Recent neural network models for algorithmic tasks have led to significant improvements in extrapolation to sequences much longer than training, but it remains an outstanding problem that the performance still degrades for very long or adversarial sequences. We present alternative architectures and loss-terms to address these issues, and our testing of these approaches has not detected any remaining extrapolation errors within memory constraints. We focus on linear time algorithmic tasks including copy, parentheses parsing, and binary addition. First, activation binning was used to discretize the trained network in order to avoid computational drift from continuous operations, and a binning-based digital loss term was added to encourage discretizable representations. In addition, a localized differentiable memory (LDM) architecture, in contrast to distributed memory access, addressed remaining extrapolation errors and avoided unbounded growth of internal computational states. Previous work has found that algorithmic extrapolation issues can also be alleviated with approaches relying on program traces, but the current effort does not rely on such traces.
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