POLYNOMIAL ACTIVATION FUNCTIONS
Activation is a nonlinearity function that plays a predominant role in the convergence and performance of deep neural networks. While Rectified Linear Unit (ReLU) is the most successful activation function, its derivatives have shown superior performance on benchmark datasets. In this work, we explore the polynomials as activation functions (order ? 2) that can approximate continuous real valued function within a given interval. Leveraging this property, the main idea is to learn the nonlinearity, accepting that the ensuing function may not be monotonic. While having the ability to learn more suitable nonlinearity, we cannot ignore the fact that it is a challenge to achieve stable performance due to exploding gradients - which is prominent with the increase in order. To handle this issue, we introduce dynamic input scaling, output scaling, and lower learning rate for the polynomial weights. Moreover, lower learning rate will control the abrupt fluctuations of the polynomials between weight updates. In experiments on three public datasets, our proposed method matches the performance of prior activation functions, thus providing insight into a network’s nonlinearity preference.
Motivation: The authors propose the use of polynomials as the choice of activation function. Clarity: The authors does not give a very clear introduction why using polynomial functions as activation functions is a good idea. Rather they say, *, we believe that the nonlinearity learned by the deep networks can provide more insight on how they can be designed.* a bit more intuition in the beginning of the introduction would make the paper a bit easier to read. *We demonstrate the stability of polynomial of orders 2 to 9 by introducing scaling functions and initialization scheme that approximates well known activation functions* Generally, a good technique is to motivate your design decisions before actually stating what those design decisions are. Atleast to me, it was not clear, why you need to introduce scaling functions and initialization scheme in the beginning of the introduction. Scaling Functions: Authors note that the polynomials of order n can explode, to circumvent this authors introduce scaling functions to dynamically scale the inputs. *The purpose of our proposal is to explore newer nonlinearities by allowing the network to choose an appropriate nonlinearity for each layer and eventually, design better activation functions on the gathered intuitions* Having this somewhere in the introduction could help. In general, the paper does not motivate well why use of polynomial activation functions is a good idea.
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
POLYNOMIAL ACTIVATION FUNCTIONS
Activation is a nonlinearity function that plays a predominant role in the convergence and performance of deep neural networks. While Rectified Linear Unit (ReLU) is the most successful activation function, its derivatives have shown superior performance on benchmark datasets. In this work, we explore the polynomials as activation functions (order ? 2) that can approximate continuous real valued function within a given interval. Leveraging this property, the main idea is to learn the nonlinearity, accepting that the ensuing function may not be monotonic. While having the ability to learn more suitable nonlinearity, we cannot ignore the fact that it is a challenge to achieve stable performance due to exploding gradients - which is prominent with the increase in order. To handle this issue, we introduce dynamic input scaling, output scaling, and lower learning rate for the polynomial weights. Moreover, lower learning rate will control the abrupt fluctuations of the polynomials between weight updates. In experiments on three public datasets, our proposed method matches the performance of prior activation functions, thus providing insight into a network’s nonlinearity preference.
user
<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>



Motivation: The authors propose the use of polynomials as the choice of activation function. Clarity: The authors does not give a very clear introduction why using polynomial functions as activation functions is a good idea. Rather they say, *, we believe that the nonlinearity learned by the deep networks can provide more insight on how they can be designed.* a bit more intuition in the beginning of the introduction would make the paper a bit easier to read. *We demonstrate the stability of polynomial of orders 2 to 9 by introducing scaling functions and initialization scheme that approximates well known activation functions* Generally, a good technique is to motivate your design decisions before actually stating what those design decisions are. Atleast to me, it was not clear, why you need to introduce scaling functions and initialization scheme in the beginning of the introduction. Scaling Functions: Authors note that the polynomials of order n can explode, to circumvent this authors introduce scaling functions to dynamically scale the inputs. *The purpose of our proposal is to explore newer nonlinearities by allowing the network to choose an appropriate nonlinearity for each layer and eventually, design better activation functions on the gathered intuitions* Having this somewhere in the introduction could help. In general, the paper does not motivate well why use of polynomial activation functions is a good idea.
assistant
Motivation: The authors propose the use of polynomials as the choice of activation function. Clarity: The authors does not give a very clear introduction why using polynomial functions as activation functions is a good idea. Rather they say, *, we believe that the nonlinearity learned by the deep networks can provide more insight on how they can be designed. * a bit more intuition in the beginning of the introduction would make the paper a bit easier to read. *We demonstrate the stability of polynomial of orders 2 to 9 by introducing scaling functions and initialization scheme that approximates well known activation functions* Generally, a good technique is to motivate your design decisions before actually stating what those design decisions are. Atleast to me, it was not clear, why you need to introduce scaling functions and initialization scheme in the beginning of the introduction. Scaling Functions: Authors note that the polynomials of order n can explode, to circumvent this authors introduce scaling functions to dynamically scale the inputs. *The purpose of our proposal is to explore newer nonlinearities by allowing the network to choose an appropriate nonlinearity for each layer and eventually, design better activation functions on the gathered intuitions* Having this somewhere in the introduction could help. In general, the paper does not motivate well why use of polynomial activation functions is a good idea.