{"id":"1d473b00-460a-4270-9fc9-aa9a520fb1f7","arxiv_id":"2508.17953","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"In six LLMs, subword representation composition is largely approximated by vector addition, and the models cluster into three distinct layer-wise composition patterns.","lead":"This paper probes how large language models combine subword pieces, such as 'sun' and 'rise', into whole-word meanings. Across six models, it finds that simply adding subword vectors often reconstructs the full word, with models falling into three distinct patterns.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Probing experiments lack any stated held-out split; with d≈4096 and n=3432, reported F1/accuracy may reflect memorization, weakening the content/form claims and the three-group taxonomy.","rationale":"The reader's dataset-representativeness concern is valid but concerns external generalization. The missing held-out evaluation in the probing sections is more load-bearing because it threatens the internal validity of two of the paper's main empirical supports: content preservation and the form-retention differences that are used to define the three composition strategies. The geometry analysis in §3 is explicitly split into train and test, so the authors know how to report held-out evaluation; the absence of this detail in §4 makes the probing results impossible to interpret. The proposed check is inexpensive and directly settles the concern: if the probes were already evaluated on held-out data, the results will survive the rerun; if they were not, the published curves are likely optimistic. I therefore keep the reader's CONDITIONAL verdict rather than moving to ACCEPT, but the revision conditions should explicitly include held-out probing evaluation in addition to the dataset-sensitivity analysis the reader requested.","tokens_in":13311,"tokens_out":15479,"duration_ms":175177,"concrete_test":"Rerun the §4.1 root/non-root classification and §4.2 length regression using the same 2745/687 train/test split as §3.2 (or 5-fold cross-validation), and report held-out weighted F1 and accuracy per layer for each model. If held-out performance drops substantially toward the random baselines (~56% F1 and ~3.5% accuracy) in layers where Figures 6–7 currently show high scores, the probing evidence for the three-group taxonomy is invalidated.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's central claims include that content (root/non-root) and form (length) information are preserved in composed representations and that this corroborates the three-group taxonomy. Sections 4.1 and 4.2 describe fitting logistic and linear probes with Adam for three epochs, but never state that the probes are evaluated on held-out words. This contrasts with §3.2, which explicitly uses a train/test split for the geometry analysis. With 3,432 examples and hidden-state dimensionality around 4,096 (3,584 for Gemma2), a linear probe trained and evaluated on the same data can memorize labels, so the high F1/accuracy in Figures 6–7 may reflect overfitting rather than encoded content/form information. Because Section 5 uses these probing curves as corroborating evidence that the same three groups appear, an overfitting artifact would remove part of the support for the taxonomy, and the claim that some models retain form information while others do not would be unsubstantiated.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies how six instruction-tuned LLMs (Llama3, Llama3.1, Aya-expanse, Gemma2, Falcon, Qwen2.5) compose subword representations into whole-word representations. Using a parallel dataset of 3,432 English words whose two subword tokens are in all six vocabularies, it applies orthogonal Procrustes analysis to compare simple composition operations (addition, multiplication, absolute difference) against whole-word representations across layers, with the transformation fit on a train split and evaluated on a test split. It also trains logistic and linear probes to predict root/non-root class and word length from composed representations. The paper claims that (i) addition is near-isometric to LLM composition in most models, (ii) content information is preserved across layers and models while form information is preserved only in some models, and (iii) the six models form three compositional groups. The three-group taxonomy is presented as the main contribution.","tokens_in":13498,"tokens_out":5043,"duration_ms":52707,"significance":"If the results hold, the finding that a simple orthogonal alignment makes subword sums retrieve whole-word vectors across layers is a meaningful constraint on how transformer representations compose, and the proposed three-way grouping could guide further analysis of training-data and architectural effects. The geometry analysis is carefully set up in one respect: the Procrustes transformation is fit on a train split and evaluated on a held-out test split, and the comparison of addition, multiplication, and absolute difference is clean. The base-versus-instruction-tuned comparison and the root/non-root breakdown are also valuable. However, the probing experiments lack an explicit held-out evaluation, and the central three-group taxonomy rests on visual inspection without quantitative support, so the paper's broader claims currently outrun the evidence.","major_comments":[{"comment":"The probing experiments are described as training logistic and linear probes for three epochs with Adam, but no held-out split or cross-validation is mentioned, unlike the geometry analysis in §3.2. With input dimensionality d≈4096 (3584 for Gemma2) and n=3432, a linear probe can memorize the training labels, so high weighted F1/accuracy on the same examples does not establish that root/non-root or length information is encoded. Since Section 5 uses these curves as corroborating evidence for the three-group taxonomy, the authors should report held-out evaluation or cross-validated performance for every layer and model, and state how the random baselines were computed under the same evaluation scheme.","section":"§4.1–§4.2, Figures 6–7"},{"comment":"The central claim that the six models fall into three distinct groups is supported only by visual inspection of layer-wise curves; no clustering, pairwise curve-distance measure, or significance test is reported. For instance, in Figure 2 the Llama and Falcon/Qwen curves overlap in early layers, and in Figure 7 the 'same three groups' are asserted without quantifying between-group versus within-group differences. The authors should provide a quantitative grouping, for example silhouette scores over curve features or permutation tests on curve differences, so that the taxonomy is not an impressionistic reading of the plots.","section":"§3.3, §5 (Figures 2, 5, 6, 7)"},{"comment":"The dataset construction—words with exactly two subword tokens and both tokens present in all six vocabularies—likely selects for short, high-frequency, morphologically transparent words, and the paper's own limitations section acknowledges the small, English-only coverage. Because the main claims ('most models', 'three groups') are about composition in general, the absence of any sensitivity analysis (for example, relaxing the two-subword constraint, using per-model vocabularies, or stratifying by frequency or morphological category) leaves open the possibility that the observed additivity and the three-group taxonomy are artifacts of the word sample. Please add at least one robustness check, or explicitly restrict the claims to this dataset in the abstract and contributions.","section":"§3.1 (dataset) and Limitations"}],"minor_comments":[{"comment":"The abstract contains typos ('effective compose' should be 'effectively compose', 'pattens' should be 'patterns'), and the author line 'Y e kun Chai' has an unusual space that should be fixed.","section":"Abstract and author line"},{"comment":"The candidate set for P@1 retrieval is not specified: it should state whether retrieval is over the test-split whole-word vectors, the full vocabulary, or some other set, and whether the target word itself is included in the candidates.","section":"§3.2"},{"comment":"The phrase 'significantly more similar' is used without a statistical test; if error bars are the only evidence, replace 'significantly' with 'consistently' or report an appropriate significance test over the three runs.","section":"§3.3 and Figure 2 caption"},{"comment":"The text says 'Table 3.1' but should refer to Table 1; also, the 'random baseline' should be described precisely, since a classifier matching class proportions and a majority-class baseline are different and the 56% figure should be reproducible from the class distribution.","section":"§4.1"},{"comment":"The contextualized-subword experiment is underspecified: please describe the exact input format (are the two subwords fed as a two-token sequence?), which hidden states are extracted, and whether the same subword combinations are used as in the non-contextualized setting.","section":"§3.3 and Figure 5"},{"comment":"The reference to the data-mixture appendix appears only as a footnote; move the pointer into the main text so readers can find the appendix information easily.","section":"§5 and Appendix A"}],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: this is a well-structured empirical study of how six LLMs compose two-subword representations. The geometry analysis is solid and the main finding — that simple addition beats multiplication and absolute difference under Procrustes alignment, and that this holds across base and instruction-tuned versions — is believable and new in its layer-wise detail. Worth a careful read.\n\nWhat's new: the layer-wise P@1 comparison across six LLMs, fit on a train split and evaluated on a test split, moves beyond earlier distance-based subword work. The base-model control is a nice touch, and the contextualization experiment adds a useful axis. The dataset is narrow (3,432 English words, two subwords, all tokens in all vocabularies), but the authors acknowledge this.\n\nWhere I'd push back. First, the three-group taxonomy is the load-bearing claim, but it's supported by visual grouping of curves. No clustering, no significance test. The groups may be real, but the paper doesn't show it statistically. Second, the probing sections (4.1, 4.2) don't state whether the logistic/linear probes were evaluated on a held-out split. With n=3,432 and d≈4,096, a linear probe trained on the same data can memorize. If the reported F1/accuracy are from the training set, the content/form preservation claims and the corroboration of the taxonomy lose force. This is likely fixable — they probably should have used the same split as §3.2 — but it's not written down. Third, the word \"isometric\" overstates what P@1 measures; nearest-neighbor retrieval is a weaker notion.\n\nCitation pattern looks fine; they engage with the relevant subword and probing literature. The paper is honest about its limitations.\n\nBottom line: the core geometry result is likely robust and worth knowing. The taxonomy and probing claims need more rigor. A serious referee should ask for a statistical check on the grouping and a clear statement about the split in the probing. I'd send it to review; with those fixes it would be a useful reference for tokenizer design and interpretability work.","headline":"Solid layer-wise geometry result on subword addition, but the three-group taxonomy rests on visual curve reading and the probing experiments never state a held-out split.","tokens_in":14006,"tokens_out":3151,"would_cite":true,"duration_ms":31011,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["68T50","68T07"],"pacs":[],"model":"deepseek-v4-flash","headline":"Most large language models compose subword representations almost exactly by vector addition, recoverable through a single linear map, and the six models tested fall into three distinct composition-strategy groups.","keywords":["subword composition","compositionality","Procrustes analysis","probing classifiers","vector addition","large language models","isometry","word length prediction"],"falsifier":"Test the same six models on words with three or more subwords, or on an agglutinative language such as Turkish, and recompute Procrustes P@1 for the sum operation: if recoverability drops toward chance, the paper's claims are limited to the two-subword English setting. The design is fully specified in the paper, so the test is runnable without new machinery.","tokens_in":1632,"feed_emoji":"➕","tokens_out":7027,"duration_ms":98744,"temperature":0.7,"pith_summary":"The paper tries to establish how LLMs build word-level representations from subword pieces, and it reports two related findings. First, in most of the six models tested, the composed representation of a word is isometric to the simple sum of its two subword representations: after fitting an orthogonal linear map, adding subword vectors and looking up the nearest whole-word vector recovers the original word with high precision. Second, the layer-by-layer geometry and probing results sort the six models into three stable groups, suggesting systematic rather than idiosyncratic differences in composition strategy. If the paper is right, subword composition in mainstream LLMs is largely linear, and a model's composition group is a measurable, fairly fixed property that is set during pre-training rather than by instruction tuning.","feed_headline":"Most LLMs compose subwords nearly by vector addition","feed_subtitle":"Six models fall into three groups; word meaning survives everywhere while surface form survives only in some.","key_machinery":"Procrustes analysis is the central instrument: given matrices $X$ of composed subword vectors and $Y$ of whole-word vectors, the orthogonal transformation $W^* = UV^T$ obtained from the SVD of $YX^T$ maps the composed space onto the word space, and recoverability is measured by Precision@1 over nearest neighbors on a held-out test split. This converts the claim 'composition behaves like addition' from a metaphor into a falsifiable geometric statement. The probing experiments use logistic regression to classify root versus non-root words and linear regression to predict word length, run layer by layer on both original and addition-composed representations.","core_discovery":"The paper claims that, in most of the models tested, the representation a model builds for a whole word from its two subword pieces is, up to a single orthogonal linear transformation, the vector sum of the two subword representations. After fitting that transformation on a training split, summing subword vectors and retrieving the nearest whole-word vector achieves high Precision@1 on a held-out test split, and addition beats multiplication and absolute difference everywhere. The same experiments divide the six models into three groups: Llama3 and Llama3.1 show little linear recoverability outside the embedding layer; Aya-expanse and Gemma2 stay linearly recoverable across nearly all layers; Falcon and Qwen2.5 start recoverable, then drop in middle layers. Probing shows that the root/non-root distinction survives in the composed vectors for all models at all layers, while word length information is reliably recoverable only in some models and some layers, with a consistent late-layer re-emergence. Instruction tuning changes the scores slightly but not the grouping, so the strategies are argued to be fixed during pre-training.","pith_inferences":["If this additivity generalizes beyond the paper's narrow two-subword English sample, mean-pooling subword embeddings—a common practical shortcut—is a much better approximation of model-internal word representations for some model families than for others.","The grouping correlates with model families' data-mixture choices, suggesting a testable hypothesis the paper stops short of: training the same architecture on two different data mixtures should move its composition group.","The late-layer re-emergence of word-length information seen in several models may reflect pressure from next-token prediction to reconstruct surface form; one could test this by ablating the final output projection and re-measuring length accuracy.","Because root words are already less recoverable than non-root words, a natural extension is to check whether additivity degrades gracefully with subword count; the paper's mechanism predicts it would."],"forward_implications":["Word-level vectors in most tested LLMs can be approximated well by adding subword vectors and applying one linear map, making linear readouts a viable route to word-level meaning for those models.","Because instruction tuning barely changes the patterns, the composition strategy is largely fixed during pre-training, pointing to pre-training data and data mixture rather than fine-tuning as the causal factor.","Semantic decomposability is preserved in all models at all layers, whereas surface form is not; for the Aya/Gemma group both content and form survive, making the input more easily derivable from the composed representation.","The three-group taxonomy offers a compact diagnostic for tokenizer and representation design: whether a model retains subword traces throughout its depth or abstracts them away early is observable from the layer-wise P@1 curves."],"supporting_citations":[{"why":"Supplies the orthogonal Procrustes solution that the geometry pipeline uses to align composed and whole-word spaces.","marker":"(Schönemann, 1966)"},{"why":"Provides the morpheme-segmentation resource from which the paper selects its parallel two-subword words.","marker":"(Batsuren et al., 2022)"},{"why":"Defines the Llama3 and Llama3.1 models and the data-mixture figures used to interpret the first group.","marker":"(Dubey et al., 2024)"},{"why":"Defines the Aya-expanse model whose data mixture is discussed in relation to the high-similarity group.","marker":"(Dang et al., 2024)"},{"why":"Technical report for Qwen2.5, one of the Falcon/Qwen group models.","marker":"(Team, 2024b)"},{"why":"Defines Falcon, the other model in the second group; its data-mixture figure is reproduced in the appendix.","marker":"(Almazrouei et al., 2023a)"},{"why":"Defines Gemma2, the model paired with Aya in the high-similarity group.","marker":"(Team, 2024a)"}],"fun_headline_variants":["LLMs: word vectors are subword sums after rotation","Six LLMs, three strategies: subword sum or not","Word meaning from subwords: mostly just addition","Subword composition in LLMs: linear sum wins","How LLMs build words: vector addition plus rotation"],"cache_read_input_tokens":16256,"weakest_assumption_plain":"The 3,432-word benchmark only includes English words that split into exactly two subwords, with both subwords present in all six vocabularies; if that selection is not representative of how words are usually tokenized, the observed additivity and the three-group grouping may be artifacts of the sample.","fun_headline_variants_meta":{"raw":{"variants":["LLMs: word vectors are subword sums after rotation","Six LLMs, three strategies: subword sum or not","Word meaning from subwords: mostly just addition","Subword composition in LLMs: linear sum wins","How LLMs build words: vector addition plus rotation"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000489,"raw_usage":{"total_tokens":2393,"prompt_tokens":918,"completion_tokens":1475,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":534,"completion_tokens_details":{"reasoning_tokens":1397}},"tokens_in":534,"tokens_out":1475,"duration_ms":11302,"temperature":1.0,"reasoning_tokens":1397,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T16:58:27.206800+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Test the same six models on words with three or more subwords, or on an agglutinative language such as Turkish, and recompute Procrustes P@1 for the sum operation: if recoverability drops toward chance, the paper's claims are limited to the two-subword English setting. The design is fully specified in the paper, so the test is runnable without new machinery.","supporting_citations":[],"review_version":2}