Venue: ICLR 2017 conference

Reviews:

final_score: rating: 5: Marginally below acceptance threshold
review_content: Authors show that a contrastive loss for a Siamese architecture can be used for learning representations for planar curves. With the proposed framework, authors are able to learn a representation which is comparable to traditional differential or integral invariants, as evaluated on few toy examples.

The paper is generally well written and shows an interesting application of the Siamese architecture. However, the experimental evaluation and the results show that these are rather preliminary results as not many of the choices are validated. My biggest concern is in the choice of the negative samples, as the network basically learns only to distinguish between shapes at different scales, instead of recognizing different shapes. It is well known fact that in order to achieve a good performance with the contrastive loss, one has to be careful about the hard negative sampling, as using too easy negatives may lead to inferior results. Thus, this may be the underlying reason for such choice of the negatives? Unfortunately, this is not discussed in the paper.

Furthermore the paper misses a more thorough quantitative evaluation and concentrates more on showing particular examples, instead of measuring more robust statistics over multiple curves (invariance to noise and sampling artifacts).

In general, the paper shows interesting first steps in this direction, however it is not clear whether the experimental section is strong and thorough enough for the ICLR conference. Also the novelty of the proposed idea is limited as Siamese networks are used for many years and this work only shows that they can be applied to a different task.
review_title: Limited theoretical novelty and evaluation

final_score: rating: 6: Marginally above acceptance threshold
review_content: I'm torn on this one. Seeing the MPEG-7 dataset and references to curvature scale space brought to mind the old saying that "if it's not worth doing, it's not worth doing well." There is no question that the MPEG-7 dataset/benchmark got saturated long ago, and it's quite surprising to see it in a submission to a modern ML conference. I brought up the question of "why use this representation" with the authors and they said their "main purpose was to connect the theory of differential geometry of curves with the computational engine of a convolutional neural network." Fair enough. I agree these are seemingly different fields, and the authors deserve some credit for connecting them. If we give them the benefit of the doubt that this was worth doing, then the approach they pursue using a Siamese configuration makes sense, and their adaptation of deep convnet frameworks to 1D signals is reasonable. To the extent that the old invariant based methods made use of smoothed/filtered representations coupled with nonlinearities, it's sensible to revisit this problem using convnets. I wouldn't mind seeing this paper accepted, since it's different from the mainstream, but I worry about there being too narrow an audience at ICLR that still cares about this type of shape representation.
review_title: filling a much needed gap?

final_score: rating: null
review_content: - Why there is no rotation for the negative samples?
- Are the negative samples always the same contour, as visualized in the table 1, only with a different scale?
- Why is the contour retrieval not computed on the 350 testing and validation contours? The precision seems to be remarkably low even for such small dataset.
- Is the method able to achieve invariance to translation and uniform scaling or does it depend on the contour pre-processing?
review_title: Pre-Review Qeustions

final_score: rating: null
review_content: Why not use a rasterized representation of the shapes rather than the parametric curve representations? In other words, you could pursue the same Siamese network based metric learning approach on pixel-domain representations of the MPEG-7 shapes. Parametric curves are of course elegant from a mathematical perspective, but when mixed with the machinery of CNNs, one wonders why not go all-in on image based representations, using spatial transformer networks, etc. I'm asking this since the sight of MPEG-7 shapes, the MATLAB bwboundaries() function and Mokhtarian citations seem oddly anachronistic in a submission to ICLR 2017.
review_title: parametric vs. rasterized representation

final_score: rating: null
review_content: First, I have to say I really did enjoy the result of the paper.

Is the number N of points fixed? If yes, this does not seem to be however a limitation thanks to Section 5, second paragraph, could you clarify this? How did you chose the red points? (via the support of the max pooling?)

Have you tried to check the stability with respect to small deformations: when applying the same deformation to different curves, are there any linearisation properties?

Why did not you use circular convolution, since this symmetry is present in your data?(the first and final points of the input of size N should not change the final result, if I'm correct?) Does the normalization of the signature makes it independent from the first point used to process the curve?

On the Figure 5, I do not understand why there is still a "spike" at the end of the curvature, for the 4th image?

Thank you.
review_title: Technical questions on the architecture

final_score: rating: 8: Top 50% of accepted papers, clear accept
review_content: Pros : 
- New representation with nice properties that are derived and compared with a mathematical baseline and background
- A simple algorithm to obtain the representation

Cons :
- The paper sounds like an applied maths paper, but further analysis on the nature of the representation could be done, for instance, by understanding the nature of each layer, or at least, the first.

review_title: An interesting representation

Meta-review: This work proposes learning of local representations of planar curves using convolutional neural networks.
 Invariance to rigid transformations and discriminability are enforced with a metric learning framework using a siamese architecture. Preliminary experiments on toy datasets compare favorably with predefined geometric invariants (both differential and integral). 
 
 The reviewers found value on the problem set-up and the proposed model, and were generally satisfied with the author's response. They also expressed concern that the experimental section is currently a bit weak and does not include any real data. Also, the paper does not offer theoretical insights that inform us about the design of the representation or about the provable invariance guarantees. All things considered, the AC recommends acceptance in the form of a poster, but strongly encourages the authors to strengthen the work both in the experimental and the theoretical aspects.
Decision: Accept (Poster)