Mirror Descent View For Neural Network Quantization
Quantizing large Neural Networks (NN) while maintaining the performance is highly desirable for resource-limited devices due to reduced memory and time complexity. NN quantization is usually formulated as a constrained optimization problem and optimized via a modified version of gradient descent. In this work, by interpreting the continuous parameters (unconstrained) as the dual of the quantized ones, we introduce a Mirror Descent (MD) framework (Bubeck (2015)) for NN quantization. Specifically, we provide conditions on the projections (i.e., mapping from continuous to quantized ones) which would enable us to derive valid mirror maps and in turn the respective MD updates. Furthermore, we discuss a numerically stable implementation of MD by storing an additional set of auxiliary dual variables (continuous). This update is strikingly analogous to the popular Straight Through Estimator (STE) based method which is typically viewed as a “trick” to avoid vanishing gradients issue but here we show that it is an implementation method for MD for certain projections. Our experiments on standard classification datasets (CIFAR-10/100, TinyImageNet) with convolutional and residual architectures show that our MD variants obtain fully-quantized networks with accuracies very close to the floating-point networks.
A good paper that uses the Mirror Descent paradigm for learning quantized networks. Though Mirror Descent is not their original idea, but using it in the context of learning quantized network is novel and interesting. Empirically, they showed better results than existing method, with comparisons with reasonable baselines including using relaxed projected gradient descent. Overall, I don’t have much concerns, but here are some more specific comment/questions (most relates to writing) In the intro, it would be great to mention some past success on using MD, as opposed to just saying it’s well-known. Also you mention MD can be used for more than quantization, but compression in general, it’d be better to add that discussion, or remove this sentence. In the beginning of Section 2.1, it*d be easier for the readers to make clear that the primal space corresponds to the quantized weights and the dual space corresponds to the unconstrained space in the rest of the paper. At the top of page 3 you describe MD for the first time, but it’s unclear to me how y^0 is handled. The end of section 3 and section 4 talk quite a bit about STE, maybe it*d be clear if the authors can provide a concise description. As someone not super familiar with NN quantization, this work seems like a good contribution. My only possible concerns would be somehow comparisons to existing methods are not comprehensive enough (if this will be pointed out by the other reviewers)
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
Mirror Descent View For Neural Network Quantization
Quantizing large Neural Networks (NN) while maintaining the performance is highly desirable for resource-limited devices due to reduced memory and time complexity. NN quantization is usually formulated as a constrained optimization problem and optimized via a modified version of gradient descent. In this work, by interpreting the continuous parameters (unconstrained) as the dual of the quantized ones, we introduce a Mirror Descent (MD) framework (Bubeck (2015)) for NN quantization. Specifically, we provide conditions on the projections (i.e., mapping from continuous to quantized ones) which would enable us to derive valid mirror maps and in turn the respective MD updates. Furthermore, we discuss a numerically stable implementation of MD by storing an additional set of auxiliary dual variables (continuous). This update is strikingly analogous to the popular Straight Through Estimator (STE) based method which is typically viewed as a “trick” to avoid vanishing gradients issue but here we show that it is an implementation method for MD for certain projections. Our experiments on standard classification datasets (CIFAR-10/100, TinyImageNet) with convolutional and residual architectures show that our MD variants obtain fully-quantized networks with accuracies very close to the floating-point networks.
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>



A good paper that uses the Mirror Descent paradigm for learning quantized networks. Though Mirror Descent is not their original idea, but using it in the context of learning quantized network is novel and interesting. Empirically, they showed better results than existing method, with comparisons with reasonable baselines including using relaxed projected gradient descent. Overall, I don’t have much concerns, but here are some more specific comment/questions (most relates to writing) In the intro, it would be great to mention some past success on using MD, as opposed to just saying it’s well-known. Also you mention MD can be used for more than quantization, but compression in general, it’d be better to add that discussion, or remove this sentence. In the beginning of Section 2.1, it*d be easier for the readers to make clear that the primal space corresponds to the quantized weights and the dual space corresponds to the unconstrained space in the rest of the paper. At the top of page 3 you describe MD for the first time, but it’s unclear to me how y^0 is handled. The end of section 3 and section 4 talk quite a bit about STE, maybe it*d be clear if the authors can provide a concise description. As someone not super familiar with NN quantization, this work seems like a good contribution. My only possible concerns would be somehow comparisons to existing methods are not comprehensive enough (if this will be pointed out by the other reviewers)
assistant
A good paper that uses the Mirror Descent paradigm for learning quantized networks. Though Mirror Descent is not their original idea, but using it in the context of learning quantized network is novel and interesting. Empirically, they showed better results than existing method, with comparisons with reasonable baselines including using relaxed projected gradient descent. Overall, I don’t have much concerns, but here are some more specific comment/questions (most relates to writing) In the intro, it would be great to mention some past success on using MD, as opposed to just saying it’s well-known. Also you mention MD can be used for more than quantization, but compression in general, it’d be better to add that discussion, or remove this sentence. In the beginning of Section 2.1, it*d be easier for the readers to make clear that the primal space corresponds to the quantized weights and the dual space corresponds to the unconstrained space in the rest of the paper. At the top of page 3 you describe MD for the first time, but it’s unclear to me how y^0 is handled. The end of section 3 and section 4 talk quite a bit about STE, maybe it*d be clear if the authors can provide a concise description. As someone not super familiar with NN quantization, this work seems like a good contribution. My only possible concerns would be somehow comparisons to existing methods are not comprehensive enough (if this will be pointed out by the other reviewers)