Invariant-equivariant representation learning for multi-class data
Representations learnt through deep neural networks tend to be highly informative, but opaque in terms of what information they learn to encode. We introduce an approach to probabilistic modelling that learns to represent data with two separate deep representations: an invariant representation that encodes the information of the class from which the data belongs, and an equivariant representation that encodes the symmetry transformation defining the particular data point within the class manifold (equivariant in the sense that the representation varies naturally with symmetry transformations). This approach to representation learning is conceptually transparent, easy to implement, and in-principle generally applicable to any data comprised of discrete classes of continuous distributions (e.g. objects in images, topics in language, individuals in behavioural data). We demonstrate qualitatively compelling representation learning and competitive quantitative performance, in both supervised and semi-supervised settings, versus comparable modelling approaches in the literature with little fine tuning.
 The paper proposes a genarative model for images which explicitly separates the within class variation (the covariant part) from the across class variation (invariant part). Functionally, this achieves a similar result as various recent works on incorporating invariances in neural nets, but the fact that it is able to explicitly construct models for both parts of the distribution is nice. Results on MNIST are good, but of course this is a very simple dataset. It would be very interesting to see how the model performs on a more realistic problem. Admittedly, I am not an expert in generative models. This is a clean paper with a clear goal, it is hard for me to judge how original the idea is. "Covariant" might not be the best word to use here because it has a very specific meaning in the context of some other neural networks related to how quantities transform according to representations of a symmetry group. This is a potential source of confusion.
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
Invariant-equivariant representation learning for multi-class data
Representations learnt through deep neural networks tend to be highly informative, but opaque in terms of what information they learn to encode. We introduce an approach to probabilistic modelling that learns to represent data with two separate deep representations: an invariant representation that encodes the information of the class from which the data belongs, and an equivariant representation that encodes the symmetry transformation defining the particular data point within the class manifold (equivariant in the sense that the representation varies naturally with symmetry transformations). This approach to representation learning is conceptually transparent, easy to implement, and in-principle generally applicable to any data comprised of discrete classes of continuous distributions (e.g. objects in images, topics in language, individuals in behavioural data). We demonstrate qualitatively compelling representation learning and competitive quantitative performance, in both supervised and semi-supervised settings, versus comparable modelling approaches in the literature with little fine tuning.
user
<think>Okay, to do a decent peer review, I should start with summarizing what the work is about. This includes novelty, contributions, clarity, and impact. I might include suggestions to issues that I find critical to the usefulness of the work. Starting with novelty, there are different types of novelty. The first aspect of novelty is scope and scale. Is the work covering a broader perspective than previous works? The second aspect is methodology. Is the proposed methodology novel compared to previous methods? Do they provide any significant advantage over previous methodologies? The third aspect is results. Are the results different compared previous work? Does this lead to any novel theories or an extension of current theories? Next is clarity, I will be reading the work in depth and analyze if any sentences can be potentially ambiguous or misleading. If any sentences are ambiguous, I will state them and give a suggestion on how to rephrase such sentence or how to make more clear to the audience. Lastly, impact is important. I will attempt to predict how such work will impact the scientific community. This might include the applications of such work and how the work might transform the way we study a certain topic. Finally, I will might only mention issues that are critical. This is to keep the review as concise and helpful as possible.</think>



 The paper proposes a genarative model for images which explicitly separates the within class variation (the covariant part) from the across class variation (invariant part). Functionally, this achieves a similar result as various recent works on incorporating invariances in neural nets, but the fact that it is able to explicitly construct models for both parts of the distribution is nice. Results on MNIST are good, but of course this is a very simple dataset. It would be very interesting to see how the model performs on a more realistic problem. Admittedly, I am not an expert in generative models. This is a clean paper with a clear goal, it is hard for me to judge how original the idea is. "Covariant" might not be the best word to use here because it has a very specific meaning in the context of some other neural networks related to how quantities transform according to representations of a symmetry group. This is a potential source of confusion.
assistant
 The paper proposes a genarative model for images which explicitly separates the within class variation (the covariant part) from the across class variation (invariant part). Functionally, this achieves a similar result as various recent works on incorporating invariances in neural nets, but the fact that it is able to explicitly construct models for both parts of the distribution is nice. Results on MNIST are good, but of course this is a very simple dataset. It would be very interesting to see how the model performs on a more realistic problem. Admittedly, I am not an expert in generative models. This is a clean paper with a clear goal, it is hard for me to judge how original the idea is. "Covariant" might not be the best word to use here because it has a very specific meaning in the context of some other neural networks related to how quantities transform according to representations of a symmetry group. This is a potential source of confusion.