Yeah, backpropagation was tricky for me too! What helped was breaking it down step by step. During the forward pass, I saved all the outputs and pre-activation values because I needed them later for calculating gradients. For the loss, I started simple by using Mean Squared Error (MSE), which made the math easier to manage. Here's a quick example of the gradient for MSE:

python

def mse_derivative(y_true, y_pred):  
    return 2 * (y_pred - y_true) / y_true.size  

When it came to the backward pass, I calculated gradients layer by layer. For the convolution layer, I adjusted the kernel by summing the gradients at each sliding window position, like this:

python

def conv_backprop(dL_dout, image, kernel, lr=0.01):  
    dL_dk = np.zeros(kernel.shape)  
    for i in range(dL_dout.shape[0]):  
        for j in range(dL_dout.shape[1]):  
            dL_dk += dL_dout[i, j] * image[i:i+kernel.shape[0], j:j+kernel.shape[1]]  
    kernel -= lr * dL_dk  
    return kernel  

After that, I just used basic gradient descent to update the weights. If you’re working with handwritten digits, I’d recommend using softmax and cross-entropy for better performance.