We study the training process of Deep Neural Networks (DNNs) from the Fourier analysis perspective. We demonstrate a very universal Frequency Principle (F-Principle) --- DNNs often fit target functions from low to high frequencies --- on high-dimensional benchmark datasets such as MNIST/CIFAR10...
The F-Principle can be observed over DNNs of various structures, activation functions, and training algorithms in our experiments. We also illustrate how the F-Principle help understand the effect of early-stopping as well as the generalization of DNNs. This F-Principle potentially provides insights...
We propose a phenomenological model of the NN training to explain this non-overfitting puzzle. Our linear frequency principle (LFP) model accounts for a key dynamical feature of NNs: they learn low frequencies first, irrespective of microscopic details. Theory based on our LFP model shows that ...
The selection of these parameters directly affects the performance of the final model [28]. These parameters are determined by both empirical knowledge, selecting appropriate ranges for setting, and reliable methods to accurately determine their final values [29]. The fundamental principle of ...
In this section we will describe the principle of reciprocity, which will allow us to measure the response at one location and derive frequency response functions corresponding to locations at which we excite the system. As discussed in the previous section (see Eq. 6.5-6), the acceleration ...
Description of Algorithm OCT Intensity and A-Line Construction Optical Coherence Tomography (OCT) is a non-invasive imaging technique that utilizes the principle of coherence to generate images along the depth of a tissue. An OCT device consists of a light source that emits a broad spectrum of ...
The TFD representation is localized in both t and f subject to the interpretation and within the limits of the uncertainty principle, as mentioned in Section I.2.3.3 of Chapter I. Before proceeding further with the (t, f) approach, for the sake of completeness, the next sections first use...
However, there is no guiding principle on how to modify each time-frequency component since randomly modifying each element may cause unexpected time-frequency information violation. Neural network can learn and tune internal neuron connections via continuous training. Therefore we propose in this work ...
Besides, the resonance characteristics of various structures of rocks are identified and analyzed based on the principle of seismic resonance measurement. This information is helpful for both environmental safety and possible formation characterization. However, since the key to realizing of the RED ...
The main limitation is the cross-sectional nature of our studies that precludes causal inferences.As in all entirely questionnaire-based studies, correlations between constructs could in principle be driven by common method variance. Future work, perhaps with physiological measurements during sleep, could...