Locally adaptive activation functions with slope recovery term for deep and physics-informed neural networks
We propose two approaches of locally adaptive activation functions namely, layer-wise and neuron-wise locally adaptive activation functions, which improve the performance of deep and physics-informed neural networks. The local adaptation of activation function is achieved by introducing scalable hyper-parameters in each layer (layer-wise) and for every neuron separately (neuron-wise), and then optimizing it using the stochastic gradient descent algorithm. Introduction of neuron-wise activation function acts like a vector activation function as opposed to the traditional scalar activation function given by fixed, global and layer-wise activations. In order to further increase the training speed, an activation slope based slope recovery term is added in the loss function, which further accelerate convergence, thereby reducing the training cost. For numerical experiments, a nonlinear discontinuous function is approximated using a deep neural network with layer-wise and neuron-wise locally adaptive activation functions with and without the slope recovery term and compared with its global counterpart. Moreover, solution of the nonlinear Burgers equation, which exhibits steep gradients, is also obtained using the proposed methods. On the theoretical side, we prove that in the proposed method the gradient descent algorithms are not attracted to sub-optimal critical points or local minima under practical conditions on the initialization and learning rate. Furthermore, the proposed adaptive activation functions with the slope recovery are shown to accelerate the training process in standard deep learning benchmarks using CIFAR-10, CIFAR-100, SVHN, MNIST, KMNIST, Fashion-MNIST, and Semeion data sets with and without data augmentation.
This paper introduces a parameter to scale the input to an activation function and a loss function to encourage the scaling parameter to be large. The authors test it to learn a discontinuous function as well as several image datasets. The concept of learnable activation functions is not new and this work is fairly incremental. However, for the image dataset results it seems the authors are using ReLU for their activation functions. Having a scaling parameter before the input to ReLU and encouraging that scaling parameter to be large is similar to increasing the learning rate. There are no experiments to verify whether or not this is the case. Also, the authors only report loss and not accuracy on these datasets.
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
Locally adaptive activation functions with slope recovery term for deep and physics-informed neural networks
We propose two approaches of locally adaptive activation functions namely, layer-wise and neuron-wise locally adaptive activation functions, which improve the performance of deep and physics-informed neural networks. The local adaptation of activation function is achieved by introducing scalable hyper-parameters in each layer (layer-wise) and for every neuron separately (neuron-wise), and then optimizing it using the stochastic gradient descent algorithm. Introduction of neuron-wise activation function acts like a vector activation function as opposed to the traditional scalar activation function given by fixed, global and layer-wise activations. In order to further increase the training speed, an activation slope based slope recovery term is added in the loss function, which further accelerate convergence, thereby reducing the training cost. For numerical experiments, a nonlinear discontinuous function is approximated using a deep neural network with layer-wise and neuron-wise locally adaptive activation functions with and without the slope recovery term and compared with its global counterpart. Moreover, solution of the nonlinear Burgers equation, which exhibits steep gradients, is also obtained using the proposed methods. On the theoretical side, we prove that in the proposed method the gradient descent algorithms are not attracted to sub-optimal critical points or local minima under practical conditions on the initialization and learning rate. Furthermore, the proposed adaptive activation functions with the slope recovery are shown to accelerate the training process in standard deep learning benchmarks using CIFAR-10, CIFAR-100, SVHN, MNIST, KMNIST, Fashion-MNIST, and Semeion data sets with and without data augmentation.
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<think>Okay, to do a decent peer review, I should start with summarizing what the work is about. This includes novelty, contributions, clarity, and impact. I might include suggestions to issues that I find critical to the usefulness of the work. Starting with novelty, there are different types of novelty. The first aspect of novelty is scope and scale. Is the work covering a broader perspective than previous works? The second aspect is methodology. Is the proposed methodology novel compared to previous methods? Do they provide any significant advantage over previous methodologies? The third aspect is results. Are the results different compared previous work? Does this lead to any novel theories or an extension of current theories? Next is clarity, I will be reading the work in depth and analyze if any sentences can be potentially ambiguous or misleading. If any sentences are ambiguous, I will state them and give a suggestion on how to rephrase such sentence or how to make more clear to the audience. Lastly, impact is important. I will attempt to predict how such work will impact the scientific community. This might include the applications of such work and how the work might transform the way we study a certain topic. Finally, I will might only mention issues that are critical. This is to keep the review as concise and helpful as possible.</think>



This paper introduces a parameter to scale the input to an activation function and a loss function to encourage the scaling parameter to be large. The authors test it to learn a discontinuous function as well as several image datasets. The concept of learnable activation functions is not new and this work is fairly incremental. However, for the image dataset results it seems the authors are using ReLU for their activation functions. Having a scaling parameter before the input to ReLU and encouraging that scaling parameter to be large is similar to increasing the learning rate. There are no experiments to verify whether or not this is the case. Also, the authors only report loss and not accuracy on these datasets.
assistant
This paper introduces a parameter to scale the input to an activation function and a loss function to encourage the scaling parameter to be large. The authors test it to learn a discontinuous function as well as several image datasets. The concept of learnable activation functions is not new and this work is fairly incremental. However, for the image dataset results it seems the authors are using ReLU for their activation functions. Having a scaling parameter before the input to ReLU and encouraging that scaling parameter to be large is similar to increasing the learning rate. There are no experiments to verify whether or not this is the case. Also, the authors only report loss and not accuracy on these datasets.