4 papers
A Geometric Measure of Linear Separability for Neural Representations
Yi Wei, Xuan Qi, Furao Shen
Modern neural classifiers commonly rely on linear readouts, yet predictive metrics alone do not characterize the class-wise geometry of the representations on which such readouts o…
AffineLens: Capturing the Continuous Piecewise Affine Functions of Neural Networks
Yi Wei, Xuan Qi, Furao Shen +3
Piecewise affine neural networks (PANNs) provide a principled geometric perspective on neural network expressivity by characterizing the input--output map as a continuous piecewise…
Training-Time Batch Normalization Reshapes Local Partition Geometry in Piecewise-Affine Networks
Xuan Qi, Yi Wei, Fanqi Yu +3
Batch normalization (BN) is central to modern deep networks, but its effect on the realized function during training remains less understood than its optimization benefits. We stud…
Region Seeding via Pre-Activation Regularization: A Geometric View of Piecewise Affine Neural Networks
Yi Wei, Xuan Qi, Furao Shen
Deep networks with continuous piecewise affine activations induce polyhedral partitions of the input space, making the number of realized affine regions a natural measure of expres…