code: 
  
  
  import copy
  import logging
  import random
  
  import joblib
  import numpy as np
  import torch
  import torch.nn as nn
  from torch.utils.data import DataLoader
  from tqdm import tqdm
  
  from transformers import AdamW, GPTaLMHeadModel, get_linear_schedule_with_warmup
  
  
  lowerCAmelCase					 =	logging.getLogger(__name__)
  
  
  
  
  
  
  
  def  _lowerCamelCase(			lowercase__			)		->			Tuple:
  
  		'''simple docstring'''
  
  
  
  
  
  
  
  		random.seed(lowercase__			)
  		np.random.seed(lowercase__			)
  		torch.manual_seed(lowercase__			)
  		torch.cuda.manual_seed_all(lowercase__			)
  
  
  
  
  
  
  
  def  _lowerCamelCase(			lowercase__     ,				lowercase__     ,				lowercase__			)		->			List[str]:
  
  		'''simple docstring'''
  
  
  
  
  
  
  
  		model.eval()
  		__lowercase=    next(model.parameters()			).device
  		__lowercase=    1
  		__lowercase=    torch.zeros((eval_batch_size, context_len)     ,				dtype=torch.long     ,				device=lowercase__			)
  		__lowercase=    DataLoader(lowercase__     ,				shuffle=lowercase__     ,				batch_size=lowercase__			)
  		__lowercase=    torch.zeros(1     ,				device=lowercase__			)
  		__lowercase=    0
  		for batch in eval_dataloader:
  				batch.to(lowercase__			)
  				# pad
  				context.zero_()
  				for i in range(lowercase__			):
  						__lowercase=    batch[i]
  				__lowercase=    model(lowercase__     ,				labels=lowercase__			)
  				eval_loss += outputs[0].sum().item()
  				nb_eval_examples += batch.size(0			)
  		__lowercase=    eval_loss / nb_eval_examples
  		__lowercase=    torch.exp(lowercase__			)
  		model.train()
  		return perplexity
  
  
  
  
  
  
  
  def  _lowerCamelCase(			lowercase__="gpt2"			)		->			str:
  
  		'''simple docstring'''
  
  
  
  
  
  
  
  		__lowercase=    GPTaLMHeadModel.from_pretrained(lowercase__     ,				output_hidden_states=lowercase__			)
  		torch.save(model.state_dict()     ,				model_name + 'local.pt'			)
  		return model
  
  
  
  
  
  
  
  def  _lowerCamelCase(			lowercase__     ,				lowercase__     ,				lowercase__			)		->			List[str]:
  
  		'''simple docstring'''
  
  
  
  
  
  
  
  		__lowercase=    copy.deepcopy(lowercase__			)
  		model.to(lowercase__			)
  
  		__lowercase=    ['bias', 'LayerNorm.weight']
  		__lowercase=    [
  		    {
  		        'params': [p for n, p in model.named_parameters() if not any(nd in n for nd in no_decay			)],
  		        'weight_decay': 0.0,
  		    },
  		    {'params': [p for n, p in model.named_parameters() if any(nd in n for nd in no_decay			)], 'weight_decay': 0.0},
  		]
  		__lowercase=    AdamW(lowercase__     ,				lr=5E-5     ,				eps=1E-8			)
  		__lowercase=    get_linear_schedule_with_warmup(lowercase__     ,				0     ,				lowercase__			)
  		torch.cuda.empty_cache()
  		return model, lm_optimizer, lm_scheduler
  
  
  
  
  
  
  
  def  _lowerCamelCase(			lowercase__     ,				lowercase__     ,				lowercase__     ,				lowercase__			)		->			Optional[Any]:
  
  		'''simple docstring'''
  
  
  
  
  
  
  
  		__lowercase=    np.array(lowercase__			).mean()
  		__lowercase=    np.array(lowercase__			).std()
  		__lowercase=    (real_perps - avg) / std
  		__lowercase=    list(zip(lowercase__     ,				lowercase__     ,				lowercase__			)			)
  		joblib.dump(lowercase__     ,				lowercase__			)
  
  
  
  
  
  
  
  def  _lowerCamelCase(			lowercase__     ,				lowercase__     ,				lowercase__     ,				lowercase__     ,				lowercase__     ,				lowercase__     ,				lowercase__     ,				lowercase__="dev.jbl"     ,				lowercase__=recopy_gpta     ,				)		->			int:
  
  		'''simple docstring'''
  
  
  
  
  
  
  
  		__lowercase=    []
  		__lowercase=    []
  		__lowercase=    []
  
  		# Initialize the transformer model
  		__lowercase=    copy.deepcopy(lowercase__			)
  		orig_model.to(device='cpu'			)
  		torch.cuda.empty_cache()
  
  		# Compute perplexity of initial transformer model for comparison
  		model.train()
  		__lowercase,							__lowercase,							__lowercase=    recopy_model(lowercase__     ,				lowercase__     ,				lowercase__			)
  
  		for step in tqdm(range(lowercase__			)			):
  				__lowercase=    torch.zeros((1, context_len)     ,				dtype=torch.long     ,				device=lowercase__			)
  				__lowercase=    random.choice(lowercase__			)
  				__lowercase=    random.randint(0     ,				len(story[0]			) - context_len - 1			)
  				__lowercase=    story[0][start : start + context_len]
  				lm_optimizer.zero_grad()
  				__lowercase=    model(lowercase__     ,				labels=lowercase__			)
  				__lowercase=    outputs[0]
  				__lowercase=    compute_perplexity(lowercase__     ,				lowercase__     ,				lowercase__			)
  				model.train()
  				lm_loss.backward()
  				# Do LM backprop
  				torch.nn.utils.clip_grad_norm_(model.parameters()     ,				3.0			)
  				lm_optimizer.step()
  				lm_scheduler.step()  # Update learning rate schedule
  
  				# Compute perplexity after back-propagating on the selected context
  				__lowercase=    compute_perplexity(lowercase__     ,				lowercase__     ,				lowercase__			)
  
  				# Periodically save the stored (X, IG(X)) pairs
  				if step % 1_0_0_0 == 0 and step > 1:
  						intermittent_save(lowercase__     ,				lowercase__     ,				lowercase__     ,				lowercase__			)
  
  				# Reset the pretrained model to the original pretrained GPT-2 weights after each iteration
  				__lowercase,							__lowercase,							__lowercase=    recopy_model(lowercase__     ,				lowercase__     ,				lowercase__			)
  
  				past_perps.append(past_perp.item()			)
  				real_perps.append(orig_perp - real_perp.item()			)
  				contexts.append(np.array(context.cpu()			)			)
  
  		intermittent_save(lowercase__     ,				lowercase__     ,				lowercase__     ,				lowercase__			)
  
  
  
  
  
  
  
  def  _lowerCamelCase(			lowercase__     ,				lowercase__="data/tokenized_stories_train_wikitext103.jbl"     ,				lowercase__=1_0_0     ,				lowercase__=1_0_2_6     ,				lowercase__=True			)		->			str:
  
  		'''simple docstring'''
  
  
  
  
  
  
  
  		__lowercase=    joblib.load(lowercase__			)
  		print('data loaded'			)
  		__lowercase=    []
  		if trim:
  				for i, example in enumerate(lowercase__			):
  						if len(example[0]			) > min_len:
  								__lowercase=    random.randint(0     ,				len(example[0]			) - context_len - 1			)
  								objective_set.append(example[0, start : start + context_len]			)
  						if len(lowercase__			) >= number:
  								break
  				__lowercase=    []
  				for j in range(i + 1     ,				len(lowercase__			)			):
  						if len(data[j][0]			) > min_len:
  								train_data.append(data[j]			)
  		else:
  				__lowercase=    data[0:number]
  				__lowercase=    data[number:]
  
  		joblib.dump(lowercase__     ,				'objective_set.jbl'			)
  		print('objective set saved'			)
  		return train_data, objective_set
  
  
  
  
  
  
  
  def  _lowerCamelCase(			lowercase__     ,				lowercase__     ,				lowercase__     ,				lowercase__     ,				lowercase__=5_0     ,				lowercase__="secondary_learner.pt"			)		->			Tuple:
  
  		'''simple docstring'''
  
  
  
  
  
  
  
  		__lowercase=    torch.device('cuda:0' if torch.cuda.is_available() else 'cpu'			)
  		# We will use the first 512 pairs from our dataset as a test set for
  		# our secondary learner and the rest to train
  		__lowercase=    train_dataset[:5_1_2]
  		__lowercase=    train_dataset[5_1_2:]
  		__lowercase=    DataLoader(lowercase__     ,				shuffle=lowercase__     ,				batch_size=lowercase__			)
  		__lowercase=    DataLoader(lowercase__     ,				shuffle=lowercase__     ,				batch_size=lowercase__			)
  
  		# secondary learner model set up
  		__lowercase=    nn.MSELoss()
  		__lowercase=    nn.MSELoss(reduction='sum'			)
  		secondary_learner.to(lowercase__			)
  		__lowercase=    torch.optim.Adam(secondary_learner.parameters()     ,				lr=0.0_0001			)
  		secondary_learner.train()
  
  		# TODO in original code this is written as number of actual batches seen
  		# not number of items seen but other places it is number of items instead.
  		# improve consistency! changed this to epochs for clarity
  		__lowercase=    float('inf'			)
  		# Iterate through batches until we've used max_steps batches
  		for epoch in range(int(lowercase__			)			):
  				__lowercase=    0.0
  				secondary_learner.train()
  				for step, batch in enumerate(lowercase__			):
  						__lowercase=    batch[0].to(lowercase__			)
  						__lowercase=    batch[1].to(lowercase__			)
  						__lowercase=    secondary_learner(lowercase__			)
  						q_optimizer.zero_grad()
  						__lowercase=    loss(lowercase__     ,				real_q.float()			)
  						q_loss.backward()
  						q_optimizer.step()
  						tr_q_loss += q_loss.item()
  
  						# model trains fairly quickly so we won't wait for a full epoch
  						# eval is triggered at eval_freq and end of epochs
  						if (step % eval_freq == 0 and step > 0) or ((step + 1) == len(lowercase__			)):
  								__lowercase=    tr_q_loss / (step + 1)
  
  								secondary_learner.eval()
  								__lowercase=    0.0
  								__lowercase=    0.0
  								__lowercase=    []
  								__lowercase=    []
  								# Compute performance of the secondary learner after this batch
  								for stepa, batcha in enumerate(lowercase__			):
  										__lowercase=    batcha[0].to(lowercase__			)
  										__lowercase=    batcha[1].to(lowercase__			)
  										__lowercase=    secondary_learner(lowercase__			)
  										q_lossa += test_loss(lowercase__     ,				lowercase__			).item()
  										sum_qa += torch.sum(lowercase__			).item()
  										for ei, i in enumerate(predicted_qa.cpu().detach().numpy()			):
  												predicted.append(i.item()			)
  										for ei, i in enumerate(real_qa.cpu().detach().numpy()			):
  												actual.append(i.item()			)
  
  								q_lossa /= len(lowercase__			)
  								print(
  								    'Epoch: '     ,				lowercase__     ,				'step: '     ,				lowercase__     ,				'Avg. q:'     ,				sum_qa / len(lowercase__			)     ,				'Train Loss: '     ,				lowercase__     ,				'Test Loss: '     ,				lowercase__     ,				)
  								if q_lossa < best_test_loss:
  										joblib.dump((predicted, actual)     ,				'pred_vs_actual.jbl'			)
  										torch.save(secondary_learner.state_dict()     ,				lowercase__			)
  										__lowercase=    q_lossa
  
  						secondary_learner.train()
  		return secondary_learner
  
  
  
  
  
  class    A					(     nn.Module				):
  
  
  							def __init__(self   ,       lowerCAmelCase      ):
  									super(lowerCAmelCase   ,       self      ).__init__()
  									__lowercase=    model.transformer.wte
  									__lowercase=    copy.deepcopy(model.transformer.wte.weight      )
  									__lowercase=    nn.Convad(self.embeddings.weight.size(1      )   ,       2_5_6   ,       3   ,       padding=1      )
  									__lowercase=    nn.Sequential(nn.Linear(2_5_6   ,       3_2      )   ,       nn.Dropout(p=0.1      )   ,       nn.Linear(3_2   ,       3_2      )   ,       nn.Linear(3_2   ,       1      )      )
  
  
  							def     _A (self   ,       lowerCAmelCase      ):
  									__lowercase=    torch.max(self.conv(self.embeddings(lowerCAmelCase      ).squeeze(1      ).transpose(1   ,       2      )      )   ,       2      )[0]
  									__lowercase=    self.fc(lowerCAmelCase      )
  									return qs.squeeze(1      )
  
  
  
  
  
  
  
  							@classmethod
  							def     _A (cls   ,       lowerCAmelCase   ,       lowerCAmelCase      ):
  									__lowercase=    cls(lowerCAmelCase      )  # this calls __init__
  									__lowercase=    torch.load(lowerCAmelCase      )
  									secondary_learner.load_state_dict(lowerCAmelCase      )
  									__lowercase=    model.transformer.wte
  									__lowercase=    copy.deepcopy(model.transformer.wte.weight      )
  									return secondary_learner
  
  
  
  
  
  
  
style_context: 
  
  
  def  _lowerCamelCase(			lowercase__			)		->			str:
  
  		'''simple docstring'''
  
  
  
  
  
  
  
  		if len(lowercase__			) == 0 or not all(len(lowercase__			) == 2 for pair in coordinates			):
  				raise ValueError('The program cannot work out a fitting polynomial.'			)
  
  		if len({tuple(lowercase__			) for pair in coordinates}			) != len(lowercase__			):
  				raise ValueError('The program cannot work out a fitting polynomial.'			)
  
  		__lowercase=    {x for x, _ in coordinates}
  		if len(lowercase__			) == 1:
  				return F'x={coordinates[0][0]}'
  
  		if len(lowercase__			) != len(lowercase__			):
  				raise ValueError('The program cannot work out a fitting polynomial.'			)
  
  		__lowercase=    len(lowercase__			)
  
  		__lowercase=    0
  		__lowercase=    []
  		# put the x and x to the power values in a matrix
  		while count_of_line < x:
  				__lowercase=    0
  				__lowercase=    coordinates[count_of_line][0]
  				__lowercase=    []
  				while count_in_line < x:
  						count_line.append(a ** (x - (count_in_line + 1))			)
  						count_in_line += 1
  				matrix.append(lowercase__			)
  				count_of_line += 1
  
  		__lowercase=    0
  		# put the y values into a vector
  		__lowercase=    []
  		while count_of_line < x:
  				vector.append(coordinates[count_of_line][1]			)
  				count_of_line += 1
  
  		__lowercase=    0
  
  		while count < x:
  				__lowercase=    0
  				while zahlen < x:
  						if count == zahlen:
  								zahlen += 1
  						if zahlen == x:
  								break
  						__lowercase=    matrix[zahlen][count] / matrix[count][count]
  						for counting_columns, item in enumerate(matrix[count]			):
  								# manipulating all the values in the matrix
  								matrix[zahlen][counting_columns] -= item * bruch
  						# manipulating the values in the vector
  						vector[zahlen] -= vector[count] * bruch
  						zahlen += 1
  				count += 1
  
  		__lowercase=    0
  		# make solutions
  		__lowercase=    []
  		while count < x:
  				solution.append(str(vector[count] / matrix[count][count]			)			)
  				count += 1
  
  		__lowercase=    0
  		__lowercase=    'f(x)='
  
  		while count < x:
  				__lowercase=    solution[count].split('E'			)
  				if len(lowercase__			) > 1:
  						__lowercase=    F'{remove_e[0]}*10^{remove_e[1]}'
  				solved += F'x^{x - (count + 1)}*{solution[count]}'
  				if count + 1 != x:
  						solved += "+"
  				count += 1
  
  		return solved
  
  
  if __name__ == "__main__":
  	print(points_to_polynomial([]))
  	print(points_to_polynomial([[]]))
  	print(points_to_polynomial([[1, 0], [2, 0], [3, 0]]))
  	print(points_to_polynomial([[1, 1], [2, 1], [3, 1]]))
  	print(points_to_polynomial([[1, 3], [2, 3], [3, 3]]))
  	print(points_to_polynomial([[1, 1], [2, 2], [3, 3]]))
  	print(points_to_polynomial([[1, 1], [2, 4], [3, 9]]))
  	print(points_to_polynomial([[1, 3], [2, 6], [3, 1_1]]))
  	print(points_to_polynomial([[1, -3], [2, -6], [3, -1_1]]))
  	print(points_to_polynomial([[1, 5], [2, 2], [3, 9]]))
  
  
  
  
  
  
  