Systematic generalization

Overview

Systematic generalization is the ability to apply known parts in combinations that were not seen together during training. The survey frames its absence as the binding problem: a network cannot route information that is spread over many units into separate, symbol-like entities that can be reused elsewhere 2012.05208 §2.3. The authors call this the root cause of weak systematic generalization 2012.05208 §1 2012.05208 §2.3. The claim is argued rather than tested in the paper 2012.05208 §7.

Every mechanism in the survey shares one requirement: object representations must stay separate from each other and use a common format, so that they can be recombined without losing their identity 2012.05208 §3.1. The mechanisms differ in how they achieve this.

A second position paper frames the same goal as a question of inductive biases. It argues that data, compute and architecture alone are not enough for out-of-distribution and systematic generalization 2011.15091 §1. It also argues that a test set drawn from the training distribution cannot reveal overfitting to that distribution, so evaluation must change as well 2011.15091 §2.

Two papers measure the symptom instead of proposing a mechanism. A benchmark tests whether vision-language models retrieve the right caption for a combination of objects, attributes and relations, and finds lower retrieval accuracy on compounds absent from the training captions 2212.07796 §5.1. A dataset paper on knowledge-base question answering defines three levels of test questions, by whether the schema items in each query were seen in training 2011.07743 §2.2. Both results are observational and author-reported, not a test of the binding account.

Variants

The first five variants are mechanisms from the binding survey, so each links the same card. The survey reviews them as options, not as tested methods. The sixth is a set of design biases from the second position paper, also untested. The last two are measurement designs, from a benchmark paper and a dataset paper.

Slot-based object representations

A fixed set of slots, each holding the features of one object. The survey treats slots as the simplest option 2012.05208 §3.3.1 2012.05208 §3.4. Card: On the Binding Problem in Artificial Neural Networks.

Distributed codes with separation

Keeps distributed neural codes and adds a mechanism that keeps objects apart 2012.05208 §3.3.2. The survey judges it harder to build than slots but more capable 2012.05208 §3.4. Card: On the Binding Problem in Artificial Neural Networks.

Tensor product representations

A binding scheme based on tensor products, reviewed as a more structured alternative to slots 2012.05208 §3.3.3. The survey places it with distributed codes in terms of build effort and expressive power 2012.05208 §3.4. Card: On the Binding Problem in Artificial Neural Networks.

Attractor dynamics

Uses attractor states to represent inputs that admit several stable interpretations 2012.05208 §3.3.4. Card: On the Binding Problem in Artificial Neural Networks.

Graph neural networks for relational composition

Graph neural networks operate on object representations and their relations. The survey calls them a promising route to relational responding 2012.05208 §5.3.1 2012.05208 §5.4. Card: On the Binding Problem in Artificial Neural Networks.

Verbalisable causal variables with sparse changes

Not an architecture. The paper proposes inductive biases taken from high-level, conscious processing. High-level variables should be verbalisable and often causal 2011.15091 §3.4 2011.15091 §3.5. Changes should be sparse and local, touching one or a few variables or mechanisms 2011.15091 §3.6. The joint distribution over those variables should be a sparse factor graph 2011.15091 §3.8, and knowledge should be stored as reusable schemas whose arguments are bound to instances 2011.15091 §3.9. Stable knowledge is learned slowly and shared, while volatile knowledge is learned fast 2011.15091 §3.7. The paper reads soft attention as a soft form of variable binding, and says discrete typed arguments and hard choices are missing 2011.15091 §3.2. It gives no algorithm and no experiments 2011.15091 §1. Card: Inductive Biases for Deep Learning of Higher-Level Cognition.

Seen versus unseen compound splits for vision-language models

Not a mechanism. CREPE builds a zero-shot image-to-text retrieval test on Visual Genome scene graphs. Atoms are objects, relations or attributes, and compounds are attribute-object or object-relation-object pairs 2212.07796 §3.1. Each test caption is placed in a split by whether its atoms and compounds occur in the training captions of CC-12M, YFCC-15M or LAION-400M 2212.07796 §3.2. Hard negatives either replace one atom or join two single-compound foils, so a model that matches loose word patterns is penalised 2212.07796 §4.1. A second axis varies caption complexity from 4 to 12 atoms 2212.07796 §3.3. Card: CREPE: Can Vision-Language Foundation Models Reason Compositionally?.

Three levels of new questions for knowledge-base question answering

Not a mechanism. GrailQA groups each question by the schema items in its logical form: relations, classes and functions 2011.07743 §2.2. A question is i.i.d. if every item occurs in training and the test questions follow the training distribution. It is compositional if every item occurs in training but this combination does not. It is zero-shot if at least one item never occurs in training 2011.07743 §2.2. The dataset has 64,331 questions. Its validation and test sets are half zero-shot, a quarter compositional and a quarter i.i.d. 2011.07743 §5.1. The authors' BERT-based ranker scores 67.0 F1 on i.i.d., 53.9 on compositional and 55.7 on zero-shot test questions 2011.07743 tab. 3. Card: Beyond I.I.D.: Three Levels of Generalization for Question Answering on Knowledge Bases.

When to use which

The survey and the causal position paper give no measured comparison between their proposals. The guidance for those rows repeats their stated judgments and is not benchmark evidence. The CREPE and GrailQA rows rest on their author-reported numbers only.

Implementation sketch

The survey gives no implementation. It does name held-out combinations of features and of parts as the way to measure separation and composition 2012.05208 §3.4 2012.05208 §5.4. The sketch below turns that into a split. It is illustrative and not from the paper.

# Illustrative only: a split that holds out whole pairings of parts
# Method named in [arxiv:2012.05208 §3.4] and [arxiv:2012.05208 §5.4]
def held_out_combination_split(examples, parts_of, test_fraction):
    # Describe each example by the set of parts it contains
    pairings = {frozenset(parts_of(ex)) for ex in examples}
    # Choose whole pairings for test, so no test pairing is seen in training
    test_pairings = sample(pairings, test_fraction)
    train = [ex for ex in examples
             if frozenset(parts_of(ex)) not in test_pairings]
    test = [ex for ex in examples
            if frozenset(parts_of(ex)) in test_pairings]
    # Every test part must still occur in training, so only pairings are new
    train_parts = {p for ex in train for p in parts_of(ex)}
    assert all(p in train_parts for ex in test for p in parts_of(ex))
    return train, test

CREPE uses a related but different rule. It holds out compounds that never occur in a named training caption set, and it also separates atoms that never occur there 2212.07796 §3.2. Its split is therefore defined against a training corpus, not against pairings within one dataset.

GrailQA labels each test question by its schema items instead. The zero-shot level is any question with an item never seen in training. The compositional level needs every item seen, plus the combination unseen 2011.07743 §2.2.

Contradictions

Tension, not a test. The survey lists disentanglement among the desiderata for object representations: factors of variation should map to features in a local, independent way 2012.05208 §3.1.3. The causal position paper rejects the assumption, common in disentangling work, that high-level variables are marginally independent, and asks instead for a sparse joint structure 2011.15091 §3.8. Neither paper tests the other's proposal.

Tension, not a test. GrailQA reports that its BERT encoder matters most on compositional and zero-shot questions 2011.07743 §5.3. CREPE reports that the models trained on the largest corpus still lose the most recall on unseen compounds, for atom-level foils 2212.07796 app. B.1. The tasks, metrics and models differ, so the two results are not compared.

Otherwise none directly. The sources do not test the same claim. The survey argues that scaling alone will not suffice 2012.05208 §7, and the causal paper argues that data, compute and architecture are not enough without further inductive biases 2011.15091 §1. Both are argued, not measured. CREPE reports that the LAION-400M models score highest in absolute recall on the combined seen-compound set and still lose recall on unseen compounds 2212.07796 app. B.1. All three facts are reported as they stand. None of the sources settles another.

Papers

• On the Binding Problem in Artificial Neural Networks: a position survey that splits the binding problem into representation, segregation and composition, and reviews mechanisms for each.
• Inductive Biases for Deep Learning of Higher-Level Cognition: a position paper that proposes inductive biases from high-level cognition for out-of-distribution and systematic generalization. It gives no experiments.
• CREPE: Can Vision-Language Foundation Models Reason Compositionally?: a retrieval benchmark that splits test captions into seen and unseen compounds and varies caption complexity.
• Beyond I.I.D.: Three Levels of Generalization for Question Answering on Knowledge Bases: a dataset and semantic parser that tests knowledge-base questions at i.i.d., compositional and zero-shot levels.