Latent Space Representations of Neural Algorithmic Reasoners

• URL: http://arxiv.org/abs/2307.08874v2
• Date: Mon, 29 Apr 2024 12:01:54 GMT
• Title: Latent Space Representations of Neural Algorithmic Reasoners
• Authors: Vladimir V. Mirjanić, Razvan Pascanu, Petar Veličković,
• Abstract summary: We perform a detailed analysis of the structure of the latent space induced by the GNN when executing algorithms. We identify two possible failure modes: (i) loss of resolution, making it hard to distinguish similar values; (ii) inability to deal with values outside the range observed during training. We show that these changes lead to improvements on the majority of algorithms in the standard CLRS-30 benchmark when using the state-of-the-art Triplet-GMPNN processor.
• Score: 15.920449080528536
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Neural Algorithmic Reasoning (NAR) is a research area focused on designing neural architectures that can reliably capture classical computation, usually by learning to execute algorithms. A typical approach is to rely on Graph Neural Network (GNN) architectures, which encode inputs in high-dimensional latent spaces that are repeatedly transformed during the execution of the algorithm. In this work we perform a detailed analysis of the structure of the latent space induced by the GNN when executing algorithms. We identify two possible failure modes: (i) loss of resolution, making it hard to distinguish similar values; (ii) inability to deal with values outside the range observed during training. We propose to solve the first issue by relying on a softmax aggregator, and propose to decay the latent space in order to deal with out-of-range values. We show that these changes lead to improvements on the majority of algorithms in the standard CLRS-30 benchmark when using the state-of-the-art Triplet-GMPNN processor. Our code is available at https://github.com/mirjanic/nar-latent-spaces

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