Florian Valentin Wunderlich, Lars Benedikt Kaesberg, Jan Philip Wahle et al.
Advances in inference methods have enabled language models to improve their predictions without additional training. These methods often prioritize raw performance over cost-effective compute usage. However, computational efficiency is key for real-world applications with resource constraints. We provide a systematic analysis of the inference scaling strategies self-consistency, self-refinement, multi-agent debate, and mixture-of-agents, to study their computational performance tradeoffs. We evaluate methods on two reasoning benchmarks (MMLU-Pro, BBH) and include extensive parameter configurations (e.g., scaling the number of parallel predictions, agents, and debate rounds) across different model sizes. Across 34 configurations and over 100 evaluations, we compute the Pareto-optimal front to select methods that achieve the best accuracy with the lowest computational budget. Notably, inference scaling improves accuracy by up to +7.1% points over chain-of-thought at the highest evaluated budgets (20x the CoT compute budget) on MMLU-Pro. With an equal computing budget, debate and mixture-of-agents outperform self-consistency by 1.3% and 2.7% points, respectively. While self-consistency saturates earlier, multi-agent gains persist, particularly on more complicated tasks. We identify a simple multi-agent design guideline: mixture-of-agents is most efficient when the number of parallel generations exceeds the number of sequential aggregations.