna
Extracted sentiment directions can vary across samples even when downstream sentiment classification remains accurate. To evaluate direction reproducibility, we measure split-half agreement in English, Hausa, and Yoruba representations across four language models using both native and translated texts. We identify layers selected for agreement using ten topics and evaluate direction agreement across separate groups of fifteen topics. Using the final token, split-half agreement ranges from 0.737 to 0.870 for English, 0.589 to 0.762 for Hausa, and 0.101 to 0.399 for Yoruba, maintaining this language rank order across all 77 complete model comparisons. Classifiers trained on these same layers consistently predict sentiment above chance, demonstrating that predictive accuracy does not imply directional consistency. Furthermore, averaging token representations yields less consistent agreement, and high agreement can partially reflect sentence length. Ultimately, our findings highlight the need to measure vector direction reproducibility independently of classification performance, though they do not establish that tokenizer fertility which is the average number of tokens per whitespace separated word causes cross-lingual differences.
Figures & tables
Figure 1: Results for natively written texts in each language using final token representations. The panels show split-half direction agreement (left) and probe classification accuracy at the selected layer (right). Bars indicate approximate 95% confidence intervals with layer selection held fixed. The dashed line marks chance accuracy.
Model
Pool
English
Hausa
Yoruba
Ordered / complete
E2B
last
20/20
20/20
18/20
18/18
E2B
mean
20/20
19/20
18/20
15/17
E4B
last
20/20
20/20
19/20
19/19
E4B
mean
20/20
19/20
19/20
16/18
12B
last
20/20
20/20
20/20
20/20
12B
mean
20/20
19/20
19/20
16/18
Table 1: Layer availability across twenty divisions of the topics at threshold 0.15. The language columns count divisions with an eligible layer. The final column counts English > Hausa > Yoruba among divisions with all three results. Unavailable comparisons are excluded from this count.
Appendix figures & tables12 assets
Supplementary material from the paper’s appendix.
Appendix
Model
Language
Layer
r [95% interval]
Accuracy [95% interval]
E2B
English
25
0.852 [0.792, 0.911]
0.983 [0.958, 1.000]
E2B
Hausa
16
0.703 [0.606, 0.800]
0.767 [0.683, 0.842]
E2B
Yoruba
16
0.101 [-0.100, 0.302]
0.625 [0.542, 0.717]
E4B
English
25
0.870 [0.827, 0.914]
1.000 [1.000, 1.000]
E4B
Hausa
25
0.762 [0.676, 0.848]
0.808 [0.742, 0.875]
E4B
Yoruba
26
0.399 [0.207, 0.591]
0.683 [0.608, 0.758]
Appendix
Table 2: Native final token results at the layer selected for reliability.
Model
Language
Layer
r [95% interval]
Accuracy [95% interval]
E2B
English
12
0.723 [0.660, 0.787]
0.942 [0.900, 0.975]
E2B
Hausa
9
0.424 [0.268, 0.580]
0.733 [0.650, 0.817]
E2B
Yoruba
22
0.317 [0.045, 0.588]
0.692 [0.617, 0.767]
E4B
English
19
0.789 [0.723, 0.855]
0.975 [0.950, 1.000]
E4B
Hausa
18
0.609 [0.489, 0.728]
0.867 [0.817, 0.917]
E4B
Yoruba
34
0.271 [-0.174, 0.716]
0.642 [0.583, 0.708]
Appendix
Table 3: Native mean pooling results at the layer selected for reliability. AfroLlama Yoruba has no eligible layer at threshold 0.15.
Model
Language
Fertility
Final token accuracy
Mean-pool accuracy
E2B
English
1.137
0.942 [0.900, 0.975]
0.925 [0.883, 0.967]
E2B
Hausa
1.783
0.775 [0.692, 0.858]
0.783 [0.708, 0.867]
E2B
Yoruba
2.572
0.592 [0.533, 0.642]
0.642 [0.592, 0.692]
E4B
English
1.137
0.975 [0.950, 1.000]
0.958 [0.917, 0.992]
E4B
Hausa
1.783
0.833 [0.775, 0.892]
0.808 [0.733, 0.883]
E4B
Yoruba
2.572
0.692 [0.608, 0.767]
0.642 [0.567, 0.717]
Appendix
Table 4: Accuracy after a separate search for a probe layer within selection data. These are distinct from the results at the same layer above. Fertility is computed on native text.
Model
Language
rlast−rmean [95% interval]
E2B
English
0.129 [0.089, 0.168]
E2B
Hausa
0.279 [0.092, 0.466]
E2B
Yoruba
-0.216 [-0.483, 0.052]
E4B
English
0.081 [0.051, 0.111]
E4B
Hausa
0.154 [0.030, 0.278]
E4B
Yoruba
0.128 [-0.378, 0.634]
Appendix
Table 5: Paired difference between final token and mean pooling reliability in the primary allocation. The two readouts may select different layers. Intervals delete the same topic in both conditions.
Model
Lang.
Pool
0.10
0.15
0.20
0.25
E2B
eng
last
25 (0.852)
25 (0.852)
25 (0.852)
25 (0.852)
E2B
eng
mean
12 (0.723)
12 (0.723)
12 (0.723)
12 (0.723)
E2B
hau
last
16 (0.703)
16 (0.703)
16 (0.703)
16 (0.703)
E2B
hau
mean
9 (0.424)
9 (0.424)
9 (0.424)
9 (0.424)
E2B
yor
last
16 (0.101)
16 (0.101)
16 (0.101)
16 (0.101)
E2B
yor
mean
23 (0.330)
22 (0.317)
22 (0.317)
22 (0.317)
Appendix
Table 6: Selected layer and reliability on evaluation data in parentheses at each threshold for length overlap. A dash indicates no eligible layer. Sixteen configurations retain the same eligible layer across all four thresholds.
Model
Lang.
Pool
Eligible
Median
Range
Layers
E2B
eng
last
20/20
0.864
[0.826, 0.892]
5
E2B
eng
mean
20/20
0.753
[0.716, 0.798]
4
E2B
hau
last
20/20
0.563
[0.309, 0.703]
6
E2B
hau
mean
19/20
0.432
[0.255, 0.524]
9
E2B
yor
last
18/20
0.099
[-0.117, 0.275]
12
E2B
yor
mean
18/20
0.208
[-0.067, 0.458]
10
Appendix
Table 7: Agreement across twenty allocations at threshold 0.15. Median and range use eligible allocations only. The final column counts distinct selected layers.
Figure 2: Agreement across topic allocations. Each dot is an eligible allocation and the horizontal mark is its configuration’s median. Counts show eligibility out of twenty.
Model
Lang.
Pool
rmeandifference
rprobeweights
Difference [95% interval]
E2B
eng
last
0.858
0.516
0.342 [0.243, 0.442]
E2B
eng
mean
0.724
0.182
0.542 [0.152, 0.932]
E2B
hau
last
0.708
0.298
0.410 [0.071, 0.750]
E2B
hau
mean
0.399
0.254
0.145 [-0.380, 0.671]
E2B
yor
last
0.105
-0.016
0.121 [-0.272, 0.513]
E2B
yor
mean
0.315
-0.039
0.354 [-0.088, 0.796]
Appendix
Table 8: Agreement of mean difference and probe coefficient vectors. The difference is paired by topic deletion. Seventeen unadjusted approximate intervals exclude zero. These comparisons use twenty partitions, so their values for mean differences need not equal the main estimates based on 100 divisions.
Model
Lang.
Pool
A
B
C
D
E2B
hau
last
0.703
0.332
0.565
0.670
E2B
hau
mean
0.424
0.347
0.403
0.520
E2B
yor
last
0.101
0.019
0.222
0.242
E2B
yor
mean
0.317
0.009
0.325
0.269
E4B
hau
last
0.762
0.457
0.633
0.734
E4B
hau
mean
0.609
0.462
0.537
0.649
Appendix
Table 9: Agreement within each arm for native writing (A), human translation (B), machine translation (C) and translation into English and back (D). AfroLlama Yoruba mean pooling is unavailable. Full arm intervals are included in the accompanying CSV tables.
Model
Lang.
Pool
c [95% interval]
h [95% interval]
h−c [95% interval]
E2B
hau
last
0.464 [-0.042, 0.970]
0.641 [0.527, 0.756]
0.178 [-0.348, 0.703]
E2B
hau
mean
0.476 [0.319, 0.634]
0.554 [0.387, 0.721]
0.078 [-0.055, 0.210]
E2B
yor
last
0.058 [-0.160, 0.276]
0.082 [–]
0.024 [–]
E2B
yor
mean
0.143 [-0.370, 0.657]
0.091 [–]
-0.052 [–]
E4B
hau
last
0.429 [-0.018, 0.877]
0.737 [0.645, 0.829]
0.307 [-0.175, 0.789]
E4B
hau
mean
0.616 [0.490, 0.741]
0.692 [0.593, 0.790]
0.076 [-0.058, 0.210]
Appendix
Table 10: Native versus human translation (A–B). Values are followed by full conditional 95% intervals. An interval marked [–] is undefined because a required reliability after a topic is removed is negative. The E4B Yoruba mean pooling reference is itself undefined because the point reliability for B is negative.
Model
Lang.
Pool
c [95% interval]
h [95% interval]
h−c [95% interval]
E2B
hau
last
0.524 [0.335, 0.713]
0.772 [0.693, 0.851]
0.248 [0.042, 0.454]
E2B
hau
mean
0.481 [0.211, 0.751]
0.585 [0.456, 0.714]
0.104 [-0.121, 0.328]
E2B
yor
last
0.296 [0.100, 0.492]
0.258 [0.000, 0.534]
-0.038 [-0.352, 0.276]
E2B
yor
mean
0.473 [0.264, 0.681]
0.486 [0.266, 0.705]
0.013 [-0.260, 0.286]
E4B
hau
last
0.576 [0.389, 0.763]
0.819 [0.755, 0.883]
0.243 [0.039, 0.447]
E4B
hau
mean
0.660 [0.546, 0.774]
0.727 [0.641, 0.813]
0.067 [-0.038, 0.173]
Appendix
Table 11: Native versus machine translation (A–C). The text is translated from English seeds. Independent errors relative to native writing are not established by this construction because the conditions share topics and evaluation choices.
Model
Lang.
Pool
c [95% interval]
h [95% interval]
h−c [95% interval]
E2B
hau
last
0.889 [0.826, 0.951]
0.814 [0.750, 0.878]
-0.075 [-0.148, -0.001]
E2B
hau
mean
0.807 [0.688, 0.925]
0.638 [0.511, 0.766]
-0.168 [-0.254, -0.083]
E2B
yor
last
0.437 [-0.001, 0.875]
0.267 [0.000, 0.556]
-0.170 [-0.633, 0.293]
E2B
yor
mean
0.696 [0.434, 0.958]
0.451 [0.108, 0.794]
-0.244 [-0.458, -0.031]
E4B
hau
last
0.926 [0.872, 0.979]
0.856 [0.792, 0.920]
-0.070 [-0.132, -0.008]
E4B
hau
mean
0.866 [0.777, 0.955]
0.772 [0.699, 0.845]
-0.094 [-0.206, 0.018]
Appendix
Table 12: Native versus translation into English and back (A–D). D is derived from A. All fifteen observed cosines exceed the attenuation reference, which must not be interpreted as a hard bound or as evidence of independent agreement.