Authors: Florian Valentin Wunderlich, Lars Benedikt Kaesberg, Jan Philip Wahle, Terry Ruas, Bela Gipp
Organizations: University of Göttingen, Germany
Abstract
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.
Mixture-of-Agents (MoA) architectures improve inference-time scaling by organizing multiple LLM agents into layered reasoning pipelines. However, existing MoA variants fail to sustain gains as depth increases, exhibiting degradation, early plateauing, or saturation. We propose ReM-MoA, a memory-augmented MoA framework that sustains scaling through two mechanisms: (1) a Ranked Reasoning Memory that persistently stores and ranks reasoning traces from all layers using a comparative Reviewer Agent, and (2) a Curated Diversified Memory Routing scheme that exposes different agents to distinct combinations of successful and failed traces, preserving exploration diversity while propagating high-quality reasoning. We further introduce an optional multi-domain Reviewer distillation pipeline that improves ranking quality through frontier-model supervision. Across five reasoning benchmarks spanning math, formal logic, code, knowledge, and commonsense, ReM-MoA consistently outperforms prior MoA variants across both depth and width scaling, and its advantage widens with depth, establishing structured cross-layer reasoning memory as a key missing mechanism for scalable multi-agent inference.
Test-time scaling has become an effective paradigm for improving the reasoning ability of large language models by allocating additional computation during inference. Recent structured approaches have further advanced this paradigm by organizing inference across multiple trajectories, refinement rounds, and verification-based feedback. However, existing structured test-time scaling methods either weakly coordinate parallel reasoning trajectories or rely on noisy historical information without explicitly deciding what should be retained and reused, limiting their ability to balance exploration and exploitation. In this work, we propose TMAS, a framework for scaling test-time compute via multi-agent synergy. TMAS organizes inference as a collaborative process among specialized agents, enabling structured information flow across agents, trajectories, and refinement iterations. To support effective cross-trajectory collaboration, TMAS introduces hierarchical memories: the experience bank reuses low-level reliable intermediate conclusions and local feedback, while the guideline bank records previously explored high-level strategies to steer subsequent rollouts away from redundant reasoning patterns. Furthermore, we design a hybrid reward reinforcement learning scheme tailored to TMAS, which jointly preserves basic reasoning capability, enhances experience utilization, and encourages exploration beyond previously attempted solution strategies. Extensive experiments on challenging reasoning benchmarks show that TMAS achieves stronger iterative scaling than existing test-time scaling baselines, with hybrid reward training further improving scaling effectiveness and stability across iterations. Code and data are available at https://github.com/IQuestLab/tmas.
Self-consistency (SC) is a widely used test-time inference technique for improving performance in chain-of-thought reasoning. It consists of generating multiple responses, or ``samples", from a large language model (LLM) and selecting the most frequent answer. This procedure can naturally be viewed as a majority vote or empirical mode estimation. Despite its effectiveness, self-consistency is prohibitively expensive at scale when naively applied to datasets, and it lacks a unified theoretical understanding of sample efficiency and scaling behavior. In this paper, we provide the first comprehensive analysis of SC's scaling behavior and its variants, drawing on mode estimation and voting theory. We derive and empirically validate power law scaling for self-consistency across datasets, and analyze the sample efficiency for fixed-allocation and dynamic-allocation sampling schemes. From these insights, we introduce Blend-ASC, a novel variant of self-consistency that dynamically allocates samples to questions during inference, achieving state-of-the-art sample efficiency. Our approach uses 4.8 times fewer samples than vanilla SC on average, outperforming both fixed- and dynamic-allocation SC baselines, thereby demonstrating the superiority of our approach in terms of efficiency. In contrast to existing variants, we note that Blend-ASC is hyperparameter-free, supports batching, and can fit any budget of samples, ensuring it can be easily applied to any self-consistency application.