Paper:
Metric embeddings are immensely useful representations of associations between entities (images, users, search queries, words, and more). Embeddings are learned by optimizing a loss objective of the general form of a sum over example associations. Typically, the optimization uses stochastic gradient updates over minibatches of examples that are arranged independently at random. In this work, we propose principled methods of structuring the arrangements of training examples aimed at accelerating the training. Our arrangements consist of randomized microbatches of examples from a distribution that is guided by the structure of the example associations but respects a specified marginal distribution of training examples. We present efficient microbatch generators and experimentally demonstrate training time acceleration of 3-30%. Structured arrangements emerge as a powerful and novel performance knob for SGD that is independent and complementary to other SGD hyperparameters and thus is a candidate for wide deployment.

Review:
The paper presents a method for improving the convergence rate of Stochastic Gradient Descent for learning embeddings by grouping similar training samples together. The basic idea is that gradients computed on a batch of highly associated samples encode related information in a single update that independent samples might take multiple updates to capture. These structured minibatches are constructed by independently combining subsets of positive examples called “microbatches”. Two methods are presented for constructing these microbaches; first by grouping positive examples by shared context (called “basic” microbatches), second by applying Locality Sensitive Hashing to further partition the microbatches into groups that are more likely to contain similar examples.
Three datasets are used for experimental analysis: a synthetic dataset generated using the stochastic block model, and two large scale recommendation datasets. The presented algorithms are compared to a baseline of independently sampled minibatches using the cosine gap and precision for the top k predictions. The authors show the measured cosine gaps over the course of training as well as the gains in training performance for several sets of hyperparameters.
The motivation and basic intuition behind the work is clearly presented in the introductory section. The theoretical justification for the structured minibatches is reasonably convincing and invites empirical verification.
General concerns:
Any method for improving the performance of an optimization process via additional preprocessing must show that the additional overhead incurred from preprocessing the data (in this case, organizing the minibatches) does not negate the achieved improvement in convergence time. This work presents no evidence that this is the case. I expected to see 1) time complexity analysis of each new algorithm proposed for preprocessing and 2) experimental results showing that the overall computation time, including the proposed preprocessing steps, was reduced by this method. Neither of these things are present in this work.
Furthermore, the measured “training gains” are, to my knowledge, not clearly defined. I assume that the authors are using the number of epochs or iterations before convergence as their measure of training performance, but this should be stated explicitly rather than implicitly.
Finally, the experimental results presented do not seem to entirely support the authors’ conclusions. Figures 2, 3, and 4, as well as several of the figures in the appendix, show some parameter settings for which the gains over the baseline are quite limited. This makes me suspect that perhaps the coordinated minibatches aren’t the only variable affecting performance.
I have organized my remaining minor concerns and requests for clarification by section, detailed below.
Section 1
- In the last paragraph, the acronym SGNS is mentioned before being defined. You should either state the full name of the method (with citation) or omit the mention altogether.
Section 2
- I would like a few sentences of additional clarification on what “focus” entities vs. “context” entities are in the more general case. I am familiar with what they mean in the context of Skip Gram, but I think more discussion on how this generalizes is necessary here. Same goes for what kappa (“association strength”) means, especially considering that this concept isn’t really present (to my understanding) in Skip Gram.
- Grammar correction:
“The negative examples provide an antigravity effect that prevents all embeddings to collapse into the same vector”
“to collapse” -> “from collapsing”
Section 3
- Maybe this is just me, but I find the mu-beta notation for the microbatch distributions rather odd. Why not just use a single symbol?
- I would like a bit more clarification on the proof for lemma 3.1, specifically on the last sentence, “the product of these events …”; that statement did not follow obviously to me.
Section 3.1
- Remove the period and colon near kappas at the end of paragraph 3. It’s visually confusing with the dot index notation right next to them.
Section 4
- Typo: “We selects a row vector …” -> “We select a row vector …”
Section 5
- I don’t understand what Figure 1 is trying to demonstrate. It doesn’t do anything (as far as I can tell) to defend the authors’ claim that COO provides a higher expected increase in cosine similarity than IND.
Section 6
- All figures in this section should have axis labels. The captions don’t sufficiently explain what they are.
Section 6.2
- How is kappa computed for the recommendations datasets? This isn’t obvious at all.