Gaussian Prototypical Networks for Few-Shot Learning on Omniglot
We propose a novel architecture for k-shot classification on the Omniglot dataset. Building on prototypical networks, we extend their architecture to what we call Gaussian prototypical networks. Prototypical networks learn a map between images and embedding vectors, and use their clustering for classification. In our model, a part of the encoder output is interpreted as a confidence region estimate about the embedding point, and expressed as a Gaussian covariance matrix. Our network then constructs a direction and class dependent distance metric on the embedding space, using uncertainties of individual data points as weights. We show that Gaussian prototypical networks are a preferred architecture over vanilla prototypical networks with an equivalent number of parameters. We report results consistent with state-of-the-art performance in 1-shot and 5-shot classification both in 5-way and 20-way regime on the Omniglot dataset. We explore artificially down-sampling a fraction of images in the training set, which improves our performance. Our experiments therefore lead us to hypothesize that Gaussian prototypical networks might perform better in less homogeneous, noisier datasets, which are commonplace in real world applications.
 This paper presents an interesting extension to Snell et al.*s prototypical networks, by introducing uncertainty through a parameterised estimation of covariance along side the image embeddings (means). Uncertainty may be particularly important in the few-shot learning case this paper examines, when it is helpful to extract more information from limited number of input samples. However, several important concepts in the paper are not well explained or motivated. For example, it is a bit misleading to use the word "covariance" throughout the paper, when the best model only employs a scalar estimate of the variance. A related, and potentially technical problem is in computing the prototype*s mean and variance (section 3.3). Eq. 5 and 6 are not well motivated, and the claim of "optimal" under eq.6 is not explained. More importantly, eq. 5 and 6 do not use any covariance information (off-diagonal elements of S) --- as a result, the model is likely to ignore the covariance structure even when using full covariance estimate. The distance function (eq. 4) is d Mahalanobis distance, instead of "linear Euclidean distance". While the paper emphasises the importance of the form of loss function, the loss function used in the model is given without explanation (and using cross-entropy over distances looks hacky). In addition, the experiments are too limited to support the claimed benefits from encoding uncertainty. Since the accuracies on omniglot data from recent models are already close to perfect, it is unclear whether the marginally improved number reported here is significant. In addition, more analysis may better support existing claims. For example, showing subsampled images indeed had higher uncertainty, rather than only the histogram for all data points. Pros: -Interesting problem and interesting direction. -Considers a number of possible alternative models -Intuitive illustration in Fig. 1 Cons: -Misleading use of "covariance" -The several important concepts including prototype mean/variance, distance, and loss are not well motivated or explained -Evaluation is too limited
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
Gaussian Prototypical Networks for Few-Shot Learning on Omniglot
We propose a novel architecture for k-shot classification on the Omniglot dataset. Building on prototypical networks, we extend their architecture to what we call Gaussian prototypical networks. Prototypical networks learn a map between images and embedding vectors, and use their clustering for classification. In our model, a part of the encoder output is interpreted as a confidence region estimate about the embedding point, and expressed as a Gaussian covariance matrix. Our network then constructs a direction and class dependent distance metric on the embedding space, using uncertainties of individual data points as weights. We show that Gaussian prototypical networks are a preferred architecture over vanilla prototypical networks with an equivalent number of parameters. We report results consistent with state-of-the-art performance in 1-shot and 5-shot classification both in 5-way and 20-way regime on the Omniglot dataset. We explore artificially down-sampling a fraction of images in the training set, which improves our performance. Our experiments therefore lead us to hypothesize that Gaussian prototypical networks might perform better in less homogeneous, noisier datasets, which are commonplace in real world applications.
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<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>



 This paper presents an interesting extension to Snell et al.*s prototypical networks, by introducing uncertainty through a parameterised estimation of covariance along side the image embeddings (means). Uncertainty may be particularly important in the few-shot learning case this paper examines, when it is helpful to extract more information from limited number of input samples. However, several important concepts in the paper are not well explained or motivated. For example, it is a bit misleading to use the word "covariance" throughout the paper, when the best model only employs a scalar estimate of the variance. A related, and potentially technical problem is in computing the prototype*s mean and variance (section 3.3). Eq. 5 and 6 are not well motivated, and the claim of "optimal" under eq.6 is not explained. More importantly, eq. 5 and 6 do not use any covariance information (off-diagonal elements of S) --- as a result, the model is likely to ignore the covariance structure even when using full covariance estimate. The distance function (eq. 4) is d Mahalanobis distance, instead of "linear Euclidean distance". While the paper emphasises the importance of the form of loss function, the loss function used in the model is given without explanation (and using cross-entropy over distances looks hacky). In addition, the experiments are too limited to support the claimed benefits from encoding uncertainty. Since the accuracies on omniglot data from recent models are already close to perfect, it is unclear whether the marginally improved number reported here is significant. In addition, more analysis may better support existing claims. For example, showing subsampled images indeed had higher uncertainty, rather than only the histogram for all data points. Pros: -Interesting problem and interesting direction. -Considers a number of possible alternative models -Intuitive illustration in Fig. 1 Cons: -Misleading use of "covariance" -The several important concepts including prototype mean/variance, distance, and loss are not well motivated or explained -Evaluation is too limited
assistant
 This paper presents an interesting extension to Snell et al. *s prototypical networks, by introducing uncertainty through a parameterised estimation of covariance along side the image embeddings (means). Uncertainty may be particularly important in the few-shot learning case this paper examines, when it is helpful to extract more information from limited number of input samples. However, several important concepts in the paper are not well explained or motivated. For example, it is a bit misleading to use the word "covariance" throughout the paper, when the best model only employs a scalar estimate of the variance. A related, and potentially technical problem is in computing the prototype*s mean and variance (section 3.3). Eq. 5 and 6 are not well motivated, and the claim of "optimal" under eq.6 is not explained. More importantly, eq. 5 and 6 do not use any covariance information (off-diagonal elements of S) --- as a result, the model is likely to ignore the covariance structure even when using full covariance estimate. The distance function (eq. 4) is d Mahalanobis distance, instead of "linear Euclidean distance". While the paper emphasises the importance of the form of loss function, the loss function used in the model is given without explanation (and using cross-entropy over distances looks hacky). In addition, the experiments are too limited to support the claimed benefits from encoding uncertainty. Since the accuracies on omniglot data from recent models are already close to perfect, it is unclear whether the marginally improved number reported here is significant. In addition, more analysis may better support existing claims. For example, showing subsampled images indeed had higher uncertainty, rather than only the histogram for all data points. Pros: -Interesting problem and interesting direction. -Considers a number of possible alternative models -Intuitive illustration in Fig. 1 Cons: -Misleading use of "covariance" -The several important concepts including prototype mean/variance, distance, and loss are not well motivated or explained -Evaluation is too limited