Venue: NeurIPS 2021 Conference

Reviews:

final_score: rating: 7: Good paper, accept
review_content: summary: This paper presents a modification to the HRR along with a novel loss that permits efficient learning in large output spaces. The approach is demonstrated on a number of extreme classification tasks and this appears to be the first work that shows the possibility of backpropagating through HRRs that bind many elements.

main_review: This paper presents a modification to the Holographic Reduced Representation that increases the precision of the unbinding operator while maintaining numerical stability and avoiding costly cleanup operations. The paper also presents a novel loss that supports learning in large label spaces. Together, these are applied to extreme classification using an approach that relies on two fixed, orthogonal, role vectors (label present / not present) and many label fillers. This approach supports the novel loss that considers all of the labels without iterating over the large label space, by checking that absent labels are not bound to the label-present role. For extreme classification tasks where few labels are present at any one time, this is significantly more efficient in terms of time and parameters than methods that explicitly model the entire label space.

Results are presented for a number of extreme classification benchmarks, and the new approach is compared to equivalent models that replace the HRR output layer with a standard logistic layer. These results show that the loss is working well and being backpropagated through theeffectively through the (fixed) HRR. There is a discussion of the effect of learning both the role and filler representations but this doesn't seem to have a big effect on the tasks studied.

Overall, I think this is a nice contribution with an interesting set of results. The paper would be even stronger with more discussion of how these results could extend to tasks beyond the current classification settings, that may more explicitly require the binding and unbinding operations made available by the HRR.

limitations_and_societal_impact: The application to extreme classification demonstrates the approach's ability to represent, and learn in, large label spaces. But it only models two roles (label present / not present) and does not investigate the HRRs ability to represent diverse role-filler combinations, or even recursive structures, in a fixed size representation. The paper would be stronger with a discussion of how these results could extend to other applications of the HRR that test its ability to bind arguments in more challenging ways.

While there hasn't been much recent work on learning with HRRs. There has been a line of recent work focused on learning with the very related Tensor Product Representation. I think that work should be mentioned in this paper.
review_title: null

final_score: rating: 6: Marginally above the acceptance threshold
review_content: summary: This paper introduces a modification to the Holographic Reduced Representation (HRR) method, which are a pair of encoding/decoding operations based on circular convolution; these operations can be used to efficiently approximate symbolic querying, information storage, and retrieval operations in a low-dimensional vector embedding space. 
used for approximating symbolic storage and retrieval operations.

The first contribution of this paper is a modification to the original HRR method (introduced by Plate 1995 and primarily used in biologically-plausible computation models) that increases its query accuracy.

The second contribution to this paper is a proof-of-concept loss function that allows the modified HRR encoding to be incorporated into differentiable neural architectures.

The final contribution of this paper is a set of experiments showing that concrete HRR-based models can be used in extreme-multi-label (XML) classification tasks, in some cases exceeding baseline accuracy with standard fully-connected layers used for lookup and retrieval (while using a comparatively smaller and more efficient encoding/decoding scheme.)
main_review: *Strengths (soundness; theoretical grounding; empirical evaluation; significance and novelty; relevance to NeurIPS community)*:
- Novelty of the proposed operation. The authors introduce a projection scheme to the original HRR operation in Plate 1995 and a means of incorporating HRR into modern learnable architectures that appears to be novel (though I am not an expert on the related work, and am comparing relative to the provided related works.) The projection modification seems to significantly improve the viability of the HRR operator over its original form -- it increases the query accuracy for the retrieval task. The usage of HRR operations in a learnable framework at all appears novel.
- Practical contribution: the authors convincingly demonstrate that the HRR operation allows a useful task (queryable lookup and retrieval of many labels in a low-dimensional vector) to be performed efficiently and relatively accurately with fewer vector parameters. 
- The empirical evaluations on the XML task use real-world datasets and demonstrate comparable (and in some cases SOTA-exceeding) performance over a fully-connected baseline for the lookup task, using several different neural architectures (FC; CNN; LSTM) as the base with the HRR layer as the final layer.	
- Significance and potential relevance. The introduction and empirical task certainly suggest that the operation could be a useful new operation in the neural toolkit that can emulate important symbolic operations. However, I believe this aspect can be clarified and tightened, as discussed next. 



*Weaknesses (soundness; theoretical grounding; empirical evaluation; significance and novelty; relevance to NeurIPS community)* :
- Paper framing and next steps using the HRR operation. While reading this paper, I found myself confused about what the goals of this paper were, which would determine the appropriate metrics for evaluating whether the proposed model had or had not succeeded, and what its prospects were as a significant new tool in vector-based computation. While the authors introduce a reasonably novel operation (the HRR framework) and provide proof-of-concept empirical evaluations demonstrating that it is viable on a practical XML task, they stop short of (and in fact explicitly say) that their goals are not to demonstrate state-of-the art XML performance. This is fine, but I believe a useful revision of this paper could paint a clearer and more precise picture of why the HRR operation is being introduced -- and what its clearest advantages are (or could be) over other approaches. The framing and goals of introducing HRR seem to change or are hard to pin down throughout the paper -- I think the introduction could benefit from a revision that crisply enumerates its advantages over other related methods (and the kinds of currently-neural operations it might be comparable to or seek replace). 

At times the authors suggest that a major goal is to improve on HRRs (eg. L306-309) . This would make sense if a focus of the paper was for neurally-plausible cognition or tackling the other cognitive tasks (but it does not seem to be.) Otherwise, it would seem that a better focus would be on how HRR itself improves over the existing symbolic and neural SOTA toolkit early on (eg. the possibility of distillation; improved accuracy on other kinds of tasks; or computational efficiency.)

In other words, I was looking for a summary that would clearly answer: what is this for; what is this intended to replace; and what are its prospects at doing so in scaled up practical applications? 

To better guide a revision, I will elaborate on several questions I had while reading this that might help with a tighter framing:
- Empirical comparisons to existing ‘competitor operators’: were the FC-final layers the best comparison for the kinds of operations HRR might seek to replace? What about other hashing and distillation approaches? The authors mention that they replaced the hierarchical-attention based head in AttentionXML with an FC layer. This seems like a pretty major change, especially since learnable attention seems like one of the closer comparisons to the kind of querying that HRR can perform. Putting attention (or another common ‘competitor’ operation) through its paces with respect to HRR -- on a variety of metrics (computational efficiency, accuracy) would be useful.
- Candidate as a useful symbolic operation in scaled up tasks and architectures: the XML task seems to be a good fit for HRR. But it would be even better if the authors could paint a picture of how or whether it could be used for other kinds of symbolic operations associated with Turing machines or modern programming languages -- for example, can HRR be used to preserve ordering and syntax, like a structured grammar? These are key reasons why symbolic components are often added to neural architectures, beyond query capacity. 
- Candidate as a practical operation in scaled up learnable tasks and architectures: the discussion of updating label vectors leaves open questions of how HRR would be practically incorporated into more complex learnable architectures -- when I think about attention-based architectures, for instance, one key aspect of their success is that they can play well with operations over implicit, learned vector representations. Beyond XML, could the authors give a picture (or suggest how future work might tackle) HRR operations in other modern tasks? Even better if these are tasks that intuitively require some learning and cannot be solved by a solely symbolic approach. 

====
*Clarity review*: the paper is relatively clear in presenting the HRR operation and modifications made by the authors, though it is also notation dense (I’m not an expert, but I had to look up the basic circular convolution and seek external references to suggest why this operation should have benefits over other attention-style operations.) We might have benefitted (even in the supplement) from a worked example on a toy lookup task, as well as some figures showing how the operation works graphically (like those on the Wikipedia page about circular convolution!)
		- The discussion of the loss, however, is clear and useful relative to the more 
common cross-entropy loss.

*Correctness review*: the approach overall appears correct. 
*Relation to prior work*: the authors extensively discuss prior work on HRRs. As discussed above, it would be useful if they could also take a step back and at least review the closest prior work outside of HRRs that we should consider this work to be comparable to in order to frame the best comparisons early on. 

Tiny nits:
	L294-295: XXX lines of code.
	HRR is sometimes misspelled as ‘HHR’ throughout. :) 

limitations_and_societal_impact: The authors make a good effort in the empirical section to discuss limitations of their existing framework on a real-world task, and against relatively reasonable baselines (though see above for a discussion of the FC choice.) They choose a variety of reasonable metrics and provide additional supplementary material discussing the additional ablations and experiments conducted.
	They complete an author checklist, and (I believe) accurately assess the potential societal impacts.
review_title: null

final_score: rating: 7: Good paper, accept
review_content: summary: The authors study a small but important modification of holographic reduced representations (HRRs) which make them practical for use in differentiable neurosymbolic systems. They do a good job exploring the implications of this modification, though on a task (multi-label classification) which does not seem like a particularly exciting domain for HRRs, in the sense that it doesn't utilize what is arguably their key feature, namely the ability to represent complex symbolic knowledge.
main_review: This paper introduces a projection operator that initializes vectors to have a complex magnitude of 1. This has important practical implications for using these vectors in a holographic reduced representation, because it enables use of the inverse operator for decoding in a numerically stable way (rather than the approximate inverse, which was traditionally use because of its greater numerical stability).

My subjective view of this paper is that it presents a useful method, and a pretty detailed comparison between architectures and parametrizations, but the application domain (multi-label classification) isn't a particularly interesting one. HRRs were invented to do represent and reason about complex symbolic expressions. It would have been more interesting to see an application to the kinds of domains where neurosymbolic approaches have been applied recently (e.g., scene understanding, knowledge graphs, natural language inference).

My other major comment is that it's not clear what problem is being solved here that wasn't already solved. The authors concede that their approach is not intended to exceed performance of other algorithms on XML tasks, but rather to understand the pros and cons of using HRRs for this task. I feel like this is a rather weak case for using HRRs (though I agree with the authors that the advantage of the HRR in their comparisons is compelling). This connects back to my previous point, which is that a better case for HRRs might be made with a different task, one where symbolic reasoning is necessary.

Minor:

abstract: "differential component" -> "differentiable component" (?)

abstract: "differential solution" -> "differentiable solution" (?)

abstract: "a output" -> "an output"

I don't understand the query example in the second paragraph of the introduction. Should this be the inverse operation applied to S and red? Why is there a convolution symbol in there?

p. 2: "it’s niche" -> "its niche"

p. 2: "takle" -> "tackle"

p. 3: "it's values" -> "its values"

p. 4: It looks odd to have an equation number (4) in the middle of an equation.

p. 7: "XXX lines of code" should be replaced with an integer.

p. 7: "overal" -> "overall"

p. 7: "project step" -> "projection step"

p. 7: "largeness" -> "size"

I was confused by Table 1. Why are different sets of models being applied to different data sets? I didn't see any explanation of these choices.
limitations_and_societal_impact: I don't see any negative societal impact of the work. They have adequately addressed limitations.
review_title: null

Meta-review: This paper shows how HRRs can be modified to enable end-to-end differentiable training at scale. While the results are not compelling that such representations will be useful in applications, the reviewers all agreed that the technical method is novel and provides a foundation for other systems to build on. 
Decision: Accept (Spotlight)