用嵌套梯度带计算 Hessian 矩阵

Question

I am attempting to calculate the Hessian matrix of the output of a neural network with respect to the input, using gradient tapes and 2 batch_jacobian functions. The first function returns the Jacobian, as expected, the second one returns a pretty meaningless error. The coordinates [:,0] in g are picked, since the Jacobian is calculated with respect to just one variable, hence the second axis only has length 1. The code does not execute past the point where the Hessian is calculated.

 def dynamics(self, x):  # compute guess of dynamics of the system, using current lagrangian model
    with tf.GradientTape() as tape2: # observing the first order derivatives
        tape2.watch(x)
        with tf.GradientTape(persistent = True) as tape:
            tape.watch(x)
            lagrangian = self.lagrangian_net(x)
            print(lagrangian)
        g = tape.batch_jacobian(lagrangian, x, unconnected_gradients='zero')[:, 0]
        print(g)
    hessian = tape2.batch_jacobian(g, x, unconnected_gradients='zero')
    print(hessian)
    U = g[:, 0, :] - tf.einsum("dij,dj->di", hessian[:, 1, :, 0, :], x[:, 1, :])  # U[d,i]
    P = hessian[:, 1, :, 1, :]
    P = tf.map_fn(tf.linalg.inv, P)  # P[d, i, k]
    A = tf.einsum("di,dik->dk", U, P)
    return A  # return accelerations for the batch

Error:

Traceback (most recent call last): File "C:\\Users\\Maks\\Anaconda3\\envs\\machine_learning\\lib\\site-packages\\tensorflow\\python\\eager\\backprop.py", line 1183, in batch_jacobian parallel_iterations=parallel_iterations) File "C:\\Users\\Maks\\Anaconda3\\envs\\machine_learning\\lib\\site-packages\\tensorflow\\python\\ops\\parallel_for\\control_flow_ops.py", line 164, in pfor return f() File "C:\\Users\\Maks\\Anaconda3\\envs\\machine_learning\\lib\\site-packages\\tensorflow\\python\\eager\\function.py", line 1323, in call graph_function, args, kwargs = self._maybe_define_function(args, kwargs) File "C:\\Users\\Maks\\Anaconda3\\envs\\machine_learning\\lib\\site-packages\\tensorflow\\python\\eager\\function.py", line 1652, in _maybe_define_function graph_function = self._create_graph_function(args, kwargs) File "C:\\Users\\Maks\\Anaconda3\\envs\\machine_learning\\lib\\site-packages\\tensorflow\\python\\eager\\function.py", line 1545, in _create_graph_function capture_by_value=self._capture_by_value), File "C:\\Users\\Maks\\Anaconda3\\envs\\machi ne_learning\\lib\\site-packages\\tensorflow\\python\\framework\\func_graph.py", line 715, in func_graph_from_py_func func_outputs = python_func(*func_args, **func_kwargs) File "C:\\Users\\Maks\\Anaconda3\\envs\\machine_learning\\lib\\site-packages\\tensorflow\\python\\framework\\func_graph.py", line 705, in wrapper raise e.ag_error_metadata.to_exception(type(e)) ValueError: in converted code: relative to C:\\Users\\Maks\\Anaconda3\\envs\\machine_learning\\lib\\site-packages\\tensorflow\\python\\ops\\parallel_for:

control_flow_ops.py:161 f *
    return _pfor_impl(loop_fn, iters, parallel_iterations=parallel_iterations)
control_flow_ops.py:214 _pfor_impl
    outputs.append(converter.convert(loop_fn_output))
pfor.py:1175 convert
    output = self._convert_helper(y)
pfor.py:1343 _convert_helper
    "which may run slower" % (y_op.type, y_op, converted_inputs))

ValueError: No converter defined for PartitionedCall
name: "loop_body/PartitionedCall"
op: "PartitionedCall"
input: "loop_body/Reshape_4"
input: "loop_body/PartitionedCall/args_1"
input: "loop_body/PartitionedCall/args_2"
input: "loop_body/PartitionedCall/args_3"
input: "loop_body/PartitionedCall/args_4"
input: "loop_body/PartitionedCall/args_5"
attr {
  key: "Tin"
  value {
    list {
      type: DT_DOUBLE
      type: DT_DOUBLE
      type: DT_DOUBLE
      type: DT_DOUBLE
      type: DT_DOUBLE
      type: DT_INT32
    }
  }
}
attr {
  key: "Tout"
  value {
    list {
      type: DT_DOUBLE
      type: DT_DOUBLE
    }
  }
}
attr {
  key: "_gradient_op_type"
  value {
    s: "PartitionedCall-385"
  }
}
attr {
  key: "config"
  value {
    s: ""
  }
}
attr {
  key: "config_proto"
  value {
    s: "\n\007\n\003CPU\020\001\n\007\n\003GPU\020\0002\002J\0008\001"
  }
}
attr {
  key: "executor_type"
  value {
    s: ""
  }
}
attr {
  key: "f"
  value {
    func {
      name: "__inference___backward_f_232_270"
    }
  }
}

inputs: [WrappedTensor(t=<tf.Tensor 'loop_body/Reshape_4/pfor/Reshape:0' shape=(4, 1, 3, 2, 2) dtype=float64>, is_stacked=True, is_sparse_stacked=False), WrappedTensor(t=<tf.Tensor 'loop_body/PartitionedCall/args_1:0' shape=(4, 1) dtype=float64>, is_stacked=False, is_sparse_stacked=False), WrappedTensor(t=<tf.Tensor 'loop_body/PartitionedCall/args_2:0' shape=(3, 1) dtype=float64>, is_stacked=False, is_sparse_stacked=False), WrappedTensor(t=<tf.Tensor 'loop_body/PartitionedCall/args_3:0' shape=(1, 3, 1) dtype=float64>, is_stacked=False, is_sparse_stacked=False), WrappedTensor(t=<tf.Tensor 'loop_body/PartitionedCall/args_4:0' shape=(1, 3, 1) dtype=float64>, is_stacked=False, is_sparse_stacked=False), WrappedTensor(t=<tf.Tensor 'loop_body/PartitionedCall/args_5:0' shape=(3,) dtype=int32>, is_stacked=False, is_sparse_stacked=False)]. 
Either add a converter or set --op_conversion_fallback_to_while_loop=True, which may run slower

During handling of the above exception, another exception occurred:

Traceback (most recent call last): File "C:/Users/Maks/Desktop/neural/lagrangian neural network.py", line 129, in N.train(2) File "C:/Users/Maks/Desktop/neural/lagrangian neural network.py", line 110, in train self.train_step(x, true_y) File "C:/Users/Maks/Desktop/neural/lagrangian neural network.py", line 98, in train_step acc = self.dynamics(x) File "C:/Users/Maks/Desktop/neural/lagrangian neural network.py", line 83, in dynamics hessian = tape2.batch_jacobian(g, x, unconnected_gradients='zero') File "C:\\Users\\Maks\\Anaconda3\\envs\\machine_learning\\lib\\site-packages\\tensorflow\\python\\eager\\backprop.py", line 1191, in batch_jacobian sys.exc_info()[2]) File "C:\\Users\\Maks\\Anaconda3\\envs\\machine_learning\\lib\\site-packages\\six.py", line 702, in reraise raise value.with_traceback(tb) File "C:\\Users\\Maks\\Anaconda3\\envs\\machine_learning\\lib\\site-packages\\tensorflow\\python\\eager\\backprop.py", line 1183, in batch_jacobian parallel_iterations=parallel_iterations) File "C:\\Users\\Maks\\Anaconda3\\en vs\\machine_learning\\lib\\site-packages\\tensorflow\\python\\ops\\parallel_for\\control_flow_ops.py", line 164, in pfor return f() File "C:\\Users\\Maks\\Anaconda3\\envs\\machine_learning\\lib\\site-packages\\tensorflow\\python\\eager\\function.py", line 1323, in call graph_function, args, kwargs = self._maybe_define_function(args, kwargs) File "C:\\Users\\Maks\\Anaconda3\\envs\\machine_learning\\lib\\site-packages\\tensorflow\\python\\eager\\function.py", line 1652, in _maybe_define_function graph_function = self._create_graph_function(args, kwargs) File "C:\\Users\\Maks\\Anaconda3\\envs\\machine_learning\\lib\\site-packages\\tensorflow\\python\\eager\\function.py", line 1545, in _create_graph_function capture_by_value=self._capture_by_value), File "C:\\Users\\Maks\\Anaconda3\\envs\\machine_learning\\lib\\site-packages\\tensorflow\\python\\framework\\func_graph.py", line 715, in func_graph_from_py_func func_outputs = python_func(*func_args, **func_kwargs) File "C:\\Users\\Maks\\Anaconda3\\envs\\machine_learning\\lib\\site-packages\\tensorflow \\python\\framework\\func_graph.py", line 705, in wrapper raise e.ag_error_metadata.to_exception(type(e)) ValueError: in converted code: relative to C:\\Users\\Maks\\Anaconda3\\envs\\machine_learning\\lib\\site-packages\\tensorflow\\python\\ops\\parallel_for:

control_flow_ops.py:161 f *
    return _pfor_impl(loop_fn, iters, parallel_iterations=parallel_iterations)
control_flow_ops.py:214 _pfor_impl
    outputs.append(converter.convert(loop_fn_output))
pfor.py:1175 convert
    output = self._convert_helper(y)
pfor.py:1343 _convert_helper
    "which may run slower" % (y_op.type, y_op, converted_inputs))

ValueError: No converter defined for PartitionedCall
name: "loop_body/PartitionedCall"
op: "PartitionedCall"
input: "loop_body/Reshape_4"
input: "loop_body/PartitionedCall/args_1"
input: "loop_body/PartitionedCall/args_2"
input: "loop_body/PartitionedCall/args_3"
input: "loop_body/PartitionedCall/args_4"
input: "loop_body/PartitionedCall/args_5"
attr {
  key: "Tin"
  value {
    list {
      type: DT_DOUBLE
      type: DT_DOUBLE
      type: DT_DOUBLE
      type: DT_DOUBLE
      type: DT_DOUBLE
      type: DT_INT32
    }
  }
}
attr {
  key: "Tout"
  value {
    list {
      type: DT_DOUBLE
      type: DT_DOUBLE
    }
  }
}
attr {
  key: "_gradient_op_type"
  value {
    s: "PartitionedCall-385"
  }
}
attr {
  key: "config"
  value {
    s: ""
  }
}
attr {
  key: "config_proto"
  value {
    s: "\n\007\n\003CPU\020\001\n\007\n\003GPU\020\0002\002J\0008\001"
  }
}
attr {
  key: "executor_type"
  value {
    s: ""
  }
}
attr {
  key: "f"
  value {
    func {
      name: "__inference___backward_f_232_270"
    }
  }
}

inputs: [WrappedTensor(t=<tf.Tensor 'loop_body/Reshape_4/pfor/Reshape:0' shape=(4, 1, 3, 2, 2) dtype=float64>, is_stacked=True, is_sparse_stacked=False), WrappedTensor(t=<tf.Tensor 'loop_body/PartitionedCall/args_1:0' shape=(4, 1) dtype=float64>, is_stacked=False, is_sparse_stacked=False), WrappedTensor(t=<tf.Tensor 'loop_body/PartitionedCall/args_2:0' shape=(3, 1) dtype=float64>, is_stacked=False, is_sparse_stacked=False), WrappedTensor(t=<tf.Tensor 'loop_body/PartitionedCall/args_3:0' shape=(1, 3, 1) dtype=float64>, is_stacked=False, is_sparse_stacked=False), WrappedTensor(t=<tf.Tensor 'loop_body/PartitionedCall/args_4:0' shape=(1, 3, 1) dtype=float64>, is_stacked=False, is_sparse_stacked=False), WrappedTensor(t=<tf.Tensor 'loop_body/PartitionedCall/args_5:0' shape=(3,) dtype=int32>, is_stacked=False, is_sparse_stacked=False)]. 
Either add a converter or set --op_conversion_fallback_to_while_loop=True, which may run slower

Encountered an exception while vectorizing the batch_jacobian computation. Vectorization can be disabled by setting experimental_use_pfor to False. Exception ignored in: <function _EagerDefinedFunctionDeleter. del at 0x0000026FE02C50D8> Traceback (most recent call last): File "C:\\Users\\Maks\\Anaconda3\\envs\\machine_learning\\lib\\site-packages\\tensorflow\\python\\eager\\function.py", line 305, in del File "C:\\Users\\Maks\\Anaconda3\\envs\\machine_learning\\lib\\site-packages\\tensorflow\\python\\eager\\context.py", line 1663, in remove_function File "C:\\Users\\Maks\\Anaconda3\\envs\\machine_learning\\lib\\site-packages\\tensorflow\\python\\eager\\context.py", line 865, in remove_function TypeError: 'NoneType' object is not callable Exception ignored in: <function _EagerDefinedFunctionDeleter. del at 0x0000026FE02C50D8> Traceback (most recent call last): File "C:\\Users\\Maks\\Anaconda3\\envs\\machine_learning\\lib\\site-packages\\tensorflow\\python\\eager\\function.py", line 305, in del File "C:\\Users\\Maks\\Anaconda3\\envs\\machine_learning\\lib\\site-packages\\tensorflow\\python\\eager\\context.py", line 1663, in remove_function File "C:\\Users\\Maks\\Anaconda3\\envs\\machine_learning\\lib\\site-packages\\tensorflow\\python\\eager\\context.py", line 865, in remove_function TypeError: 'NoneType' object is not callable Exception ignored in: <function _EagerDefinedFunctionDeleter. del at 0x0000026FE02C50D8> Traceback (most recent call last): File "C:\\Users\\Maks\\Anaconda3\\envs\\machine_learning\\lib\\site-packages\\tensorflow\\python\\eager\\function.py", line 305, in del File "C:\\Users\\Maks\\Anaconda3\\envs\\machine_learning\\lib\\site-packages\\tensorflow\\python\\eager\\context.py", line 1663, in remove_function File "C:\\Users\\Maks\\Anaconda3\\envs\\machine_learning\\lib\\site-packages\\tensorflow\\python\\eager\\context.py", line 865, in remove_function TypeError: 'NoneType' object is not callable

Answer 1

通过更新到 tensorflow 2.1 解决