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Concept Direction Reliability Across Languages with Different Tokenizer Fertility

Muhammad Abdullahi Said, Abass Oguntade, Elisha Komolafe, Babangida Sani, Fatima Muhammad Adam, Muhammad Sammani Sani

arXiv:2609.36194v1cs.CL

TL;DR

Extracted sentiment directions can vary across samples even when sentiment remains predictable, so the paper asks whether the directions themselves are reproducible. It measures split-half agreement across languages, models, and text sources, finding a stable final-token language ordering while prediction remains viable at weak-agreement layers.

  • Problem

    Concept directions are used to identify and manipulate properties such as sentiment, but it is important to know whether independent samples yield similar vectors before interpreting or steering with them.

    Source: §1 · p. 1

  • Method

    The study measures split-half cosine agreement for sentiment directions across English, Hausa, and Yoruba representations, using separate topic sets for layer selection and evaluation.

    Source: §1 · p. 1

  • Results

    Final-token agreement ranks English > Hausa > Yoruba across all 77 valid comparisons, while probes predict sentiment above chance even at weak-agreement layers.

    Source: §3 · p. 3

  • Takeaways & Limitations

    Direction reproducibility should be assessed alongside classification performance, with explicit reporting of topic partitions, layer-selection rules, and sentence-length constraints.

    Source: §7 · p. 5

    The findings cover one sentiment contrast across three languages, with three native authors per language completing distinct topic blocks.

    Source: §6 · p. 5

Abstract

from arXiv · show

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.

1 Introduction

The introduction asks whether sentiment directions extracted from contrastive texts are reproducible across independent samples, not merely useful for prediction. It evaluates split-half agreement alongside probes and examines factors associated with agreement, including tokenizer fertility.

1 Introduction

  • Reliable interpretation or steering with an extracted concept direction requires checking whether an independent sample yields a similar vector.The paper describes the common extraction approach as the difference in means between representations of contrastive text pairs.Source: §1 · p. 1
  • Split-half agreement measures consistency by estimating sentiment directions from separate, non-overlapping topic subsets.Each contrast pair contains a pleased and an annoyed message about the same topic; keeping topics intact prevents shared-topic inflation.Source: §1 · p. 1
  • Probe accuracy measures whether sentiment is linearly recoverable, whereas direction agreement measures whether an extraction method reliably isolates the same vector.Source: §1 · p. 1
  • The analysis examines representation method, text source, sentence length, topic selection, and tokenizer fertility, measuring fertility's association with agreement without claiming causation.Source: §1 · p. 1

2 Study design

The study evaluates sentiment directions across four open-weight models and, for Hausa and Yoruba, four independently analyzed text sources. It selects layers using direction agreement and assesses reproducibility on separate topic partitions, while checking length effects and probe accuracy.

2 Study design

  • Each language dataset contains 100 sentiment contrast pairs across 25 topics; Hausa and Yoruba include native, human-translated, machine-translated, and back-translated text arms.English contains source pairs only; texts are Unicode NFC-normalized and each arm is evaluated independently.Source: §2 · p. 2
  • Representations come from Gemma 4 E2B, E4B, and 12B variants and AfroLlama V1, using final-token or mean-pooled vectors at each layer.Inference uses unquantized float16 precision and sequences capped at 128 tokens.Source: §2 · p. 2
  • For each topic subset, the method normalizes an average positive-minus-negative representation difference and compares directions from non-overlapping topic halves by cosine similarity.Ten topics select layers and fifteen separate topics evaluate them; agreement averages cosine similarity over 100 random partitions, keeping all pairs from a topic together.Source: §2 · p. 2
  • Layer selection also limits absolute cosine overlap with a sentence-length direction to below 0.15; results are unavailable when no layer meets the threshold.The check addresses one possible length influence but does not eliminate every source of bias.Source: §2 · p. 2
  • Logistic regression probes train on 40 selection pairs and test on 60 evaluation pairs, with accuracy assessed at reliability-selected and classification-selected layers.Topic-based jackknife and bootstrap intervals hold layer selection or the fitted classifier fixed, respectively; the intervals do not adjust for multiple comparisons.Source: §2 · p. 2

3 Sentiment prediction and direction agreement

With final-token representations, split-half agreement ranks English above Hausa and Yoruba, while sentiment remains predictable even at layers with weak agreement. Mean pooling does not consistently improve directional agreement, particularly for Yoruba.

3 Sentiment prediction and direction agreement

  • 0.737–0.870 for English, 0.589–0.762 for Hausa, and 0.101–0.399 for Yoruba: final-token split-half agreement follows English > Hausa > Yoruba across all four models.Figure 1 shows agreement in its left panel and probe accuracy at the selected layer in its right panel for native texts.Source: Figure 1 · p. 3, §3 · p. 3
  • Across all 24 model, language, and representation combinations, separately selected probes have accuracy interval lower bounds above chance (0.50), despite weak direction agreement in some cases.At reliability-selected layers, this also holds for all 23 eligible combinations; Gemma 4 E2B on Yoruba has final-token agreement 0.101 and accuracy 0.625.Source: §3 · p. 3
  • Final-token agreement exceeds mean-pooling agreement for every English and Hausa model, while Yoruba trends are mixed and all three available intervals overlap zero.The fourth Yoruba comparison is unavailable because no AfroLlama layer meets the 0.15 length-overlap threshold under mean pooling; the results establish no fertility threshold favoring pooling.Source: §3 · p. 3

4 Sensitivity to selection and estimation choices

Topic-division sensitivity analyses preserve the final-token language ordering across valid comparisons, although individual agreement values and layer availability vary. The section also shows that the length-overlap threshold and direction-estimation choice affect reported results.

4 Sensitivity to selection and estimation choices

  • Twenty specified topic divisions assess sensitivity to topic selection, not replication on independent data, because they split the same underlying observations.Source: §4 · p. 4
  • 77 of 77 valid final-token comparisons preserve English > Hausa > Yoruba; Table 1 summarizes layer availability and the complete-comparison ordering across twenty topic divisions.Three comparisons lack an eligible Yoruba layer; with mean pooling, the ordering holds in 56 of 65 complete comparisons, with fifteen unavailable cases.Source: §4 · p. 4, Table 1 · p. 4
  • Agreement values vary substantially across topic divisions: E2B Yoruba final-token agreement ranges from −0.117 to 0.275 across eighteen eligible divisions.These ranges represent empirical variability, not statistical confidence bounds, so the paper presents the primary division alongside the sensitivity analysis.Source: §4 · p. 4
  • At length-overlap thresholds 0.10, 0.15, 0.20, and 0.25, sixteen of 24 combinations retain the same eligible layer, while eight change layer choice or availability.Without the length check, AfroLlama Yoruba mean pooling selects layer 2 with selection agreement 0.943 and length overlap 0.997.Source: §4 · p. 4
  • Mean-difference vectors have higher split-half agreement than logistic-probe weight vectors in all 23 eligible combinations, with paired difference intervals excluding zero in seventeen.The authors caution that this result applies to their probe parameters and layer-selection protocol, not all extraction settings.Source: §4 · p. 4

5 Comparisons between text sources

Across the fifteen eligible Hausa and Yoruba comparisons, back-translated texts align most closely with native writing, while human translations show the lowest within-arm agreement in most combinations. The attenuation reference provides context but is assumption-dependent and does not establish equivalence or a strict upper bound.

5 Comparisons between text sources

  • 0.338, 0.398, and 0.756 are the median cosine similarities for human translation, machine translation, and translation into English and back, respectively, against native writing.Human translation has the lowest within-arm agreement in fourteen of fifteen combinations.Source: §5 · p. 5
  • All fifteen back-translated comparisons exceed the attenuation reference, but their shared native-sentence origins prevent this similarity from independently confirming the extracted direction.Texts translated into English and back remain closest to native writing across all fifteen combinations.Source: §5 · p. 5
  • The attenuation reference uses classical measurement-error assumptions, may be undefined when reliability is negative, and is neither a strict upper bound nor a test of statistical equivalence.Human and machine translations may also have dependent errors because text sources share topic content.Source: §5 · p. 5

6 Discussion

Direction agreement can reveal sample sensitivity even when sentiment remains accurately classifiable, and high agreement can reflect text properties rather than sentiment. The discussion recommends evaluating direction reliability alongside classification while noting limits in language, authorship, topic coverage, and causal interpretation.

6 Discussion

  • Accurate sentiment probes do not establish that extracted directions are reproducible, since distinct topic samples may contain different predictive features and support multiple decision boundaries.These are potential explanations that the experimental design does not evaluate directly.Source: §6 · p. 5
  • Sentence-length checks show that a consistently estimated vector can reflect surface properties rather than sentiment, so representation analyses should inspect sentence length and use separate topic sets for layer selection and evaluation.The discussion recommends assessing classification performance alongside direction agreement.Source: §6 · p. 5
  • The evidence covers one sentiment contrast across three languages; three native authors per language wrote distinct topic blocks, and fifteen topics per split yield approximate confidence intervals.Incomplete writer tracking prevented evaluation of generalization across separate authors.Source: §6 · p. 5
  • Tokenizer and model comparisons do not isolate a causal mechanism because subword fertility covaries with pretraining exposure, language family, and structural features.The paper frames reporting agreement with topic partitioning, layer-selection rules, and sentence-length constraints as a reliability check for probe interpretation [7] [4].Source: §6 · p. 5

7 Conclusion

Across valid topic divisions, final-token agreement ranks English highest, Hausa next, and Yoruba lowest, even though sentiment remains predictable when directions have weak agreement. The conclusion calls for measuring direction reproducibility separately from classification and says tokenizer causation remains unresolved.

7 Conclusion

  • Final-token split-half agreement is consistently highest for English, followed by Hausa and Yoruba, across valid comparisons, while sentiment remains predictable even with weak direction agreement.The conclusion recommends reporting agreement metrics with topic partitioning, layer-selection rules, and sentence-length constraints; controlled experiments are needed to determine whether tokenizer characteristics cause cross-lingual variation.Source: §7 · p. 5

A Extraction and evaluation protocol

The protocol uses native writing for primary agreement and probe experiments, with other text sources used for comparisons. It specifies token extraction and pooling, model variants, tokenization details, and length-overlap settings.

A Extraction and evaluation protocol

  • Arm A supplies primary direction-agreement and probe-classification experiments, while Arms B, C, and D support comparisons across text sources.Sources are aligned by topic, but independently authored pairs do not share identical identifier strings.Source: A Extraction and evaluation protocol · p. 7
  • Sequences are tokenized without chat formatting or prompt wrappers; final-token extraction uses the last attended position, while mean pooling includes all attended positions, including special tokens.Special tokens are retained and padding is applied on the right.Source: A Extraction and evaluation protocol · p. 7
  • E2B and E4B are treated as distinct architectures, and layer index zero denotes the embedding-layer output.The passage points to the reproducibility code repository for checkpoints, dependencies, and random seeds.Source: A Extraction and evaluation protocol · p. 7
  • Subword fertility is calculated as aggregate non-special-token count divided by whitespace-word count across both sides of all native pairs.No text required truncation; maximum sequence lengths were 68 tokens for Gemma architectures and 79 for AfroLlama.Source: A Extraction and evaluation protocol · p. 7
  • The primary length-overlap threshold is 0.15, with 0.10, 0.20, and 0.25 used for sensitivity checks.Analysis scripts and plotting code are available in the repository.Source: A Extraction and evaluation protocol · p. 7

B Uncertainty and numerical checks

The section quantifies uncertainty with topic-deletion and bootstrap intervals, checks interval behavior in simulations, and independently validates numerical calculations.

B Uncertainty and numerical checks

  • Jackknife intervals recompute each statistic after deleting one of 15 evaluation topics, while keeping the selected layer and original topic divisions fixed.Cosine, paired-reliability-difference, and attenuation-reference intervals are clipped to specified ranges; an undefined deletion result leaves its interval unavailable.Source: B Uncertainty and numerical checks · p. 7
  • Probe accuracy intervals bootstrap 15 topics with replacement over 1,000 iterations, keeping classifier parameters and layer selection fixed.When every resample yields perfect classification, identical interval bounds do not prove perfect general accuracy.Source: B Uncertainty and numerical checks · p. 7
  • Matched estimator intervals use paired differences under identical topic deletions, but are approximate and unadjusted, with probe-vector coverage not independently validated.Both probe halves are retrained for each deletion, with standardization parameters recomputed on the remaining training sequences.Source: B Uncertainty and numerical checks · pp. 7–8
  • 93.3%–99.7% empirical coverage was observed across synthetic checks, but this finite simulation does not guarantee coverage for text, probe-weight, or attenuation-reference intervals.The checks covered seven scenario configurations and 300 synthetic datasets per scenario.Source: B Uncertainty and numerical checks · p. 8
  • Numerical calculations were independently validated using a parallel codebase operating on saved activation tensors.The reproducibility repository documents these checks and their operational bounds.Source: B Uncertainty and numerical checks · p. 8

C Native results and probe evaluation

The appendix reports native reliability and probe tables, readout and threshold sensitivity, repeated-allocation variation, and matched estimator comparisons. The estimator ranking remains conditional on layers selected for mean-difference agreement.

C Native results and probe evaluation

D Readout and threshold sensitivity

  • Table 5 pairs final-token and mean-pooling reliability by topic deletion; Table 6 reports selected layers and evaluation reliability across overlap thresholds, with 16 configurations retaining one layer at every threshold.A dash denotes no eligible layer.Source: Table 5 · p. 9, Table 6 · p. 10

E Repeated topic allocations

F Matched direction estimators

  • Matched estimator comparisons use twenty partitions, with 17 unadjusted approximate intervals excluding zero; rankings remain conditional on mean-difference-selected layers and fixed regularization.Probe coefficients are divided by training-scaler feature standard deviations before cosine calculation, returning both estimators to activation coordinates while probe regularization still depends on training standardization.Source: Table 8 · p. 12, F Matched direction estimators · p. 12

G Provenance comparisons

The provenance comparisons assess native writing against translated text using observed cosine and an attenuation reference. Their estimates are qualified by dependence among conditions and by the limited interpretation of cross-model and readout medians.

G Provenance comparisons

  • Shared topics and derived text can induce dependent errors, so the comparisons do not establish independent agreement across provenance conditions.Back-translated text is derived from native writing, while machine translations come from English seeds.Source: G Provenance comparisons · p. 12, Table 12 · p. 14, Table 11 · p. 14
  • Tables 10–12 compare native writing with human translation, machine translation, and translation into English and back, using observed cosine against an attenuation reference.The reference assumes a relationship between split-half agreement and full-sample reliability that is not established for these representations.Source: G Provenance comparisons · p. 12, Table 10 · p. 13, Table 11 · p. 14
  • Section 5 medians summarize different models and readouts; they are not independent estimates of a population translation effect.Source: G Provenance comparisons · p. 14
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