Out-of-distribution Generalisation is Hard: Evidence from ARC-like Tasks

Conference: NeurIPS 2025 arXiv: 2505.09716 Code: None Area: Other Keywords: OOD generalisation, compositional generalisation, ARC tasks, inductive bias, feature learning

TL;DR

By constructing ARC-like tasks with well-defined OOD metrics, this paper demonstrates that standard neural networks (MLP/CNN/Transformer) fail to achieve compositional OOD generalisation. Moreover, even architectures designed with correct inductive biases that attain near-perfect OOD performance may still learn incorrect compositional features.

Background & Motivation

Out-of-distribution (OOD) generalisation is widely regarded as a hallmark of human and animal intelligence. Achieving OOD generalisation through composition requires a system to: 1. Identify input-output mapping properties that are invariant across environments 2. Transfer them to novel inputs

However, existing research has a critical gap: - Testing on OOD settings alone is insufficient to prove that an algorithm has learned compositional structure - One must additionally verify that the identified features are genuinely compositional - When a system performs well on OOD tests, it remains unclear whether it has truly learned the correct compositional rules

The authors' central argument: validating OOD generalisation requires jointly verifying both performance and feature correctness.

Method

Overall Architecture

1. Design two tasks with clearly defined OOD metrics
2. Evaluate the OOD capabilities of three standard networks (MLP, CNN, Transformer)
3. Design two novel architectures with correct inductive biases
4. Analyse whether feature learning remains correct even when OOD performance is perfect

Key Designs

Task Design: - Inspired by the ARC (Abstraction and Reasoning Corpus) benchmark - Tasks possess decomposable compositional structure - OOD metrics are clearly defined: whether novel combinations of input features are handled correctly

Task 1 — Geometric Transformation Task: - Input: grid patterns with specific geometric properties - Output: patterns after deterministic transformations - OOD setting: the combinations of geometric properties differ between training and test sets - Key property: transformations can be decomposed into independent sub-operations

Task 2 — Colour–Shape Composition Task: - Inputs involve independent variation in colour and shape - Correct compositional generalisation requires learning invariant features for colour and shape separately

Two Novel Architectures: - Architecture A: embeds geometric invariance biases, enabling the network to process transformations along each dimension independently - Architecture B: embeds compositional decomposition biases, forcing the network to factorize the feature space into independent subspaces

Loss & Training

• Standard cross-entropy / MSE loss
• All architectures use identical training data and optimisation strategies
• Train–test splits strictly control the degree of OOD shift

Key Experimental Results

Main Results

OOD generalisation of standard networks:

Network	Task 1 ID Acc.	Task 1 OOD Acc.	Task 2 ID Acc.	Task 2 OOD Acc.
MLP	~100%	~0%	~100%	~0%
CNN	~100%	~0%	~100%	~0%
Transformer	~100%	~0%	~100%	~0%

Novel architectures with correct inductive biases:

Architecture	Task 1 OOD Acc.	Task 2 OOD Acc.	Feature Correctness
Biased Arch. A	~100%	~100%	Partially incorrect
Biased Arch. B	~100%	~100%	Partially incorrect

Ablation Study

Condition	OOD Performance	Correct Compositional Features Learned
No inductive bias	Fails	No
Weak inductive bias	Partial success	Uncertain
Strong inductive bias	Succeeds	Not guaranteed
Perfect inductive bias	Near-perfect	May still be incorrect

Key Findings

1. Standard networks fail comprehensively: MLP, CNN, and Transformer all achieve near-zero OOD accuracy on both tasks.
2. Correct bias ≠ correct features: Even when embedding correct inductive biases yields near-perfect OOD performance, networks may still learn incorrect compositional features.
3. OOD performance ≠ compositional generalisation: High OOD performance does not prove that an algorithm has learned the underlying compositional structure.
4. Necessity of verifying feature correctness: Testing OOD performance alone is insufficient to confirm compositional generalisation capability.

Highlights & Insights

1. Methodological contribution: Proposes a new standard for evaluating compositional generalisation — one must not only measure performance but also verify feature correctness.
2. Counter-intuitive finding: Near-perfect OOD performance can be achieved through "incorrect" means, i.e., without relying on correct compositional features.
3. Implications for ARC: Provides an explanation for why current AI systems perform poorly on ARC tasks — they lack genuine compositional reasoning ability.
4. Theory–practice gap: Inductive biases are necessary but not sufficient, underscoring the importance of understanding what models actually learn.

Limitations & Future Work

1. The designed tasks are relatively simple and limited in complexity compared to real ARC tasks.
2. Only three standard architectures and two custom architectures are evaluated.
3. The verification of feature correctness relies heavily on manual inspection, lacking automated evaluation tools.
4. The compositional generalisation capabilities of larger-scale or pretrained models are not explored.
5. The influence of new paradigms such as in-context learning on OOD generalisation is not considered.

Related Work & Insights

• ARC Challenge: The abstract reasoning benchmark proposed by François Chollet.
• Compositional generalisation: Compositional generalisation benchmarks in semantic parsing, such as SCAN and COGS.
• Systematic generalisation: Lake & Baroni's discussion on systematic generalisation in neural networks.
• Insight: In-depth analysis on simple tasks is often more informative than surface-level testing on complex ones.

Rating

• Novelty: ⭐⭐⭐⭐ (significant methodological contribution)
• Technical depth: ⭐⭐⭐⭐ (rigorous analysis)
• Experimental thoroughness: ⭐⭐⭐ (tasks could be more diverse)
• Value: ⭐⭐⭐ (primarily theoretical insights)

Related Papers

• [NeurIPS 2025] Redundancy-Aware Test-Time Graph Out-of-Distribution Detection
• [NeurIPS 2025] Double Descent Meets Out-of-Distribution Detection: Theoretical Insights and Empirical Analysis
• [NeurIPS 2025] Harnessing Feature Resonance under Arbitrary Target Alignment for Out-of-Distribution Node Detection
• [NeurIPS 2025] Product Distribution Learning with Imperfect Advice
• [NeurIPS 2025] Brain-Like Processing Pathways Form in Models With Heterogeneous Experts