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Pretrained language models encode grammaticality as a single linear direction in their sentence representations, a direction that generalizes across phenomena and languages and cannot be reduced to string probability or the tested extra-gra

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2026-08-01 23:54 UTC pith:J7METGEB

load-bearing objection The paper's core finding—mass-mean probes generalize across benchmarks and survive probability deconfounding—is real, but the abstract's 'cannot be fully explained' overreaches: the acceptability deconfounding removes only one direction. the 3 major comments →

arxiv 2607.15175 v1 pith:J7METGEB submitted 2026-07-16 cs.CL

Linear representations of grammaticality in neural language models

Jane Li , Najoung Kim This is my paper
classification cs.CL
keywords grammaticalitymass-mean probinglinear representationsneural language modelssyntactic knowledgeacceptabilitydeconfoundingcross-linguistic generalization
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper argues that pretrained neural language models encode grammaticality as a coherent linear dimension in their sentence representations. Using a mass-mean probe—a single direction defined by the difference between the average representation of grammatical and ungrammatical sentences—the authors show that a direction learned on one set of acceptability judgments generalizes to held-out datasets covering a wide range of syntactic phenomena. They show that this direction is not just a proxy for string probability: when probes are fit on deliberately counterfactual subsets (low-probability grammatical vs. high-probability ungrammatical), performance barely drops. They also find that the direction is only mildly entangled with other acceptability-related properties such as plausibility, truth, imageability, and arousal, and that removing the shared signal with those properties still leaves a usable grammaticality direction. For the strongest models, the encoding transfers across languages, suggesting grammaticality is a major organizing axis of the representational space.

Core claim

The central claim is that a single mass-mean difference vector, computed as the difference between the mean hidden-state representations of grammatical and ungrammatical sentences, captures a robust and generalizable grammaticality signal in the final-layer sentence representations of pretrained language models. This direction, fitted on a mixed set of acceptability judgments, succeeds on unseen minimal-pair tests across many syntactic phenomena; it is largely unaffected by counterfactual manipulation of string probability during probe fitting; and after regressing out the shared component with several extra-grammatical acceptability factors via boundary tilting, it still classifies grammati

What carries the argument

The key object is the mass-mean probe direction θ, defined as the difference between the mean representations of the positive (grammatical) and negative (ungrammatical) classes. Classification is done by thresholding the inner product θ·x at zero. The paper also uses token-region-of-interest extraction (critical, pre-critical, final) to localize when the grammaticality signal appears, and a boundary-tilting operation in which the projection of θ onto an extra-grammatical difference vector is subtracted from θ, isolating the component of the direction that is not shared with acceptability-related properties.

Load-bearing premise

The grammaticality labels in the benchmarks used to fit and evaluate probes are taken as ground truth; if those labels are systematically contaminated by plausibility, frequency, or other extra-grammatical factors that were not deconfounded, what the probe isolates could be a direction for acceptability rather than grammar per se.

What would settle it

Train a mass-mean probe on grammaticality contrasts using only sentences whose ungrammaticality arises from purely syntactic violations (e.g., agreement mismatches with matched lexical content and plausibility), then apply it to a held-out set of word-shuffle ungrammatical sentences after regressing out length, word-frequency, and plausibility from the representations. If the probe's success drops to chance, the claim that a single robust grammaticality direction exists would be undercut.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

  • Probability-based targeted syntactic evaluation may underestimate the grammatical knowledge of language models, since representational separation does not always propagate to output probabilities.
  • The existence of a single, generalizable direction makes grammaticality a candidate for activation steering, analogous to other linearly encoded properties.
  • Grammaticality representations are incrementally updated: the signal is already present at the critical word, not only at the final token.
  • Cross-linguistic transfer suggests that, in multilingual models, grammaticality is encoded in a way that is at least partially shared across languages, bearing on claims about a universal grammar-like abstraction.
  • The deconfounding methodology provides a template for separating a target linguistic property from correlated sentence-level properties in representation space.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the grammaticality direction is as robust as claimed, the same mass-mean probe could be used as a training signal or regularizer to encourage syntactic generalisation in smaller models.
  • The paper leaves open whether the direction emerges from co-occurrence statistics in training data; a direct test would be to track the probe's success during the training of an autoregressive model from checkpoints.
  • The boundary-tilting method could be extended to a systematic atlas of extra-grammatical factors (e.g., length, word frequency, surprisal) beyond the handful tested; the claim would be strengthened if the direction survives tilting against all of them.
  • One natural next experiment is jabberwocky or nonce-word stimuli: if the direction still separates grammatical from ungrammatical nonsense sentences, that would confirm the abstraction is syntactic rather than lexical.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

3 major / 6 minor

Summary. This paper asks whether grammaticality is linearly encoded in the sentence representations of pretrained neural language models, going beyond probability-based targeted syntactic evaluation. The authors fit mass-mean probes on the LI-Adger acceptability dataset and evaluate them on held-out BLiMP and SCaMP datasets, finding above-null probe success across 25 models (Experiment 1). They then localize the signal to the critical region and show cross-phenomenon generalization (Experiment 2), deconfound scalar string probability via Counter/Favour sampling (Experiment 3), test whether the probe is reducible to plausibility/truth/imageability/arousal etc. via cross-probing and boundary tilting (Experiment 4), and report partial cross-linguistic generalization for five stronger models (Experiment 5). The paper concludes that grammaticality is a robust, generalizable linear representational dimension that 'cannot be fully explained by alternative sentence-level factors.'

Significance. The study is a serious and mostly well-designed contribution to the debate on whether NLMs represent grammaticality. Its strengths include the external probe-transfer design (fit on LI-Adger, evaluate on BLiMP/SCaMP), the 100-run resampling protocol, the inclusion of 25 models across families and scales, and the attempt to deconfound probability and several extra-grammatical factors. The probability-decorrelation experiment (Experiment 3) is a particularly clean test, and the cross-linguistic analysis, while limited, is a useful step. If the central claim is suitably calibrated, the paper would provide a valuable representation-based complement to probability-based benchmarks. The main weakness is that the abstract's 'cannot be fully explained' claim is stronger than what the deconfounding experiments can support, given that the boundary-tilting procedure removes only a single direction at a time and the set of extra-grammatical factors tested is finite.

major comments (3)
  1. [§6.3 / §6.1] The abstract's 'cannot be fully explained by alternative sentence-level factors' rests mainly on Experiment 4, but the boundary-tilting analysis removes from θ only the projection onto a single ϕ: either the mean of all extra-grammatical difference vectors (Tilt-all) or the single most collinear vector (Tilt-one). If extra-grammatical acceptability is a multidimensional subspace (plausibility, truth, imageability, arousal, frequency, length are correlated but distinct), a grammaticality direction could lie in that subspace while having low cosine with each individual ϕ and with their mean. The Control condition shows only that the projection operation can destroy a grammaticality signal when ϕ is itself a grammaticality direction; it does not establish that the 26 extra-grammatical ϕs span the relevant subspace. The paper also does not report the cosine between θ and the extra-grammatica
  2. [Abstract / §5 / §6.1] The phrase 'alternative sentence-level factors' is broader than the factors actually deconfounded at the representation level. Experiment 3 deconfounds scalar string probability, and Experiment 4 covers the extra-grammatical datasets in Table 2 (Shades, Drive, Truth), but lexical frequency and length — both cited in §1 as documented confounds — are only used as similarity regressors in §4.3, not as probe-fitting contrasts whose direction is removed from θ. A probe direction could therefore still be partially aligned with a frequency or length contrast. The conclusion should either test these additional contrasts or be reformulated as conditional on the factors examined.
  3. [§8.4] The discussion states that the results settle the premise that NLMs can represent grammaticality distinctions at all. Given that the probe is fitted on benchmark labels and evaluated on the same kind of benchmark, and that the deconfounding evidence is partial (see above), this framing is too strong. The paper itself in §8.1.1 notes that the link between the grammaticality boundary and syntactic representations 'has yet to be established.' Please align the strength of the conclusion with this acknowledged limitation.
minor comments (6)
  1. [§2.5] The 5% probe-success threshold is calibrated from the Pre-critical region results of Experiment 2. Since this threshold is used throughout the paper, please report sensitivity of the main conclusions to the threshold choice (e.g., 2% or 10%) or justify more formally why 5% is conservative beyond the observed null range.
  2. [§2.2] Models are pre-selected for above-chance BLiMP probability comparisons. This is a reasonable precondition, but it means the claims about 'a wide range of pretrained NLMs' are conditional on prior behavioral sensitivity. Please state this explicitly and discuss whether pre-selection could inflate the Experiment 1 success rates.
  3. [§6] The text refers to 'Table A.1' for the extra-grammatical datasets, but the relevant table is Table 2. Please fix the cross-reference.
  4. [Figure 14] Typo in the caption: 'Experiemnt' should be 'Experiment.'
  5. [Conclusion] The final paragraph contains 'and and model classes' — remove the duplicated 'and.'
  6. [Figures 2–12] Several correlation values are reported without confidence intervals or p-values. Please add these, or at least indicate which correlations are significant under a multiple-comparison correction.

Circularity Check

1 steps flagged

Minor circularity: Pre-critical control failure is guaranteed by the 5% threshold calibrated to that control; central claims are external.

specific steps
  1. fitted input called prediction [§2.5 (success threshold) applied in §4.1 (Result #1)]
    "Observing that probes fitted on single BLiMP datasets at the Pre-Critical region (a manipulation in Experiment 2) are in the range [-2.62%, 1.65%], we set the threshold to 5% as a conservative estimate of false positives. ... We find that all 25 models we examine demonstrate sensitivity to grammaticality in the Critical and Final regions and not the Pre-critical region."

    Success is defined as probing accuracy being at least 5% above the null distribution. The 5% threshold is explicitly calibrated to exceed the Pre-critical range of [-2.62%, 1.65%]. Consequently, any Pre-critical probe necessarily falls below the success threshold, making the 'not the Pre-critical region' result true by definition rather than by evidence. This is a fitted parameter (threshold) used to certify a closely related null outcome. The main Critical/Final and cross-dataset results are not forced by this threshold, so the circularity is minor and non-load-bearing.

full rationale

The central claim is supported by held-out and cross-benchmark evaluation: the mass-mean direction θ is fit on LI-Adger and evaluated on BLiMP/SCaMP; cross-linguistic probes are fit on English benchmarks and tested on non-English benchmarks; deconfounding experiments use external datasets (Shades, Drive, Truth). These evaluations are external to the fitted direction, so the main results are not circular. The only circular step is the Pre-critical control: the 5% success threshold is set from the observed Pre-critical range, which guarantees Pre-critical probes are classified as unsuccessful. This is a control-condition artifact rather than a load-bearing step, since the paper's positive claims concern Critical/Final sensitivity and generalization. Model pre-selection on BLiMP probability success is a sampling filter, not a fitted parameter, and does not make the probe results equivalent to its inputs.

Axiom & Free-Parameter Ledger

4 free parameters · 6 axioms · 0 invented entities

The paper introduces no new entities. Its central assumptions are that benchmark labels capture grammaticality, that the mass-mean direction is a good probe, that the null/shuffle baseline is valid, and that projection deconfounding works. The main free parameters are the success threshold and model selection choices.

free parameters (4)
  • probe success threshold = 5% above null
    Set in §2.5 based on observed Pre-critical false-positive range [-2.62%, 1.65%]; determines whether a probing configuration counts as successful.
  • top-5 model selection for cross-lingual experiment = Llama-3.2-3B, Llama-3.1-8B, Qwen3-4B, OLMo-7B-hf, OLMo-2-1124-7B
    Section 7 selects models with strongest English grammaticality signals; this selection biases the cross-lingual generalization results.
  • probability quantiles for Counter/Favour conditions = top/bottom 20%
    Experiment 3 samples the 20% most/least probable sentences; this arbitrary cut affects the deconfounding manipulation but is not itself fitted to the outcome.
  • Drive grammaticality cutoff = 4.0 Likert
    Appendix A.1 filters Drive stimuli to sentences rated above 4.0 on grammaticality; affects the extra-grammatical dataset used in Experiment 4.
axioms (6)
  • domain assumption Benchmark labels are valid ground truth for grammaticality
    All probing uses BLiMP/SCaMP/LI-Adger labels as the target; if these labels reflect acceptability or artifact, the probe measures that instead. Introduced in §2.1 and throughout.
  • domain assumption Mass-mean vector (class centroid difference) is a sufficient linear probe for the encoding
    The paper equates linear separability with a 'grammaticality dimension' using θ=μ1−μ0 (§2.4); more complex linear probes might find different directions.
  • standard math Null distribution from label shuffling is the correct baseline
    Used to define probe success (§2.5); assumes shuffled-label probes estimate chance performance for this geometry.
  • domain assumption Projection out of extra-grammatical vectors isolates grammaticality
    Boundary tilting in §6.3 assumes shared variance between θ and extra-grammatical ϕ is acceptability signal, and removing it leaves grammaticality; if grammaticality and acceptability share structure, this can remove grammaticality too.
  • domain assumption Models above chance on BLiMP probability comparisons are the population of interest
    §2.2 pre-selects 25 models based on BLiMP performance; conclusions do not apply to models that fail BLiMP.
  • domain assumption Final-token representation is a valid sentence representation
    §2.3 uses final punctuation token when region annotations are unavailable; this representation may encode sentence-level properties beyond grammaticality.

pith-pipeline@v1.3.0-alltime-deepseek · 28528 in / 13246 out tokens · 100614 ms · 2026-08-01T23:54:47.026658+00:00 · methodology

0 comments
read the original abstract

Whether neural language models (NLMs) possess the ability to distinguish strings on the basis of their grammaticality remains a debated topic in the computational linguistics literature. Existing evidence has largely relied on probability-based measures, testing whether models assign higher probabilities to grammatical than ungrammatical strings. However, probability comparisons have been criticized as a measure for grammatical knowledge based on the assumption that grammaticality is inherently entangled with likelihood. Model-assigned probability is a function of many related sentence properties, such as lexical frequency, plausibility, and world knowledge. In this work, we move beyond probability-based evaluations and investigate whether grammaticality is encoded in the internal representations of NLMs. Using mass-mean probing, we test whether grammatical and ungrammatical sentences are systematically separated in representational space. We further examine the extent to which these representations are independent of sentence properties that are correlated with grammaticality, as well as their generalization across grammatical phenomena and languages. Our results provide evidence that grammaticality is robustly encoded in sentence representations of a wide range of pretrained NLMs, yielding clear representational separation on the dimension of grammaticality that cannot be fully explained by alternative sentence-level factors. Moreover, this encoding generalizes across a broad range of grammatical phenomena and to some degree, across languages, suggesting that grammaticality constitutes a coherent representational dimension in contemporary NLMs. These findings contribute new evidence to debates about the nature of syntactic knowledge in language models and offer a complementary framework for evaluating grammatical competence that is not dependent on string probabilities alone.

Figures

Figures reproduced from arXiv: 2607.15175 by Jane Li, Najoung Kim.

Figure 1
Figure 1. Figure 1: A step-by-step summary of the methods used in the experiments of this paper. [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Model-level results from Experiment 1. R reports the Pearson correlation between model size (log10 parameter count) and the main measure of each subplot. (A) Percentage of successful probes out of the 67 BLiMP datasets. (B) Average accuracy (in %) of each probe. (C) Average accuracy within the set of successful probes. We find that all 25 models we examine demonstrate some probe sensitivity to grammaticali… view at source ↗
Figure 3
Figure 3. Figure 3: (A) Comparisons between accuracy measures. Each point represents an aggregate measure of accuracy for a model. (B) A dataset-level comparison of MP Rep advantage, ordered on the x-axis by the proportion of models that exhibit advantage on that dataset. (C) The magnitude of the MP Rep advantage, following the ordering as sub-figure 3B. based comparisons tend to detect grammaticality contrasts more effective… view at source ↗
Figure 4
Figure 4. Figure 4: The success rate (as defined by §2.5) of mass-mean probes on detecting grammaticality across models (A) and [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Probing accuracies of Experiment 2 in the Critical and Final region. ( [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: The relationship between surface-level similarity measures between BLiMP datasets and the probing [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Results from Experiment 3. (A) The distribution of average fitting sentence probabilities for Llama-3.1-8B, across conditions. Each datapoint in the plot represents the mean sentence probability per fitting subset, separated by grammaticality label. (B-D) Probing performance between conditions: success, mean probe accuracy, and the rate of success given that the Original probe was successful. probability: … view at source ↗
Figure 8
Figure 8. Figure 8: Probing results when grammaticality probes are tested on extra-grammatical datasets and vice versa. [PITH_FULL_IMAGE:figures/full_fig_p012_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Probing results on SCaMP plausible and implausible datasets. The fitting datasets are always in the [PITH_FULL_IMAGE:figures/full_fig_p012_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Probing results across different θ, pre- and post- tilting. All probes are evaluated on grammaticality datasets (BLiMP and SCaMP). (A) Success rates across conditions. (B) Accuracy scores across conditions. (C) Success rates of tilted and control probes, given success of the original probe. The results indicate that grammaticality is a distinct signal from acceptability. First, we see that the equivalent … view at source ↗
Figure 11
Figure 11. Figure 11: Within-language (left bars) and cross-language (right bars) probing success rates across the five models [PITH_FULL_IMAGE:figures/full_fig_p014_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Probing results across six languages, across five high-performant models. “*” marked in a grid indicates that [PITH_FULL_IMAGE:figures/full_fig_p015_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Minimal pair probability comparison-based BLiMP accuracies for each model we examine. Each dot on the [PITH_FULL_IMAGE:figures/full_fig_p024_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Critical and Final region accuracies on BLiMP dataset-level probing (Experiemnt 2) on Pythia-14m, OLMo [PITH_FULL_IMAGE:figures/full_fig_p025_14.png] view at source ↗

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