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I'm currently reading the paper Federated Learning with Matched Averaging (2020), where the authors claim:

A basic fully connected (FC) NN can be formulated as: $\hat{y} = \sigma(xW_1)W_2$ [...]

Expanding the preceding expression $\hat{y} = \sum_{i=1}^{L} W_{2, r \cdot } \sigma(\langle x, W_{1,\cdot i} \rangle))$, where $\cdot i$ and $\cdot i$ denote the ith row and column correspondingly and $L$ is the number of hidden units.

I'm having a hard time wrapping my head around how it can be boiled down to this. Is this rigorous? Specifically, what is meant by the ith row and column? Is this formula for only one layer or does it work with multiple layers?

Any clarification would be helpful.

I'm currently reading the paper Federated Learning with Matched Averaging (2020), where the authors claim:

A basic fully connected (FC) NN can be formulated as: $\hat{y} = \sigma(xW_1)W_2$ [...]

Expanding the preceding expression $\hat{y} = \sum_{i=1}^{L} W_{2, i \cdot } \sigma(\langle x, W_{1,\cdot i} \rangle))$, where $ i\cdot$ and $\cdot i$ denote the ith row and column correspondingly and $L$ is the number of hidden units.

I'm having a hard time wrapping my head around how it can be boiled down to this. Is this rigorous? Specifically, what is meant by the ith row and column? Is this formula for only one layer or does it work with multiple layers?

Any clarification would be helpful.

I'm currently reading the paper Federated Learning with Matched Averaging (2020), where the authors claim:

A basic fully connected (FC) NN can be formulated as: $\hat{y} = \sigma(xW_1)W_2$ [...]

Expanding the preceding expression $\hat{y} = \sum_{i=1}^{L} W_{2, r \cdot } \sigma(\langle x, W_{1,\cdot i} \rangle))$, where $\cdot i$ and $\cdot i$ denote the ith row and column correspondingly and L is the number of hidden units.

I'm having a hard time wrapping my head around how it can be boiled down to this. Is this rigorous? Specifically, what is meant by the ith row and column? Is this formula for only one layer or does it work with multiple layers?

Any clarification would be helpful.

I'm currently reading the paper Federated Learning with Matched Averaging (2020), where the authors claim:

A basic fully connected (FC) NN can be formulated as: $\hat{y} = \sigma(xW_1)W_2$ [...]

Expanding the preceding expression $\hat{y} = \sum_{i=1}^{L} W_{2, r \cdot } \sigma(\langle x, W_{1,\cdot i} \rangle))$, where $\cdot i$ and $\cdot i$ denote the ith row and column correspondingly and $L$ is the number of hidden units.

I'm having a hard time wrapping my head around how it can be boiled down to this. Is this rigorous? Specifically, what is meant by the ith row and column? Is this formula for only one layer or does it work with multiple layers?

Any clarification would be helpful.