Large Language models are comprised of billions of parameters (weights). For every word it generates, the model has to perform computationally expensive calculations across all of those parameters.
Large Language models accept a sentence, or sequence of tokens, and generate a probability distribution of the following almost certainly token.
Thus, typically decoding n tokens (or generating n words from the model) requires running the model n variety of times. At each iteration, the brand new token is appended to the input sentence and passed to the model again. This might be costly.
Moreover, decoding strategy can influence the standard of the generated words. Generating tokens in a straightforward way, by just taking the token with the best probability within the output distribution, may end up in repetitive text. Random sampling from the distribution may end up in unintended drift.
Thus, a solid decoding strategy is required to make sure each:
- High Quality Outputs
- Fast Inference Time
Each requirements might be addressed by utilizing a mixture of a giant and small language model, so long as the amateur and expert models are similar (e.g., same architecture but different sizes).
- Goal/Large Model: Important LM with larger variety of parameters (e.g. OPT-13B)
- Amateur/Small Model: Smaller version of Important LM with fewer parameters (e.g. OPT-125M)
Speculative and contrastive decoding leverage large and small LLMs to attain reliable and efficient text generation.
Contrastive Decoding is a technique that exploits the incontrovertible fact that that failures in large LLMs (reminiscent of repetition, incoherence) are much more pronounced in small LLMs. Thus, this strategy optimizes for the tokens with the best probability difference between the small and huge model.
For a single prediction, contrastive decoding generates two probability distributions:
- q = logit probabilities for amateur model
- p = logit probabilities for expert model
The subsequent token is chosen based on the next criteria:
- Discard all tokens that wouldn’t have sufficiently high probability under the expert model (discard p(x) < alpha * max(p))
- From the remaining tokens, select the one the with the most important difference between large model and small model log probabilities, max(p(x) – q(x)).
Implementing Contrastive Decoding
from transformers import AutoTokenizer, AutoModelForCausalLM
import torch# Load models and tokenizer
tokenizer = AutoTokenizer.from_pretrained('gpt2')
amateur_lm = AutoModelForCausalLM.from_pretrained('gpt2')
expert_lm = AutoModelForCausalLM.from_pretrained('gpt2-large')
def contrastive_decoding(prompt, max_length=50):
input_ids = tokenizer(prompt, return_tensors="pt").input_ids
while input_ids.shape[1] < max_length:
# Generate amateur model output
amateur_outputs = amateur_lm(input_ids, return_dict=True)
amateur_logits = torch.softmax(amateur_outputs.logits[:, -1, :], dim=-1)
log_probs_amateur = torch.log(amateur_logits)
# Generate expert model output
expert_outputs = expert_lm(input_ids, return_dict=True)
expert_logits = torch.softmax(expert_outputs.logits[:, -1, :], dim=-1)
log_probs_exp = torch.log(expert_logits)
log_probs_diff = log_probs_exp - log_probs_amateur
# Set an alpha threshold to eliminate less confident tokens in expert
alpha = 0.1
candidate_exp_prob = torch.max(expert_logits)
# Mask tokens below threshold for expert model
V_head = expert_logits < alpha * candidate_exp_prob
# Select the following token from the log-probabilities difference, ignoring masked values
token = torch.argmax(log_probs_diff.masked_fill(V_head, -torch.inf)).unsqueeze(0)
# Append token and accumulate generated text
input_ids = torch.cat([input_ids, token.unsqueeze(1)], dim=-1)
return tokenizer.batch_decode(input_ids)
prompt = "Large Language Models are"
generated_text = contrastive_decoding(prompt, max_length=25)
print(generated_text)
Speculative decoding is predicated on the principle that the smaller model must sample from the identical distribution because the larger model. Thus, this strategy goals to just accept as many predictions from the smaller model as possible, provided they align with the distribution of the larger model.
The smaller model generates n tokens in sequence, as possible guesses. Nevertheless, all n sequences are fed into the larger expert model as a single batch, which is quicker than sequential generation.
This leads to a cache for every model, with n probability distributions in each cache.
- q = logit probabilities for amateur model
- p = logit probabilities for expert model
Next, the sampled tokens from the amateur model are accepted or rejected based on the next conditions:
- If probability of the token is higher in expert distribution (p) than amateur distribution (q), or p(x) > q(x), accept token
- If probability of token is lower in expert distribution (p) than amateur distribution (q), or p(x) < q(x), reject token with probability 1 – p(x) / q(x)
If a token is rejected, the following token is sampled from the expert distribution or adjusted distribution. Moreover, the amateur and expert model reset the cache and re-generate n guesses and probability distributions p and q.
Implementing Speculative Decoding
from transformers import AutoTokenizer, AutoModelForCausalLM
import torch# Load models and tokenizer
tokenizer = AutoTokenizer.from_pretrained('gpt2')
amateur_lm = AutoModelForCausalLM.from_pretrained('gpt2')
expert_lm = AutoModelForCausalLM.from_pretrained('gpt2-large')
# Sample next token from output distribution
def sample_from_distribution(logits):
sampled_index = torch.multinomial(logits, 1)
return sampled_index
def generate_cache(input_ids, n_tokens):
# Store logits at each step for amateur and expert models
amateur_logits_per_step = []
generated_tokens = []
batch_input_ids = []
with torch.no_grad():
for _ in range(n_tokens):
# Generate amateur model output
amateur_outputs = amateur_lm(input_ids, return_dict=True)
amateur_logits = torch.softmax(amateur_outputs.logits[:, -1, :], dim=-1)
amateur_logits_per_step.append(amateur_logits)
# Sampling from amateur logits
next_token = sample_from_distribution(amateur_logits)
generated_tokens.append(next_token)
# Append to input_ids for next generation step
input_ids = torch.cat([input_ids, next_token], dim=-1)
batch_input_ids.append(input_ids.squeeze(0))
# Feed IDs to expert model as batch
batched_input_ids = torch.nn.utils.rnn.pad_sequence(batch_input_ids, batch_first=True, padding_value=0 )
expert_outputs = expert_lm(batched_input_ids, return_dict=True)
expert_logits = torch.softmax(expert_outputs.logits[:, -1, :], dim=-1)
return amateur_logits_per_step, expert_logits, torch.cat(generated_tokens, dim=-1)
def speculative_decoding(prompt, n_tokens=5, max_length=50):
input_ids = tokenizer(prompt, return_tensors="pt").input_ids
while input_ids.shape[1] < max_length:
amateur_logits_per_step, expert_logits, generated_ids = generate_cache(
input_ids, n_tokens
)
accepted = 0
for n in range(n_tokens):
token = generated_ids[:, n][0]
r = torch.rand(1).item()
# Extract probabilities
p_x = expert_logits[n][token].item()
q_x = amateur_logits_per_step[n][0][token].item()
# Speculative decoding acceptance criterion
if ((q_x > p_x) and (r > (1 - p_x / q_x))):
break # Reject token and restart the loop
else:
accepted += 1
# Check length
if (input_ids.shape[1] + accepted) >= max_length:
return tokenizer.batch_decode(input_ids)
input_ids = torch.cat([input_ids, generated_ids[:, :accepted]], dim=-1)
if accepted < n_tokens:
diff = expert_logits[accepted] - amateur_logits_per_step[accepted][0]
clipped_diff = torch.clamp(diff, min=0)
# Sample a token from the adjusted expert distribution
normalized_result = clipped_diff / torch.sum(clipped_diff, dim=0, keepdim=True)
next_token = sample_from_distribution(normalized_result)
input_ids = torch.cat([input_ids, next_token.unsqueeze(1)], dim=-1)
else:
# Sample directly from the expert logits for the last accepted token
next_token = sample_from_distribution(expert_logits[-1])
input_ids = torch.cat([input_ids, next_token.unsqueeze(1)], dim=-1)
return tokenizer.batch_decode(input_ids)
# Example usage
prompt = "Large Language models are"
generated_text = speculative_decoding(prompt, n_tokens=3, max_length=25)
print(generated_text)
Evaluation
We are able to evaluate each decoding approaches by comparing them to a naive decoding method, where we randomly pick the following token from the probability distribution.
def sequential_sampling(prompt, max_length=50):
"""
Perform sequential sampling with the given model.
"""
# Tokenize the input prompt
input_ids = tokenizer(prompt, return_tensors="pt").input_idswith torch.no_grad():
while input_ids.shape[1] < max_length:
# Sample from the model output logits for the last token
outputs = expert_lm(input_ids, return_dict=True)
logits = outputs.logits[:, -1, :]
probabilities = torch.softmax(logits, dim=-1)
next_token = torch.multinomial(probabilities, num_samples=1)
input_ids = torch.cat([input_ids, next_token], dim=-1)
return tokenizer.batch_decode(input_ids)
To guage contrastive decoding, we are able to use the next metrics for lexical richness.
- n-gram Entropy: Measures the unpredictability or diversity of n-grams within the generated text. High entropy indicates more diverse text, while low entropy suggests repetition or predictability.
- distinct-n: Measures the proportion of unique n-grams within the generated text. Higher distinct-n values indicate more lexical diversity.
from collections import Counter
import mathdef ngram_entropy(text, n):
"""
Compute n-gram entropy for a given text.
"""
# Tokenize the text
tokens = text.split()
if len(tokens) < n:
return 0.0 # Not enough tokens to form n-grams
# Create n-grams
ngrams = [tuple(tokens[i:i + n]) for i in range(len(tokens) - n + 1)]
# Count frequencies of n-grams
ngram_counts = Counter(ngrams)
total_ngrams = sum(ngram_counts.values())
# Compute entropy
entropy = -sum((count / total_ngrams) * math.log2(count / total_ngrams)
for count in ngram_counts.values())
return entropy
def distinct_n(text, n):
"""
Compute distinct-n metric for a given text.
"""
# Tokenize the text
tokens = text.split()
if len(tokens) < n:
return 0.0 # Not enough tokens to form n-grams
# Create n-grams
ngrams = [tuple(tokens[i:i + n]) for i in range(len(tokens) - n + 1)]
# Count unique and total n-grams
unique_ngrams = set(ngrams)
total_ngrams = len(ngrams)
return len(unique_ngrams) / total_ngrams if total_ngrams > 0 else 0.0
prompts = [
"Large Language models are",
"Barack Obama was",
"Decoding strategy is important because",
"A good recipe for Halloween is",
"Stanford is known for"
]
# Initialize accumulators for metrics
naive_entropy_totals = [0, 0, 0] # For n=1, 2, 3
naive_distinct_totals = [0, 0] # For n=1, 2
contrastive_entropy_totals = [0, 0, 0]
contrastive_distinct_totals = [0, 0]
for prompt in prompts:
naive_generated_text = sequential_sampling(prompt, max_length=50)[0]
for n in range(1, 4):
naive_entropy_totals[n - 1] += ngram_entropy(naive_generated_text, n)
for n in range(1, 3):
naive_distinct_totals[n - 1] += distinct_n(naive_generated_text, n)
contrastive_generated_text = contrastive_decoding(prompt, max_length=50)[0]
for n in range(1, 4):
contrastive_entropy_totals[n - 1] += ngram_entropy(contrastive_generated_text, n)
for n in range(1, 3):
contrastive_distinct_totals[n - 1] += distinct_n(contrastive_generated_text, n)
# Compute averages
naive_entropy_averages = [total / len(prompts) for total in naive_entropy_totals]
naive_distinct_averages = [total / len(prompts) for total in naive_distinct_totals]
contrastive_entropy_averages = [total / len(prompts) for total in contrastive_entropy_totals]
contrastive_distinct_averages = [total / len(prompts) for total in contrastive_distinct_totals]
# Display results
print("Naive Sampling:")
for n in range(1, 4):
print(f"Average Entropy (n={n}): {naive_entropy_averages[n - 1]}")
for n in range(1, 3):
print(f"Average Distinct-{n}: {naive_distinct_averages[n - 1]}")
print("nContrastive Decoding:")
for n in range(1, 4):
print(f"Average Entropy (n={n}): {contrastive_entropy_averages[n - 1]}")
for n in range(1, 3):
print(f"Average Distinct-{n}: {contrastive_distinct_averages[n - 1]}")
The next results show us that contrastive decoding outperforms naive sampling for these metrics.
Naive Sampling:
Average Entropy (n=1): 4.990499826537679
Average Entropy (n=2): 5.174765791328267
Average Entropy (n=3): 5.14373124004409
Average Distinct-1: 0.8949694135740648
Average Distinct-2: 0.9951219512195122Contrastive Decoding:
Average Entropy (n=1): 5.182773920916605
Average Entropy (n=2): 5.3495681172235665
Average Entropy (n=3): 5.313720275712986
Average Distinct-1: 0.9028425204970866
Average Distinct-2: 1.0
To guage speculative decoding, we are able to have a look at the common runtime for a set of prompts for various n values.
import time
import matplotlib.pyplot as plt# Parameters
n_tokens = range(1, 11)
speculative_decoding_times = []
naive_decoding_times = []
prompts = [
"Large Language models are",
"Barack Obama was",
"Decoding strategy is important because",
"A good recipe for Halloween is",
"Stanford is known for"
]
# Loop through n_tokens values
for n in n_tokens:
avg_time_naive, avg_time_speculative = 0, 0
for prompt in prompts:
start_time = time.time()
_ = sequential_sampling(prompt, max_length=25)
avg_time_naive += (time.time() - start_time)
start_time = time.time()
_ = speculative_decoding(prompt, n_tokens=n, max_length=25)
avg_time_speculative += (time.time() - start_time)
naive_decoding_times.append(avg_time_naive / len(prompts))
speculative_decoding_times.append(avg_time_speculative / len(prompts))
avg_time_naive = sum(naive_decoding_times) / len(naive_decoding_times)
# Plotting the outcomes
plt.figure(figsize=(8, 6))
plt.bar(n_tokens, speculative_decoding_times, width=0.6, label='Speculative Decoding Time', alpha=0.7)
plt.axhline(y=avg_time_naive, color='red', linestyle='--', label='Naive Decoding Time')
# Labels and title
plt.xlabel('n_tokens', fontsize=12)
plt.ylabel('Average Time (s)', fontsize=12)
plt.title('Speculative Decoding Runtime vs n_tokens', fontsize=14)
plt.legend()
plt.grid(axis='y', linestyle='--', alpha=0.7)
# Show the plot
plt.show()
plt.savefig("plot.png")
We are able to see that the common runtime for the naive decoding is far higher than for speculative decoding across n values.
Combining large and small language models for decoding strikes a balance between quality and efficiency. While these approaches introduce additional complexity in system design and resource management, their advantages apply to conversational AI, real-time translation, and content creation.
These approaches require careful consideration of deployment constraints. As an illustration, the extra memory and compute demands of running dual models may limit feasibility on edge devices, though this might be mitigated through techniques like model quantization.
Unless otherwise noted, all images are by the writer.
