ABGD parametrizes piecewise linear functions as difference of max-affine functions and converges linearly to an epsilon-accurate solution with O(d max(sigma/epsilon,1)^2) samples under sub-Gaussian noise, which is minimax optimal up to logs.
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The Linear Centroids Hypothesis reframes network features as directions in centroid spaces of local affine experts, unifying interpretability methods and yielding sparser, more faithful dictionaries, circuits, and saliency maps.
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Locally Near Optimal Piecewise Linear Regression in High Dimensions via Difference of Max-Affine Functions
ABGD parametrizes piecewise linear functions as difference of max-affine functions and converges linearly to an epsilon-accurate solution with O(d max(sigma/epsilon,1)^2) samples under sub-Gaussian noise, which is minimax optimal up to logs.
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The Linear Centroids Hypothesis: Features as Directions Learned by Local Experts
The Linear Centroids Hypothesis reframes network features as directions in centroid spaces of local affine experts, unifying interpretability methods and yielding sparser, more faithful dictionaries, circuits, and saliency maps.