5 papers
Directional Linear Separability of Neural Representations: Geometry and Transformations
Yi Wei, Xuan Qi, Furao Shen +1
Neural networks build representations through affine maps and nonlinear activations. Injective affine maps preserve linear separability, raising the problem of how they prepare dat…
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…
The Evolution of the Interplay Between Input Distributions and Linear Regions in Networks
Xuan Qi, Yi Wei
It is commonly recognized that the expressiveness of deep neural networks is contingent upon a range of factors, encompassing their depth, width, and other relevant considerations.…