MAS reveals that numeric representations differ between GRUs trained on Multi-Object, Rounding, and Modulo tasks

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• MAS successfully aligns the Count variable from Multi-Object GRUs with the Rem Ops variable from Arithmetic GRUs with moderate IIAfinding0.835
  Shows MAS can compare specific numeric variables across tasks with different domains/codomains.
• MAS successfully aligns behavior between Multi-Object GRU models in both embedding and hidden state layers with high IIAfinding0.812
  Demonstrates MAS's ability to bidirectionally transfer behavior where RSA shows low embedding correlation.
• There are fewer representations competent for N tasks than M<N tasks, so training more general models should yield fewer possible solutionshypothesis0.793
  Selective pressure toward convergence via task generality
• How do representations differ or converge between architectures, tasks, and modalities?question0.787
  Broader research question MAS is positioned to address, citing multiple recent works.
• GRU behavior can be compressed to as few as 4 dimensions using DAS and MAS with comparable IIAsfinding0.782
  Shows that behaviorally relevant information is low-dimensional; contrasted with model stitching achieving near-perfect IIA at rank 2.
• We hypothesize that degraded generalization on benchmarks like MMLU may reflect the computational demands of the tasks.hypothesis0.771
  Connecting the paper's task-difficulty findings to prior observations of weak generalization on complex QA benchmarks.
• There is a bidirectional relationship between the geometry of representation and behavior across tasks and modalities.claim0.768
  Author’s interpretive claim that the shared geometry is general and robust.
• MAS reduces number of required alignment matrices for n-model comparison from n(n-1) or n^2 (stitching) to nfinding0.768
  Key computational efficiency advantage of MAS over traditional model stitching for multi-model comparisons.