# Fitting Every Hint Is Not Enough: Premature Floods in Recurrent Algorithmic Reasoners

arXiv: https://arxiv.org/abs/2610.14982 · HTML: https://mlsanity.com/paper/2610.14982/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 29 of its 31 references that are in the map.
- First posted on arXiv 10 Oct 2026.

## Builds on (most cited first, 29 of 29)

- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Sigmoid-Weighted Linear Units for Neural Network Function Approximation in Reinforcement Learning](https://mlsanity.com/paper/1702.03118/) (2017)
- [Underspecification Presents Challenges for Credibility in Modern Machine Learning](https://mlsanity.com/paper/2011.03395/) (2020)
- [Scaling up Test-Time Compute with Latent Reasoning: A Recurrent Depth Approach](https://mlsanity.com/paper/2502.05171/) (2025)
- [How Neural Networks Extrapolate: From Feedforward to Graph Neural Networks](https://mlsanity.com/paper/2009.11848/) (2020)
- [Hierarchical Reasoning Model](https://mlsanity.com/paper/2506.21734/) (2025)
- [From Local Structures to Size Generalization in Graph Neural Networks](https://mlsanity.com/paper/2010.08853/) (2020)
- [Can You Learn an Algorithm? Generalizing from Easy to Hard Problems with Recurrent Networks](https://mlsanity.com/paper/2106.04537/) (2021)
- [The CLRS Algorithmic Reasoning Benchmark](https://mlsanity.com/paper/2205.15659/) (2022)
- [A Generalist Neural Algorithmic Learner](https://mlsanity.com/paper/2209.11142/) (2022)
- [Pointer Graph Networks](https://mlsanity.com/paper/2006.06380/) (2020)
- [Path Independent Equilibrium Models Can Better Exploit Test-Time Computation](https://mlsanity.com/paper/2211.09961/) (2022)
- [Neural Algorithmic Reasoning with Causal Regularisation](https://mlsanity.com/paper/2302.10258/) (2023)
- [Towards Better Out-of-Distribution Generalization of Neural Algorithmic Reasoning Tasks](https://mlsanity.com/paper/2211.00692/) (2022)
- [Understanding and Improving Length Generalization in Recurrent Models](https://mlsanity.com/paper/2507.02782/) (2025)
- [Neural Algorithmic Reasoning Without Intermediate Supervision](https://mlsanity.com/paper/2306.13411/) (2023)
- [SALSA-CLRS: A Sparse and Scalable Benchmark for Algorithmic Reasoning](https://mlsanity.com/paper/2309.12253/) (2023)
- [On the Markov Property of Neural Algorithmic Reasoning: Analyses and Methods](https://mlsanity.com/paper/2403.04929/) (2024)
- [Discrete Neural Algorithmic Reasoning](https://mlsanity.com/paper/2402.11628/) (2024)
- [Think Shallow, Solve Deep: Controlling Recurrent Dynamics for Reliable Test-Time Depth](https://mlsanity.com/paper/2608.18222/) (2026)
- [Thinking with Looped Flows](https://mlsanity.com/paper/2609.11801/) (2026)
- [Latent Space Representations of Neural Algorithmic Reasoners](https://mlsanity.com/paper/2307.08874/) (2023)
- [Learning Graph Algorithms With Recurrent Graph Neural Networks](https://mlsanity.com/paper/2212.04934/) (2022)
- [Deep Equilibrium Algorithmic Reasoning](https://mlsanity.com/paper/2410.15059/) (2024)
- [Which Algorithms Can Graph Neural Networks Learn?](https://mlsanity.com/paper/2602.13106/) (2026)
- [Flood and Echo Net: Algorithmically Aligned GNNs that Generalize](https://mlsanity.com/paper/2310.06970/) (2023)
- [From Shortcut Learning to Discrete Neural Insertion Sort](https://mlsanity.com/paper/2609.31114/) (2026)

## Abstract (arXiv)

Recurrent algorithmic reasoners are trained with per-step hints on small graphs and run for many more steps on large ones. On breadth-first search in SALSA-CLRS, we find that a reasoner can reproduce every training hint and still fail on deep graphs: after some exact steps, it declares nodes reached before the search gets there. We call this a premature flood and trace two routes to it. In our GRU processor with a degree input, the flood is carried in the hidden state and set off when that input is in the tail of the training distribution. Setting the input higher at inference brings the flood sooner, and none of the six flooding models counts steps. Without the input, summing the neighbors' states instead of averaging them also breaks the processor. In the benchmark's own GIN and PGN, trained with its code, some seeds instead flood from a fixed step, on sparse and dense graphs alike. Clamping the degree input or adding 200 dense training graphs removes every failure of the GRU processor. Detaching the state between steps avoids the flood in that processor (0 of 23 seeds, against 6 under full backpropagation) but not with sums or a residual update, and two published remedies leave floods. None of the benchmark's test sets is both deep and dense, but its deepest one shows the second route: on its Delaunay graphs at 1,600 nodes, one GIN seed floods from step 18. We therefore recommend auditing the range of every input and aggregate, which catches the first route, and testing on deep graphs, which catches both.