Estimating Nonplanar Flow from 2D Motion-blurred Widefield Microscopy Images via Deep Learning

Optical flow is a method aimed at predicting the movement velocity of any pixel in the image and is used in medicine and biology to estimate flow of particles in organs or organelles. However, a precise optical flow measurement requires images taken at high speed and low exposure time, which induces phototoxicity due to the increase in illumination power. We are looking here to estimate the three-dimensional movement vector field of moving out-of-plane particles using normal light conditions and a standard microscope camera. We present a method to predict, from a single textured wide-field microscopy image, the movement of out-of-plane particles using the local characteristics of the motion blur. We estimated the velocity vector field from the local estimation of the blur model parameters using an deep neural network and achieved a prediction with a regression coefficient of 0.92 between the ground truth simulated vector field and the output of the network. This method could enable microscopists to gain insights about the dynamic properties of samples without the need for high-speed cameras or high-intensity light exposure.

Jamming transition as a paradigm to understand the loss landscape of deep neural networks

Mario Geiger, Levent Dogus Sagun, Stefano Spigler, Matthieu Wyart

Deep learning has been immensely successful at a variety of tasks, ranging from classification to artificial intelligence. Learning corresponds to fitting training data, which is implemented by descending a very high-dimensional loss function. Understanding under which conditions neural networks do not get stuck in poor minima of the loss, and how the landscape of that loss evolves as depth is increased, remains a challenge. Here we predict, and test empirically, an analogy between this landscape and the energy landscape of repulsive ellipses. We argue that in fully connected deep networks a phase transition delimits the over- and underparametrized regimes where fitting can or cannot be achieved. In the vicinity of this transition, properties of the curvature of the minima of the loss (the spectrum of the Hessian) are critical. This transition shares direct similarities with the jamming transition by which particles form a disordered solid as the density is increased, which also occurs in certain classes of computational optimization and learning problems such as the perceptron. Our analysis gives a simple explanation as to why poor minima of the loss cannot be encountered in the overparametrized regime. Interestingly, we observe that the ability of fully connected networks to fit random data is independent of their depth, an independence that appears to also hold for real data. We also study a quantity Delta which characterizes how well (Delta < 0) or badly (Delta > 0) a datum is learned. At the critical point it is power-law distributed on several decades, P+(Delta) similar to Delta(theta) for Delta > 0 and P_(Delta) similar to (-Delta)(-gamma) for Delta < 0, with exponents that depend on the choice of activation function. This observation suggests that near the transition the loss landscape has a hierarchical structure and that the learning dynamics is prone to avalanche-like dynamics, with abrupt changes in the set of patterns that are learned.

AMER PHYSICAL SOC2019

Jamming transition as a paradigm to understand the loss landscape of deep neural networks

Mario Geiger, Levent Dogus Sagun, Stefano Spigler, Matthieu Wyart

AMER PHYSICAL SOC2019