我正在尝试理解和熟悉嵌入。
我创建了一个由5个数据集组成的5000个观察值的人工数据集:
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从均值= 1,标准差= 0.1的正态分布中提取的1000个值的样本
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从均值= 5,标准差= 0.1的正态分布中提取的1000个值的样本
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从均值= 7,标准差= 0.1的正态分布中提取的1000个值的样本
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从均值= 1,标准差= 1的正态分布中提取的1000个值的样本
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从均值= 7,标准差= 1的正态分布中提取的1000个值的样本
代码如下:
from scipy.stats import norm
y1 = norm.rvs(loc=1,scale=.1,size=1000)
y2 = norm.rvs(loc=5,size=1000)
y3 = norm.rvs(loc=7,size=1000)
y4 = norm.rvs(loc=5,scale= 1,size=1000)
y5 = norm.rvs(loc=1,size=1000)
df1 = pd.DataFrame({'x' : 1,'y': y1 })
df2 = pd.DataFrame({'x' : 2,'y': y2 })
df3 = pd.DataFrame({'x' : 3,'y': y3 })
df4 = pd.DataFrame({'x' : 4,'y': y4 })
df5 = pd.DataFrame({'x' : 5,'y': y5 })
df = pd.concat([df1,df2,df3,df4,df5],axis = 0)
df= df.sample(frac=1)
我的目的是使用嵌入来表示代表二维空间中5个数据集(即1、2、3、4、5)的代码值。
我很想知道这种表示形式是否会以某种方式反映每个数据集的内部性质,即它们都是从正态分布中抽取的样本,但均值和标准差有5种不同的组合。
我的处理方式如下:
inputs = Input(shape=(1,))
x1 = Embedding(6,2,input_length=1,name = 'embeddings')(inputs)
x2 = flatten()(x1)
x3 = Dense(10,activation = 'relu')(x2)
x4 = Dense(10,activation = 'relu')(x3)
x5 = Dropout(0.5)(x4)
prediction = Dense(1)(x5)
model = Model(inputs = inputs,outputs = prediction)
model.compile(optimizer='Adam',loss='mse',metrics=['mae'])
model.fit(x = df.x.values,y = df.y.values,epochs = 10,batch_size = 16)
然后我提取训练后的图层的权重并进行检查:
for layer in model.layers:
if layer.name == 'embeddings':
embedding_layer = layer
所以在这里,我们有一个6行的矩阵,对应于输入的唯一值,如我们所见,它们是{1、2、3、4、5}。
但是哪一行对应于哪个值?
第六行“冗余”对应于什么?
您能提供对特定重量的直观解释吗?
如果这对您有帮助,我可以画出权重,因为它们是在2D空间中表示的。
ax = embeddings_df.reset_index().plot.scatter(x = 'x',y = 'y')
for i,txt in enumerate(embeddings_df.index):
ax.annotate(txt,(embeddings_df.x.iat[i],embeddings_df.y.iat[i]))
实际上,唯一输入值似乎对应于权重矩阵的各个索引。嵌入向量的位置似乎与生成分布的平均值有关(沿着从左上角高到右下角的对角线)。尽管尚不清楚映射的工作原理,但std的差异沿水平轴的位置不同。
一般而言,尽管我们如何知道权重矩阵的哪一行对应于输入向量中的唯一值?总是1对应权重矩阵的索引为1的行吗?
索引为0的行的作用是什么?
事实上,我尝试使用数字5作为嵌入数字来创建嵌入,该数字在拟合期间导致错误:
Train on 5000 samples
Epoch 1/10
16/5000 [..............................] - eta: 2:53
---------------------------------------------------------------------------
InvalidArgumentError Traceback (most recent call last)
<ipython-input-44-ec152436476c> in <module>
----> 1 model.fit(x = df.x.values,batch_size = 16)
~\Anaconda3\envs\tf2\lib\site-packages\tensorflow_core\python\keras\engine\training.py in fit(self,x,y,batch_size,epochs,verbose,callbacks,validation_split,validation_data,shuffle,class_weight,sample_weight,initial_epoch,steps_per_epoch,validation_steps,validation_freq,max_queue_size,workers,use_multiprocessing,**kwargs)
726 max_queue_size=max_queue_size,727 workers=workers,--> 728 use_multiprocessing=use_multiprocessing)
729
730 def evaluate(self,~\Anaconda3\envs\tf2\lib\site-packages\tensorflow_core\python\keras\engine\training_v2.py in fit(self,model,**kwargs)
322 mode=ModeKeys.TRAIN,323 training_context=training_context,--> 324 total_epochs=epochs)
325 cbks.make_logs(model,epoch_logs,training_result,ModeKeys.TRAIN)
326
~\Anaconda3\envs\tf2\lib\site-packages\tensorflow_core\python\keras\engine\training_v2.py in run_one_epoch(model,iterator,execution_function,dataset_size,strategy,num_samples,mode,training_context,total_epochs)
121 step=step,mode=mode,size=current_batch_size) as batch_logs:
122 try:
--> 123 batch_outs = execution_function(iterator)
124 except (StopIteration,errors.OutOfRangeError):
125 # TODO(kaftan): File bug about tf function and errors.OutOfRangeError?
~\Anaconda3\envs\tf2\lib\site-packages\tensorflow_core\python\keras\engine\training_v2_utils.py in execution_function(input_fn)
84 # `numpy` translates Tensors to values in Eager mode.
85 return nest.map_structure(_non_none_constant_value,---> 86 distributed_function(input_fn))
87
88 return execution_function
~\Anaconda3\envs\tf2\lib\site-packages\tensorflow_core\python\eager\def_function.py in __call__(self,*args,**kwds)
455
456 tracing_count = self._get_tracing_count()
--> 457 result = self._call(*args,**kwds)
458 if tracing_count == self._get_tracing_count():
459 self._call_counter.called_without_tracing()
~\Anaconda3\envs\tf2\lib\site-packages\tensorflow_core\python\eager\def_function.py in _call(self,**kwds)
518 # lifting succeeded,so variables are initialized and we can run the
519 # stateless function.
--> 520 return self._stateless_fn(*args,**kwds)
521 else:
522 canon_args,canon_kwds = \
~\Anaconda3\envs\tf2\lib\site-packages\tensorflow_core\python\eager\function.py in __call__(self,**kwargs)
1821 """Calls a graph function specialized to the inputs."""
1822 graph_function,args,kwargs = self._maybe_define_function(args,kwargs)
-> 1823 return graph_function._filtered_call(args,kwargs) # pylint: disable=protected-access
1824
1825 @property
~\Anaconda3\envs\tf2\lib\site-packages\tensorflow_core\python\eager\function.py in _filtered_call(self,kwargs)
1139 if isinstance(t,(ops.Tensor,1140 resource_variable_ops.BaseResourceVariable))),-> 1141 self.captured_inputs)
1142
1143 def _call_flat(self,captured_inputs,cancellation_manager=None):
~\Anaconda3\envs\tf2\lib\site-packages\tensorflow_core\python\eager\function.py in _call_flat(self,cancellation_manager)
1222 if executing_eagerly:
1223 flat_outputs = forward_function.call(
-> 1224 ctx,cancellation_manager=cancellation_manager)
1225 else:
1226 gradient_name = self._delayed_rewrite_functions.register()
~\Anaconda3\envs\tf2\lib\site-packages\tensorflow_core\python\eager\function.py in call(self,ctx,cancellation_manager)
509 inputs=args,510 attrs=("executor_type",executor_type,"config_proto",config),--> 511 ctx=ctx)
512 else:
513 outputs = execute.execute_with_cancellation(
~\Anaconda3\envs\tf2\lib\site-packages\tensorflow_core\python\eager\execute.py in quick_execute(op_name,num_outputs,inputs,attrs,name)
65 else:
66 message = e.message
---> 67 six.raise_from(core._status_to_exception(e.code,message),None)
68 except TypeError as e:
69 keras_symbolic_tensors = [
~\Anaconda3\envs\tf2\lib\site-packages\six.py in raise_from(value,from_value)
InvalidArgumentError: 2 root error(s) found.
(0) Invalid argument: indices[1,0] = 5 is not in [0,5)
[[node model_4/embeddings/embedding_lookup (defined at C:\Users\Alienware\Anaconda3\envs\tf2\lib\site-packages\tensorflow_core\python\framework\ops.py:1751) ]]
[[Adam/Adam/update/AssignSubVariableOp/_39]]
(1) Invalid argument: indices[1,5)
[[node model_4/embeddings/embedding_lookup (defined at C:\Users\Alienware\Anaconda3\envs\tf2\lib\site-packages\tensorflow_core\python\framework\ops.py:1751) ]]
0 successful operations.
0 derived errors ignored. [Op:__inference_distributed_function_33376]
Function call stack:
distributed_function -> distributed_function
这使我感到困惑,因为实际上输入的维数为5,因为我有5个以向量形式表示的不同/唯一值。
您能解释一下吗?