LLMs are becoming increasingly capable at reasoning, but the cost is rising accordingly. To make models "think deeper," the common approach is to increase the number of samples or extend the reasoning chain—but this directly translates to more tokens, higher costs, and slower speeds.
Is there a way to maintain reasoning quality while drastically cutting costs?
A paper submitted on May 14, Dual-Dimensional Consistency (DDC), offers a refreshing solution.
Where the Problem Lies
Existing inference-time scaling strategies suffer from two common flaws:
Width-based consensus methods (sampling multiple candidates and then voting) tend to reinforce hallucinations—if most samples head in the same wrong direction, the voting mechanism actually "confirms" the error.
Depth-pruning methods (prematurely terminating overly long reasoning chains) risk cutting off complex yet correct reasoning paths too early.
In short: widening risks hallucinations, while deepening risks waste. DDC aims to solve both problems simultaneously.
How DDC Works
DDC introduces two core components:
Confidence-Weighted Bayesian Protocol: Instead of simple voting, it performs weighted aggregation based on the confidence of each reasoning path. This way, even if multiple paths converge in the same direction, the system won't blindly confirm it if the overall confidence is low.
Trend-Aware Stratified Pruning: Rather than applying a one-size-fits-all cutoff to long reasoning chains, it analyzes the trend in reasoning quality. If a long chain hasn't produced a result yet but shows an upward quality trend, it is kept; if the trend is declining, it is decisively pruned.
Together, these two components form a closed loop: concentrating computational resources on high-quality reasoning paths, filtering out hallucinations while accelerating consensus.
Results
Across 5 benchmarks, DDC reduces token consumption by over 10x while maintaining or surpassing strong baseline accuracy. Moreover, this performance holds across a variety of different LLMs.
A 10x reduction is staggering in the field of inference optimization. Typically, saving 30-50% is already considered a publishable achievement.
Authors
The paper is authored by researchers including Bo Li and Hang Yan. Submitted on May 14, 2026.
Practical Implications
For teams using LLMs for complex reasoning in production environments, DDC's appeal is straightforward: with the same budget, you can run more inference tasks; or for the same number of tasks, you spend significantly less.
Inference-time scaling is one of the hottest research directions in 2026. Models like OpenAI's o1/o3 series, DeepSeek's R1, and Google's Gemini Thinking all employ similar approaches. DDC's contribution lies in making this path far more cost-effective.