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Context: Prototypical networks compute an M-dimensional representation \mathbf{c}_{k}\in\mathbb{R}^{M}, or prototype, of each class through an embedding function f_{\bm{\phi}}:\mathbb{R}^{D}\rightarrow\mathbb{R}^{M} with learnable parameters \bm{\phi}. Each prototype is the mean vector of the embedded support points belonging to its class:\mathbf{c}_{k}=\frac{1}{|S_{k}|}\sum_{(\mathbf{x}_{i},y_{i})\in S_{k}}f_{\bm{\phi}}(\mathbf{x}_{i})(1)Given a distance function d:\mathbb{R}^{M}\times\mathbb{R}^{M}\rightarrow[0,+\infty), prototypical networks produce a distribution over classes for a query point \mathbf{x} based on a softmax over distances to the prototypes in the embedding space:p_{\bm{\phi}}(y=k\,|\,\mathbf{x})=\frac{\exp(-d(f_{\bm{\phi}}(\mathbf{x}),\mathbf{c}_{k}))}{\sum_{k^{\prime}}\exp(-d(f_{\bm{\phi}}(\mathbf{x}),\mathbf{c}_{k^{\prime}}))}(2)Learning proceeds by minimizing the negative log-probability J(\bm{\phi})=-\log p_{\bm{\phi}}(y=k\,|\,\mathbf{x}) of the true class k via SGD. Training episodes are formed by randomly selecting a subset of classes from the training set, then choosing a subset of examples within each class to act as the support set and a subset of the remainder to serve as query points. Pseudocode to compute the loss J(\bm{\phi}) for a training episode is provided in Algorithm 1.

Question: What is the value of M?
[Prototypical networks compute an M-dimensional representation \mathbf{c}_{k}\in\mathbb{R}^{M}, or prototype, of each class through an embedding function f_{\bm{\phi}}:\mathbb{R}^{D}\rightarrow\mathbb{R}^{M} with learnable parameters \bm{\phi}. Each prototype is the mean vector of the embedded support points belonging to its class:\mathbf{c}_{k}=\frac{1}{|S_{k}|}\sum_{(\mathbf{x}_{i},y_{i})\in S_{k}}f_{\bm{\phi}}(\mathbf{x}_{i}). Hence M=Dimension of the prototype.]