Smooth Loss Functions for Deep Top-k Classification
The top- error is a common measure of performance in machine learning and computer vision. In practice, top- classification is typically performed with deep neural networks trained with the cross-entropy loss. Theoretical results indeed suggest that cross-entropy is an optimal learning objective for such a task in the limit of infinite data. In the context of limited and noisy data however, the use of a loss function that is specifically designed for top- classification can bring significant improvements. Our empirical evidence suggests that the loss function must be smooth and have non-sparse gradients in order to work well with deep neural networks. Consequently, we introduce a family of smoothed loss functions that are suited to top- optimization via deep learning. The widely used cross-entropy is a special case of our family. Evaluating our smooth loss functions is computationally challenging: a na{"i}ve algorithm would require operations, where is the number of classes. Thanks to a connection to polynomial algebra and a divide-and-conquer approach, we provide an algorithm with a time complexity of . Furthermore, we present a novel approximation to obtain fast and stable algorithms on GPUs with single floating point precision. We compare the performance of the cross-entropy loss and our margin-based losses in various regimes of noise and data size, for the predominant use case of . Our investigation reveals that our loss is more robust to noise and overfitting than cross-entropy.
 This paper introduces a smooth surrogate loss function for the top-k SVM, for the purpose of plugging the SVM to the deep neural networks. The idea is to replace the order statistics, which is not smooth and has a lot of zero partial derivatives, to the exponential of averages, which is smooth and is a good approximation of the order statistics by a good selection of the "temperature parameter". The paper is well organized and clearly written. The idea deserves a publication. On the other hand, there might be better and more direct solutions to reduce the combinatorial complexity. When the temperature parameter is small enough, both of the original top-k SVM surrogate loss (6) and the smooth loss (9) can be computed precisely by sorting the vector s first, and take a good care of the boundary around s_{[k]}.
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
Smooth Loss Functions for Deep Top-k Classification
The top- error is a common measure of performance in machine learning and computer vision. In practice, top- classification is typically performed with deep neural networks trained with the cross-entropy loss. Theoretical results indeed suggest that cross-entropy is an optimal learning objective for such a task in the limit of infinite data. In the context of limited and noisy data however, the use of a loss function that is specifically designed for top- classification can bring significant improvements. Our empirical evidence suggests that the loss function must be smooth and have non-sparse gradients in order to work well with deep neural networks. Consequently, we introduce a family of smoothed loss functions that are suited to top- optimization via deep learning. The widely used cross-entropy is a special case of our family. Evaluating our smooth loss functions is computationally challenging: a na{"i}ve algorithm would require operations, where is the number of classes. Thanks to a connection to polynomial algebra and a divide-and-conquer approach, we provide an algorithm with a time complexity of . Furthermore, we present a novel approximation to obtain fast and stable algorithms on GPUs with single floating point precision. We compare the performance of the cross-entropy loss and our margin-based losses in various regimes of noise and data size, for the predominant use case of . Our investigation reveals that our loss is more robust to noise and overfitting than cross-entropy.
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>



 This paper introduces a smooth surrogate loss function for the top-k SVM, for the purpose of plugging the SVM to the deep neural networks. The idea is to replace the order statistics, which is not smooth and has a lot of zero partial derivatives, to the exponential of averages, which is smooth and is a good approximation of the order statistics by a good selection of the "temperature parameter". The paper is well organized and clearly written. The idea deserves a publication. On the other hand, there might be better and more direct solutions to reduce the combinatorial complexity. When the temperature parameter is small enough, both of the original top-k SVM surrogate loss (6) and the smooth loss (9) can be computed precisely by sorting the vector s first, and take a good care of the boundary around s_{[k]}.
assistant
 This paper introduces a smooth surrogate loss function for the top-k SVM, for the purpose of plugging the SVM to the deep neural networks. The idea is to replace the order statistics, which is not smooth and has a lot of zero partial derivatives, to the exponential of averages, which is smooth and is a good approximation of the order statistics by a good selection of the "temperature parameter". The paper is well organized and clearly written. The idea deserves a publication. On the other hand, there might be better and more direct solutions to reduce the combinatorial complexity. When the temperature parameter is small enough, both of the original top-k SVM surrogate loss (6) and the smooth loss (9) can be computed precisely by sorting the vector s first, and take a good care of the boundary around s_{[k]}.