The tokenizer, Byte-Pair Encoding on this occasion, interprets every token within the enter textual content right into a corresponding token ID. Then, GPT-2 makes use of these token IDs as enter and tries to foretell the subsequent most definitely token. Lastly, the mannequin generates logits, that are transformed into possibilities utilizing a softmax operate.
For instance, the mannequin assigns a likelihood of 17% to the token for “of” being the subsequent token after “I’ve a dream”. This output primarily represents a ranked checklist of potential subsequent tokens within the sequence. Extra formally, we denote this likelihood as P(of | I’ve a dream) = 17%.
Autoregressive fashions like GPT predict the subsequent token in a sequence primarily based on the previous tokens. Think about a sequence of tokens w = (w₁, w₂, …, wₜ). The joint likelihood of this sequence P(w) may be damaged down as:
For every token wᵢ within the sequence, P(wᵢ | w₁, w₂, …, wᵢ₋₁) represents the conditional likelihood of wᵢ given all of the previous tokens (w₁, w₂, …, wᵢ₋₁). GPT-2 calculates this conditional likelihood for every of the 50,257 tokens in its vocabulary.
This results in the query: how will we use these possibilities to generate textual content? That is the place decoding methods, equivalent to grasping search and beam search, come into play.
Grasping search is a decoding methodology that takes probably the most possible token at every step as the subsequent token within the sequence. To place it merely, it solely retains the most definitely token at every stage, discarding all different potential choices. Utilizing our instance:
- Step 1: Enter: “I’ve a dream” → Most certainly token: “ of”
- Step 2: Enter: “I’ve a dream of” → Most certainly token: “ being”
- Step 3: Enter: “I’ve a dream of being” → Most certainly token: “ a”
- Step 4: Enter: “I’ve a dream of being a” → Most certainly token: “ physician”
- Step 5: Enter: “I’ve a dream of being a health care provider” → Most certainly token: “.”
Whereas this strategy would possibly sound intuitive, it’s essential to notice that the grasping search is short-sighted: it solely considers probably the most possible token at every step with out contemplating the general impact on the sequence. This property makes it quick and environment friendly because it doesn’t must hold observe of a number of sequences, but it surely additionally implies that it may miss out on higher sequences which may have appeared with barely much less possible subsequent tokens.
Subsequent, let’s illustrate the grasping search implementation utilizing graphviz and networkx. We choose the ID with the best rating, compute its log likelihood (we take the log to simplify calculations), and add it to the tree. We’ll repeat this course of for 5 tokens.
import matplotlib.pyplot as plt
import networkx as nx
import numpy as np
import timedef get_log_prob(logits, token_id):
# Compute the softmax of the logits
possibilities = torch.nn.practical.softmax(logits, dim=-1)
log_probabilities = torch.log(possibilities)
# Get the log likelihood of the token
token_log_probability = log_probabilities[token_id].merchandise()
return token_log_probability
def greedy_search(input_ids, node, size=5):
if size == 0:
return input_ids
outputs = mannequin(input_ids)
predictions = outputs.logits
# Get the anticipated subsequent sub-word (right here we use top-k search)
logits = predictions[0, -1, :]
token_id = torch.argmax(logits).unsqueeze(0)
# Compute the rating of the anticipated token
token_score = get_log_prob(logits, token_id)
# Add the anticipated token to the checklist of enter ids
new_input_ids = torch.cat([input_ids, token_id.unsqueeze(0)], dim=-1)
# Add node and edge to graph
next_token = tokenizer.decode(token_id, skip_special_tokens=True)
current_node = checklist(graph.successors(node))[0]
graph.nodes[current_node]['tokenscore'] = np.exp(token_score) * 100
graph.nodes[current_node]['token'] = next_token + f"_{size}"
# Recursive name
input_ids = greedy_search(new_input_ids, current_node, length-1)
return input_ids
# Parameters
size = 5
beams = 1
# Create a balanced tree with peak 'size'
graph = nx.balanced_tree(1, size, create_using=nx.DiGraph())
# Add 'tokenscore', 'cumscore', and 'token' attributes to every node
for node in graph.nodes:
graph.nodes[node]['tokenscore'] = 100
graph.nodes[node]['token'] = textual content
# Begin producing textual content
output_ids = greedy_search(input_ids, 0, size=size)
output = tokenizer.decode(output_ids.squeeze().tolist(), skip_special_tokens=True)
print(f"Generated textual content: {output}")
Generated textual content: I've a dream of being a health care provider.
Our grasping search generates the identical textual content because the one from the transformers library: “I’ve a dream of being a health care provider.” Let’s visualize the tree we created.
import matplotlib.pyplot as plt
import networkx as nx
import matplotlib.colours as mcolors
from matplotlib.colours import LinearSegmentedColormapdef plot_graph(graph, size, beams, rating):
fig, ax = plt.subplots(figsize=(3+1.2*beams**size, max(5, 2+size)), dpi=300, facecolor='white')
# Create positions for every node
pos = nx.nx_agraph.graphviz_layout(graph, prog="dot")
# Normalize the colours alongside the vary of token scores
if rating == 'token':
scores = [data['tokenscore'] for _, information in graph.nodes(information=True) if information['token'] just isn't None]
elif rating == 'sequence':
scores = [data['sequencescore'] for _, information in graph.nodes(information=True) if information['token'] just isn't None]
vmin = min(scores)
vmax = max(scores)
norm = mcolors.Normalize(vmin=vmin, vmax=vmax)
cmap = LinearSegmentedColormap.from_list('rg', ["r", "y", "g"], N=256)
# Draw the nodes
nx.draw_networkx_nodes(graph, pos, node_size=2000, node_shape='o', alpha=1, linewidths=4,
node_color=scores, cmap=cmap)
# Draw the sides
nx.draw_networkx_edges(graph, pos)
# Draw the labels
if rating == 'token':
labels = {node: information['token'].cut up('_')[0] + f"n{information['tokenscore']:.2f}%" for node, information in graph.nodes(information=True) if information['token'] just isn't None}
elif rating == 'sequence':
labels = {node: information['token'].cut up('_')[0] + f"n{information['sequencescore']:.2f}" for node, information in graph.nodes(information=True) if information['token'] just isn't None}
nx.draw_networkx_labels(graph, pos, labels=labels, font_size=10)
plt.field(False)
# Add a colorbar
sm = plt.cm.ScalarMappable(cmap=cmap, norm=norm)
sm.set_array([])
if rating == 'token':
fig.colorbar(sm, ax=ax, orientation='vertical', pad=0, label='Token likelihood (%)')
elif rating == 'sequence':
fig.colorbar(sm, ax=ax, orientation='vertical', pad=0, label='Sequence rating')
plt.present()
# Plot graph
plot_graph(graph, size, 1.5, 'token')
