tf.compat.v1.estimator.tpu.TPUEstimator Estimator with TPU support. Inherits From: Estimator 
tf.compat.v1.estimator.tpu.TPUEstimator(
    model_fn=None, model_dir=None, config=None, params=None, use_tpu=True,
    train_batch_size=None, eval_batch_size=None, predict_batch_size=None,
    batch_axis=None, eval_on_tpu=True, export_to_tpu=True, export_to_cpu=True,
    warm_start_from=None, embedding_config_spec=None,
    export_saved_model_api_version=ExportSavedModelApiVersion.V1
)
 TPUEstimator also supports training on CPU and GPU. You don't need to define a separate tf.estimator.Estimator. TPUEstimator handles many of the details of running on TPU devices, such as replicating inputs and models for each core, and returning to host periodically to run hooks. TPUEstimator transforms a global batch size in params to a per-shard batch size when calling the input_fn and model_fn. Users should specify global batch size in constructor, and then get the batch size for each shard in input_fn and model_fn by params['batch_size'].  For training, model_fn gets per-core batch size; input_fn may get per-core or per-host batch size depending on per_host_input_for_training in TPUConfig (See docstring for TPUConfig for details). For evaluation and prediction, model_fn gets per-core batch size and input_fn get per-host batch size.  Evaluation model_fn should return TPUEstimatorSpec, which expects the eval_metrics for TPU evaluation. If eval_on_tpu is False, the evaluation will execute on CPU or GPU; in this case the following discussion on TPU evaluation does not apply. TPUEstimatorSpec.eval_metrics is a tuple of metric_fn and tensors, where tensors could be a list of any nested structure of Tensors (See TPUEstimatorSpec for details). metric_fn takes the tensors and returns a dict from metric string name to the result of calling a metric function, namely a (metric_tensor, update_op) tuple. One can set use_tpu to False for testing. All training, evaluation, and predict will be executed on CPU. input_fn and model_fn will receive train_batch_size or eval_batch_size unmodified as params['batch_size']. Current limitations:  TPU evaluation only works on a single host (one TPU worker) except BROADCAST mode. input_fn for evaluation should NOT raise an end-of-input exception (OutOfRangeError or StopIteration). And all evaluation steps and all batches should have the same size.  Example (MNIST): # The metric Fn which runs on CPU.
def metric_fn(labels, logits):
  predictions = tf.argmax(logits, 1)
  return {
    'accuracy': tf.compat.v1.metrics.precision(
        labels=labels, predictions=predictions),
  }

# Your model Fn which runs on TPU (eval_metrics is list in this example)
def model_fn(features, labels, mode, config, params):
  ...
  logits = ...

  if mode = tf.estimator.ModeKeys.EVAL:
    return tpu_estimator.TPUEstimatorSpec(
        mode=mode,
        loss=loss,
        eval_metrics=(metric_fn, [labels, logits]))

# or specify the eval_metrics tensors as dict.
def model_fn(features, labels, mode, config, params):
  ...
  final_layer_output = ...

  if mode = tf.estimator.ModeKeys.EVAL:
    return tpu_estimator.TPUEstimatorSpec(
        mode=mode,
        loss=loss,
        eval_metrics=(metric_fn, {
            'labels': labels,
            'logits': final_layer_output,
        }))
 Prediction Prediction on TPU is an experimental feature to support large batch inference. It is not designed for latency-critical system. In addition, due to some usability issues, for prediction with small dataset, CPU .predict, i.e., creating a new TPUEstimator instance with use_tpu=False, might be more convenient. 
Note: In contrast to TPU training/evaluation, the input_fn for prediction should raise an end-of-input exception (OutOfRangeError or StopIteration), which serves as the stopping signal to TPUEstimator. To be precise, the ops created by input_fn produce one batch of the data. The predict() API processes one batch at a time. When reaching the end of the data source, an end-of-input exception should be raised by one of these operations. The user usually does not need to do this manually. As long as the dataset is not repeated forever, the tf.data API will raise an end-of-input exception automatically after the last batch has been produced.


Note: Estimator.predict returns a Python generator. Please consume all the data from the generator so that TPUEstimator can shutdown the TPU system properly for user.
 Current limitations:  TPU prediction only works on a single host (one TPU worker). input_fn must return a Dataset instance rather than features. In fact, .train() and .evaluate() also support Dataset as return value.  Example (MNIST): height = 32
width = 32
total_examples = 100

def predict_input_fn(params):
  batch_size = params['batch_size']

  images = tf.random.uniform(
      [total_examples, height, width, 3], minval=-1, maxval=1)

  dataset = tf.data.Dataset.from_tensor_slices(images)
  dataset = dataset.map(lambda images: {'image': images})

  dataset = dataset.batch(batch_size)
  return dataset

def model_fn(features, labels, params, mode):
   # Generate predictions, called 'output', from features['image']

  if mode == tf.estimator.ModeKeys.PREDICT:
    return tf.contrib.tpu.TPUEstimatorSpec(
        mode=mode,
        predictions={
            'predictions': output,
            'is_padding': features['is_padding']
        })

tpu_est = TPUEstimator(
    model_fn=model_fn,
    ...,
    predict_batch_size=16)

# Fully consume the generator so that TPUEstimator can shutdown the TPU
# system.
for item in tpu_est.predict(input_fn=input_fn):
  # Filter out item if the `is_padding` is 1.
  # Process the 'predictions'
 Exporting export_saved_model exports 2 metagraphs, one with saved_model.SERVING, and another with saved_model.SERVING and saved_model.TPU tags. At serving time, these tags are used to select the appropriate metagraph to load. Before running the graph on TPU, the TPU system needs to be initialized. If TensorFlow Serving model-server is used, this is done automatically. If not, please use session.run(tpu.initialize_system()). There are two versions of the API: 1 or 2. In V1, the exported CPU graph is model_fn as it is. The exported TPU graph wraps tpu.rewrite() and TPUPartitionedCallOp around model_fn so model_fn is on TPU by default. To place ops on CPU, tpu.outside_compilation(host_call, logits) can be used. Example: def model_fn(features, labels, mode, config, params):
  ...
  logits = ...
  export_outputs = {
    'logits': export_output_lib.PredictOutput(
      {'logits': logits})
  }

  def host_call(logits):
    class_ids = math_ops.argmax(logits)
    classes = string_ops.as_string(class_ids)
    export_outputs['classes'] =
      export_output_lib.ClassificationOutput(classes=classes)

  tpu.outside_compilation(host_call, logits)

  ...
 In V2, export_saved_model() sets up params['use_tpu'] flag to let the user know if the code is exporting to TPU (or not). When params['use_tpu'] is True, users need to call tpu.rewrite(), TPUPartitionedCallOp and/or batch_function(). Alternatively use inference_on_tpu() which is a convenience wrapper of the three. def model_fn(features, labels, mode, config, params):
  ...
  # This could be some pre-processing on CPU like calls to input layer with
  # embedding columns.
  x2 = features['x'] * 2

  def computation(input_tensor):
    return layers.dense(
        input_tensor, 1, kernel_initializer=init_ops.zeros_initializer())

  inputs = [x2]
  if params['use_tpu']:
    predictions = array_ops.identity(
        tpu_estimator.inference_on_tpu(computation, inputs,
        num_batch_threads=1, max_batch_size=2, batch_timeout_micros=100),
        name='predictions')
  else:
    predictions = array_ops.identity(
        computation(*inputs), name='predictions')
  key = signature_constants.DEFAULT_SERVING_SIGNATURE_DEF_KEY
  export_outputs = {
      key: export_lib.PredictOutput({'prediction': predictions})
  }
  ...
 TIP: V2 is recommended as it is more flexible (eg: batching, etc).
 


 Args
  model_fn   Model function as required by Estimator which returns EstimatorSpec or TPUEstimatorSpec. training_hooks, 'evaluation_hooks', and prediction_hooks must not capure any TPU Tensor inside the model_fn.  
  model_dir   Directory to save model parameters, graph and etc. This can also be used to load checkpoints from the directory into a estimator to continue training a previously saved model. If None, the model_dir in config will be used if set. If both are set, they must be same. If both are None, a temporary directory will be used.  
  config   An tpu_config.RunConfig configuration object. Cannot be None.  
  params   An optional dict of hyper parameters that will be passed into input_fn and model_fn. Keys are names of parameters, values are basic python types. There are reserved keys for TPUEstimator, including 'batch_size'.  
  use_tpu   A bool indicating whether TPU support is enabled. Currently, - TPU training and evaluation respect this bit, but eval_on_tpu can override execution of eval. See below.  
  train_batch_size   An int representing the global training batch size. TPUEstimator transforms this global batch size to a per-shard batch size, as params['batch_size'], when calling input_fn and model_fn. Cannot be None if use_tpu is True. Must be divisible by total number of replicas.  
  eval_batch_size   An int representing evaluation batch size. Must be divisible by total number of replicas.  
  predict_batch_size   An int representing the prediction batch size. Must be divisible by total number of replicas.  
  batch_axis   A python tuple of int values describing how each tensor produced by the Estimator input_fn should be split across the TPU compute shards. For example, if your input_fn produced (images, labels) where the images tensor is in HWCN format, your shard dimensions would be [3, 0], where 3 corresponds to the N dimension of your images Tensor, and 0 corresponds to the dimension along which to split the labels to match up with the corresponding images. If None is supplied, and per_host_input_for_training is True, batches will be sharded based on the major dimension. If tpu_config.per_host_input_for_training is False or PER_HOST_V2, batch_axis is ignored.  
  eval_on_tpu   If False, evaluation runs on CPU or GPU. In this case, the model_fn must return EstimatorSpec when called with mode as EVAL.  
  export_to_tpu   If True, export_saved_model() exports a metagraph for serving on TPU. Note that unsupported export modes such as EVAL will be ignored. For those modes, only a CPU model will be exported. Currently, export_to_tpu only supports PREDICT.  
  export_to_cpu   If True, export_saved_model() exports a metagraph for serving on CPU.  
  warm_start_from   Optional string filepath to a checkpoint or SavedModel to warm-start from, or a tf.estimator.WarmStartSettings object to fully configure warm-starting. If the string filepath is provided instead of a WarmStartSettings, then all variables are warm-started, and it is assumed that vocabularies and Tensor names are unchanged.  
  embedding_config_spec   Optional EmbeddingConfigSpec instance to support using TPU embedding.  
  export_saved_model_api_version   an integer: 1 or 2. 1 corresponds to V1, 2 corresponds to V2. (Defaults to V1). With V1, export_saved_model() adds rewrite() and TPUPartitionedCallOp() for user; while in v2, user is expected to add rewrite(), TPUPartitionedCallOp() etc in their model_fn. A helper function inference_on_tpu is provided for V2. brn_tpu_estimator.py includes examples for both versions i.e. TPUEstimatorExportTest and TPUEstimatorExportV2Test.   
 


 Raises
  ValueError   params has reserved keys already.   
 


 Attributes
  config  
 
  model_dir  
 
  model_fn   Returns the model_fn which is bound to self.params.  
  params  
   Methods eval_dir View source 
eval_dir(
    name=None
)
 Shows the directory name where evaluation metrics are dumped.
 


 Args
  name   Name of the evaluation if user needs to run multiple evaluations on different data sets, such as on training data vs test data. Metrics for different evaluations are saved in separate folders, and appear separately in tensorboard.   
 


 Returns   A string which is the path of directory contains evaluation metrics.  
 evaluate View source 
evaluate(
    input_fn, steps=None, hooks=None, checkpoint_path=None, name=None
)
 Evaluates the model given evaluation data input_fn. For each step, calls input_fn, which returns one batch of data. Evaluates until:  
steps batches are processed, or 
input_fn raises an end-of-input exception (tf.errors.OutOfRangeError or StopIteration). 
 


 Args
  input_fn   A function that constructs the input data for evaluation. See Premade Estimators for more information. The function should construct and return one of the following:  A tf.data.Dataset object: Outputs of Dataset object must be a tuple (features, labels) with same constraints as below. A tuple (features, labels): Where features is a tf.Tensor or a dictionary of string feature name to Tensor and labels is a Tensor or a dictionary of string label name to Tensor. Both features and labels are consumed by model_fn. They should satisfy the expectation of model_fn from inputs. 

 
  steps   Number of steps for which to evaluate model. If None, evaluates until input_fn raises an end-of-input exception.  
  hooks   List of tf.train.SessionRunHook subclass instances. Used for callbacks inside the evaluation call.  
  checkpoint_path   Path of a specific checkpoint to evaluate. If None, the latest checkpoint in model_dir is used. If there are no checkpoints in model_dir, evaluation is run with newly initialized Variables instead of ones restored from checkpoint.  
  name   Name of the evaluation if user needs to run multiple evaluations on different data sets, such as on training data vs test data. Metrics for different evaluations are saved in separate folders, and appear separately in tensorboard.   
 


 Returns   A dict containing the evaluation metrics specified in model_fn keyed by name, as well as an entry global_step which contains the value of the global step for which this evaluation was performed. For canned estimators, the dict contains the loss (mean loss per mini-batch) and the average_loss (mean loss per sample). Canned classifiers also return the accuracy. Canned regressors also return the label/mean and the prediction/mean.  

 


 Raises
  ValueError   If steps <= 0.    experimental_export_all_saved_models View source 
experimental_export_all_saved_models(
    export_dir_base, input_receiver_fn_map, assets_extra=None, as_text=False,
    checkpoint_path=None
)
 Exports a SavedModel with tf.MetaGraphDefs for each requested mode. For each mode passed in via the input_receiver_fn_map, this method builds a new graph by calling the input_receiver_fn to obtain feature and label Tensors. Next, this method calls the Estimator's model_fn in the passed mode to generate the model graph based on those features and labels, and restores the given checkpoint (or, lacking that, the most recent checkpoint) into the graph. Only one of the modes is used for saving variables to the SavedModel (order of preference: tf.estimator.ModeKeys.TRAIN, tf.estimator.ModeKeys.EVAL, then tf.estimator.ModeKeys.PREDICT), such that up to three tf.MetaGraphDefs are saved with a single set of variables in a single SavedModel directory. For the variables and tf.MetaGraphDefs, a timestamped export directory below export_dir_base, and writes a SavedModel into it containing the tf.MetaGraphDef for the given mode and its associated signatures. For prediction, the exported MetaGraphDef will provide one SignatureDef for each element of the export_outputs dict returned from the model_fn, named using the same keys. One of these keys is always tf.saved_model.signature_constants.DEFAULT_SERVING_SIGNATURE_DEF_KEY, indicating which signature will be served when a serving request does not specify one. For each signature, the outputs are provided by the corresponding tf.estimator.export.ExportOutputs, and the inputs are always the input receivers provided by the serving_input_receiver_fn. For training and evaluation, the train_op is stored in an extra collection, and loss, metrics, and predictions are included in a SignatureDef for the mode in question. Extra assets may be written into the SavedModel via the assets_extra argument. This should be a dict, where each key gives a destination path (including the filename) relative to the assets.extra directory. The corresponding value gives the full path of the source file to be copied. For example, the simple case of copying a single file without renaming it is specified as {'my_asset_file.txt': '/path/to/my_asset_file.txt'}.
 


 Args
  export_dir_base   A string containing a directory in which to create timestamped subdirectories containing exported SavedModels.  
  input_receiver_fn_map   dict of tf.estimator.ModeKeys to input_receiver_fn mappings, where the input_receiver_fn is a function that takes no arguments and returns the appropriate subclass of InputReceiver.  
  assets_extra   A dict specifying how to populate the assets.extra directory within the exported SavedModel, or None if no extra assets are needed.  
  as_text   whether to write the SavedModel proto in text format.  
  checkpoint_path   The checkpoint path to export. If None (the default), the most recent checkpoint found within the model directory is chosen.   
 


 Returns   The path to the exported directory as a bytes object.  

 


 Raises
  ValueError   if any input_receiver_fn is None, no export_outputs are provided, or no checkpoint can be found.    export_saved_model View source 
export_saved_model(
    export_dir_base, serving_input_receiver_fn, assets_extra=None, as_text=False,
    checkpoint_path=None, experimental_mode=ModeKeys.PREDICT
)
 Exports inference graph as a SavedModel into the given dir. For a detailed guide, see SavedModel from Estimators. This method builds a new graph by first calling the serving_input_receiver_fn to obtain feature Tensors, and then calling this Estimator's model_fn to generate the model graph based on those features. It restores the given checkpoint (or, lacking that, the most recent checkpoint) into this graph in a fresh session. Finally it creates a timestamped export directory below the given export_dir_base, and writes a SavedModel into it containing a single tf.MetaGraphDef saved from this session. The exported MetaGraphDef will provide one SignatureDef for each element of the export_outputs dict returned from the model_fn, named using the same keys. One of these keys is always tf.saved_model.signature_constants.DEFAULT_SERVING_SIGNATURE_DEF_KEY, indicating which signature will be served when a serving request does not specify one. For each signature, the outputs are provided by the corresponding tf.estimator.export.ExportOutputs, and the inputs are always the input receivers provided by the serving_input_receiver_fn. Extra assets may be written into the SavedModel via the assets_extra argument. This should be a dict, where each key gives a destination path (including the filename) relative to the assets.extra directory. The corresponding value gives the full path of the source file to be copied. For example, the simple case of copying a single file without renaming it is specified as {'my_asset_file.txt': '/path/to/my_asset_file.txt'}. The experimental_mode parameter can be used to export a single train/eval/predict graph as a SavedModel. See experimental_export_all_saved_models for full docs.
 


 Args
  export_dir_base   A string containing a directory in which to create timestamped subdirectories containing exported SavedModels.  
  serving_input_receiver_fn   A function that takes no argument and returns a tf.estimator.export.ServingInputReceiver or tf.estimator.export.TensorServingInputReceiver.  
  assets_extra   A dict specifying how to populate the assets.extra directory within the exported SavedModel, or None if no extra assets are needed.  
  as_text   whether to write the SavedModel proto in text format.  
  checkpoint_path   The checkpoint path to export. If None (the default), the most recent checkpoint found within the model directory is chosen.  
  experimental_mode   tf.estimator.ModeKeys value indicating with mode will be exported. Note that this feature is experimental.   
 


 Returns   The path to the exported directory as a bytes object.  

 


 Raises
  ValueError   if no serving_input_receiver_fn is provided, no export_outputs are provided, or no checkpoint can be found.    export_savedmodel View source 
export_savedmodel(
    export_dir_base, serving_input_receiver_fn, assets_extra=None, as_text=False,
    checkpoint_path=None, strip_default_attrs=False
)
 Exports inference graph as a SavedModel into the given dir. (deprecated) Warning: THIS FUNCTION IS DEPRECATED. It will be removed in a future version. Instructions for updating: This function has been renamed, use export_saved_model instead. For a detailed guide, see SavedModel from Estimators. This method builds a new graph by first calling the serving_input_receiver_fn to obtain feature Tensors, and then calling this Estimator's model_fn to generate the model graph based on those features. It restores the given checkpoint (or, lacking that, the most recent checkpoint) into this graph in a fresh session. Finally it creates a timestamped export directory below the given export_dir_base, and writes a SavedModel into it containing a single tf.MetaGraphDef saved from this session. The exported MetaGraphDef will provide one SignatureDef for each element of the export_outputs dict returned from the model_fn, named using the same keys. One of these keys is always tf.saved_model.signature_constants.DEFAULT_SERVING_SIGNATURE_DEF_KEY, indicating which signature will be served when a serving request does not specify one. For each signature, the outputs are provided by the corresponding tf.estimator.export.ExportOutputs, and the inputs are always the input receivers provided by the serving_input_receiver_fn. Extra assets may be written into the SavedModel via the assets_extra argument. This should be a dict, where each key gives a destination path (including the filename) relative to the assets.extra directory. The corresponding value gives the full path of the source file to be copied. For example, the simple case of copying a single file without renaming it is specified as {'my_asset_file.txt': '/path/to/my_asset_file.txt'}.
 


 Args
  export_dir_base   A string containing a directory in which to create timestamped subdirectories containing exported SavedModels.  
  serving_input_receiver_fn   A function that takes no argument and returns a tf.estimator.export.ServingInputReceiver or tf.estimator.export.TensorServingInputReceiver.  
  assets_extra   A dict specifying how to populate the assets.extra directory within the exported SavedModel, or None if no extra assets are needed.  
  as_text   whether to write the SavedModel proto in text format.  
  checkpoint_path   The checkpoint path to export. If None (the default), the most recent checkpoint found within the model directory is chosen.  
  strip_default_attrs   Boolean. If True, default-valued attributes will be removed from the NodeDefs. For a detailed guide, see Stripping Default-Valued Attributes.   
 


 Returns   The path to the exported directory as a bytes object.  

 


 Raises
  ValueError   if no serving_input_receiver_fn is provided, no export_outputs are provided, or no checkpoint can be found.    get_variable_names View source 
get_variable_names()
 Returns list of all variable names in this model.
 


 Returns   List of names.  

 


 Raises
  ValueError   If the Estimator has not produced a checkpoint yet.    get_variable_value View source 
get_variable_value(
    name
)
 Returns value of the variable given by name.
 


 Args
  name   string or a list of string, name of the tensor.   
 


 Returns   Numpy array - value of the tensor.  

 


 Raises
  ValueError   If the Estimator has not produced a checkpoint yet.    latest_checkpoint View source 
latest_checkpoint()
 Finds the filename of the latest saved checkpoint file in model_dir.
 


 Returns   The full path to the latest checkpoint or None if no checkpoint was found.  
 predict View source 
predict(
    input_fn, predict_keys=None, hooks=None, checkpoint_path=None,
    yield_single_examples=True
)
 Yields predictions for given features. Please note that interleaving two predict outputs does not work. See: issue/20506
 


 Args
  input_fn   A function that constructs the features. Prediction continues until input_fn raises an end-of-input exception (tf.errors.OutOfRangeError or StopIteration). See Premade Estimators for more information. The function should construct and return one of the following:  
tf.data.Dataset object -- Outputs of Dataset object must have same constraints as below. features -- A tf.Tensor or a dictionary of string feature name to Tensor. features are consumed by model_fn. They should satisfy the expectation of model_fn from inputs. A tuple, in which case the first item is extracted as features. 

 
  predict_keys   list of str, name of the keys to predict. It is used if the tf.estimator.EstimatorSpec.predictions is a dict. If predict_keys is used then rest of the predictions will be filtered from the dictionary. If None, returns all.  
  hooks   List of tf.train.SessionRunHook subclass instances. Used for callbacks inside the prediction call.  
  checkpoint_path   Path of a specific checkpoint to predict. If None, the latest checkpoint in model_dir is used. If there are no checkpoints in model_dir, prediction is run with newly initialized Variables instead of ones restored from checkpoint.  
  yield_single_examples   If False, yields the whole batch as returned by the model_fn instead of decomposing the batch into individual elements. This is useful if model_fn returns some tensors whose first dimension is not equal to the batch size.   
 


 Yields   Evaluated values of predictions tensors.  

 


 Raises
  ValueError   If batch length of predictions is not the same and yield_single_examples is True.  
  ValueError   If there is a conflict between predict_keys and predictions. For example if predict_keys is not None but tf.estimator.EstimatorSpec.predictions is not a dict.    train View source 
train(
    input_fn, hooks=None, steps=None, max_steps=None, saving_listeners=None
)
 Trains a model given training data input_fn.
 


 Args
  input_fn   A function that provides input data for training as minibatches. See Premade Estimators for more information. The function should construct and return one of the following:  A tf.data.Dataset object: Outputs of Dataset object must be a tuple (features, labels) with same constraints as below. A tuple (features, labels): Where features is a tf.Tensor or a dictionary of string feature name to Tensor and labels is a Tensor or a dictionary of string label name to Tensor. Both features and labels are consumed by model_fn. They should satisfy the expectation of model_fn from inputs. 

 
  hooks   List of tf.train.SessionRunHook subclass instances. Used for callbacks inside the training loop.  
  steps   Number of steps for which to train the model. If None, train forever or train until input_fn generates the tf.errors.OutOfRange error or StopIteration exception. steps works incrementally. If you call two times train(steps=10) then training occurs in total 20 steps. If OutOfRange or StopIteration occurs in the middle, training stops before 20 steps. If you don't want to have incremental behavior please set max_steps instead. If set, max_steps must be None.  
  max_steps   Number of total steps for which to train model. If None, train forever or train until input_fn generates the tf.errors.OutOfRange error or StopIteration exception. If set, steps must be None. If OutOfRange or StopIteration occurs in the middle, training stops before max_steps steps. Two calls to train(steps=100) means 200 training iterations. On the other hand, two calls to train(max_steps=100) means that the second call will not do any iteration since first call did all 100 steps.  
  saving_listeners   list of CheckpointSaverListener objects. Used for callbacks that run immediately before or after checkpoint savings.   
 


 Returns   self, for chaining.  

 


 Raises
  ValueError   If both steps and max_steps are not None.  
  ValueError   If either steps or max_steps <= 0.