def METHOD_NAME(rs_options: Dict[str, Any]) -> Dict[str, Dict[str, Any]]:
    """
    Generate random parameters for a random architecture (convolutional part).
    Args:
        rs_options: parameters of the random search
    Returns
        parameters of the convolutions
    """
    n_convblocks = sampling_fn(rs_options["n_convblocks"], "randint")
    first_conv_width = sampling_fn(rs_options["first_conv_width"], "choice")
    d_reduction = sampling_fn(rs_options["d_reduction"], "choice")
    # Sampling the parameters of each convolutional block
    convolutions = dict()
    current_in_channels = None
    current_out_channels = first_conv_width
    for i in range(n_convblocks):
        conv_dict = dict()
        conv_dict["in_channels"] = current_in_channels
        conv_dict["out_channels"] = current_out_channels
        current_in_channels, current_out_channels = update_channels(
            current_out_channels, rs_options["channels_limit"]
        )
        conv_dict["n_conv"] = sampling_fn(rs_options["n_conv"], "choice")
        conv_dict["d_reduction"] = d_reduction
        convolutions["conv" + str(i)] = conv_dict
    return convolutions