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On the Markov Property of Neural Algorithmic Reasoning: Analyses and Methods
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Proposes ForgetNet, which removes historical hidden-state embeddings from the CLRS-30 encoder-processor-decoder to match the Markov nature of algorithmic execution, and G-ForgetNet, which adds a learned sigmoid gate on historical embeddings with an L2 penalty to ease early training.
Problem
Neural algorithmic reasoning models on CLRS-30 feed historical processor embeddings into each execution step, which conflicts with the Markov nature of algorithmic execution and can hurt out-of-distribution generalization.
Approach
Remove the recurrent use of previous-step hidden states so the processor sees only the current encoded state (ForgetNet), then use a learnable, L2-penalized gate on historical embeddings (G-ForgetNet) to keep useful pathways early in training while converging toward Markov behavior.
Key results
- G-ForgetNet reaches 82.89% overall average OOD micro-F1 on CLRS-30 versus 75.98% for Triplet-GMPNN and 38.03% for Memnet.
- G-ForgetNet outperforms the baseline on all 30 algorithms, and ForgetNet beats the baseline on 23/30 tasks.
- G-ForgetNet scores above 99% on 9/30 algorithms versus 1/30 for the prior best.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Replace Triplet-GMPNN with G-ForgetNet | CLRS-30 OOD evaluation across all 30 algorithms · CLRS-30 OOD overall average | micro-F1: 75.98% to 82.89% | Helped |
| Remove historical embeddings | Baseline neural algorithm learner · CLRS-30 OOD across algorithm tasks | micro-F1 | Mixed |
| Add gated historical embeddings with gate-magnitude regularization | ForgetNet-style neural algorithm learner · CLRS-30 OOD across algorithm tasks | micro-F1: 78.98% to 82.89% | Helped |
| Add gated historical embeddings with gate-magnitude regularization | Baseline neural algorithm learner · CLRS-30 OOD across algorithm tasks | micro-F1 | Helped |
| Remove historical embeddings | Baseline neural algorithm learner · CLRS-30 OOD: Floyd-Warshall | micro-F1: 53.00% to 38.14% | Hurt |
| Add gated historical embeddings with gate-magnitude regularization | Baseline neural algorithm learner · CLRS-30 OOD: Floyd-Warshall | micro-F1: 53.00% to 56.32% | Helped |
| Add gated historical embeddings with gate-magnitude regularization | Baseline neural algorithm learner · CLRS-30 OOD: Naïve String Matcher | micro-F1: 80.32% to 97.02% | Helped |
| Remove the gate-magnitude loss penalty (ablation) | G-ForgetNet · CLRS-30 OOD overall average | micro-F1: 82.88% to 79.31% | Hurt |
| Remove the gate-magnitude loss penalty (ablation) | G-ForgetNet · CLRS-30 OOD across algorithm tasks | micro-F1: 28/30 algorithms | Mixed |
| Remove historical embeddings | Baseline learner in the multi-task setup · CLRS-30 multi-task OOD | micro-F1: 20/30 algorithms | Mixed |
| Add the gate-magnitude penalty (ablation) | G-ForgetNet · CLRS-30 OOD: Activity Selector | micro-F1: 96.76% to 99.03% | Helped |
Surprising findings
- ForgetNet underperforms the baseline on several tasks such as Floyd-Warshall and naive string matcher, and is worse in the multi-task setting on 10/30 algorithms.
- Without the L2 penalty, the gated model still beats the baseline on 28/30 algorithms but averages 79.31% versus 82.88% with the penalty.
Limitations
- The lambda penalty is set by a heuristic per algorithm and is unlikely to be optimal.
- ForgetNet suffers from inaccurate intermediate predictions and slower early training, underperforming on some tasks.
- Hint-ReLIC could not be directly compared because its code is not public and its setup differs.
Experimental setup
Datasets: CLRS-30
Benchmarks: CLRS-30
Metrics: micro-F1 (OOD test)
Baselines: Memnet MPNN PGN Triplet-GMPNN ForgetNet (baseline encoder-processor-decoder)
Builds on: CLRS-30 Triplet-GMPNN Hint-ReLIC
Closest papers by meaning
- Emergent Symbolic Mechanisms Support Abstract Reasoning in Large Language Models (ICML 2025 · similarity 0.86)
- Deep Equilibrium Algorithmic Reasoning (NeurIPS 2024 · similarity 0.86)
- Open-Book Neural Algorithmic Reasoning (NeurIPS 2024 · similarity 0.85)
- A mathematical theory of balancing relational generalization and memorization (NeurIPS 2026 · similarity 0.85)
- Boosting Inference with Guided Reasoning: Stochastic Exploration for Recursive Models (NeurIPS 2026 · similarity 0.85)
- Discrete Neural Algorithmic Reasoning (ICML 2025 · similarity 0.85)
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