I think the paper has several weaknesses. Please see the following list and the questions sections.
* The statement in the introduction regarding the biological plausibility of backpropagation may be too weak ("While the backpropagation ..., its biological plausibility remains a subject of debate."). It is widely accepted that backpropagation is biologically implausible.
* Regarding the following sentence in Section 3 "We further define a readout ... ,i.e., $\mathbf{m}^t = f(y^t).$", did you mean to write $\mathbf{m}^t = f(\mathbf{y}^t)$ ($\mathbf{y}^t$ with boldsymbol)?
* On page 4, "setting $\theta_{110} = 1$ and $\theta_{012} = -1$," the second term should be $\theta_{021}$ rather than $\theta_{012}$.
* The initialization of polynomial coefficient parameters is not clear, and it seems they are initialized close to zero according to Figure 2. It would be valuable to explain how they were initialized.
* The paper models synaptic plasticity rules only for feedforward connections. It would be interesting to explore the impact of lateral connections (by adding additional terms in Equation 6). Have you experimented with such a setup?
* In page 7, the authors state that "In the case of the MLP, we tested various architectures and highlight results for a 3-10-1 neuron topology." What are the results for other various architectures? Putting them into the paper would also be valuable (as ablation studies).
* The hyperparameters for the experiments are missing? What is the learning rate, what is the optimizer, etc.?
* I do not see that much difference between the experiment presented in Section 4 and the experiment in (Confavreux et al., 2020) (Section 3.1) except the choice of optimization method. In your experimental setup, you also do not model the global reward. Therefore, I think it makes it more similar to the experiment in (Confavreux et al., 2020).
* Comparison to previous work is missing.
* The statement in the introduction regarding the biological plausibility of backpropagation may be too weak ("While the backpropagation ..., its biological plausibility remains a subject of debate."). It is widely accepted that backpropagation is biologically implausible.