def test_cpd_jtjvp_optimized(benchmark): for datatype in BACKEND_TYPES: T.set_backend(datatype) A_list, input_tensor, loss, residual = cpd_graph(dim, size, rank) A, B, C = A_list v_A = ad.Variable(name="v_A", shape=[size, rank]) v_B = ad.Variable(name="v_B", shape=[size, rank]) v_C = ad.Variable(name="v_C", shape=[size, rank]) A_list, input_tensor_val = init_rand_cp(dim, size, rank) A_val, B_val, C_val = A_list v_A_list, _ = init_rand_cp(dim, size, rank) v_A_val, v_B_val, v_C_val = v_A_list JtJvps = ad.jtjvps(output_node=residual, node_list=[A, B, C], vector_list=[v_A, v_B, v_C]) JtJvps = [optimize(JtJvp) for JtJvp in JtJvps] dedup(*JtJvps) for node in JtJvps: assert isinstance(node, ad.AddNode) executor_JtJvps = ad.Executor(JtJvps) jtjvp_val = benchmark(executor_JtJvps.run, feed_dict={ A: A_val, B: B_val, C: C_val, input_tensor: input_tensor_val, v_A: v_A_val, v_B: v_B_val, v_C: v_C_val })
def test_cpd_hessian_optimize_offdiag(backendopt): dim = 3 for datatype in backendopt: T.set_backend(datatype) A_list, input_tensor, loss, residual = cpd_graph(dim, size, rank) A, B, C = A_list A_list, input_tensor_val = init_rand_cp(dim, size, rank) A_val, B_val, C_val = A_list hessian = ad.hessian(loss, [A, B, C]) hessian_offdiag = [hessian[0][1], hessian[1][0]] for node in hessian_offdiag: optimize(node) assert isinstance(node, ad.AddNode) num_operations = len( list( filter(lambda x: isinstance(x, ad.OpNode), find_topo_sort([node])))) # This is currently non-deterministic. # assert num_operations == 14 executor = ad.Executor(hessian_offdiag) hes_diag_vals = executor.run(feed_dict={ A: A_val, B: B_val, C: C_val, input_tensor: input_tensor_val, })
def test_cpd_hessian_optimize_diag(backendopt): dim = 3 for datatype in backendopt: T.set_backend(datatype) A_list, input_tensor, loss, residual = cpd_graph(dim, size, rank) A, B, C = A_list A_list, input_tensor_val = init_rand_cp(dim, size, rank) A_val, B_val, C_val = A_list hessian = ad.hessian(loss, [A, B, C]) hessian_diag = [hessian[0][0], hessian[1][1], hessian[2][2]] for node in hessian_diag: node = optimize(node) assert isinstance(node, ad.AddNode) num_operations = len( list( filter(lambda x: isinstance(x, ad.OpNode), find_topo_sort([node])))) """ Use this assertion to test the optimize function. 5 operations: 1. T.einsum('ca,cb->ab',A,A), 2. T.einsum('ca,cb->ab',B,B), 3. T.einsum('ab,ab->ab',T.einsum('ca,cb->ab',A,A),T.einsum('ca,cb->ab',B,B)), 4. T.einsum('bd,ac->abcd',T.einsum('ab,ab->ab',T.einsum('ca,cb->ab',A,A),T.einsum('ca,cb->ab',B,B)),T.identity(10)), 5. (T.einsum('bd,ac->abcd',T.einsum('ab,ab->ab',T.einsum('ca,cb->ab',A,A),T.einsum('ca,cb->ab',B,B)),T.identity(10))+ T.einsum('bd,ac->abcd',T.einsum('ab,ab->ab',T.einsum('ca,cb->ab',A,A),T.einsum('ca,cb->ab',B,B)),T.identity(10))) """ assert num_operations == 5 executor = ad.Executor(hessian_diag) hes_diag_vals = executor.run(feed_dict={ A: A_val, B: B_val, C: C_val, input_tensor: input_tensor_val, }) expected_hes_diag_val = [ 2 * T.einsum('eb,ed,fb,fd,ac->abcd', B_val, B_val, C_val, C_val, T.identity(size)), 2 * T.einsum('eb,ed,fb,fd,ac->abcd', A_val, A_val, C_val, C_val, T.identity(size)), 2 * T.einsum('eb,ed,fb,fd,ac->abcd', A_val, A_val, B_val, B_val, T.identity(size)) ] assert T.norm(hes_diag_vals[0] - expected_hes_diag_val[0]) < 1e-8 assert T.norm(hes_diag_vals[1] - expected_hes_diag_val[1]) < 1e-8 assert T.norm(hes_diag_vals[2] - expected_hes_diag_val[2]) < 1e-8
def test_cpd_grad(backendopt): dim = 3 for datatype in backendopt: T.set_backend(datatype) A_list, input_tensor, loss, residual = cpd_graph(dim, size, rank) A, B, C = A_list grad_A, grad_B, grad_C = ad.gradients(loss, [A, B, C]) executor = ad.Executor([loss, grad_A, grad_B, grad_C]) A_list, input_tensor_val = init_rand_cp(dim, size, rank) A_val, B_val, C_val = A_list loss_val, grad_A_val, grad_B_val, grad_C_val = executor.run( feed_dict={ input_tensor: input_tensor_val, A: A_val, B: B_val, C: C_val }) expected_output_tensor = T.einsum("ia,ja,ka->ijk", A_val, B_val, C_val) expected_residual = expected_output_tensor - input_tensor_val expected_norm_error = T.norm(expected_residual) expected_loss = expected_norm_error * expected_norm_error expected_contract_residual_A = 2 * T.einsum("ijk,ia->ajk", expected_residual, A_val) expected_contract_residual_B = 2 * T.einsum("ijk,ja->iak", expected_residual, B_val) expected_contract_residual_C = 2 * T.einsum("ijk,ka->ija", expected_residual, C_val) expected_grad_A = T.einsum("iak,ka->ia", expected_contract_residual_B, C_val) expected_grad_B = T.einsum("ajk,ka->ja", expected_contract_residual_A, C_val) expected_grad_C = T.einsum("ajk,ja->ka", expected_contract_residual_A, B_val) assert abs(loss_val - expected_loss) < 1e-8 assert T.norm(grad_A_val - expected_grad_A) < 1e-8 assert T.norm(grad_B_val - expected_grad_B) < 1e-8 assert T.norm(grad_C_val - expected_grad_C) < 1e-8
def test_cpd_jtjvp_optimize(backendopt): dim = 3 for datatype in backendopt: T.set_backend(datatype) A_list, input_tensor, loss, residual = cpd_graph(dim, size, rank) A, B, C = A_list v_A = ad.Variable(name="v_A", shape=[size, rank]) v_B = ad.Variable(name="v_B", shape=[size, rank]) v_C = ad.Variable(name="v_C", shape=[size, rank]) A_list, input_tensor_val = init_rand_cp(dim, size, rank) A_val, B_val, C_val = A_list v_A_list, _ = init_rand_cp(dim, size, rank) v_A_val, v_B_val, v_C_val = v_A_list JtJvps = ad.jtjvps(output_node=residual, node_list=[A, B, C], vector_list=[v_A, v_B, v_C]) JtJvps = [optimize(JtJvp) for JtJvp in JtJvps] dedup(*JtJvps) for node in JtJvps: assert isinstance(node, ad.AddNode) executor_JtJvps = ad.Executor(JtJvps) jtjvp_val = executor_JtJvps.run( feed_dict={ A: A_val, B: B_val, C: C_val, input_tensor: input_tensor_val, v_A: v_A_val, v_B: v_B_val, v_C: v_C_val }) expected_hvp_val = expect_jtjvp_val(A_val, B_val, C_val, v_A_val, v_B_val, v_C_val) assert T.norm(jtjvp_val[0] - expected_hvp_val[0]) < 1e-8 assert T.norm(jtjvp_val[1] - expected_hvp_val[1]) < 1e-8 assert T.norm(jtjvp_val[2] - expected_hvp_val[2]) < 1e-8
def test_cpd_hessian_simplify(backendopt): dim = 3 for datatype in backendopt: T.set_backend(datatype) A_list, input_tensor, loss, residual = cpd_graph(dim, size, rank) A, B, C = A_list A_list, input_tensor_val = init_rand_cp(dim, size, rank) A_val, B_val, C_val = A_list hessian = ad.hessian(loss, [A, B, C]) # TODO (issue #101): test the off-diagonal elements hessian_diag = [hessian[0][0], hessian[1][1], hessian[2][2]] for node in hessian_diag: node = simplify(node) input_node = node.inputs[0] assert len(input_node.inputs) == 5 executor = ad.Executor(hessian_diag) hes_diag_vals = executor.run(feed_dict={ A: A_val, B: B_val, C: C_val, input_tensor: input_tensor_val, }) expected_hes_diag_val = [ 2 * T.einsum('eb,ed,fb,fd,ac->abcd', B_val, B_val, C_val, C_val, T.identity(size)), 2 * T.einsum('eb,ed,fb,fd,ac->abcd', A_val, A_val, C_val, C_val, T.identity(size)), 2 * T.einsum('eb,ed,fb,fd,ac->abcd', A_val, A_val, B_val, B_val, T.identity(size)) ] assert T.norm(hes_diag_vals[0] - expected_hes_diag_val[0]) < 1e-8 assert T.norm(hes_diag_vals[1] - expected_hes_diag_val[1]) < 1e-8 assert T.norm(hes_diag_vals[2] - expected_hes_diag_val[2]) < 1e-8