A Max-Affine Spline Perspective of Recurrent Neural Networks
We develop a framework for understanding and improving recurrent neural networks (RNNs) using max-affine spline operators (MASOs). We prove that RNNs using piecewise affine and convex nonlinearities can be written as a simple piecewise affine spline operator. The resulting representation provides several new perspectives for analyzing RNNs, three of which we study in this paper. First, we show that an RNN internally partitions the input space during training and that it builds up the partition through time. Second, we show that the affine slope parameter of an RNN corresponds to an input-specific template, from which we can interpret an RNN as performing a simple template matching (matched filtering) given the input. Third, by carefully examining the MASO RNN affine mapping, we prove that using a random initial hidden state corresponds to an explicit L2 regularization of the affine parameters, which can mollify exploding gradients and improve generalization. Extensive experiments on several datasets of various modalities demonstrate and validate each of the above conclusions. In particular, using a random initial hidden states elevates simple RNNs to near state-of-the-art performers on these datasets.
 In this paper, the authors provide a novel approach towards understanding RNNs using max-affine spline operators (MASO). Specifically, they rewrite RNNs with piecewise affine and convex activations MASOs and provide some explanation to the use of noisy initial hidden state. The paper can be improved in presentation. More high level explanation should be given on MASOs and why this new view of RNN is better. To best of my knowledge, this is the first paper that related RNNs with MASOs and provides insights on this re-formulation. However, the authors failed to find more useful applications of this new formulation other than finding that noisy initial hidden state helps in regularization. Also, the re-formulation is restricted to piecewise affine and convex activation functions (Relu and leaky-Relu). In general, I think this is an original work providing interesting viewing point, but could be further improved if the authors find more applications of the MASO form.
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
A Max-Affine Spline Perspective of Recurrent Neural Networks
We develop a framework for understanding and improving recurrent neural networks (RNNs) using max-affine spline operators (MASOs). We prove that RNNs using piecewise affine and convex nonlinearities can be written as a simple piecewise affine spline operator. The resulting representation provides several new perspectives for analyzing RNNs, three of which we study in this paper. First, we show that an RNN internally partitions the input space during training and that it builds up the partition through time. Second, we show that the affine slope parameter of an RNN corresponds to an input-specific template, from which we can interpret an RNN as performing a simple template matching (matched filtering) given the input. Third, by carefully examining the MASO RNN affine mapping, we prove that using a random initial hidden state corresponds to an explicit L2 regularization of the affine parameters, which can mollify exploding gradients and improve generalization. Extensive experiments on several datasets of various modalities demonstrate and validate each of the above conclusions. In particular, using a random initial hidden states elevates simple RNNs to near state-of-the-art performers on these datasets.
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>



 In this paper, the authors provide a novel approach towards understanding RNNs using max-affine spline operators (MASO). Specifically, they rewrite RNNs with piecewise affine and convex activations MASOs and provide some explanation to the use of noisy initial hidden state. The paper can be improved in presentation. More high level explanation should be given on MASOs and why this new view of RNN is better. To best of my knowledge, this is the first paper that related RNNs with MASOs and provides insights on this re-formulation. However, the authors failed to find more useful applications of this new formulation other than finding that noisy initial hidden state helps in regularization. Also, the re-formulation is restricted to piecewise affine and convex activation functions (Relu and leaky-Relu). In general, I think this is an original work providing interesting viewing point, but could be further improved if the authors find more applications of the MASO form.
assistant
 In this paper, the authors provide a novel approach towards understanding RNNs using max-affine spline operators (MASO). Specifically, they rewrite RNNs with piecewise affine and convex activations MASOs and provide some explanation to the use of noisy initial hidden state. The paper can be improved in presentation. More high level explanation should be given on MASOs and why this new view of RNN is better. To best of my knowledge, this is the first paper that related RNNs with MASOs and provides insights on this re-formulation. However, the authors failed to find more useful applications of this new formulation other than finding that noisy initial hidden state helps in regularization. Also, the re-formulation is restricted to piecewise affine and convex activation functions (Relu and leaky-Relu). In general, I think this is an original work providing interesting viewing point, but could be further improved if the authors find more applications of the MASO form.