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REVIEW 2 major objections 4 minor 98 references

Behavioural vs. Representational Systematicity in End-to-End Models: An Opinionated Survey

T0 review · 2 major / 4 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read Systematic behaviour on a benchmark does not show that a model has systematic internal representations, and most current benchmarks do not require the strong form of systematicity that comes closest to human generalization.

desk verdict A useful survey that cleanly separates behavioural from representational systematicity, but its classification of visual benchmarks under a syntax-free Hadley taxonomy is underdetermined. read the letter →

arxiv 2506.04461 v1 pith:IMUHCEJ4 submitted 2025-06-04 cs.LG cs.AIcs.CL

Ivan Vegner , Sydelle de Souza , Valentin Forch , Martha Lewis , Leonidas A.A. Doumas This is my paper
classification cs.LGcs.AIcs.CL
keywords systematicitycompositionalitybehaviouralrepresentationalHadley'staxonomymechanisticinterpretabilitysystematicgeneralizationFodorandPylyshyn
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

Machine-learning papers routinely cite Fodor and Pylyshyn's challenge as a reason to build or test compositional models, but this survey argues that the community is answering a different question. Fodor and Pylyshyn asked for systematic mental representations; the paper contends that nearly all current benchmarks and training studies measure systematic behaviour only. Using Hadley's three-level scale of weak, quasi, and strong systematicity, the authors classify representative language and vision benchmarks and conclude that many never require strong systematicity, the level closest to human generalization. Their constructive recommendation is that behavioural success must be paired with mechanistic interpretability, evidence about the internal representations that actually drive a model's output.

What carries the argument

The load-bearing machinery is Hadley's (1994) three-level taxonomy of systematicity—weak, quasi, and strong—which classifies what a training set has already shown a learner. Weak systematicity permits novel combinations of familiar words only in familiar syntactic positions; quasi-systematicity adds recursion over structurally familiar clauses; strong systematicity requires handling words in syntactic positions never seen in training, the level Hadley ties to human generalization. The authors use this scale to operationalize Fodor and Pylyshyn's representational systematicity, and they pair it with the competence/performance distinction: behavioural success is evidence, not proof, and mechanistic interpretability supplies the causal evidence needed to move from behaviour to representations.

What would settle it

Enumerate the train and test splits of a benchmark the paper classifies as testing only weak systematicity, for example SCAN Split 1, and count the test items in which some word appears in a syntactic position never attested in any training sentence; if that fraction is substantial rather than near zero, the weak-systematicity classification is false. The same position-coverage calculation, published for each benchmark, would settle which of the survey's classifications are correct.

Watch

Extended reading notes

Core claim

The central claim is that Fodor and Pylyshyn defined compositionality through systematicity of representations, not behaviour, and that the machine-learning literature invoking them has largely substituted behavioural systematicity for representational systematicity. On the authors' reading, a model can pass systematicity benchmarks through memorization or task-specific heuristics while lacking the structured internal representations Fodor and Pylyshyn argued are necessary. The survey adopts Hadley's weak/quasi/strong taxonomy as the operationalization of that distinction and uses it to classify benchmarks: SCAN's Split 1 and PCFG SET's systematicity split test weak systematicity; productivity-oriented splits require quasi-systematicity; COGS and ReCOGS-style structural generalization approach strong systematicity; most visual benchmarks do not reach it. The conclusion is that claims to have answered the Fodor–Pylyshyn challenge should be backed by mechanistic interpretability of the model's representations, not by benchmark scores alone.

Load-bearing premise

Everything downstream rests on the assumption that Hadley's 1994 three-level scale, built for connectionist language learning, transfers to modern end-to-end models and especially to visual benchmarks, where the paper concedes there is no agreed syntax of images to anchor the levels.

Editorial extensions

If this is right

  • Benchmark reports should state which level of Hadley's taxonomy the train/test split actually demands, rather than treating any compositional split as evidence of Fodor–Pylyshyn systematicity.
  • A claim that a model addresses the Fodor–Pylyshyn challenge should be accompanied by mechanistic evidence that the identified representations are causally responsible for the systematic behaviour.
  • New language benchmarks should be built to target strong systematicity by controlling which words appear in which syntactic positions during training.
  • For large pre-trained models, claims of strong behavioural systematicity are hard to support because the training distribution is not controlled.
  • Visual systematicity benchmarks cannot be fully scored on Hadley's scale until a theory of the syntax of images is available.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A natural extension the authors do not develop is a quantitative distance-to-strong measure: for any train/test split, compute the fraction of test items whose words appear only in syntactic positions absent from all training sentences; benchmarks could then be ordered by how much beyond weak systematicity they demand.
  • If the survey is right, cross-benchmark model rankings should not be read as rankings of systematic generalization; the same model may exploit different shortcuts on different benchmarks, which is a direct explanation for the disagreement across benchmarks the paper cites.
  • The paper's position implies a testable criterion for representational systematicity: causal interventions on internal representations, for example swapping role or binding vectors, should change the model's output exactly as the compositional operation predicts; where they do not, the behavioural success is probably shortcut-driven.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 4 minor

Summary. This paper argues that much of the machine-learning literature on systematicity measures behavioural systematicity, whereas Fodor and Pylyshyn's original challenge concerned systematicity of representations. The authors adopt Hadley's (1994) weak/quasi/strong taxonomy as an operational framework, apply it to a selection of language and vision benchmarks, and conclude that many current benchmarks fall short of strong systematicity, the level closest to human systematic generalization. They then review evidence for and against representational systematicity in end-to-end Transformer models, drawing on mechanistic interpretability, and close with recommendations for evaluating systematicity claims.

Significance. If the central distinction is accepted, the paper provides an important corrective to the field's frequent invocation of Fodor and Pylyshyn. Its strengths are the clear separation of behavioural from representational systematicity, the concrete examples illustrating the dangers of conflating the two (e.g., Bastings et al.'s SCAN shortcuts and ReCOGS's impact on COGS results), and the constructive emphasis on mechanistic interpretability as a complement to behavioural benchmarks. The paper is an opinionated survey, so its soundness rests on the accuracy and internal consistency of its interpretive claims; the main argument is well supported by the historical discussion and the case studies in language, though the visual-benchmark analysis is less secure.

major comments (2)
  1. [§4.2] The classification of visual benchmarks under Hadley's taxonomy is underdetermined because the paper itself acknowledges that no strong theory of image syntax exists. The text states, 'Lacking a strong theory of the syntax of images, it is unclear how Hadley's levels of systematicity apply to visual concepts,' yet it immediately assigns 'weak systematicity' to disentanglement datasets on the grounds that they 'lack a hierarchical structure' and do not place concepts in novel contexts. Hierarchical structure, syntactic position, and novel context are not defined for image contents. As a result, the weak/quasi/strong labels for visual benchmarks are not well grounded, and the Section 6 conclusion that 'many current benchmarks fall short of testing strong systematicity' is not supported for the visual half of the survey. I recommend either providing a working visual syntax (e.g., scene graphs or a grammar over generative factors) or explicitly limiting the Hadley-based classification to linguistic benchmarks and presenting the visual discussion as exploratory.
  2. [§2.3 and §4.1] The classification of productivity splits as requiring at least quasi-systematicity rests on an unproven conjecture. The paper asserts that weak systematicity yields no productivity because a sentence of unseen length 'will necessarily' contain at least one word in a novel syntactic position. This is not established for arbitrary phrase-structure grammars; under recursive grammars, arguments may occupy the same positions at all depths, and whether a word is in a novel position depends on the grammar's definition of positions. The classification of the PCFG SET Productivity split and SCAN's Split 2 depends on this step. Please either prove the claim under explicit grammar assumptions or soften the classification to 'may require at least quasi-systematicity'.
minor comments (4)
  1. [§3.1] The informal phrase 'Mike Young and colleagues' should be replaced with a formal citation, since the text later cites Young and Wasserman (1997, 2001) by name.
  2. [References] Several reference entries contain formatting errors in author names (e.g., 'DeV os', 'V on Kügelgen'); these should be corrected before publication.
  3. [§4.2] The sentence 'ARC may constitute a test for strong compositionality but cannot be judged on an objective basis' is ambiguous; please separate the hedged claim from the justification that the construction process is not systematically described.
  4. [§4.1] For SCAN Split 1, the classification as weak systematicity relies on the statistical claim that even 2% of the training data exhibits all possible commands in all possible positions; please state explicitly that this is an empirical judgment about the dataset rather than a formal property of the split.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the survey's central distinction and benchmark classifications are imported from external sources (Fodor & Pylyshyn; Hadley), not derived from its own conclusion.

full rationale

This is an opinionated survey rather than a derivation, and its central claims are backed by external, non-self-authored sources. The behavioural-vs-representational distinction is attributed to Fodor and Pylyshyn (1988), and the weak/quasi/strong taxonomy is Hadley's (1994); the paper explicitly adopts these frameworks rather than defining them in terms of its own target conclusion. The benchmark classifications in Sections 4.1 and 4.2 are applications of Hadley's externally defined levels to specific datasets, and the observation that many benchmarks 'fall short of testing strong systematicity' follows from inspecting those datasets under Hadley's definitions; it is a classification, not a forced equivalence. The paper itself flags the main threat to this application in Section 4.2: 'lacking a strong theory of the syntax of images, it is unclear how Hadley's levels of systematicity apply to visual concepts,' which is an acknowledged limitation on the validity of the visual extension, not a circular step. Self-citations (Lewis et al. 2024; Doumas et al. 2022) appear only as examples or as out-of-scope footnotes and are not load-bearing; they do not supply the framework or the uniqueness of the taxonomy. No fitted parameters are renamed as predictions, and no uniqueness theorem from the authors' prior work is invoked. The productivity conjectures in Section 2.3 are consequences of the definitions of weak/quasi/strong systematicity and unseen-length sentences, not circular inputs. The least secure part of the paper is the transfer of Hadley's linguistic taxonomy to visual benchmarks, but that is an underdetermination/correctness concern, not circularity.

Assumptions & free parameters 0 free parameters · 4 assumptions · 0 invented entities

The paper's central claim rests on four main interpretive assumptions: the representational reading of Fodor and Pylyshyn, the validity of Hadley's taxonomy, the requirement of controlled operationalisation, and the conditional inference from valid behavioural success to representational systematicity. There are no free parameters or invented entities. The assumptions are largely explicit, but the strongest one, the validity of Hadley's taxonomy, receives less critical scrutiny than it needs.

assumptions (4)
  • domain assumption Fodor and Pylyshyn's systematicity is fundamentally a property of representations, not behaviour.
    This is the foundational interpretive claim of the paper, stated in Section 2.1 and used throughout. It is not proven but is attributed to Fodor and Pylyshyn.
  • domain assumption Hadley's three levels of systematicity provide a valid operationalization of Fodor and Pylyshyn's representational systematicity.
    Adopted in Section 3.1 and Section 4. The paper treats Hadley's taxonomy as a robust framework, but it is a theoretical choice and the paper itself notes uncertainty for visual tasks.
  • domain assumption A valid behavioural operationalisation requires principled control over dataset syntax and semantics.
    Stated in Section 3.2, Case 1. This assumption underlies the paper's critique of benchmarks that lack such control.
  • domain assumption Behavioural success under a valid operationalisation is evidence of representational systematicity only if Fodor and Pylyshyn's position is accepted.
    Discussed in Section 3.2, Case 2. The paper notes that this is a conditional conclusion, not an independently established fact.

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Cite this review

Pith. "Pith review of Behavioural vs. Representational Systematicity in End-to-End Models: An Opinionated Survey." pith.science (2026). https://pith.science/paper/IMUHCEJ4

@misc{pith2026250604461,
  author       = {Pith},
  title        = {Pith review of: Behavioural vs. Representational Systematicity in End-to-End Models: An Opinionated Survey},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/IMUHCEJ4}},
  note         = {Machine review of arXiv:2506.04461}
}
read the original abstract

A core aspect of compositionality, systematicity is a desirable property in ML models as it enables strong generalization to novel contexts. This has led to numerous studies proposing benchmarks to assess systematic generalization, as well as models and training regimes designed to enhance it. Many of these efforts are framed as addressing the challenge posed by Fodor and Pylyshyn. However, while they argue for systematicity of representations, existing benchmarks and models primarily focus on the systematicity of behaviour. We emphasize the crucial nature of this distinction. Furthermore, building on Hadley's (1994) taxonomy of systematic generalization, we analyze the extent to which behavioural systematicity is tested by key benchmarks in the literature across language and vision. Finally, we highlight ways of assessing systematicity of representations in ML models as practiced in the field of mechanistic interpretability.

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Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.