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Tracing Multilingual Representations in LLMs with Cross-Layer Transcoders

Abir Harrasse, Florent Draye, Punya Syon Pandey, Zhijing Jin, Bernhard Schölkopf

arXiv:2511.10840v3cs.CL

TL;DR

The paper investigates how multilingual LLMs represent different languages internally and why performance still favors English. Using Cross-Layer Transcoders and Attribution Graphs, it finds shared multilingual representations alongside late-layer language-specific decoding, and traces performance differences to feature strength and tokenization-related mechanisms.

  • Problem

    How multilingual LLMs represent different languages internally, and why their performance favors the dominant training language, remain poorly understood.

    Source: §1 · p. 2

  • Method

    The authors analyze models trained on different multilingual mixtures with Cross-Layer Transcoders and Attribution Graphs, including model-diffing of base and language-finetuned models.

    Source: §1 · p. 2, §4.3 · p. 7

  • Results

    The models form shared multilingual representations and use high-frequency late-layer features for language-specific decoding, while targeted interventions can shift output language.

    Source: §1 · p. 2, §5 · p. 8

  • Takeaways & Limitations

    Cross-Layer Transcoders provide a practical basis for more focused investigations of cross-language processing and where multilingual disparities emerge.

    Source: §5 · p. 8

    The primary analyses use relatively small models trained from scratch, so the findings may not fully generalize to production-scale models or different architectures.

    Source: Limitations · p. 8

Abstract

from arXiv · show

Multilingual Large Language Models (LLMs) can process many languages, yet how they internally represent this diversity remains unclear. Do they form shared multilingual representations with language-specific decoding, and if so, why does performance favor the dominant training language? To address this, we train models on different multilingual mixtures and analyze their internal mechanisms using Cross-Layer Transcoders (CLTs) and Attribution Graphs. Our results reveal multilingual shared representations: the model employs highly similar features across languages, while language-specific decoding emerges in later layers. Training models without English shows identical multilingual shared space structures. Decoding relies partly on a small set of high-frequency features in the final layers, which linearly encode language identity from early layers. Intervening on these features allows one language to be suppressed and another substituted. Finally, to explain non-English failures, we perform a Model-Diffing experiment: underperformance arises from dim late-layer features, weak middle-layer clusters, and tokenizer bias toward English that forces early layers to specialize in word reassembly. Finetuning strengthens these features and their links, improving token assembly and language-specific decoding, providing a mechanistic explanation for multilingual gaps. Our models and CLTs are available at https://huggingface.co/collections/CausalNLP/multilingual-clts and https://huggingface.co/collections/CausalNLP/multilingual-gpt2-models. Our code is available at: https://github.com/abirharrasse/MultilingualCLTs

1. Introduction

The paper uses Cross-Layer Transcoders and Attribution Graphs to investigate how multilingual processing changes across model layers. It reports shared representations across languages alongside language-specific decoding and identifies mechanisms related to multilingual performance gaps.

1. Introduction

  • Cross-Layer Transcoders and Attribution Graphs track feature interactions across layers to analyze transitions between shared and language-specific processing.The paper presents this as a mechanistic account of multilingual processing.Source: §1 · p. 2
  • The authors vary English-to-multilingual training-data ratios and intervene on language features to study their effects on representations and output language.They also release multilingual models, finetuned models, corresponding CLTs, and code.Source: §1 · p. 2
  • Shared multilingual representations emerge even without English or another dominant language, suggesting pivot mechanisms are not a consequence of language dominance.English-dominant models may still preferentially align with English.Source: §1 · p. 2
  • Language decoding relies partly on a small set of high-frequency late-layer features that read information from early-layer features and token embeddings.The paper also reports that intervening on these features can change the output language.Source: §1 · p. 2
  • The paper characterizes language-specific failure modes in which models succeed in English but fail on equivalent inputs in other languages.These disparities are linked to underlying mechanisms.Source: §1 · p. 2

2. Related Work

Prior work documents multilingual performance disparities and offers competing accounts of internal representations, including English-aligned and shared cross-lingual structures. Mechanistic interpretability provides tools for circuit analysis, but multilingual CLT studies remain sparse.

2.1. Multilingual Language Models

  • English outperforms other languages, especially low-resource languages and on complex reasoning tasks, while mechanisms underlying these disparities remain poorly understood.Prior work has documented gaps across language families in benchmarks including XTREME and XNLI.Source: §2.1 · p. 2

2.2. Internal Representations and the Pivot Hypothesis

  • Prior studies report English-aligned intermediate representations, while other work finds shared grammatical structures and more language-specific lexical and semantic processing.The English-pivot account has also informed alignment, translation-based fine-tuning, romanization, and prompting strategies; the shared-space account is related to the Platonic hypothesis.Source: §2.2 · pp. 2–3

2.3. Mechanistic Interpretability in LLMs

  • Mechanistic interpretability uses circuits and learned features to study model internals, while CLTs simplify feature graphs through distinct decoder matrices for downstream layers.Multilingual mechanistic analyses are sparse, and fair cross-language comparisons require CLTs trained on balanced multilingual distributions.Source: §2.3 · p. 3

3. Experimental Setup and Methods

The experiments compare multilingual models trained on five languages and varying data mixtures, then use CLTs to trace feature interactions and measure feature multilinguality. The setup includes model training, graph attribution, and an entropy-based score.

3.1. Mixture of multilingual LLMs

  • The study covers English, German, French, Arabic, and Chinese using GPT-2-style and TinyStories-style models, with English proportions varying from 20% to 90%.Models use debiased tokenizers trained on evenly distributed five-language data, separating training-mixture effects from tokenization artifacts.Source: §3.1 · p. 3

3.2. Cross-Layer Transcoders (CLTs)

  • CLTs map activations between layers and reconstruct an MLP output from a layer’s MLP input using encoder and decoder components.The training objective combines MSE reconstruction, L0 sparsity, and a dead-feature penalty; training uses activation samples drawn uniformly across languages.Source: §3.2 · pp. 3–4

3.3. Graph attribution

  • Graph attribution scores feature-to-feature effects across layers, then prunes graphs to retain features accounting for 80% of final-logit effect and edges accounting for 95% of edge effect.The attribution calculation uses a Jacobian with nonlinearities frozen by stop-gradient operations.Source: §3.3 · p. 4

3.4. Multilingual Score

  • The multilingual score is the entropy of a feature’s normalized activation distribution across languages, with higher entropy indicating more multilingual features.Scores are computed for top-activated sequences and a balanced sample of 600k sequences across five languages, each of length 16, then normalized to 0–1.Source: §3.4 · p. 4

4. Results

Across mixtures, multilingual models form shared middle-layer representations while retaining language-specific processing at the edges. The results trace language decoding and non-English performance gaps to late-layer features, tokenization, and how finetuning changes feature connections.

4.1.1. GENERALIZATION UNDER DATA IMBALANCE

  • Models trained with up to 90% English tokens still achieve competitive validation performance in English and minority languages such as Arabic.The authors interpret this as evidence that learned representations capture transferable features under data imbalance.Source: §4.1.1 · p. 4

4.1.2. LANGUAGE ENTROPY ACROSS LAYERS

  • Middle-layer entropy rises between language-specific early and late layers, a pattern stable across mixtures and model scales.The pattern is also observed in balanced non-English training, but is absent in the 4-layer TinyStories model.Source: §4.1.2 · pp. 4–5, Figure 2 · p. 5

4.1.3. MULTILINGUAL CIRCUITS ACROSS DATA MIXTURES

  • Circuits form multilingual middle-layer clusters while early and late layers are mostly language-specific.Semantic alignment can occur from layer 0 when tokenization is clean; in some 90%-English cases, the late-layer English cluster is absent, while determiners remain largely language-specific.Source: Figure 3 · p. 5, §4.1.3 · pp. 5–6

4.2. Mechanisms of Language Decoding

  • Late-layer language clusters drive decoding through high-frequency features whose activations can be read linearly from early-layer features and embeddings.Zeroing one language’s features and adding a target language’s features substantially raises the target-language logit rank; perfect prediction may require further intervention.Source: §4.2 · p. 6
  • A small number of features activate on 50–100% of within-language tokens, while dominant languages show fewer such features.English feature overlap rises from 77% to 84% with English training proportion; non-English languages have 89% mutual feature overlap.Source: §4.2 · p. 6, Figure 5 · p. 7

4.3. Failure Mechanisms in Non-English Languages

  • Model-diffing compares base and language-finetuned models to probe why non-English performance gaps persist despite shared circuits.The largest feature-dictionary changes occur in later layers, where finetuning strengthens connections between language-specific representations and the shared middle-layer space.Source: §4.3 · p. 7, §4.3.1 · p. 7

4.3.2. REPAIR THROUGH MULTILINGUAL FEATURE CHANGES

  • Finetuning preserves layer-0 embeddings, alters Chinese reductions at layer 1, and concentrates transformative target-language adjustments at layer 11.Changes also cross language boundaries: German finetuning increases Arabic features among high-change features, while Chinese shows similar interactions with French and Arabic.Source: §4.3.2 · p. 7

4.3.4. CIRCUIT-LEVEL ILLUSTRATION

  • Finetuning strengthens high-change features and increases early-layer token assembly, while English-biased tokenization weakens non-English circuit links.Circuit interventions can improve retrieval of correct answers; sub-tokenization weakens edges to important clusters despite a tokenizer trained on equal amounts of data per language.Source: §4.1.3 · p. 6, §4.3.3 · p. 8, §4.3.4 · p. 8

5. Conclusion

The paper uses Cross-Layer Transcoders to trace shared multilingual representations and language-specific decoding. It connects multilingual performance differences to tokenization and downstream feature strength, offering a basis for more focused mechanistic investigation.

5. Conclusion

  • Cross-Layer Transcoders reveal shared middle-layer multilingual representations alongside language-specific decoding by small sets of high-frequency features.The features linearly read out language identity from earlier layers, and targeted interventions can shift output language.Source: §5 · p. 8
  • The paper attributes multilingual performance differences less to missing shared circuits than to tokenization and downstream activation strength.Source: §5 · p. 8
  • The analysis provides a practical basis for focused investigation of cross-language processing in LLMs.Source: §5 · p. 8

Limitations

The analysis is bounded by model scale and architecture, a single tokenizer strategy, and substantial training costs with incompletely characterized reproducibility.

Model Scale and Architecture

  • The primary analyses use 68M- and 177M-parameter models; patterns observed with LLaMA-3.2-1B may not generalize to 10B+ models or other architectures.Larger models may have mechanisms or multilingual representations not captured by this analysis.Source: Limitations · p. 8

Tokenization Analysis

  • The tokenization study uses one balanced-data BPE tokenizer and does not systematically compare alternatives, leaving the optimal multilingual tokenization approach open.The untested alternatives include character-level, morpheme-aware, and language-specific tokenizers.Source: Limitations · pp. 8–9

Reproducibility Constraints

  • Training base models and CLTs requires thousands of GPU-hours, while sensitivity to random seeds, hardware variations, and implementation details remains uncharacterized.The models and CLTs are released, but the specific training dynamics have not been exhaustively characterized.Source: Limitations · p. 9

Impact Statement

The paper presents CLTs as a way to trace shared and language-specific multilingual processing and identify mechanisms associated with language disparities. Its scope and resource demands constrain how broadly its findings can be applied.

Impact Statement

  • CLTs trace processing from early encoding through shared representations to language-specific decoding, making cross-language circuit differences inspectable.The analysis can identify circuits described as weaker, missing, or more fragmented for particular languages.Source: Impact Statement · p. 9
  • Even with balanced training data, the models show systematic gaps; Arabic sub-tokenization requires early layers to reconstruct fragmented words.The paper presents this as an example of how the mechanistic analysis can connect performance disparities to processing mechanisms.Source: Impact Statement · p. 9
  • The experiments cover five languages and relatively small models; training also required thousands of GPU-hours, and interventions raise fairness and misuse considerations.The authors describe their approach as a foundation for further research into multilingual processing and more equitable multilingual AI systems.Source: Impact Statement · p. 9

Supplementary Materials

The supplementary materials cover methods, complementary analyses, case studies, and model diffing and tokenizer analysis, alongside details of tokenization, training, and model configurations.

Supplementary Materials

  • The supplementary materials are organized into methodological details, complementary analyses, case studies, and model-diffing and tokenizer analyses.These are listed as four parts of the supplement.Source: Supplementary Materials · p. 15

A.1. Tokenization Strategy

A.2.1. MODEL ARCHITECTURE SPECIFICATIONS

  • The models use two transformer architectures, with detailed architecture hyperparameters provided in Table 2.The text frames the architectures as enabling comparisons across model families and scales.Source: §A.2.1 · p. 16, Table 2 · p. 16

A.2.2. TRAINING SCALE AND COMPUTE OPTIMIZATION

  • Training data sizes are computed using Chinchilla scaling laws, with the compute-optimal specifications reported in Table 3.The supplied passage does not specify the table's values.Source: §A.2.2 · p. 16, Table 3 · p. 16

A.2.3. TRAINING IMPLEMENTATION

  • Training uses the nanoGPT codebase, and its hyperparameters are reported in Table 4.The supplied passages do not give the table's hyperparameter values.Source: §A.2.3 · p. 16, Table 4 · p. 17

Optimization Configuration

  • Models are trained on 4×H100 80GB GPUs using data parallelism, gradient synchronization, and mixed precision with automatic loss scaling.The passage specifies FP16 mixed precision.Source: Optimization Configuration · p. 17

A.2.4. TRAINING DYNAMICS

  • As English data proportions rise, English validation loss falls while performance on other languages can decline slightly.The passage refers to training and validation loss plots across English proportions.Source: §A.2.4 · p. 17

A.2.5. TRAINING PROCEDURE AND MODELS TRAINED

  • Each architecture is trained with 20%, 50%, 70%, and 90% English mixtures, alongside a model trained on non-English data only.The non-English mixture divides data equally among Arabic, Chinese, German, and French; a pretrained LLaMA-3.2-1B is also included for comparison.Source: §A.2.5 · p. 17

B.1. Training Configuration

The appendix describes CLT training and reports performance diagnostics across model families, including dead-feature counts and explained variance.

B.1. Training Configuration

  • The LLaMA CLT uses fewer features, with an expansion factor of 4, because of GPU memory constraints.The LLaMA CLT is trained using torch.float32.Source: §B.1 · p. 18
  • CLTs mostly follow Anthropic guidelines, stop below an L0 sparsity coefficient of 10 and above 70% explained variance, and train on approximately 200M tokens.Attribution graphs retain 80% of cumulative node scores and 85% of cumulative edge scores.Source: §B.1 · pp. 17–18

B.2. Performance

C.1. GPT2-Models

Validation results show robust multilingual prediction under extreme English imbalance at both standard and small training scales. The feature analysis defines language-specific features through activation frequency and language association, then measures their overlap across languages.

C.1. GPT2-Models

  • Despite extreme English imbalance, Chinese validation prediction remains competitive, and multilingual performance stays robust across five languages in TinyStories models.The TinyStories result persists despite reduced, synthetic training data, extending the observed trend to small-scale training.Source: §C.1 · p. 19, Figure 12 · p. 20, §C.2 · p. 20

C.2. TinyStories Models

  • TinyStories-trained models retain robust multilingual performance across English, Arabic, German, French, and Chinese despite reduced, synthetic training data.Source: §C.2 · p. 20, Figure 13 · p. 20

D. Language Feature Analysis

  • The feature analysis examines high-frequency feature language specificity and cross-language sharing using activation statistics from models trained with 20%, 50%, 70%, or 90% English.Source: D. Language Feature Analysis · p. 21

D.1. Methodology and Definitions

  • A feature is language-specific when its activation frequency is at least 0.03 and its activation sequences are at least 50% from that language; overlap is computed by set intersection.The language distribution is conditioned on feature activation; a sequence counts when the feature activates at least once.Source: §D.1 · p. 21

D.2. Feature Overlap Results

Feature overlap shifts toward English as English training data increases, while a shared multilingual space also emerges without English dominance. Circuit analyses show that multilingual clusters are most evident in middle layers, with language-specific decoding or exceptions in other settings.

D.2. Feature Overlap Results

  • Non-English/English feature overlap rises from approximately 77% at 20% English to 84% at 90%; non-English overlap averages 89% versus 77% at 20%, and all pairs exceed 78% at 90%.At 90% English, Chinese–Arabic overlap is 86.6%, compared with 78.1% for French–German; English overlap with other languages is 83–84%.Source: Figure 14 · p. 21, §D.2 · pp. 21–22, Figure 15 · p. 22

E. Multilingual Score

  • Top-100-sequence and large-subset multilingual entropy measures show the same layerwise trend, though the top-100 measure is lower, especially in early layers.Early-layer activations often correspond to single tokens, motivating the authors’ use of the top-100 score; the Llama-3.2-1B graph also has a final-layer jump potentially tied to training dynamics.Source: E. Multilingual Score · p. 23, Figure 19 · p. 24, Figure 20 · p. 24

F. Shared Multilingual Space Independence from English Dominance

  • A model trained without English shows the same weighted multilingual entropy rise-and-fall pattern as the English-dominant model, peaking in layers 5–6.The non-English mixture comprises 25% each French, German, Arabic, and Chinese.Source: F. Shared Multilingual Space… · p. 23, Figure 22 · p. 25

G. Case Studies: Multilingual Circuits

  • The appendix’s circuit examples are manually clustered using feature descriptions and activations, then validated through interventions; some interventions strengthen existing features to guide correct outputs.Additional case studies use translation and culturally contextualized prompts on LLaMA-3.2-1B.Source: G. Case Studies: Multilingual Circuits · p. 25, §G.1 · p. 25

G.1. Multilingual Circuits: U-shaped Entropy

  • Circuits generally show language-specific processing in early and late layers and high-entropy multilingual clusters in middle layers, with determinants and prepositions as exceptions.Source: §G.1 · p. 25

G.1.1. PREPOSITION SENTENCES (ENGLISH: “It was a piece”)

G.1.2. PREPOSITION SENTENCES (FRENCH: “J’ai bu une tasse”)

  • Content-word, calendar-term, and analogy predictions reuse multilingual clusters in middle layers, while early and late layers are often more language-specific.The French preposition case tests whether English-preposition patterns generalize to another language.Source: §G.1.3 · p. 26, §G.1.4 · p. 26, §G.1.2 · p. 26

G.2. Multilingual Circuits: Failure Modes

  • The failure-mode analysis tests antonym and category reasoning across five languages and four English-dominance mixtures to examine non-English failures.Source: §G.2 · p. 27

G.2.1. ANTONYM TASK

Across lexical, translation, and cultural tasks, circuits show shared multilingual structure while performance gaps track task-cluster strength and token fragmentation. Targeted interventions can restore failed predictions.

G.2.2. CATEGORY COMPLETION TASK

  • In Category Completion, Arabic token fragmentation forces early layers to reconstruct words rather than activate answer clusters, but scaling those clusters restores correct predictions.English produces stronger task-specific circuit responses; the gap narrows with balanced mixtures, while fragmented tokens have weaker embedding-to-cluster edges.Source: §G.2.2 · p. 28

G.3. Intervention Validation

  • Failures often lack or underactivate the reasoning circuit; boosting it while suppressing the copying circuit consistently yields correct predictions.The proposed competition is between a circuit predicting “Women” and one copying “Men” from the input.Source: §G.2.1 · p. 28, §G.3 · p. 29

H. Extended Task Analysis: Translation and Cultural Prompts

  • Across complex tasks, circuits retain a three-phase pattern: early language-specific features, middle language-neutral semantics, and late language-specific output clusters.Translation circuits show the same rise-and-fall pattern across layers, and cultural-prompt circuits show the same multilinguality pattern.Source: H. Extended Task Analysis: Translation… · p. 29, §H.1 · p. 29, §H.2 · p. 29

I. Why English Performs Better: A Case Study

  • English produces higher activations in task-relevant clusters than other languages; the disparity decreases toward the 20% mixture but is not eliminated.Highly sub-tokenized languages show weaker embedding-to-target-cluster edge strengths, with semantic information spread across multiple sub-tokens.Source: §I.1 · p. 29, §I.2 · p. 30

J.2. Token Assembly in Early Layers

  • Finetuning improves word assembly in Arabic and German but increases fragmentation in Chinese.Language distributions for rarely activated repair features cannot be reliably characterized because there are insufficient samples.Source: §J.2 · p. 30, §J.1 · p. 30

K. Tokenizer Analysis: BPE Constraints on Multilingual Processing

  • Arabic has 4× lower morphological coherence than English despite fair vocabulary allocation; English “reading” preserves morpheme structure.The tokenizer analyses attribute fragmentation disparities to linguistic properties rather than vocabulary-allocation bias.Source: §K.1 · p. 30, Table 6 · p. 31, §K.2 · p. 31

K.3. Mechanistic Implications

  • Fragmented tokens force early layers (0–3) to reconstruct word boundaries, weakening initial circuit signals, yet Arabic develops the same shared representations in middle layers (5–6).The shared middle-layer mechanism persists despite Arabic’s tokenization disadvantage, while degraded early signals accompany weaker circuit activation and lower downstream performance.Source: §K.3 · p. 31

G.2.1. ANTONYM TASK

  • Antonym circuits share structure, but Arabic lacks the Men&Women cluster at 90% English; it appears from 50% onward, and adding it restores correct predictions.At the 20% mixture, clusters and performance improve, especially for Latin-script languages, while non-Latin-script languages still show weaker circuit formation.Source: §G.2.1 · p. 28, Figure 29 · p. 35
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