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Towards Generative Abstract Reasoning: Completing Raven’s Progressive Matrix via Rule Abstraction and Selection
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Proposes RAISE, a conditional deep latent variable model that abstracts atomic rules into a shared global knowledge set and selects one per latent concept to generate RPM answers at bottom-right and arbitrary positions.
Problem
Generative answer prediction on realistic Raven's Progressive Matrices (discrete attributes and rules, RAVEN/I-RAVEN), where existing solvers either select answers from candidates, rely on artificial priors, or cannot generate answers at arbitrary positions.
Approach
A DLVM encodes image attributes as independent latent concepts and learns a global set of K atomic rules (learnable convolutional rule operators); for each concept it selects one atomic rule via a categorical latent variable inferred from row/column representations, then executes it to predict target latent concepts, trained with an ELBO plus rule-annotation supervision and no candidate sets.
Key results
- RAISE reaches 90.0% average bottom-right selection accuracy on RAVEN and 92.1% on I-RAVEN, the best among compared generative solvers including PrAE (80.0/85.7) and ALANS (54.3/62.8).
- On the Center-Held-Out OOD split RAISE gets 99.2% versus 99.8% for PrAE, and on O-IC-Held-Out it gets 56.1% versus 40.5% for PrAE.
- On 2x2Grid, RAISE (68.2/71.3) trails PrAE (82.0/84.5), a noted weakness on grid configurations with attribute noise.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use RAISE instead of PrAE | Bottom-right answer selection · RAVEN/I-RAVEN average | selection accuracy (%): 80.0/85.7 -> 90.0/92.1 | Helped |
| Use RAISE instead of PrAE | Bottom-right answer selection · RAVEN/I-RAVEN 2×2Grid | selection accuracy (%): 82.0/84.5 -> 68.2/71.3 | Hurt |
| Use RAISE instead of PrAE | Bottom-right answer selection · RAVEN/I-RAVEN 3×3Grid | selection accuracy (%): 23.2/45.1 -> 77.7/78.7 | Helped |
| Use RAISE instead of PrAE | Held-out configuration evaluation · Center-Held-Out | selection accuracy (%): 99.8 -> 99.2 | Hurt |
| Use RAISE instead of PrAE | Held-out configuration evaluation · O-IC-Held-Out | selection accuracy (%): 40.5 -> 56.1 | Helped |
Surprising findings
- Grid-shaped configurations with attribute noise substantially degrade generative solvers, including RAISE and Transformer; removing object-attribute noise helps RAISE reach high accuracy with only 20% rule annotations.
Limitations
- Performance drops on 2x2Grid and 3x3Grid due to attribute noise in object grids.
- Candidate-free training may be weaker under noise; the authors leave systematic study of noise to future work.
- Non-grid configurations rely on partial rule annotations (5% to 20%) for semi-supervised training.
Experimental setup
Datasets: RAVEN I-RAVEN
Benchmarks: RAVEN I-RAVEN
Metrics: selection accuracy
Baselines: GCA ALANS PrAE Transformer ANP LGPP CLAP
Builds on: variational autoencoder LGPP CLAP ALANS PrAE
Closest papers by meaning
- Stratified Rule-Aware Network for Abstract Visual Reasoning (AAAI 2021 · similarity 0.92)
- Raven’s Progressive Matrices Completion with Latent Gaussian Process Priors (AAAI 2021 · similarity 0.91)
- GenVP: Generating Visual Puzzles with Contrastive Hierarchical VAEs (ICLR 2025 · similarity 0.88)
- PotARCin: Multi-Dimensional Evaluation of Skill Acquisition in Abstract Reasoning Tasks (NeurIPS 2026 · similarity 0.86)
- StemBind: When MLLMs Get Lost Between Rules and Instances in Abstract Visual Reasoning (NeurIPS 2026 · similarity 0.86)
- SLVR: Structured Latent Visual Reasoning via Human-like Reasoning Flows (NeurIPS 2026 · similarity 0.86)
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