Paper:
Incorporating Side Information by Adaptive Convolution
Computer vision tasks often have side information available that is helpful to solve the task. For example, for crowd counting, the camera perspective (e.g., camera angle and height) gives a clue about the appearance and scale of people in the scene. While side information has been shown to be useful for counting systems using traditional hand-crafted features, it has not been fully utilized in counting systems based on deep learning. In order to incorporate the available side information, we propose an adaptive convolutional neural network (ACNN), where the convolution filter weights adapt to the current scene context via the side information. In particular, we model the filter weights as a low-dimensional manifold within the high-dimensional space of filter weights. The filter weights are generated using a learned "filter manifold" sub-network, whose input is the side information. With the help of side information and adaptive weights, the ACNN can disentangle the variations related to the side information, and extract discriminative features related to the current context (e.g. camera perspective, noise level, blur kernel parameters). We demonstrate the effectiveness of ACNN incorporating side information on 3 tasks: crowd counting, corrupted digit recognition, and image deblurring. Our experiments show that ACNN improves the performance compared to a plain CNN with a similar number of parameters. Since existing crowd counting datasets do not contain ground-truth side information, we collect a new dataset with the ground-truth camera angle and height as the side information.

Review:
Summary of the Paper:
This work proposes to use adaptive convolutions (also called 'cross convolutions') to incorporate side information (e.g., camera angle) into CNN architectures for vision tasks (e.g., crowd counting). The filter weights in each adaptive convolution layer are predicted using a separate neural network (one network for each set of filter weights) with is a multi-layer perceptron. This network is referred to as 'Filter Manifold Network' which takes the auxiliary side information as input and predicts the filter weights. Experiments on three vision tasks of crowd counting, digit recognition and image deconvolution indicate the potential of the proposed technique for incorporating auxiliary information. In addition, this paper contributes a new dataset for crowd counting with different camera heights and angles.
Paper Strengths:
- A simple yet working technique for incorporating auxiliary information into CNNs with adaptive convolutions.
- With this technique, a single network is sufficient for different dataset settings (for instance, denoising with different blur kernel parameters) and authors demonstrated generalization capability of the proposed technique to interpolate between auxiliary information.
- Experiments on 3 different vision tasks with good results compared to similar CNN architectures with non-adaptive convolutions.
- A new dataset on crowd counting.
Weaknesses:
- There is almost no discussion or analysis on the 'filter manifold network' (FMN) which forms the main part of the technique. Did authors experiment with any other architectures for FMN? How does the adaptive convolutions scale with the number of filter parameters? It seems that in all the experiments, the number of input and output channels is small (around 32). Can FMN scale reasonably well when the number of filter parameters is huge (say, 128 to 512 input and output channels which is common to many CNN architectures)?
- From the experimental results, it seems that replacing normal convolutions with adaptive convolutions in not always a good. In Table-3, ACNN-v3 (all adaptive convolutions) performed worse that ACNN-v2 (adaptive convolutions only in the last layer). So, it seems that the placement of adaptive convolutions is important, but there is no analysis or comments on this aspect of the technique.
- The improvements on image deconvolution is minimal with CNN-X working better than ACNN when all the dataset is considered. This shows that the adaptive convolutions are not universally applicable when the side information is available. Also, there are no comparisons with state-of-the-art network architectures for digit recognition and image deconvolution.
Suggestions:
- It would be good to move some visual results from supplementary to the main paper. In the main paper, there is almost no visual results on crowd density estimation which forms the main experiment of the paper. At present, there are 3 different figures for illustrating the proposed network architecture. Probably, authors can condense it to two and make use of that space for some visual results.
- It would be great if authors can address some of the above weaknesses in the revision to make this a good paper.
Review Summary:
- Despite some drawbacks in terms of experimental analysis and the general applicability of the proposed technique, the paper has several experiments and insights that would be interesting to the community.
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After the Rebuttal:
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My concern with this paper is insufficient analysis of 'filter manifold network' architecture and the placement of adaptive convolutions in a given CNN. Authors partially addressed these points in their rebuttal while promising to add the discussion into a revised version and deferring some other parts to future work. 
With the expectation that authors would revise the paper and also since other reviewers are fairly positive about this work, I recommend this paper for acceptance.