From Tokens to Thoughts: How LLMs and Humans Trade Compression for Meaning — part 4/4

Cleaned-text code points [47341, 61829). Bibliography omitted here; source.md includes it.

This analysis complements the main text findings by showing that LLMs do not simply achieve above-chance alignment with human categories but rather so through a systematic progression from basic to sophisticated conceptual representations, with contextual processing serving as an amplifier rather than a generator of semantic understanding.

We also tested the robustness of our results to different clustering seeds (Figure 9 ). We found AMI to be highly stable across seeds, with negligible variation in the peak values and layer-wise profiles, indicating that our conclusions are not sensitive to the choice of clustering initialization.

Lastly, we plot the peak AMI against the number of FLOPS per token and find no systematic correlation, suggesting that computational cost alone does not predict human-aligned conceptual representations (Figure 10 .)

## Appendix G Multilingual Analysis

To further explore conceptual understanding across languages, we translated our dataset into Spanish, German, Italian, and Russian using Google Translate’s API and repeated our analyses with the same LLMs and methods. In RQ1, a clear scale effect emerges for all non-English languages, while English shows no such trend (Figures 11 , 12 ). We interpret this as a consequence of limited non-English training data: larger models are more likely to have been exposed to sufficient multilingual data, improving their conceptual alignment. In RQ2, all models struggle to preserve the internal geometry of human concepts across languages (Figure 13 ). RQ3 shows that non-English languages exhibit greater compression (Figure 14 ), consistent with our explanation for RQ1: smaller exposure to non-English data leads to more compressed representations, reducing flexibility and interpretability.

## Appendix H Training Dynamics

The OLMo analysis examines how semantic structure develops during training by analyzing 57 intermediate checkpoints from the OLMo-7B model, representing evenly spaced sampling (every 10K training steps) spanning from 1K to 557K steps (covering approximately 4B to 2.5T tokens).

The analysis employs two complementary sampling strategies: representative sampling (6 checkpoints) captures major developmental phases at 1K, 101K, 201K, 301K, 401K, and 501K steps, while high-resolution sampling (57 checkpoints) reveals the inherent noise and fluctuations in training. Despite significant training noise, the overall semantic development follows a stable, predictable pattern captured by the representative sampling, as shown in Figure 16 . The complete training trajectory with all 57 checkpoints is presented in Figure 17 .

Moreover, this double-phase dynamics occurs when testing attention sparsity, effective rank, and ℒ \mathcal{L} values (Figures 18 , 19 ). Meaning, all of which exhibit the same early rapid shift followed by a slower restructuring phase. This convergence across independent metrics indicates that the model is not merely improving categorical alignment, but reorganizing its internal representations toward increasingly efficient structure.

## Appendix I Datasets Polysemy

Scope. We quantify lexical ambiguity in our psycholinguistic stimuli by counting the distinct WordNet synsets associated with each lemma. This polysemy score lets us estimate how many alternative senses a model must implicitly conflate when it produces a single embedding for a word.

Why it matters. Consider bat , which can denote either a flying mammal or a piece of sports equipment. The same vector must account for both senses. Aggregating semantically distant senses can blur the representation and thus confound model-human comparisons, especially in tasks that rely on fine-grained semantic similarity. Explicitly tracking polysemy allows us to verify that any performance effects we observe are not artefacts of lexical ambiguity.

Results Figure 20 shows the distribution of polysemy scores. The majority of items are unambiguous (1-2 senses), but a heavy-tailed minority (e.g. Running (52 senses), Saw (28), Block (28)) is highly polysemous. This suggests that our findings are due to real differences between the models rather than polysemy-related artifacts. An additional 141 lemmas that are not in WordNet were omitted.

][t]

## Appendix J Tokenizer Analysis

Rational. The tokenizer of a model has a significant influence over the representations: segmentation rules (WordPiece vs. BPE), vocabulary size and special control tokens can inflate sequence length, skew frequency statistics, and shape error patterns. To ensure fair cross-model comparisons, we therefore (i) cluster checkpoints by the tokenizer they use and (ii) quantify how much those tokenizers overlap when applied to our datasets.

Procedure. Before computing overlap, we normalize the vocabulary, stripping tokenizer-specific characters; SentencePiece prefixes (_), GPT-style BPE space prefixes ( Ġ/ġ ) and newline markers ( Ċ ), WordPiece continuations markers (##), and related block characters. After this cleanup, tokens differing only by such prefixes collapse to a shared canonical form (e.g. _house , Ġhouse , and ##house all become house ). We then compute pair-wise Jaccard similarity on these cleaned vocabularies.

Table 1 summarizes the core statistics and information regarding the tokenizer types, while Figure 21 visualizes the resulting pairwise vocabulary overlap.

Findings. We find that most tokenizer families share substantial lexical overlap, often exceeding 60 % \,60\% , suggesting a de-facto common token inventory across recent open-source models. First-generation BERT WordPiece (bert-large-uncased and bert-base-uncased) are an outlier, sharing under 16 % 16\% of tokens with any other group.

##### Model Clustering By Tokenizer Family

• Llama: Llama-3.2-1B (representative), Llama-3.1-8B, Meta-Llama-3-8B, Llama-3.1-70B, Meta-Llama-3-70B

• Gemma: gemma-2-9b (representative), gemma-7b, gemma-2b, gemma-2-2b

• Mistral: Mistral-7B-v0.3 (unique)

• Phi: phi-2 (representative), phi-1, phi-1.5

• RoBERTa: roberta-large (unique)

• DeBERTa: deberta-large (unique)

• GPT : gpt2-medium (representative), gpt2

• BERT: bert-large-uncased (representative), bert-base-uncased

• Qwen: Qwen1.5-0.5B (representative), Qwen1.5-1.8B, Qwen1.5-14B, Qwen2-0.5B, Qwen2-7B, Qwen2.5-0.5B, Qwen2.5-1.5B, Qwen2.5-32B, Qwen1.5-32B, phi-4 3 3 3 phi-4 has a different tokenizer than the rest of Phi family. The results of its tokenizer match the tokenizer of the Qwen family.

## Appendix K Additional Clustering Metrics

To further validate our cluster alignment findings (Section 5.1 ), in addition to Adjusted Mutual Information (AMI) and the Normalized Mutual Information (NMI), we also computed the Adjusted Rand Index (ARI) for the k-means clusters derived from LLM embeddings against human-defined categories. ARI measures the similarity between two data clusterings, correcting for chance. Like AMI, a score of 1 indicates perfect agreement and 0 indicates chance agreement.

Across all tested LLMs, the ARI and NMI scores largely mirrored the trends observed with AMI, showing significantly above-chance alignment with human categories and similar relative model performances. Silhouette scores, while more variable, generally indicated reasonable cluster cohesion for both LLM-derived and human categories. Detailed tables of these scores are provided below.

These supplementary metrics reinforce the conclusion that LLMs capture broad human-like conceptual groupings.

## Appendix L Mini-Controlled Experiment (Matched Training Data)

To evaluate the extent to which dataset differences might account for the architectural patterns we report, we conducted matched-family analyses involving the only model families that can be aligned in both training data: GPT, Pythia, Cerebras, and T5. While these comparisons cannot rule out all confounds, they substantially reduce the influence of dataset variation. Across all matched settings, encoder models continue to outperform decoder models, yielding higher AMI and lower ℒ \mathcal{L} . This indicates that the architectural effects observed throughout the paper cannot be explained by differences in training data alone.

## Appendix M Detailed AMI Scores per Model and Dataset

Table 2 provides a more granular view of the static AMI scores for each LLM across the three individual psychological datasets.

## Appendix N Correlation between Human Typicality Judgments and LLM Internal Cluster Geometry

The following tables present the Spearman correlation coefficients ( ρ \rho ) between human typicality judgments and LLM internal representations across different analysis approaches:

Table 3 : Static analysis correlations using embeddings from the E matrix. This approach captures the baseline semantic relationships between items and categories without contextual processing.

Table 4 : Peak AMI layer analysis correlations using contextual embeddings from the layer that maximized AMI scores (as identified in RQ1). This approach leverages the optimal layer for semantic clustering to assess fine-grained semantic fidelity.

Both tables present correlations across three cognitive science datasets: Rosch (1973), Rosch (1975), and McCloskey (1978), with asterisks (*) indicating statistically significant correlations ( p < 0.05 p<0.05 ). The modest correlation values across most models suggest limited alignment between LLM internal representations and human-perceived semantic nuances.

## Appendix O Typicality and Cosine Similarity [RQ2]

Figure 25 shows representative scatter plots illustrating the relationship between human typicality scores (or psychological distances) and the LLM-derived item-centroid cosine similarities for selected categories and models. These plots visually demonstrate the often modest correlations discussed in Section 5.2 .

Figure 26 shows the aggregated Spearman correlation across model families and datasets. These correlations are very weak and mostly non-significant.

## Appendix P Theoretical Extreme Case Exploration for ℒ \mathcal{L}

In the case where | C | = | X | |C|=|X| (each data point is a cluster of size 1 1 , so | C c | = 1 ​ ∀ c ∈ C |C_{c}|=1\ \forall c\in C ), then H ⁡ ( X | C ) = 1 | X | ​ ∑ c ∈ C 1 ⋅ log 2 ⁡ 1 = 0 H(X|C)=\frac{1}{|X|}\sum_{c\in C}1\cdot\log_{2}1=0 . The distortion term σ c 2 = 0 \sigma_{c}^{2}=0 for each cluster as the item is its own centroid. Thus, ℒ = I ⁡ ( X , C ) + β ⋅ 0 = H ⁡ ( X ) − H ⁡ ( X | C ) = H ⁡ ( X ) = log 2 ⁡ | X | \mathcal{L}=I(X;C)+\beta\cdot 0=H(X)-H(X|C)=H(X)=\log_{2}|X| . This represents the cost of encoding each item perfectly without any compression via clustering, and zero distortion.

In the case where | C | = 1 |C|=1 (one cluster C X C_{X} contains all | X | |X| data points, so | C C X | = | X | |C_{C_{X}}|=|X| ), then H ⁡ ( X | C ) = 1 | X | ​ | X | ​ log 2 | X | = log 2 ⁡ | X | H(X|C)=\frac{1}{|X|}|X|\log_{2}|X|=\log_{2}|X| . Thus, I ⁡ ( X , C ) = H ⁡ ( X ) − H ⁡ ( X | C ) = log 2 ⁡ | X | − log 2 | X | = 0 I(X;C)=H(X)-H(X|C)=\log_{2}|X|-\log_{2}|X|=0 . This represents maximum compression (all items are treated as one). The distortion term becomes β ⋅ 1 | X | ​ | X | ⋅ σ X 2 = β ⋅ σ X 2 \beta\cdot\frac{1}{|X|}|X|\cdot\sigma_{X}^{2}=\beta\cdot\sigma_{X}^{2} , where σ X 2 \sigma_{X}^{2} is the variance of all items X X with respect to the global centroid of X X . So, ℒ = 0 + β ⋅ σ X 2 = β ⋅ σ X 2 \mathcal{L}=0+\beta\cdot\sigma_{X}^{2}=\beta\cdot\sigma_{X}^{2} . This represents the scenario of maximum compression where the cost is purely the distortion incurred by representing all items by a single prototype.

## Appendix Q Compression Figures

Figure 28 depicts the IB-RDT objective ( ℒ \mathcal{L} ) vs. K K . Lower ℒ \mathcal{L} indicates a more optimal balance between compression ( I ⁡ ( X , C ) I(X;C) ) and semantic fidelity (distortion). Human categories (fixed K K ) show higher ℒ \mathcal{L} values.

## Appendix R Complexity-Distortion Ratio (on the importance of β \beta )

Figure 29 provides an additional sensitivity analysis in which we examine the ratio between the distortion and complexity components of ℒ \mathcal{L} as β \beta varies. Across all three datasets, encoder models maintain flat profiles, indicating stable conceptual structure under compression, whereas decoder models exhibit stronger shifts, reflecting greater reallocation of representational capacity.

## Appendix S ℒ \mathcal{L} objective vs. downstream task performance

Analysis of 13 instruction-tuned models across 5 families (Qwen, Llama, Gemma, Phi, Mistral; see Table 5 for results) indicates no statistical significance ( r = − 0.202 r=-0.202 , p = 0.508 p=0.508 ). This finding suggests that while the ℒ \mathcal{L} objective successfully identifies models that compress semantic categories more effectively, this compression ability does not directly translate to improved performance on standard NLP benchmarks. The lack of correlation implies that concept compression and benchmark accuracy represent distinct aspects of model capability, with the former capturing semantic organization efficiency and the latter measuring general knowledge and reasoning abilities. We specifically chose instruction-tuned models to ensure fair comparison on MMLU, as base models would likely perform poorly on this instruction-following benchmark. While our analysis covers a diverse range of model families and sizes, this represents a subset of available models due to the limited availability of instruction-tuned variants.

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