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Deep learning models evolve through training to learn the manifold in which the data exists to satisfy an objective. It is well known that evolution leads to different final states which produce inconsistent predictions of the same test data points. This calls for techniques to be able to empirically quantify the difference in the trajectories and highlight problematic regions. While much focus is placed on discovering what models learn, the question of how a model learns is less studied beyond theoretical landscape characterizations and local geometric approximations near optimal conditions. Here, we present a toolkit for the Dynamical Organization Of Deep Learning Loss Landscapes, or DOODL3. DOODL3 formulates the training of neural networks as a dynamical system, analyzes the learning process, and presents an interpretable global view of trajectories in the loss landscape. Our approach uses the coarseness of topology to capture the granularity of geometry to mitigate against states of instability or elongated training. Overall, our analysis presents an empirical framework to extract the global dynamics of a model and to use that information to guide the training of neural networks.
We describe a computational method for constructing a coarse combinatorial model of some dynamical system in which the macroscopic states are given by elementary cycling motions of the system. Our method is in particular applicable to time series dat
Despite many of the most common chaotic dynamical systems being continuous in time, it is through discrete time mappings that much of the understanding of chaos is formed. Henri Poincare first made this connection by tracking consecutive iterations o
In this work, we investigate the system of three species ecological model involving one predator-prey subsystem coupling with a generalist predator with negative effect on the prey. Without diffusive terms, all global dynamics of its corresponding re
Understanding the structure of loss landscape of deep neural networks (DNNs)is obviously important. In this work, we prove an embedding principle that the loss landscape of a DNN contains all the critical points of all the narrower DNNs. More precise
We present a learning-based method for extracting whistles of toothed whales (Odontoceti) in hydrophone recordings. Our method represents audio signals as time-frequency spectrograms and decomposes each spectrogram into a set of time-frequency patche