Quantile Data Pooling Method for a Neural Network

A neural network incorporating a quantile pooling layer for permutation-equivariant set data analysis, the neural network comprising:

• means for receiving an input tensor comprising a set of unordered data points;
• means for processing the input tensor through one or more permutation-equivariant transformations and/or one or more non-linear layers;
• and
• means for processing the input tensor through a quantile pooling layer to produce a pooled output to provide a pooled output vector;
• wherein the means for processing the input tensor through a quantile pooling layer is configured to implement the steps of:
• receiving an input tensor formed from a set of data points obtained from an input space, the input tensor having a plurality of input space dimensions;
• segmenting the input tensor over each of its input space dimensions into equal-sized segments, each set of corresponding segments over the input space dimensions comprising a partition;
• determining, selecting, or calculating a respective quantile level for each partition;
• determining or calculating a quantile value for each segment based on the quantile level for its partition;
• and
• creating a pooled output vector by concatenating the quantile values for the segments of each partition, the output vector comprising a pooled output for each partition.

A computer-implemented system for set data analysis, the computer system comprising:

• means for collecting a set of data points;
• means for performing permutation-equivariant transformations and quantile pooling on the collected data points;
• and
• means for utilizing the output vector or tensor to implement operations or tasks involving set-structured data;
• wherein the means for performing permutation-equivariant transformations and quantile pooling on the collected data points is configured to perform the steps of:
• receiving at the means for collecting a set of data points an input tensor comprising a set of unordered data points;
• processing the input tensor through one or more permutation-equivariant transformations and/or one or more non-linear layers;
• and
• processing the input tensor through a quantile pooling layer to produce a pooled output to provide a pooled output vector;
• wherein the step of processing the input tensor through a quantile pooling layer comprises the steps of:
• receiving an input tensor formed from a set of data points obtained from an input space, the input tensor having a plurality of input space dimensions;
• segmenting the input tensor over each of its input space dimensions into equal-sized segments, each set of corresponding segments over the input space dimensions comprising a partition;
• determining, selecting, or calculating a respective quantile level for each partition;
• determining or calculating a quantile value for each segment based on the quantile level for its partition;
• and
• creating a pooled output vector by concatenating the quantile values for the segments of each partition, the output vector comprising a pooled output for each partition.