Method backward

include/instance/model/knowledge_graph.h:226–257

    template<OptimizerType optimizer_type>
    __host__ __device__
    static void backward(Vector &head, Vector &tail, Vector &relation,
                         float l3_regularization, Float gradient, const Optimizer &optimizer,
                         float relation_lr_multiplier = 1, Float weight = 1) {
        auto update = get_update_function<Float, optimizer_type>();
        l3_regularization *= 3;
        FOR(i, dim / 2) {
            Float h_re = head[i * 2];
            Float h_im = head[i * 2 + 1];
            Float t_re = tail[i * 2];
            Float t_im = tail[i * 2 + 1];
            Float r_re = relation[i * 2];
            Float r_im = relation[i * 2 + 1];
            // head
            Float h_re_grad = gradient * (r_re * t_re + r_im * t_im);
            Float h_im_grad = gradient * (-r_im * t_re + r_re * t_im);
            head[i * 2] -= (optimizer.*update)(h_re, h_re_grad + l3_regularization * abs(h_re) * h_re, weight);
            head[i * 2 + 1] -= (optimizer.*update)(h_im, h_im_grad + l3_regularization * abs(h_im) * h_im, weight);
            // tail
            Float t_re_grad = gradient * (h_re * r_re - h_im * r_im);
            Float t_im_grad = gradient * (h_re * r_im + h_im * r_re);
            tail[i * 2] -= (optimizer.*update)(t_re, t_re_grad + l3_regularization * abs(t_re) * t_re, weight);
            tail[i * 2 + 1] -= (optimizer.*update)(t_im, t_im_grad + l3_regularization * abs(t_im) * t_im, weight);
            // relation
            Float r_re_grad = gradient * (h_re * t_re + h_im * t_im);
            Float r_im_grad = gradient * (-h_im * t_re + h_re * t_im);
            relation[i * 2] -= relation_lr_multiplier *
                    (optimizer.*update)(r_re, r_re_grad + l3_regularization * abs(r_re) * r_re, weight);
            relation[i * 2 + 1] -= relation_lr_multiplier *
                    (optimizer.*update)(r_im, r_im_grad + l3_regularization * abs(r_im) * r_im, weight);
        }
    }

    template<OptimizerType optimizer_type>
    __host__ __device__