Efficient Test-Time Inference via Deterministic Exploration of Truncated Decoding Trees

Apr 22, 2026•Xueyan Li, Johannes Zenn, Ekaterina Fadeeva +3•View PDF

TL;DR Highlight

Deterministic Leaf Enumeration (DLE) cuts self-consistency’s redundant sampling by deterministically exploring a tree of possible sequences, simultaneously improving math/code reasoning performance and speed.

Who Should Read

ML engineers seeking to reduce LLM inference costs while maintaining accuracy, particularly developers currently using self-consistency (multiple answer generation followed by majority voting) for tasks like solving math problems or generating code.

Core Mechanics

Self-consistency suffers from significant waste due to repeatedly generating the same prefix. With code generation, approximately 17% of all prefix tokens are duplicated when k=32.
DLE (Distinct Leaf Enumeration) is a deterministic method that views the space of possible sequences as a tree and explores only new, distinct leaves without redundancy.
DLE functions as a drop-in replacement for existing truncation methods like top-p, min-p, and ε-sampling, operating without requiring additional model calls or separate evaluations.
For a given number of sequences, DLE achieves higher probability mass coverage than stochastic self-consistency, and a positive correlation exists between coverage and accuracy.
DLE is compatible with prefix caching in inference engines like SGLang/vLLM, allowing for KV cache sharing of prefixes, and achieving near-theoretical maximum cache hit rates.
Early stopping prevents waste by terminating branches when 10 consecutive tokens match a previous sibling branch; over 85% of terminated branches would have yielded the same final answer.

Evidence

"On Qwen2.5-0.5B-Instruct, DLE (with ε-sampling) achieves 44.05% on GSM8K maj@8 versus 40.94% for Self-consistency (with ε-sampling), a 3-9% improvement. On HumanEval pass@8, DLE achieves 52.44% versus 47.56% for Self-consistency, a 4-7% improvement."

How to Apply

"If you’re currently implementing self-consistency with vLLM or SGLang, DLE can be integrated by replacing only the sampling loop while maintaining the same truncation sampler settings (top-p, min-p, ε-sampling). Combining it with SGLang’s RadixAttention or vLLM’s automatic prefix caching can further reduce latency."

Code Example

snippet

# DLE core logic pseudocode (based on ε-sampling)
# Step 1: greedy generation to create the first leaf and track branching points
def dle_decode(model, prompt, k, epsilon=0.05):
    leaves = []
    # Priority queue: (negative probability, prefix, next alternative token to explore)
    branch_queue = []  # (score, prefix_tokens, alt_token)
    
    # First greedy generation
    prefix, branch_points = greedy_generate_with_branches(model, prompt, epsilon)
    leaves.append(prefix)
    
    # Add branch points to the queue based on probability (PROBFIRST)
    for pos, token, prob in branch_points:
        heapq.heappush(branch_queue, (-prob, prefix[:pos], token))
    
    while len(leaves) < k and branch_queue:
        neg_prob, branch_prefix, alt_token = heapq.heappop(branch_queue)
        
        # Start a new prefix with the alternative token and greedy completion
        new_prefix = branch_prefix + [alt_token]
        
        # Early stopping: terminate if it overlaps with a previous sibling branch by 10+ tokens
        if check_early_stop(new_prefix, leaves, n=10):
            continue
        
        new_leaf, new_branches = greedy_generate_with_branches(
            model, new_prefix, epsilon, 
            kv_cache=get_shared_prefix_cache(new_prefix)  # Reuse prefix cache
        )
        leaves.append(new_leaf)
        
        for pos, token, prob in new_branches:
            path_prob = abs(neg_prob) * prob  # accumulated path probability
            heapq.heappush(branch_queue, (-path_prob, new_leaf[:pos], token))
    
    # Majority voting (uniform weight)
    answers = [extract_answer(leaf) for leaf in leaves]
    return Counter(answers).most_common(1)[0][0]

# Example usage (SGLang based)
# SGLang's RadixAttention automatically shares the prefix KV cache
import sglang as sgl

@sgl.function
def dle_with_sglang(s, question, leaves_prefixes):
    s += sgl.system("You are a math solver.")
    s += sgl.user(question)
    # Cache hit until the shared prefix, new generation only after that
    for branch_prefix in leaves_prefixes:
        with s.fork() as branch:
            branch += sgl.assistant(branch_prefix)
            branch += sgl.gen("completion", max_tokens=512)

Terminology

Self-consistencyA technique where multiple answers are generated for the same question, and the most frequent answer is selected. Similar to solving a test question multiple times and choosing the most common answer.

Truncated samplingA method of sampling from the next token candidates by cutting off those with lower probabilities and sampling only from the top candidates. Top-p, min-p, and ε-sampling fall into this category.

KV cacheA cache that stores intermediate calculations of tokens already processed by the LLM. Using the cached values when the same prefix appears again speeds up processing.

CoverageA metric measuring how much of the total possible sequence space is covered by the generated sequences. Higher coverage indicates that more important candidates have been explored.

prefix cachingAn optimization technique that reuses the KV cache of the common prefix when multiple generation requests share a common beginning. Supported by vLLM and SGLang.

maj@kAccuracy when the final answer is selected by majority voting from k generated answers. A larger k means more answers are generated for voting.

pass@kA metric used primarily in code generation evaluation, where success is determined if at least one of the k generated answers is correct.

Original Abstract (Expand)

Self-consistency boosts inference-time performance by sampling multiple reasoning traces in parallel and voting. However, in constrained domains like math and code, this strategy is compute-inefficient because it samples with replacement, repeatedly revisiting the same high-probability prefixes and duplicate completions. We propose Distinct Leaf Enumeration (DLE), a deterministic decoding method that treats truncated sampling as traversal of a pruned decoding tree and systematically enumerates distinct leaves instead of sampling with replacement. This strategy improves inference efficiency in two ways. Algorithmically, it increases coverage of the truncated search space under a fixed budget by exploring previously unvisited high-probability branches. Systemically, it reuses shared prefixes and reduces redundant token generation. Empirically, DLE explores higher-quality reasoning traces than stochastic self-consistency, yielding better performance on math, coding, and general reasoning tasks.