Zhengqing Wu

Ben Lonnqvist, Zhengqing Wu, Michael H. Herzog

Humans are able to segment images effortlessly without supervision using perceptual grouping. Here, we propose a counter-intuitive computational approach to solving unsupervised perceptual grouping and segmentation: that they arise because of neural noise, rather than in spite of it. We (1) mathematically demonstrate that under realistic assumptions, neural noise can be used to separate objects from each other; (2) that adding noise in a DNN enables the network to segment images even though it was never trained on any segmentation labels; and (3) that segmenting objects using noise results in segmentation performance that aligns with the perceptual grouping phenomena observed in humans, and is sample-efficient. We introduce the Good Gestalt (GG) datasets -- six datasets designed to specifically test perceptual grouping, and show that our DNN models reproduce many important phenomena in human perception, such as illusory contours, closure, continuity, proximity, and occlusion. Finally, we (4) show that our model improves performance on our GG datasets compared to other tested unsupervised models by $24.9\%$. Together, our results suggest a novel unsupervised segmentation method requiring few assumptions, a new explanation for the formation of perceptual grouping, and a novel potential benefit of neural noise.

Frank Zhengqing Wu, Berfin Simsek, Francois Gaston Ged

In this paper, we study the loss landscape of one-hidden-layer neural networks with ReLU-like activation functions trained with the empirical squared loss using gradient descent (GD). We identify the stationary points of such networks, which significantly slow down loss decrease during training. To capture such points while accounting for the non-differentiability of the loss, the stationary points that we study are directional stationary points, rather than other notions like Clarke stationary points. We show that, if a stationary point does not contain "escape neurons", which are defined with first-order conditions, it must be a local minimum. Moreover, for the scalar-output case, the presence of an escape neuron guarantees that the stationary point is not a local minimum. Our results refine the description of the saddle-to-saddle training process starting from infinitesimally small (vanishing) initialization for shallow ReLU-like networks: By precluding the saddle escape types that previous works did not rule out, we advance one step closer to a complete picture of the entire dynamics. Moreover, we are also able to fully discuss how network embedding, which is to instantiate a narrower network with a wider network, reshapes the stationary points.