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Replace parallel self-consistency with sequential reasoning where chains iteratively build on previous attempts, weighted by inverse entropy to prioritize confident solutions, achieving 46.7 pp accuracy gains over parallel approaches.
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| name | sequential-edge-inverse-entropy-voting |
| title | Sequential Edge: Inverse-Entropy Voting Beats Parallel Self-Consistency |
| version | 0.0.2 |
| engine | skillxiv-v0.0.2-claude-opus-4.6 |
| license | MIT |
| url | https://arxiv.org/abs/2511.02309 |
| keywords | ["Test-Time Scaling","Inference Optimization","Reasoning Chains","Entropy","Voting"] |
| description | Replace parallel self-consistency with sequential reasoning where chains iteratively build on previous attempts, weighted by inverse entropy to prioritize confident solutions, achieving 46.7 pp accuracy gains over parallel approaches. |
The dominant paradigm for improving language model reasoning is parallel self-consistency: run N independent reasoning chains, then vote. Sequential Edge shows this is suboptimal. By running chains sequentially where each explicitly builds on previous attempts, models achieve 95.6% superiority rates over parallel approaches. Further, weighting solutions by inverse entropy (favoring low-entropy/confident chains) outperforms majority voting universally.
This is a pure inference-time technique requiring no model retraining.
Sequential Reasoning With Entropy-Weighted Aggregation:
1. Implement Sequential Chain Generation
Generate reasoning chains that explicitly reference previous attempts.
class SequentialReasoningGenerator:
def __init__(self, model, tokenizer, max_chains=6):
self.model = model
self.tokenizer = tokenizer
self.max_chains = max_chains
():
chains = []
entropies = []
prompt_1 =
chain_1, entropy_1 = .generate_chain_with_entropy(prompt_1)
chains.append(chain_1)
entropies.append(entropy_1)
i (, num_chains):
previous_solution = chains[-]
prompt_n =
chain_n, entropy_n = .generate_chain_with_entropy(prompt_n)
chains.append(chain_n)
entropies.append(entropy_n)
chains, entropies
():
input_ids = .tokenizer.encode(prompt, return_tensors=)
outputs = .model.generate(
input_ids,
max_new_tokens=,
return_dict_in_generate=,
output_scores=,
pad_token_id=.tokenizer.eos_token_id
)
generated_ids = outputs.sequences[][input_ids.shape[]:]
generated_text = .tokenizer.decode(generated_ids, skip_special_tokens=)
entropy = .compute_sequence_entropy(outputs.scores)
generated_text, entropy
():
entropies = []
token_scores scores:
probs = F.softmax(token_scores, dim=-)
entropy = -(probs * torch.log(probs + )).(dim=-)
entropies.append(entropy.item())
np.mean(entropies) entropies
2. Implement Inverse-Entropy Voting
Weight answers by confidence (inverse of entropy).
class InverseEntropyVoter:
def __init__(self, extraction_fn):
"""extraction_fn: function that extracts answer from solution text"""
self.extract_answer = extraction_fn
def extract_answers_and_weights(self, chains, entropies):
"""Extract final answers and compute entropy-based weights"""
answers = []
weights = []
for chain, entropy in zip(chains, entropies):
# Extract answer from chain
answer = self.extract_answer(chain)
answers.append(answer)
# Weight inversely to entropy: low entropy -> high weight
# Use exponential scaling for sharper differences
weight = np.exp(-entropy)
weights.append(weight)
# Normalize weights to sum to 1
total_weight = sum(weights)
weights = [w / total_weight for w in weights]
return answers, weights
def weighted_vote(self, chains, entropies, answer_similarity_fn=None):
"""Aggregate answers weighted by inverse entropy"""
answers, weights = self.extract_answers_and_weights(chains, entropies)
# Group similar answers
if answer_similarity_fn:
answer_groups = self.group_similar_answers(answers, answer_similarity_fn)
else:
answer_groups = {ans: [i for i, a in enumerate(answers) if a == ans]
for ans in set(answers)}
# Compute weighted score for each answer group
group_scores = {}
for answer, indices in answer_groups.items():
score = sum(weights[i] for i in indices)
group_scores[answer] = score
# Return highest-scoring answer
final_answer = max(group_scores, key=group_scores.get)
confidence = group_scores[final_answer]
return final_answer, confidence, group_scores
def group_similar_answers(self, answers, similarity_fn):
"""Group answers that are semantically similar"""
groups = {}
for i, answer in enumerate(answers):
# Find most similar existing group
best_group = None
best_similarity = 0
for group_answer in groups:
sim = similarity_fn(answer, group_answer)
if sim > best_similarity:
best_similarity = sim
best_group = group_answer
if best_group and best_similarity > 0.8:
groups[best_group].append(i)
else:
groups[answer] = [i]
return groups
3. Implement Hybrid Sequential-Parallel Strategy
Combine approaches for complex problems.
class HybridReasoningStrategy:
def __init__(self, model, tokenizer, num_sequential=3, num_parallel=3):
self.sequential_gen = SequentialReasoningGenerator(model, tokenizer)
self.voter = InverseEntropyVoter(self.extract_final_answer)
self.num_seq = num_sequential
self.num_par = num_parallel
def solve_with_budget(self, question, token_budget=10000):
"""Solve using hybrid strategy within token budget"""
# Phase 1: Sequential reasoning (focus on quality)
seq_chains, seq_entropies = self.sequential_gen.generate_sequential_chains(
question, self.num_seq
)
tokens_used = sum(len(c.split()) for c in seq_chains) * 1.3 # Estimate
# Phase 2: Parallel chains if budget remains
if tokens_used < token_budget * 0.7:
parallel_chains = []
for _ in range(self.num_par):
prompt = f"Solve: {question}\nSolution:"
chain, _ = self.sequential_gen.generate_chain_with_entropy(prompt)
parallel_chains.append(chain)
# Combine all chains
all_chains = seq_chains + parallel_chains
all_entropies = seq_entropies + [0.0] * len(parallel_chains) # Parallel have no reference entropy
else:
all_chains = seq_chains
all_entropies = seq_entropies
# Aggregate
answer, confidence, scores = self.voter.weighted_vote(all_chains, all_entropies)
return answer, confidence
def extract_final_answer(self, solution_text):
"""Extract final answer from solution"""
# Simple strategy: last numeric value or final sentence
import re
numbers = re.findall(r'-?\d+\.?\d*', solution_text)
if numbers:
return float(numbers[-1])
# Fallback: last sentence
sentences = solution_text.split('.')
return sentences[-2] if len(sentences) > 1 else solution_text
4. Evaluate Sequential vs Parallel
Compare efficiency and accuracy.
def compare_strategies(model, tokenizer, test_questions):
"""Benchmark sequential vs parallel approaches"""
results = {
'sequential': {'accuracy': [], 'tokens': []},
'parallel': {'accuracy': [], 'tokens': []},
'hybrid': {'accuracy': [], 'tokens': []}
}
seq_gen = SequentialReasoningGenerator(model, tokenizer)
voter = InverseEntropyVoter(extract_answer_fn)
for question, ground_truth in test_questions:
# Sequential approach
seq_chains, seq_entropies = seq_gen.generate_sequential_chains(question, num_chains=6)
seq_answer, _ = voter.weighted_vote(seq_chains, seq_entropies)
seq_correct = seq_answer == ground_truth
seq_tokens = sum(len(c.split()) * 1.3 for c in seq_chains)
results['sequential']['accuracy'].append(seq_correct)
results['sequential']['tokens'].append(seq_tokens)
# Parallel approach (independent chains)
par_chains = []
for _ in range(6):
chain, entropy = seq_gen.generate_chain_with_entropy(
f"Solve: {question}\nSolution:"
)
par_chains.append(chain)
par_entropies = [0.0] * len(par_chains)
par_answer, _ = voter.weighted_vote(par_chains, par_entropies)
par_correct = par_answer == ground_truth
par_tokens = sum(len(c.split()) * 1.3 for c in par_chains)
results['parallel']['accuracy'].append(par_correct)
results['parallel']['tokens'].append(par_tokens)
# Compute statistics
for strategy in results:
acc = np.mean(results[strategy]['accuracy'])
tokens = np.mean(results[strategy]['tokens'])
print(f"{strategy}: {acc:.1%} accuracy, {tokens:.0f} tokens/problem")
return results
When to Use:
Hyperparameters:
When NOT to Use:
Pitfalls:
Key Insight: This is one of the few inference-time tricks that consistently beats the dominant approach. The mechanism is simple: sequential reasoning enables error correction that parallel approaches miss.