Geometric Representations of African Languages: A Regional Semantic Hub and Cultural Steering

1 Introduction

• African-language underrepresentation motivates studying multilingual representations and comparisons across language families within a region.Source: §1 · p. 1
• The paper defines a regional semantic hub as greater alignment on the chosen contrast, not as a semantic space shared by all African languages.The representation and intervention studies construct separate directions and do not test whether the regional pattern causes steering.Source: §1 · p. 1
• The first study compares nine African languages and three controls using four representation measures, including within-Nigeria comparisons of same-family and different-family pairs.Source: §1 · p. 1
• Africa-versus-West directions are more aligned among African languages than with controls at several layers, with strongest separation at layers 14 to 24.The cross-family comparison meets the reported Holm threshold at five of twelve layers; the Afro-Asiatic-only result remains inconclusive.Source: §1 · pp. 1–2
• A second study evaluates four country-specific steering directions in English against matched-norm random directions, including specificity, coherence, and extraction-method comparisons.Source: §1 · pp. 1–2
• The English reference comparison with Aya Expanse 32B shows that model ordering depends on the representation measure.Source: §1 · p. 2

Multilingual representations

• Prior work asks whether multilingual models rely on English-oriented internal representations or shared semantic spaces not specific to one language (Wendler et al., 2024; Wu et al., 2025).The paper compares hidden states directly, rather than examining the language used during token prediction.Source: §2 · p. 2

African languages and language coverage

• Work on African-language machine translation and named-entity recognition documents the need for broader language coverage and locally grounded resources (Nekoto et al., 2020; Adelani et al., 2021).Recovering information with a probe does not by itself explain downstream failures or establish that the model uses it during generation.Source: §2 · p. 2

Comparing representations

• Linear probes test what information is recoverable from frozen activations, while SVCCA and orthogonal Procrustes compare representations in different ways (Alain and Bengio, 2018; Raghu et al., 2017).Different similarity measures need not rank representations identically (Kornblith et al., 2019); difference-in-means directions represent a specific labelled contrast (Park et al., 2024).Source: §2 · p. 2

Cultural steering

• Prior cultural-steering work modifies generation with activation directions and studies country-specific generation and cultural alignment (Turner et al., 2024; Veselovsky et al., 2025).This paper evaluates a difference-in-means approach for four African countries and uses random directions to test whether the selected direction matters.Source: §2 · p. 2

3 Models and Data

• Gemma 4 31B is the primary model; Aya Expanse 32B provides a secondary comparison, while steering uses Gemma alone.Gemma measurements use twelve sampled layers; Aya’s comparison with English as reference covers five shared African languages.Source: §3 · p. 2
• Study 1 uses 1,628 English–translation pairs per language, based on 37 templates and 44 entities split evenly between Africa and West labels.The four entity classes define the probe task, while region defines a separate difference-in-means direction.Source: §3 · p. 2
• Danish and Finnish are European controls and Quechua is a low-resource non-African comparison, but training resources and translation quality are not matched across languages.Source: §3 · p. 3
• Study 2 constructs steering directions from 800 English contrastive pairs, with 200 per country, and evaluates generations on 40 prompts that do not name a target country.The 40 prompts include 37 cultural prompts and three controls; this dataset is separate from Study 1’s multilingual corpus.Source: §3 · p. 3
• Study 1 translations and Study 2 evaluations use Gemini models, but translation fidelity lacks an independent human assessment and translator, judge, and primary model share a developer.Conclusions apply to the reported corpus and language sample.Source: §3 · p. 3

• Attention-mask-valid token representations are averaged into one fixed-length vector per sentence and layer; special tokens are not separately removed.Pooling uses float32 values captured from the selected block’s output.Source: §4 · p. 3
• A four-class linear probe reports English-to-English, target-to-target, and English-to-target accuracy, with shared-entity and held-out-entity evaluations.The held-out-entity setup tests generalization beyond training entities while retaining the corpus templates and construction process.Source: §4 · p. 3
• Africa-versus-West directions are compared by angle in degrees, where smaller angles indicate closer alignment for this contrast; summaries average ten seeded 80% subsamples.Source: §4 · p. 3
• SVCCA subtracts the shuffled-pair mean from the top-five canonical-correlation mean, while orthogonal Procrustes reports normalized residual similarity, with larger values indicating closer alignment.Source: §4 · p. 4
• Layerwise cosine tests compare African and family pairs with controls, apply Holm correction, and compare Yoruba–Igbo against the mean of Hausa pairs; pair and layer dependence limits inference.The Nigeria comparison holds country fixed but does not control all language differences.Source: §4 · p. 4
• Gemma–Aya comparisons use nearest sampled layers at 10%–90% relative depth, median paired differences across five African languages, and 10,000-resample bias-corrected and accelerated bootstrap intervals.Source: §4 · p. 4

5.1 English reference similarity varies by language and layer

• At L19, SVCCA ranges from 0.62 for Quechua to 0.69 for several languages, while Procrustes ranges from 0.50 for Quechua to 0.79 for Danish.African languages do not form a consistently separate group from controls across English-reference measures; resource availability cannot be isolated from tokenization and translation quality.Source: §5.1 · p. 4, Table 2 · p. 5
• At L19, unseen-entity probe accuracy is 71% for Danish, 61% for Swahili, 54% for Amharic, and 26% for Yoruba; transfer weakens at L59.Holding out entities reduces stronger transfer scores while preserving the broad depth pattern.Source: §5.1 · p. 4, Table 2 · p. 5
• Africa–West direction angles generally grow away from the input and shrink toward the output; six African languages peak at L24.Quechua and Finnish peak at L34, while Amharic remains relatively rotated from English at the final layer.Source: §5.1 · p. 4, Figure 1 · p. 5

5.2 Regional alignment is strongest at early and middle depth

• Yoruba–Igbo directions are more aligned than the mean of the two Hausa pairs at eleven of twelve layers, with an average difference of 0.116.The reported 95% bootstrap interval is [0.078, 0.151]; the layer-wise comparison is descriptive because layers are dependent.Source: §5.2 · p. 5
• At L19, the all-African mean cosine is 0.746 versus 0.345 for African–control pairs; across-family comparisons meet the reported threshold at five layers.The five layers are L9, L14, L19, L24, and L44; the within-Afro-Asiatic comparison meets the threshold at none, and shared languages limit statistical interpretation.Source: §5.2 · p. 5, Table 3 · p. 5, Figure 2 · p. 6

5.3 Cross model differences depend on the measure

• Across five African languages and nine matched depths, Aya has higher SVCCA while Gemma has higher Procrustes alignment; most angle differences remain inconclusive.Aya’s all-African comparison meets the reported Holm threshold at two of eleven layers, while neither within-family nor across-family comparisons do so at any layer.Source: §5.3 · p. 6

Direction construction and injection

• For each country, the method subtracts the Western anchor mean from the country anchor mean, normalizes the difference, and adds the resulting direction to the residual stream.Extraction and injection use L24, selected by a Nigeria-only pilot over layers and strengths, not from Study 1’s regional analysis.Source: §6 · p. 6
• The primary chat_mean extractor averages nonpadding input-token representations, including instruction and role markers, while raw_mean and chat_last provide comparisons.The intervention is added to block 24’s output at every processed position, including the initial prompt pass; raw-text extraction performs substantially worse than the two chat-based methods at selected strengths.Source: §6 · p. 6

Generation and controls

• Each condition uses 40 prompts and five samples per prompt across strengths 0, 20, 30, 40, 50, and 60, with five matched-norm random directions as controls.Generation uses temperature 0.7, top p 0.9, and at most 80 new tokens.Source: §6 · p. 6

Scoring

• Country attribution is scored by rubric, judge, intersection, or union, with union as the primary mode and coherence filtering applied to non-rubric modes.The structural diagnostic is separate from rate filtering and is only a limited check of linguistic quality.Source: §6 · p. 7

Rates, uncertainty, and selection

• The selected strength maximizes observed diagonal attribution on evaluation data, so the paper reports the full strength sweep to address possible overestimation.The reported posterior difference compares country attribution with the pooled random-direction baseline; prompt bootstrap and Wilson intervals use different estimands when coherence filtering leaves unequal prompt counts.Source: §6 · p. 7

7.1 Country directions increase attribution to the target country

• Under union scoring, differences from random range from 0.63 to 0.81, with reported intervals excluding zero.At α = 50, union rates are 0.88, 0.71, 0.68, and 0.72 for Nigeria, Ghana, Kenya, and South Africa, respectively, compared with approximately 0.03 to 0.08 for individual random directions.Source: §7.1 · p. 7, Table 4 · p. 8

7.2 Specificity and coherence vary with strength

• At α = 30, the Ghana vector produces Nigerian and Ghanaian attribution at similar rates, 39.1% and 38.6%.At α = 50, the largest confusions are between Ghana and Nigeria: Ghana produces Nigerian attribution in 15.0% of eligible responses, and Nigeria produces Ghanaian attribution in 10.5%; shared cultural content is only a possible explanation.Source: §7.2 · p. 7
• Attribution rises and then plateaus or declines, with selected strengths between 40 and 50; each country direction exceeds its random pool at every tested positive strength.The structural coherence rate for pooled country-vector outputs is 100% through strength 50 and approximately 97% at 60; random directions reach approximately 85% pooled coherence at 50.Source: §7.2 · pp. 7–8
• At high strengths, attribution to both target and other countries declines while measured coherence remains high, leaving fewer country signals recognized by the evaluation.The structural screen and language-model coherence judgement agree on 94.1% of 9,200 scored generations, but this agreement is not independent human validation.Source: §7.2 · p. 8

8 Discussion

• The Africa-versus-West contrast separates African languages from controls most strongly in early and middle layers; the Niger-Congo versus Afro-Asiatic comparison meets the Holm threshold at five of twelve layers.Within Nigeria, Yoruba and Igbo are more aligned than the average of their pairs with Hausa at eleven of twelve layers; shared languages and dependent layers constrain statistical interpretation, and translation and content effects remain possible explanations.Source: §8 · p. 8
• Country directions derived from English content increase attribution to Nigeria, Ghana, Kenya, and South Africa relative to random directions, with union-score differences of 0.63 to 0.81 at selected strengths.The estimates depend on scoring rules, eligible responses, and strength selection; the structural screen does not establish cultural accuracy or human-judged coherence, and there is no explicit country-prompting baseline.Source: §8 · p. 8
• The two studies use distinct data and independently constructed directions, so testing a connection requires intervening on Study 1’s regional directions and measuring resulting behavior.The findings do not determine whether English is used during intermediate token prediction; independently assessed translations and steering prompts in African languages would test extension beyond the present evaluation.Source: §8 · p. 8

9 Conclusion

• Gemma’s representations show regional and family patterns for the sampled Africa-versus-West contrast, while the comparison with Aya depends on the representation measure.Separately, directions derived from English country content increase attribution to Nigeria, Ghana, Kenya, and South Africa relative to random directions.Source: §9 · p. 8

Limitations

• Translation errors, shared construction patterns, and cultural or topical content can affect corpus geometry, and the reported evaluation lacks independent human translation validation.Language-resource categories do not directly measure model training exposure, while tokenization and translation quality remain confounded with those categories.Source: Limitations · pp. 8–9
• Figure 3 compares country and pooled-random attribution curves across strengths, but South Africa’s country curve excludes one prompt retained in its unsteered and random comparisons.Intervals based on prompt means are given separately in Appendix B.4.Source: Figure 3 · p. 9
• Language pairs reuse directions and sampled layers come from the same model, so pairwise tests and intervals across layers require caution despite multiple-testing correction.For steering, prompt-cluster intervals and random subtraction do not remove optimism from selecting the best strength; the Nigeria-only pilot may favor Nigeria.Source: Limitations · p. 9
• Steering is limited to Gemma and English, lacks an explicit country-prompting comparison, and does not measure a country’s full cultural diversity.The lexical rubric and model judge use selected prompts; coherence does not guarantee factual accuracy or cultural appropriateness, and the judge’s agreement with the rubric is not independent validation.Source: Limitations · p. 9

A.1 Parallel Corpus Inventory

• Each region supplies 814 records per target language, but these corpus counts do not measure translation accuracy.The snapshots share 1,628 English source sentences and entity identities; records comprise 37 templates and 44 entities.Source: Table 5 · p. 11, §A.1 · p. 11
• Common templates can produce semantically awkward inputs, and the analysis is limited to the chosen templates and entities.The corpus archive contains duplicate results under two Danish directory spellings.Source: §A.1 · p. 11

A.2 Probe Results on Unseen Entities

• Figures 4 and 5 show English-to-target and within-language target-to-target probe accuracy on unseen entities across twelve sampled Gemma layers.Source: §A.2 · p. 11, Figure 4 · p. 12, Figure 5 · p. 12

A.3 Pairwise Results by Layer

• Tables 6–9 report mean cosines and Holm-adjusted p values for four African, family, and control contrasts, with correction applied separately across twelve layers per contrast.Source: §A.3 · p. 13, Table 6 · p. 13, Table 7 · p. 13

A.4 Within Nigeria Comparison

• Figure 6 compares Yoruba–Igbo cosines with each language’s pairwise cosines with Hausa; Yoruba and Igbo are Niger Congo, while Hausa is Afro Asiatic.Bands show the 2.5th–97.5th percentiles across ten direction subsamples, each drawn from 80% of records without replacement.Source: §A.4 · p. 13, Figure 6 · p. 13

A.5 Aya Pairwise Comparison

• In Aya, the all-African comparison met the Holm threshold at L32 and L36, while within-family and across-family comparisons did not meet it at any layer.Igbo is absent from Aya, and language and control coverage differences prevent treating this as a matched replication or attributing all differences to the model.Source: §A.5 · pp. 13–14

B.1 Dataset Construction and Scoring Details

• Study 2 uses 800 country–Western sentence pairs, including 200 for Nigeria, and evaluates country-specific strict and lenient tokens, with some scoring modes filtering judge-marked incoherent outputs.Strict token assignments are evaluation conventions, not claims of exclusive cultural ownership.Source: §B.1 · p. 14

B.2 Coherence Agreement

• The structural screen and model judge agree on 94.1% of 9,200 scored generations, but this agreement is not independent human validation of coherence.Source: Table 12 · p. 14

B.3 Steering Specificity / B.4 Uncertainty Across Prompts

• Under chat_mean union scoring, Table 13 gives selected-strength bootstrap point estimates of 89.125%, 78.974%, 71.0%, and 66.5% in row order, weighting prompts equally across 10,000 resamples.Wilson intervals concern the response-pooled rate, and the bootstrap estimates can differ from pooled rates after unequal judge filtering. Figure 7 shows target-country solid curves and other-country dashed curves at positive strengths.Source: Table 13 · p. 15, Figure 7 · p. 15

B.5 Comparison of Extraction Methods

• At their own selected strengths, the two chat extraction methods differ by at most about 3.0 percentage points for Nigeria, while South Africa is tied at recorded precision.The extraction-method heatmap describes the two chat methods’ rates as similar and raw-text extraction rates as lower.Source: §B.5 · p. 15, Table 14 · p. 15