Homogeneous Linear Inequality Constraints for Neural Network Activations
We propose a method to impose homogeneous linear inequality constraints of the form on neural network activations. The proposed method allows a data-driven training approach to be combined with modeling prior knowledge about the task. One way to achieve this task is by means of a projection step at test time after unconstrained training. However, this is an expensive operation. By directly incorporating the constraints into the architecture, we can significantly speed-up inference at test time; for instance, our experiments show a speed-up of up to two orders of magnitude over a projection method. Our algorithm computes a suitable parameterization of the feasible set at initialization and uses standard variants of stochastic gradient descent to find solutions to the constrained network. Thus, the modeling constraints are always satisfied during training. Crucially, our approach avoids to solve an optimization problem at each training step or to manually trade-off data and constraint fidelity with additional hyperparameters. We consider constrained generative modeling as an important application domain and experimentally demonstrate the proposed method by constraining a variational autoencoder.
The paper proposes a new faster algorithm to add inequality constraints to neural layers. The paper focuses on a novel constraining approach with seemingly superior scalability, and this is potentially a significant contribution. However the paper does not motivate the constraining at all. I am baffled by this, since one would assume at least some benefits from all of this work could be presented. The only mentions are binarization of the predictions (which softmax already does), and monotonicity/convexity of neurons, with no proposed benefits. The running example of the paper is the chessboard constraint, which is either pointless (fig1) or harmful (fig5). Without justification and motivation the method has no merit and won’t have any impact in the machine learning community. The monotonicity constraint could have a huge impact for MCMC sampling of neural parameters since it can reduce away all multimodalities of the posterior caused by reordering nodes or layers. I had hard time following the method, and I its not clear how the neural network is modified and how backpropagation is performed with the contraints. It is not defined properly how the constrained optimisation works. Apparently additional neural layers are added that map z*s to r*s. The backpropagation in the constrained case is undefined. Here an algorithm box or schematic figure comparing unconstrained and constrained NN architectures would be extremely helpful. It’s also not explained how are modelling/domain constraints different. The paper does not compare to the earlier constrained methods (Marquaz-Neila or OptNet), and thus there is no demonstration of the methods claimed superior computational efficiency. The paper also does not make very clear the different constraining approach advantages and tradeoffs. A comparison table would be help a lot. The method is interesting, novel and seemingly efficient; but it is insufficiently defined, the method is not motivated and experiments are quite weak with little comparisons and no experiments with practical value.
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
Homogeneous Linear Inequality Constraints for Neural Network Activations
We propose a method to impose homogeneous linear inequality constraints of the form on neural network activations. The proposed method allows a data-driven training approach to be combined with modeling prior knowledge about the task. One way to achieve this task is by means of a projection step at test time after unconstrained training. However, this is an expensive operation. By directly incorporating the constraints into the architecture, we can significantly speed-up inference at test time; for instance, our experiments show a speed-up of up to two orders of magnitude over a projection method. Our algorithm computes a suitable parameterization of the feasible set at initialization and uses standard variants of stochastic gradient descent to find solutions to the constrained network. Thus, the modeling constraints are always satisfied during training. Crucially, our approach avoids to solve an optimization problem at each training step or to manually trade-off data and constraint fidelity with additional hyperparameters. We consider constrained generative modeling as an important application domain and experimentally demonstrate the proposed method by constraining a variational autoencoder.
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>



The paper proposes a new faster algorithm to add inequality constraints to neural layers. The paper focuses on a novel constraining approach with seemingly superior scalability, and this is potentially a significant contribution. However the paper does not motivate the constraining at all. I am baffled by this, since one would assume at least some benefits from all of this work could be presented. The only mentions are binarization of the predictions (which softmax already does), and monotonicity/convexity of neurons, with no proposed benefits. The running example of the paper is the chessboard constraint, which is either pointless (fig1) or harmful (fig5). Without justification and motivation the method has no merit and won’t have any impact in the machine learning community. The monotonicity constraint could have a huge impact for MCMC sampling of neural parameters since it can reduce away all multimodalities of the posterior caused by reordering nodes or layers. I had hard time following the method, and I its not clear how the neural network is modified and how backpropagation is performed with the contraints. It is not defined properly how the constrained optimisation works. Apparently additional neural layers are added that map z*s to r*s. The backpropagation in the constrained case is undefined. Here an algorithm box or schematic figure comparing unconstrained and constrained NN architectures would be extremely helpful. It’s also not explained how are modelling/domain constraints different. The paper does not compare to the earlier constrained methods (Marquaz-Neila or OptNet), and thus there is no demonstration of the methods claimed superior computational efficiency. The paper also does not make very clear the different constraining approach advantages and tradeoffs. A comparison table would be help a lot. The method is interesting, novel and seemingly efficient; but it is insufficiently defined, the method is not motivated and experiments are quite weak with little comparisons and no experiments with practical value.
assistant
The paper proposes a new faster algorithm to add inequality constraints to neural layers. The paper focuses on a novel constraining approach with seemingly superior scalability, and this is potentially a significant contribution. However the paper does not motivate the constraining at all. I am baffled by this, since one would assume at least some benefits from all of this work could be presented. The only mentions are binarization of the predictions (which softmax already does), and monotonicity/convexity of neurons, with no proposed benefits. The running example of the paper is the chessboard constraint, which is either pointless (fig1) or harmful (fig5). Without justification and motivation the method has no merit and won’t have any impact in the machine learning community. The monotonicity constraint could have a huge impact for MCMC sampling of neural parameters since it can reduce away all multimodalities of the posterior caused by reordering nodes or layers. I had hard time following the method, and I its not clear how the neural network is modified and how backpropagation is performed with the contraints. It is not defined properly how the constrained optimisation works. Apparently additional neural layers are added that map z*s to r*s. The backpropagation in the constrained case is undefined. Here an algorithm box or schematic figure comparing unconstrained and constrained NN architectures would be extremely helpful. It’s also not explained how are modelling/domain constraints different. The paper does not compare to the earlier constrained methods (Marquaz-Neila or OptNet), and thus there is no demonstration of the methods claimed superior computational efficiency. The paper also does not make very clear the different constraining approach advantages and tradeoffs. A comparison table would be help a lot. The method is interesting, novel and seemingly efficient; but it is insufficiently defined, the method is not motivated and experiments are quite weak with little comparisons and no experiments with practical value.