Loss That Will Not Fall

Task

This is a small classifier written with plain Python lists: one linear layer, a softmax cross-entropy loss and mini-batch gradient descent. It runs with no errors. On ten classes its loss starts near 2.30 and stays there, however long it trains. Find out why it does not learn, and fix the causes. The learning rate, the number of epochs and the seed come with each request and are not the problem.

Requirements

1. classifier(request) takes one request with xs (a non-empty list of equal-length lists of numbers; ValueError containing xs otherwise), ys (one label from 0 to classes - 1 per example; ValueError containing ys otherwise) and classes (a positive integer; ValueError containing classes otherwise). Any other op raises ValueError containing op. Do not change the arguments.
2. {op: "batches", batch_size, seed} returns {batches}: one epoch as a list of {xs, ys}. An epoch calls permutation(len(xs), generator) once, on a Generator(seed), and takes the examples in that order, batch_size at a time. The last batch may be smaller. batch_size is at least 1 (ValueError containing batch_size otherwise).
3. {op: "loss", model} returns {loss}: the mean softmax cross-entropy of the model on xs and ys. The score of class c for an example x is weights[c] . x + bias[c]. model is {weights, bias} (ValueError containing model when the shape is wrong); without it, every weight and bias is 0.
4. {op: "gradient", model} returns {weights, bias}: the gradient of that loss with respect to the weights and the bias.
5. {op: "fit", model, epochs, lr, batch_size, seed} trains with mini-batch gradient descent: one Generator(seed) for the whole run, one call to batches per epoch, and for each batch the model moves by lr times the gradient, downhill. It returns {loss_before, loss_after, accuracy} on xs and ys. lr is above 0 (ValueError containing lr otherwise).
6. Every number in a result is rounded to 6 decimals with rounded(). The Generator, permutation and the starting weights must stay as they are, and every setting must be used as the request gives it.