Do the features learned by Sparse Autoencoders (SAEs) represent abstract meaning, or are they tied to how text is written? We investigate this question using Serbian digraphia as a controlled testbed: Serbian is written interchangeably in Latin and Cyrillic scripts with a near-perfect character mapping between them, enabling us to vary orthography while holding meaning exactly constant. Crucially, these scripts are tokenized completely differently, sharing no tokens whatsoever. Analyzing SAE feature activations across the Gemma model family (270M-27B parameters), we find that identical sentences in different Serbian scripts activate highly overlapping features, far exceeding random baselines. Strikingly, changing script causes less representational divergence than paraphrasing within the same script, suggesting SAE features prioritize meaning over orthographic form. Cross-script cross-paraphrase comparisons provide evidence against memorization, as these combinations rarely co-occur in training data yet still exhibit substantial feature overlap. This script invariance strengthens with model scale. Taken together, our findings suggest that SAE features can capture semantics at a level of abstraction above surface tokenization, and we propose Serbian digraphia as a general evaluation paradigm for probing the abstractness of learned representations.
Figures & tables
Comparison Type
Mean Jaccard Similarity
Cross-Script Original (Latin ↔ Cyrillic, same sentence)
0.58
Cross-Script Paraphrase (Latin ↔ Cyrillic, same paraphrase)
Cross-Language Random (Serbian ↔ English, unrelated)
0.19
Table 1: Evidence for script-invariant representations. Results averaged across all models and layers.
Figure 1: Baseline semantic discrimination across model scales. Larger models achieve greater separation between paraphrase and random similarity, with Serbian Latin and Serbian Cyrillic following nearly parallel trajectories.
Figure 2: Cross-script similarity across model scales. Cross-script original and paraphrase similarity increase with model size while cross-script random decreases, indicating increasingly robust script-invariant representations. Notably, cross-script cross-paraphrase remains stable across scales.
Appendix figures & tables3 assets
Supplementary material from the paper’s appendix.
Appendix
Figure 3: Mean token counts by script and sentence type.
Figure 4: Token count difference vs. SAE feature Jaccard similarity.
Figure 5: LaBSE sentence similarity verification. (a) Histogram of similarity scores showing clear separation between random pairs and semantically related pairs. (b) Box plots of similarity distributions by condition. Cross-script original pairs achieve near-ceiling similarity, confirming semantic equivalence across scripts.
Large language model (LLM) interpretability studies how internal representations and computations produce outputs, and how they can be explained or controlled.
Sparse autoencoder (SAE) features are increasingly used to interpret language models, with auto-generated natural-language labels serving as the primary interface for understanding what each feature represents. We ask whether these labels generalize: does a feature labeled for a concept actually track that concept across languages and scripts? Using Serbian digraphia as a controlled testbed -- the same language written in both Latin and Cyrillic via deterministic transliteration -- we first find that SAE feature sets activated by the same content in different languages, scripts, and wordings share substantial overlap (mean Jaccard 0.39 vs 0.13 random baseline, peaking at 0.57), suggesting genuine cross-lingual semantic features. We then test whether auto-interpretation labels keep pace. They often do not: features whose labels describe semantic content miss the same meaning in Serbian up to 4× more often than within English, and miss Serbian Cyrillic more than Serbian Latin -- two scripts that are deterministic transliterations of each other. The gap grows with network depth, yet the labels give no indication that they fail. These results suggest that auto-interpretation labels reflect a feature's behavior on the languages and scripts a model has seen most in training, rather than the concept itself.
Sparse Autoencoders (SAEs) extract features from LLM internal activations, meant to correspond to interpretable concepts. A core SAE training hyperparameter is L0: how many SAE features should fire per token on average. Existing work compares SAE algorithms using sparsity-reconstruction tradeoff plots, implying L0 is a free parameter with no inherently correct value aside from its effect on reconstruction. In this work we study the effect of L0 on SAEs, and show that if L0 is not set correctly, the SAE fails to disentangle the underlying features of the LLM. If L0 is too low, the SAE will mix correlated features to improve reconstruction. If L0 is too high, the SAE finds degenerate solutions that also mix features. Further, we present a proxy metric that can help guide the search for the correct L0 for an SAE on a given training distribution. We show that our method finds the correct L0 in toy models and coincides with peak sparse probing performance in LLM SAEs. We find that most commonly used SAEs have an L0 that is too low. Our work shows that practitioners must set L0 correctly to train SAEs with monosemantic features.
Sparse autoencoders (SAEs) are widely used to interpret language model activations, but SAE training and latent labelling are typically repeated for every model. Here, we show that a single shared SAE can replace a collection of dedicated per-model SAEs. Our method, SharedSAE, combines a shared dictionary with model-specific encoder-decoder pairs. Unlike the closest prior method, which discards activation magnitudes and requires all models at inference, SharedSAE instead normalizes only selection scores, preserving magnitudes, and uses model dropout for single-model inference. We train SharedSAE on four 1B-scale base language models spanning distinct families and tokenizers. Despite sharing its latents across models, SharedSAE retains 96.6% of dedicated SAEs' mean explained variance; its latent activations exhibit cross-model correlations 1.8 times as high as separate SAEs aligned post-hoc, and its latent descriptions transfer across models. After the dictionary is frozen, new models can be efficiently adapted to it, achieving near-dedicated-SAE reconstruction quality while reusing the shared latent descriptions.
Daniil Ognev, Célian Vasson, Lijie Hu +2
MBZUAI · Sorbonne Université · Tohoku University +1