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Nth farthest problem

As explained in Sutskever's List

A synthetic sequence task requiring a model to identify the item at a specified distance rank from a reference vector.

The nth farthest problem tests whether a sequence model can compare items relationally rather than merely memorize them. Given vectors and a reference, it asks which item ranks nth farthest from that reference. section 7.4.1

Solving the task requires the model to:

  • Compute distances between the reference vector and the other sequence items. section 7.4.1
  • Rank those distances and identify the requested position, such as the second farthest item. section 7.4.1
  • Maintain relational information over time; memorizing the sequence alone is insufficient. section 7.4.1

A representative question

After receiving a sequence of vectors, the model might be asked: “Which item is the second farthest from item X?” Standard LSTMs and differentiable neural computers remained below 30% accuracy, while a relational memory core reached about 91%. section 7.4.1

How Sutskever's List covers it

How deep it goes
Requires distance computation, ranking, and selection, but does not specify the underlying training procedure.
Examples
Uses vector sequences and questions such as identifying the second farthest item from a reference vector.
What it assumes
Assumes vectors, distances, ranking, and basic sequence-model terminology.
What you can do after
Evaluate whether a sequence model learns relationships among items instead of only storing and recalling them.
How it connects
Connects relational reasoning with recurrent neural networks, attention, relational memory, LSTMs, and differentiable neural computers.
Cover of Sutskever's List
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Related concepts

This explainer was generated by Manning's knowledge graph from the text of Sutskever's List. The section links point to the parts of the book it draws on.