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Efficiently Learning Branching Networks for Multitask Algorithmic Reasoning

Algorithmic reasoning -- the ability to perform step-by-step logical inference -- is a synthetic benchmark for evaluating multi-step reasoning abilities, designed for graph neural networks and also for transformer models. Prior work has evaluated reasoning for executing a single algorithmic task, whereas a more desirable objective is to perform multiple algorithmic reasoning tasks simultaneously. We start by noting that this is inherently difficult due to differences arising from the execution traces of the algorithms (such as depth- vs. breadth-first search), which cause interference when they are trained together. In this paper, we introduce {branching neural networks}, a new architecture for multitask algorithmic reasoning. The main idea is to search for a recursive tree-structured partition of $n$ algorithmic tasks into a $k$-ary tree (divided into $L$ layers). Naive search requires $O(k^{nL})$ complexity; we develop an algorithm that reduces this to $O(nL)$ by solving a convex relaxation at each layer to approximate an optimal partition. Our approach clusters these tasks using gradient-based affinity and can be used on top of any base model. We validate our approach on algorithmic reasoning benchmarks and their extensions with text descriptions. We show that gradient-based affinity scores help estimate true performance with less than 5% error, measured across eight different architectures with up to 34 billion parameters. On the CLRS benchmark, our approach outperforms existing graph neural networks by 3.7% and baselines by 1.2%, while reducing runtime by 48% and memory usage by 26%. The learned branching structure shows a hierarchical clustering of related algorithms. On three text-based graph reasoning benchmarks, our approach improves over baseline methods by 3.2%. Finally, we validate our approach for overlapping community detection.

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