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DARR: A Dual-Branch Arithmetic Regression Reasoning Framework for Solving Machine Number Reasoning
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Builds a Machine Number Reasoning (MNR) dataset and proposes DARR, a dual-branch regression network (intra-image and cross-image arithmetic regression with gates) that outperforms prior abstract visual reasoning models on MNR and RAVEN benchmarks.
Problem
Abstract visual reasoning over number sense is under-studied: models must infer the arithmetic expression and number order shared by context images and pick the matching candidate, which brute-force search does not capture well.
Approach
Dual-branch network: an Intra-Image Arithmetic Regression Reasoning module regresses a held-out patch from the others over all patch permutations, with an Order Gate choosing the correct number order; a Cross-Image module regresses the candidate's features from context images using a '3-to-1' regressor and gated '2-to-1' regressors fused by Selection and Gated Fusion gates.
Key results
- DARR achieves 55.0% average accuracy on the MNR dataset under Protocol I, versus 49.0% for the second-best PredRNet.
- DARR reaches 99.0%, 99.4% and 99.2% on RAVEN, I-RAVEN and RAVEN-FAIR respectively (average 99.2%).
- Plugging DARR in as the reasoner improves every compared perception backbone on MNR, e.g. PredRNet's perception rises from 49.0 to 53.3.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Replace PredRNet with DARR | MNR · MNR Protocol I | accuracy: 49.0 -> 55.0 | Helped |
| Replace PredRNet with DARR | MNR · MNR Protocol II | accuracy: 48.1 -> 53.8 | Helped |
| Use DARR instead of PredRNet | MNR with reduced training data · MNR, 10% training data | accuracy: 29.8 -> 31.0 | Helped |
| Use DARR instead of PredRNet | MNR with reduced training data · MNR, 20% training data | accuracy: 31.7 -> 32.7 | Helped |
| Use DARR instead of PredRNet | MNR with reduced training data · MNR, 50% training data | accuracy: 44.2 -> 51.4 | Helped |
| Use DARR instead of PredRNet | RAVEN benchmarks · RAVEN | accuracy: 95.8 -> 99.0 | Helped |
| Use DARR instead of PredRNet | RAVEN benchmarks · I-RAVEN | accuracy: 96.5 -> 99.4 | Helped |
| Use DARR instead of PredRNet | RAVEN benchmarks · RAVEN-FAIR | accuracy: 97.1 -> 99.2 | Helped |
| Add IIARR to the baseline (ablation) | MNR baseline · MNR | accuracy: 48.7 -> 53.4 | Helped |
| Add CIARR to the baseline (ablation) | MNR baseline · MNR | accuracy: 48.7 -> 53.0 | Helped |
| Add both IIARR and CIARR (ablation) | MNR baseline · MNR | accuracy: 48.7 -> 55.0 | Helped |
| Add the Order Gate (ablation) | DARR IIARR · MNR | accuracy: 52.4 -> 53.4 | Helped |
Surprising findings
- WReN and SCL perform near random guess (about 12.5%) on MNR.
- Performance under the out-of-distribution Protocol II is lower on average than under Protocol I for all models.
Limitations
- Performance on MNR remains around 55%, indicating the task is far from solved.
- Accuracy drops sharply with limited training data (31.0% at 10% of training data).
Experimental setup
Datasets: MNR RAVEN I-RAVEN RAVEN-FAIR
Benchmarks: MNR RAVEN I-RAVEN RAVEN-FAIR
Metrics: accuracy
Baselines: WReN SCL STSN RelBase MRNet SCAR PredRNet
Builds on: PredRNet RAVEN And-Or Graph
Closest papers by meaning
- DynaMath: A Dynamic Visual Benchmark for Evaluating Mathematical Reasoning Robustness of Vision Language Models (ICLR 2025 · similarity 0.86)
- MathCoder2: Better Math Reasoning from Continued Pretraining on Model-translated Mathematical Code (ICLR 2025 · similarity 0.86)
- We-Math 2.0: A Versatile MathBook System for Incentivizing Visual Mathematical Reasoning (ICLR 2026 · similarity 0.85)
- MV-MATH: Evaluating Multimodal Math Reasoning in Multi-Visual Contexts (CVPR 2025 · similarity 0.85)
- Benchmarking Multimodal Mathematical Reasoning with Explicit Visual Dependency (NeurIPS 2026 · similarity 0.85)
- MINT-CoT: Enabling Interleaved Visual Tokens in Mathematical Chain-of-Thought Reasoning (NeurIPS 2025 · similarity 0.85)
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