This from-scratch NumPy logistic regression doesn't train. Debug the sigmoid, its derivative and the gradient computation.

import numpy as np

def sigmoid(z):
    out = np.empty_like(z, dtype=float)
    pos = z >= 0
    out[pos] = 1 / (1 + np.exp(-z[pos]))
    ez = np.exp(z[~pos])
    out[~pos] = ez / (1 + ez)
    return out

def train(X, y, lr=0.1, steps=1000):
    # X (N, D), y (N,) of 0/1
    w, b = np.zeros(X.shape[1]), 0.0
    for _ in range(steps):
        p = sigmoid(X @ w + b)
        err = p - y          # dLoss/dz for log loss
        w -= lr * X.T @ err / len(y)
        b -= lr * err.mean()
    return w, b

The usual bugs: a sigmoid that overflows for large negative inputs; a derivative written as s(1 minus z) instead of s(1 minus s); and multiplying by that derivative again, when log loss already gives a logit gradient of exactly p minus y. Also check the sign of the update, dividing by N, and a y of shape (N, 1) silently broadcasting to (N, N). Confirm with a finite-difference gradient check.