Maximizing a quadratic objective over unitriangular bases with non-negative 1+s action recovers the Kazhdan-Lusztig basis for all partitions of n≤7 and is conjectured to do so more generally, while minimization recovers Young's seminormal basis.
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Benchmark finds location encoders recover primary spatial coefficients consistently but secondary ones vary by scale, with raw-coordinate baseline competitive throughout.
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Kazhdan-Lusztig Basis and Optimization
Maximizing a quadratic objective over unitriangular bases with non-negative 1+s action recovers the Kazhdan-Lusztig basis for all partitions of n≤7 and is conjectured to do so more generally, while minimization recovers Young's seminormal basis.
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Do Location Encoders Capture Spatial Effects? A GeoShapley Benchmark Across Scales
Benchmark finds location encoders recover primary spatial coefficients consistently but secondary ones vary by scale, with raw-coordinate baseline competitive throughout.