Paper: Competition Priors for Object-Centric Learning (ICLR-2024)

Reviewer comment (Novelty):
All components of COP are not new. The non-iterative attention operation is common. For example in SAVi, they also perform single iteration Slot Attention. The primitive slots come from image features, which are conceptually similar to the conditional initialization in SAVi, with the only difference that they are not from initial frame hints.

Author response:
We thank the reviewer for their feedback and glad that the reviewer appreciates the non-iterative design and the results on the small datasets. 

**Regarding SAVI:**
Yes, SAVI is non-iterative. But, a lot of “initial” features in SAVI are manually selected. For example, centre of mass, bounding box, segmentation etc. This makes the problem much easier.

Reviewer comment (Experiments):
The datasets used in this paper are too simple. OCL has witnessed tremendous progress in recent years, where OCL methods have proven effective on more complex datasets [3]. The simple images tested in this paper make it hard to assess the capacity of COP. A necessary experiment is to incorporate COP with better OCL models such as STEVE, and test it on complex datasets like MOVi.

Author response:
We thank the reviewer for their feedback and glad that the reviewer appreciates the non-iterative design and the results on the small datasets. 

**Regarding other datasets and experiments:**
We do not have results for these datasets currently. We intend to add them in the new version of the manuscript.

Reviewer comment (Experiments):
It is not clear to me from the experiments the importance of max-pooling or if some other method to learn primitive slots from the input would also work well. This is a central part of the algorithm and it would strengthen the evidence for using max-pooling if this is compared with other ways of pooling such as average-pooling or strided convolutions.

Author response:
In our experiments replacing max pooling with average pooling lower the performance considerably.

Reviewer comment (Evaluation):
Have you noticed significant wall-clock time difference between COP and Slot Attention?

Author response:
For the tetro dataset (where we have most of our experiments), we had results in half the walk clock time as Slot Attention.

Reviewer comment (Experiments):
For the "COP w/ Attn as in Slot Attention" ablation, is the main difference the addition of the weight normalization after the softmax?

Author response:
Yes, in this case we add the weight normalisation after the softmax.

Reviewer comment (Novelty):
The mechanism of Soft-Winner-Takes-All (SWTA) is not explained clearly and the comparison with Slot Attention is misleading. Slot attention takes the softmax over the queries first and then normalizes over the keys by dividing each row by its sum. As I interpret the paper, SWTA seem to perform the first operation, i.e. the softmax over the queries, but skips the normalization. Therefore, what is the novelty? Skipping the normalization? Running a single iteration instead of multiple ones? In both Slot Attention and SWTA there is competition for the patches between queries: if a patch is assigned to one query/slot it can not be assigned to others.

Author response:
Yes, you are right. SWTA-Attention skips the normalisation part after the softmax. 
But we also remove the following parts from the Slot-Attention module: 
a) Gated Recurrent Unit
b) Skip Connection
c) We use the same projection weights for Keys and Values. Thus reducing the number of parameters. 
d) Also, remove the iterations, which are necessary for Slot-Attention to work.

This makes our method very simple, it is just, as you said, “Softmax over the queries”. Our novelty lies in showing that many of these design choices made in Slot-Attention are not necessary.

Reviewer comment (Theory):
I strongly disagree with the analysis performed in section 3.2 about the "competition through MaxPool layers". In particular, the discussion about "sub-networks" in the following sentences: "This results in sub-networks competing to have higher activations. During back-propagation, units that win and the subnetworks that are responsible for this will get updated. As a result, a winning sub-network is reinforced to win more if it predicts correctly." I'd like to point out the CNN layers before MaxPool share the same weights across locations therefore there are no sub-networks in competition, only one network. I would like the authors to provide references to the "sub-networks" interpretation to support their claim in the paper.

Author response:
We have alternating CNN and Max Pool layers. At the end of these layers, a primitive slot is obtained by taking features across the “channel”. We are implying a competition between sub-networks across filters in a CNN layer, not in the shared weights. We will be improving our writing in the next version and hopefully explain it better.

Reviewer comment (Experiments):
Scope of Dataset Evaluation: The empirical validation of the COP model is confined to synthetic datasets. While the authors posit that COP's attributes render it highly scalable for larger datasets, the absence of real-world dataset assessments renders the claims of its object-centric representation less compelling.

Author response:
**Regarding real world datasets:**
We are currently working towards testing our method on real world datasets and will include the results in the updated manuscript.

Reviewer comment (Experiments):
Contemporaneity of Baselines: The baselines utilized in the study are somewhat dated. A comparative analysis with more recent methodologies would be beneficial for a comprehensive evaluation, and such comparisons should be reflected in the results table.

Author response:
**Regarding Baselines:** 
We will also be updating the baselines we compare against. Thank you for the feedback.