Cited by 233Neural Networks and ApplicationsDomain Adaptation and Few-Shot LearningPsychiatry, Mental Health, Neuroscience

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Human-like systematic generalization through a meta-learning neural network

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Abstract

The power of human language and thought arises from systematic compositionality—the algebraic ability to understand and produce novel combinations from known components. Fodor and Pylyshyn 1 famously argued that artificial neural networks lack this capacity and are therefore not viable models of the mind. Neural networks have advanced considerably in the years since, yet the systematicity challenge persists. Here we successfully address Fodor and Pylyshyn’s challenge by providing evidence that neural networks can achieve human-like systematicity when optimized for their compositional skills. To do so, we introduce the meta-learning for compositionality (MLC) approach for guiding training through a dynamic stream of compositional tasks. To compare humans and machines, we conducted human behavioural experiments using an instruction learning paradigm. After considering seven different models, we found that, in contrast to perfectly systematic but rigid probabilistic symbolic models, and perfectly flexible but unsystematic neural networks, only MLC achieves both the systematicity and flexibility needed for human-like generalization. MLC also advances the compositional skills of machine learning systems in several systematic generalization benchmarks. Our results show how a standard neural network architecture, optimized for its compositional skills, can mimic human systematic generalization in a head-to-head comparison.

Overview

AI snapshot

Written from the paper’s full text.

TL;DR

The paper introduces meta-learning for compositionality (MLC), an optimization procedure that trains a standard transformer over a dynamic stream of few-shot compositional tasks. In head-to-head human experiments and machine-learning benchmarks, MLC achieves human-like systematic generalization and reproduces human-like inductive biases and error patterns, though it still fails on some productivity and structural-generalization challenges.

Key findings

  • On the few-shot instruction-learning task, the most systematic MLC run achieved 100% exact-match accuracy; when sampling, MLC produced systematic outputs at 82.4% versus 80.7% for humans, and handled longer output sequences at 77.8% versus 72.5% for humans.
  • MLC reproduced human-like errors: one-to-one translation errors were 56.3% of MLC errors versus 24.4% for people, and iconic-concatenation errors involving function 3 were 13.8% versus 23.3% for people.
  • In the open-ended task, MLC matched the modal human response in 65.0% of samples; across samples, 66.0% followed one-to-one (62.1% for people), 85.0% followed iconic concatenation (79.3% for people), and 99.0% chose a unique response for each unique command (93.1% for people).
  • On benchmarks, MLC reached error rates of 0.22% on SCAN “add jump,” 0.04% on “around right,” 0.06% on “opposite right,” and 0.87% on COGS lexical generalization; however, it failed SCAN length and three COGS structural splits with 100% error.

Methods

  • Human behavioural experiments were run on Amazon Mechanical Turk using a pseudolanguage instruction-learning paradigm: n = 25 participants completed a few-shot task with 14 study instructions and 10 query instructions, and n = 29 different participants completed an open-ended task with seven unknown instructions.
  • MLC used a standard seq2seq transformer with 3 encoder/decoder layers, 8 attention heads per layer, embeddings of size 128, feedforward hidden size 512, and about 1.4 million parameters; it was meta-trained over episodes generated from randomly generated interpretation grammars, with frozen weights at test.
  • MLC variants included algebraic-only, copy-only, behaviourally informed, and joint training; benchmark experiments used SCAN and COGS with surface-level word-type permutations and a modular procedure for long in-context sequences, scoring exact-match error rates.

Limitations

  • The paper states that MLC does not automatically handle unpractised forms of generalization or concepts outside the meta-learning distribution, fails SCAN length and three COGS structural splits at 100% error, lacks a mechanism for emitting new symbols, and is untested on the full complexity of natural language and other modalities.
  • The paper also states that optimizing over many related grammar-based tasks is not developmentally plausible, and that MLC does not solve every challenge raised by Fodor and Pylyshyn.
  • Evident from the text: the human experiments use modest samples (n = 25 and n = 29) and a pseudolanguage with abstract coloured-circle outputs rather than natural language; some MLC variants are optimized directly on human behavioural data, so human-like error patterns may partly reflect those training targets.

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Figures

Fig. 1 MLC for acquiring compositional skills through a dynamic stream of compositional tasks (episodes). a, During training, episode a presents a neural network with a set of study examples and a query instruction, all provided as a simultaneous input. The study examples demonstrate how to ‘jump twice’, ‘skip’ and so on with both instructions and corresponding outputs provided as words and text-based action symbols (solid arrows guiding the stick figures), respectively. The query instruction involves compositional use of a word (‘skip’) that is presented only in isolation in the study examples, and no intended output is provided. The network produces a query output that is compared (hollow arrows) with a behavioural target. b, Episode b introduces the next word (‘tiptoe’) and the network is asked to use it compositionally (‘tiptoe backwards around a cone’), and so on for many more training episodes. The colours highlight compositional reuse of words. Stick figures were adapted from art created by D. Chappard (OpenClipArt.org).
Fig. 1 MLC for acquiring compositional skills through a dynamic stream of compositional tasks (episodes). a, During training, episode a presents a neural network with a set of study examples and a query instruction, all provided as a simultaneous input. The study examples demonstrate how to ‘jump twice’, ‘skip’ and so on with both instructions and corresponding outputs provided as words and text-based action symbols (solid arrows guiding the stick figures), respectively. The query instruction involves compositional use of a word (‘skip’) that is presented only in isolation in the study examples, and no intended output is provided. The network produces a query output that is compared (hollow arrows) with a behavioural target. b, Episode b introduces the next word (‘tiptoe’) and the network is asked to use it compositionally (‘tiptoe backwards around a cone’), and so on for many more training episodes. The colours highlight compositional reuse of words. Stick figures were adapted from art created by D. Chappard (OpenClipArt.org).CC BY · PubMed Central
Fig. 2 Few-shot instruction-learning task that involves responding to instructions (linguistic strings) by generating sequences of abstract outputs (coloured circles). a,b, Based on the study instructions (a; headings were not provided to the participants), humans and MLC executed query instructions (b; 4 of 10 shown). The four most frequent responses are shown, marked in parentheses with response rates (counts for people and the percentage of samples for MLC). The superscript notes indicate the algebraic answer (asterisks), a one-to-one error (1-to-1) or an iconic concatenation error (IC). The words and colours were randomized for each participant and a canonical assignment is therefore shown here. A black circle indicates a colour that was unused in the study set.
Fig. 2 Few-shot instruction-learning task that involves responding to instructions (linguistic strings) by generating sequences of abstract outputs (coloured circles). a,b, Based on the study instructions (a; headings were not provided to the participants), humans and MLC executed query instructions (b; 4 of 10 shown). The four most frequent responses are shown, marked in parentheses with response rates (counts for people and the percentage of samples for MLC). The superscript notes indicate the algebraic answer (asterisks), a one-to-one error (1-to-1) or an iconic concatenation error (IC). The words and colours were randomized for each participant and a canonical assignment is therefore shown here. A black circle indicates a colour that was unused in the study set.CC BY · PubMed Central
Fig. 3 Open-ended instruction task. a,b, The participants produced responses (sequences of coloured circles) to the queries (linguistic strings) without seeing any study examples. Each column shows a different word assignment and a different response, either from a different participant (a) or MLC sample (b). The leftmost pattern (in both a and b) was the most common output for both people and MLC, translating the queries in a one-to-one (1-to-1) and left-to-right manner consistent with iconic concatenation (IC). The rightmost patterns (in both a and b) are less clearly structured but still generate a unique meaning for each instruction (mutual exclusivity (ME)).
Fig. 3 Open-ended instruction task. a,b, The participants produced responses (sequences of coloured circles) to the queries (linguistic strings) without seeing any study examples. Each column shows a different word assignment and a different response, either from a different participant (a) or MLC sample (b). The leftmost pattern (in both a and b) was the most common output for both people and MLC, translating the queries in a one-to-one (1-to-1) and left-to-right manner consistent with iconic concatenation (IC). The rightmost patterns (in both a and b) are less clearly structured but still generate a unique meaning for each instruction (mutual exclusivity (ME)).CC BY · PubMed Central
Fig. 4 MLC architecture. A standard transformer encoder (bottom) processes the query input along with a set of study examples (input/output pairs; examples are delimited by a vertical line (∣) token). The standard decoder (top) receives the encoder’s messages and produces an output sequence in response. After optimization on episodes generated from various grammars, the transformer performs novel tasks using frozen weights. Each box is an embedding (vector); input embeddings are light blue (latent are dark).
Fig. 4 MLC architecture. A standard transformer encoder (bottom) processes the query input along with a set of study examples (input/output pairs; examples are delimited by a vertical line (∣) token). The standard decoder (top) receives the encoder’s messages and produces an output sequence in response. After optimization on episodes generated from various grammars, the transformer performs novel tasks using frozen weights. Each box is an embedding (vector); input embeddings are light blue (latent are dark).CC BY · PubMed Central
Extended Data Fig. 1 Few-shot instruction learning task with full set of queries. Based on the study instructions (A; headings were not provided to participants), humans and the MLC model executed 10 query instructions by generating coloured circles from a fixed inventory (B; headings were not provided to participants). The percent of participants who produced each sequence exactly as prescribed algebraically is shown. Similarly, the percent of samples from MLC that match the prescribed sequence is shown in parentheses, which correlates with the human values (Pearson’s r = 0.788, p = 0.031 via permutation test, two-tailed, n = 10 items). The words and colours were randomized for each participant.
Extended Data Fig. 1 Few-shot instruction learning task with full set of queries. Based on the study instructions (A; headings were not provided to participants), humans and the MLC model executed 10 query instructions by generating coloured circles from a fixed inventory (B; headings were not provided to participants). The percent of participants who produced each sequence exactly as prescribed algebraically is shown. Similarly, the percent of samples from MLC that match the prescribed sequence is shown in parentheses, which correlates with the human values (Pearson’s r = 0.788, p = 0.031 via permutation test, two-tailed, n = 10 items). The words and colours were randomized for each participant.CC BY · PubMed Central
Extended Data Fig. 2 The gold interpretation grammar that defines the human instruction learning task. The double brackets (⟦⟧) denote the interpretation function for translating linguistic instructions into sequences of abstract outputs (colour circles). Each human participant received a different permutation of words and colours. Symbols xi and ui denote variables: xi applies to arbitrary non-empty strings, while ui applies only to ‘dax’, ‘wif’, ‘lug’, and ‘zup’.
Extended Data Fig. 2 The gold interpretation grammar that defines the human instruction learning task. The double brackets (⟦⟧) denote the interpretation function for translating linguistic instructions into sequences of abstract outputs (colour circles). Each human participant received a different permutation of words and colours. Symbols xi and ui denote variables: xi applies to arbitrary non-empty strings, while ui applies only to ‘dax’, ‘wif’, ‘lug’, and ‘zup’.CC BY · PubMed Central
Extended Data Fig. 3 Using the gold interpretation grammar for processing ‘zup blicket wif kiki dax fep’. Each step is annotated with the next re-write rules to be applied, and how many times (e.g., 3 × , since some steps have multiple parallel applications). A rule’s condition is met if and only if it matches the entire string inside the brackets (⟦ ⟧); for instance, only the ‘kiki’ rule applies on the first step because its condition matches two arbitrary non-empty sequences on either side of ‘kiki,’ thus being able to encompass the entire input.
Extended Data Fig. 3 Using the gold interpretation grammar for processing ‘zup blicket wif kiki dax fep’. Each step is annotated with the next re-write rules to be applied, and how many times (e.g., 3 × , since some steps have multiple parallel applications). A rule’s condition is met if and only if it matches the entire string inside the brackets (⟦ ⟧); for instance, only the ‘kiki’ rule applies on the first step because its condition matches two arbitrary non-empty sequences on either side of ‘kiki,’ thus being able to encompass the entire input.CC BY · PubMed Central
Extended Data Fig. 4 Example meta-learning episode and how it is processed by different MLC variants. The interpretation grammar defines the episode but is not observed directly and must be inferred implicitly. Set 1 has 14 input/output examples consistent with the grammar, used as Study examples for all MLC variants. Set 2 has 10 examples, used as Query examples for most MLC variants (except copy only). Pseudocode for the bias-based transformation process is shown here for the instruction ‘tufa lug fep’. This transformation is applied to the query outputs before MLC and MLC (joint) process them. Here, flip (p) is a coin flip that returns True with probability p.
Extended Data Fig. 4 Example meta-learning episode and how it is processed by different MLC variants. The interpretation grammar defines the episode but is not observed directly and must be inferred implicitly. Set 1 has 14 input/output examples consistent with the grammar, used as Study examples for all MLC variants. Set 2 has 10 examples, used as Query examples for most MLC variants (except copy only). Pseudocode for the bias-based transformation process is shown here for the instruction ‘tufa lug fep’. This transformation is applied to the query outputs before MLC and MLC (joint) process them. Here, flip (p) is a coin flip that returns True with probability p.CC BY · PubMed Central
Extended Data Fig. 5 Human responses for the (A) few-shot learning task and (B) open-ended task that most favour MLC (joint) compared to a MLC model optimized for individual tasks only. Panel (A) shows the average log-likelihood advantage for MLC (joint) across five patterns (that is, ll(MLC (joint)) - ll(MLC)), with the algebraic target shown here only as a reference. A black circle indicates a colour that was unused in the study set. Panel (B) shows three participant responses.
Extended Data Fig. 5 Human responses for the (A) few-shot learning task and (B) open-ended task that most favour MLC (joint) compared to a MLC model optimized for individual tasks only. Panel (A) shows the average log-likelihood advantage for MLC (joint) across five patterns (that is, ll(MLC (joint)) - ll(MLC)), with the algebraic target shown here only as a reference. A black circle indicates a colour that was unused in the study set. Panel (B) shows three participant responses.CC BY · PubMed Central
Extended Data Fig. 6 Handling long in-context sequences with a MLC transformer. The query input sequence (shown as ‘jump twice after run twice’) is copied and concatenated to each of the m study examples, leading to m separate source sequences (3 shown here). A shared standard transformer encoder (bottom) processes each source sequence to produce latent (contextual) embeddings. The contextual embeddings are marked with the index of their study example, combined with a set union to form a single set of source messages, and passed to the decoder. The standard decoder (top) receives this message from the encoder, and then produces the output sequence for the query. Each box is an embedding (vector); input embeddings are light blue and latent embeddings are dark blue.
Extended Data Fig. 6 Handling long in-context sequences with a MLC transformer. The query input sequence (shown as ‘jump twice after run twice’) is copied and concatenated to each of the m study examples, leading to m separate source sequences (3 shown here). A shared standard transformer encoder (bottom) processes each source sequence to produce latent (contextual) embeddings. The contextual embeddings are marked with the index of their study example, combined with a set union to form a single set of source messages, and passed to the decoder. The standard decoder (top) receives this message from the encoder, and then produces the output sequence for the query. Each box is an embedding (vector); input embeddings are light blue and latent embeddings are dark blue.CC BY · PubMed Central
Extended Data Fig. 7 Example SCAN meta-training (top) and test (bottom) episodes for the ‘add jump’ split. The word and action meanings are changing across the meta-training episodes (‘look’, ‘walk’, etc.) and must be inferred from the study examples. During the test episode, the meanings are fixed to the original SCAN forms. Here, the latter probes a compositional use of ‘jump’.
Extended Data Fig. 7 Example SCAN meta-training (top) and test (bottom) episodes for the ‘add jump’ split. The word and action meanings are changing across the meta-training episodes (‘look’, ‘walk’, etc.) and must be inferred from the study examples. During the test episode, the meanings are fixed to the original SCAN forms. Here, the latter probes a compositional use of ‘jump’.CC BY · PubMed Central
Extended Data Fig. 8 Example COGS meta-training (top) and test (bottom) episodes. Word meanings are changing across the meta-training episodes (here, ‘driver’ means ‘PILLOW’, ‘shoebox’ means ‘SPEAKER’ etc.) and must be inferred from the study examples. The meanings are fixed to the original forms during the test episode. This test episode probes the understanding of ‘Paula’ (proper noun), which just occurs in one of COGS’s original training patterns.
Extended Data Fig. 8 Example COGS meta-training (top) and test (bottom) episodes. Word meanings are changing across the meta-training episodes (here, ‘driver’ means ‘PILLOW’, ‘shoebox’ means ‘SPEAKER’ etc.) and must be inferred from the study examples. The meanings are fixed to the original forms during the test episode. This test episode probes the understanding of ‘Paula’ (proper noun), which just occurs in one of COGS’s original training patterns.CC BY · PubMed Central

Verification

Claims the paper makes

39 Own result · 26 Own method · 13 No basis given · 11 Own interpretation · 5 Supported · 4 Partly supported · 4 Sources not found · 4 No full text of the sources · 3 Not checked yet · 2 Supported so far · accuracy not yet measured

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  • Probably not a substantial claim. 43
  • It may state two separate claims as one. 38
  • The quote only partly states this claim. 1
65 of 65
  • The paper relies on this without support.

    The algebraic interpretation grammar provides the correct normative standard for the few-shot instruction-learning task.

    “The study instructions were consistent with an underlying interpretation grammar, which derives outputs from inputs through a set of compositional rewrite rules (see the ‘Interpretation grammars’ section of the Methods).”
  • The paper relies on this without support.

    Human participants recruited via Amazon Mechanical Turk are representative of the broader human population for these compositional skills.

    “All experiments were run on Amazon Mechanical Turk, and detailed procedures are described in the ‘Behavioural methods: few-shot learning task’ and ‘Behavioural methods: open-ended task’ sections of the Methods.”
  • The authors state this as an assumption.

    Broad lexical classes (common nouns, proper nouns, dative verbs, infinitive verbs) are assumed.

    “Importantly, although the broad classes are assumed and could plausibly arise through simple distributional learning68,69, the correspondence between input and output word types is unknown and not used.”
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Citations

Cites

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Research works printed but not linked: 21

  1. Marcus, G. F. The Algebraic Mind: Integrating Connectionism and Cognitive Science (MIT Press, 2003).
  2. Hill, F. et al. Environmental drivers of systematicity and generalisation in a situated agent. In Proc. International Conference on Learning Representations (ICLR) (2020).
  3. Lake, B. M. & Baroni, M. Generalization without systematicity: on the compositional skills of sequence-to-sequence recurrent networks. In Proc. International Conference on Machine Learning (ICML) (eds. Dy, J. & Krause, A.) 2873–2882 (PMLR, 2018).
  4. Ettinger, A., Elgohary, A., Phillips, C. & Resnik, P. Assessing composition in sentence vector representations. In Proc. 7th International Conference on Computational Linguistics, (COLING 2018) 1790–1801 (Association for Computational Linguistics, 2018).
  5. Stuhlmuller, A., Tenenbaum, J. B. & Goodman, N. D. Learning structured generative concepts. In Proc. Thirty-Second Annual Conference of the Cognitive Science Society, 2296–2301 (2010).
  6. Sutskever, I., Vinyals, O. & Le, Q. V. Sequence to sequence learning with neural networks. In Proc. Advances in Neural Information Processing Systems (eds Ghahramani, Z. et al.) (Curran Associates, 2014).
  7. Lake, B. M. Compositional generalization through meta sequence-to-sequence learning. In Proc. Advances in Neural Information Processing Systems (NeurIPS) 32 (eds Wallach, H. et al.) 9791–9801 (Curran Associates, 2019).
  8. Myung, J. I. & Pitt, M. A. in Stevens’ Handbook of Experimental Psychology and Cognitive Neuroscience (ed. Wixted, J. T.) 85–118 (John Wiley & Sons, 2018).
  9. Chen, X., Liang, C., Yu, A. W., Song, D. & Zhou, D. Compositional generalization via neural-symbolic stack machines. In Proc. Advances in Neural Information Processing Systems 33 (eds Larochelle, H. et al.) 1690–1701 (Curran Associates, 2020).
  10. Russin, J., Jo, J., O’Reilly, R. C. & Bengio, Y. Systematicity in a recurrent neural network by factorizing syntax and semantics. In Proc. 42nd Annual Meeting of the Cognitive Science Society (eds Denison, S. et al.) (Cognitive Science Society. 2020).
  11. Nye, M. I., Solar-Lezama, A., Tenenbaum, J. B. & Lake, B. M. Learning compositional rules via neural program synthesis. In Proc. Advances in Neural Information Processing Systems (NeurIPS) 33 (eds Larochelle, H. et al.) (Curran Associates, 2020).
  12. Singh, G., Deng, F. & Ahn, S. Illiterate DALL-E learns to compose. In Proc. ICLR https://openreview.net/group?id=ICLR.cc/2022/Conference (2022).
  13. Gandhi, K. & Lake, B. M. Mutual exclusivity as a challenge for deep neural networks. In Proc. Advances in Neural Information Processing Systems (NeurIPS) 33 (eds Larochelle, H. et al.) 14182–14192 (Curran Associates, 2020).
  14. Grant, E., Finn, C., Levine, S., Darrell, T. & Griffiths, T. Recasting gradient-based meta-learning as hierarchical bayes. In Proc. International Conference on Learning Representations (ICLR) (2019).
  15. Grant, E., Peterson, J. C. & Griffiths, T. Learning deep taxonomic priors for concept learning from few positive examples. In Proc. Annual Meeting of the Cognitive Science Society (eds Goel, A. K. et al.) 1865–1870 (Cognitive Science Society, 2019).
  16. Santoro, A., Bartunov, S., Botvinick, M., Wierstra, D. & Lillicrap, T. Meta-learning with memory-augmented neural networks. In Proc. International Conference on Machine Learning (ICML) 1842–1850 (PMLR, 2016).
  17. McCoy, R. T., Grant, E., Smolensky, P., Griffiths, T. L. & Linzen, T. Universal linguistic inductive biases via meta-learning. In Proc. 42nd Annual Conference of the Cognitive Science Society (eds Denison, S. et al.) (Cognitive Science Society, 2020).
  18. Vinyals, O., Fortunato, M. & Jaitly, N. Pointer networks. In Proc. Advances in Neural Information Processing Systems (eds Cortes, C. et al.) (Curran Associates, 2015).
  19. Radford, A., Narasimhan, K. R., Salimans, T. & Sutskever, I. Improving language understanding by generative pre-training. Preprint at https://openai.com/research/language-unsupervised (2018).
  20. Mitchell, E., Finn, C. & Manning, C. Challenges of acquiring compositional inductive biases via meta-learning. In Proc. AAAI Workshop on Meta-Learning and MetaDL Challenge 138–148 (2021).
  21. Lake, B. M., Linzen, T. & Baroni, M. Human few-shot learning of compositional instructions. In Proc. 41st Annual Conference of the Cognitive Science Society (eds Goel, A. K. et al.) 611–617 (Cognitive Science Society, 2019).

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Metadata

Authors
Lake, B. M., & Baroni, M.
Affiliations
  • New York University (US)
  • Institució Catalana de Recerca i Estudis Avançats (ES)
Corresponding author
Lake, Brenden M.
Venue
Nature
Published
2023-10-25
Volume
623
Issue
7985
Pages
115-121
ISSN
  • 0028-0836 (ISSN-L)
  • 1476-4687
OpenAlex
W4387949708
Cited by
230
References
48
Citations by year
2026: 66 · 2025: 87 · 2024: 71 · 2023: 6
FWCI
16.38
Type
journal article
Language
en
Open access
Locations
  • Nature (publishedVersion, cc-by)
  • PubMed Central (publishedVersion, cc-by)
  • PubMed (publishedVersion)
  • RePEc: Research Papers in Economics (submittedVersion)
  • Repositori digital de la UPF (Universitat Pompeu Fabra) (submittedVersion, cc-by)
Topics
  • Physical Sciences › Computer Science › Artificial Intelligence › Neural Networks and Applications
  • Physical Sciences › Computer Science › Artificial Intelligence › Domain Adaptation and Few-Shot Learning
  • Physical Sciences › Computer Science › Artificial Intelligence › Psychiatry, Mental Health, Neuroscience
Keywords
systematic generalization, compositional generalization, meta-learning, human-machine comparison
MeSH terms
Machine Learning, Humans, Language, Verbal Behavior, Neural Networks, Computer

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