Unbiased scalable softmax optimization
Recent neural network and language models have begun to rely on softmax distributions with an extremely large number of categories. In this context calculating the softmax normalizing constant is prohibitively expensive. This has spurred a growing literature of efficiently computable but biased estimates of the softmax. In this paper we present the first two unbiased algorithms for maximizing the softmax likelihood whose work per iteration is independent of the number of classes and datapoints (and does not require extra work at the end of each epoch). We compare our unbiased methods* empirical performance to the state-of-the-art on seven real world datasets, where they comprehensively outperform all competitors.
 The problem of numerical instability in applying SGD to soft-max minimization is the motivation. It would have been helpful if the author(s) could have made a formal statement. Since the main contributions are two algorithms for stable SGD it is not clear how one can formally say that they are stable. For this a formal problem statement is necessary. The discussion around eq (7) is helpful but is intuitive and it is difficult to get a formal problem which we can use later to examine the proposed algorithms. The proposed algorithms are variants of SGD but it is not clear why they should converge faster than existing strategies. Some parts of the text are badly written, see for example the following line(see paragraph before Sec 3) "Since the converge of SGD is inversely proportional to the magnitude of its gradients (Lacoste-Julien et al., 2012), we expect the formulation to converge faster." which could have shed more light on the matter. The title is also misleading in using the word "exact". I have understand it correct the proposed SGD method solves the optimization problem to an additive error. In summary the algorithms are novel variants of SGD but the associated claims of numerical stability and speed of convergence vis-a-vis existing methods are missing. The choice of word exact is also not clear.
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
Unbiased scalable softmax optimization
Recent neural network and language models have begun to rely on softmax distributions with an extremely large number of categories. In this context calculating the softmax normalizing constant is prohibitively expensive. This has spurred a growing literature of efficiently computable but biased estimates of the softmax. In this paper we present the first two unbiased algorithms for maximizing the softmax likelihood whose work per iteration is independent of the number of classes and datapoints (and does not require extra work at the end of each epoch). We compare our unbiased methods* empirical performance to the state-of-the-art on seven real world datasets, where they comprehensively outperform all competitors.
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 problem of numerical instability in applying SGD to soft-max minimization is the motivation. It would have been helpful if the author(s) could have made a formal statement. Since the main contributions are two algorithms for stable SGD it is not clear how one can formally say that they are stable. For this a formal problem statement is necessary. The discussion around eq (7) is helpful but is intuitive and it is difficult to get a formal problem which we can use later to examine the proposed algorithms. The proposed algorithms are variants of SGD but it is not clear why they should converge faster than existing strategies. Some parts of the text are badly written, see for example the following line(see paragraph before Sec 3) "Since the converge of SGD is inversely proportional to the magnitude of its gradients (Lacoste-Julien et al., 2012), we expect the formulation to converge faster." which could have shed more light on the matter. The title is also misleading in using the word "exact". I have understand it correct the proposed SGD method solves the optimization problem to an additive error. In summary the algorithms are novel variants of SGD but the associated claims of numerical stability and speed of convergence vis-a-vis existing methods are missing. The choice of word exact is also not clear.
assistant
 The problem of numerical instability in applying SGD to soft-max minimization is the motivation. It would have been helpful if the author(s) could have made a formal statement. Since the main contributions are two algorithms for stable SGD it is not clear how one can formally say that they are stable. For this a formal problem statement is necessary. The discussion around eq (7) is helpful but is intuitive and it is difficult to get a formal problem which we can use later to examine the proposed algorithms. The proposed algorithms are variants of SGD but it is not clear why they should converge faster than existing strategies. Some parts of the text are badly written, see for example the following line(see paragraph before Sec 3) "Since the converge of SGD is inversely proportional to the magnitude of its gradients (Lacoste-Julien et al., 2012), we expect the formulation to converge faster." which could have shed more light on the matter. The title is also misleading in using the word "exact". I have understand it correct the proposed SGD method solves the optimization problem to an additive error. In summary the algorithms are novel variants of SGD but the associated claims of numerical stability and speed of convergence vis-a-vis existing methods are missing. The choice of word exact is also not clear.