FusioN: Generative Synthesis from N Candidates

• FusioN is a generation-aggregation method that synthesizes a new answer from multiple LLM outputs, leveraging complementary strengths.
• It employs a training-free, judge-based two-stage process that first compares candidate quality and then fuses the best content fragments.
• Empirical results show FusioN outperforms Best-of-N in multilingual test settings and synthetic data generation, enhancing overall LLM response quality.

Searching arXiv for papers on "Fusion-of-N" / "FusioN". Fusion-of-$N$ (FusioN) is a generation-aggregation method for LLMs in which a set of $N$ candidate outputs is not reduced by selection to a single pre-existing winner, but instead provided to a generative judge that synthesizes a new final output from the pool. In the formulation introduced in “Making, not Taking, the Best of N” (Khairi et al., 1 Oct 2025), FusioN is positioned as an alternative to Best-of-$N$ (BoN): rather than treating candidate generations as mutually exclusive competitors scored by a selector, it treats them as sources of complementary evidence whose informative parts may be recombined into a superior response. The method is presented as training-free, judge-based, multilingual, and applicable both to test-time scaling and to synthetic data generation for downstream supervised fine-tuning (Khairi et al., 1 Oct 2025).

1. Definition and conceptual framing

FusioN denotes the mapping from an input prompt $x$ and a candidate pool $Y$ to a synthesized answer $y^\star$, written in the paper as

$y^\star = F(x, Y), \quad y^\star \notin Y.$

This distinguishes it from BoN, which is described as

$y^* = \argmax_{y \in Y} S(y, x).$

In BoN, aggregation is scalar selection: each candidate is independently scored and the highest-scoring sample is returned. In FusioN, aggregation is generative synthesis: the system may combine fragments, phrases, and ideas from several candidates into a new answer (Khairi et al., 1 Oct 2025).

The paper’s central motivation is that BoN is “inherently zero-sum,” because it discards all but one sample, whereas candidate pools often contain distinct partial strengths. It therefore argues that quality is often “polylithic,” meaning that different candidates may be locally strong in different respects and can be combined into a better whole (Khairi et al., 1 Oct 2025). This suggests a shift in inference-time reasoning about sample pools: not merely ranking alternatives, but performing structured consolidation across them.

A common misconception is that FusioN is simply BoN with a more sophisticated judge. The paper does not describe it that way. The distinguishing feature is not a better scalar evaluator, but a change in the aggregation primitive itself—from winner-takes-all selection to collaborative refinement (Khairi et al., 1 Oct 2025).

2. Methodological structure

The method consists of three core elements: candidate generation, judge-mediated comparison, and final synthesis. For a prompt $x$, multiple outputs are sampled from one or more models to form the pool $Y$. A strong instruction-following LLM then acts as the “fusor,” receiving the prompt and the full pool, and producing a fused answer (Khairi et al., 1 Oct 2025).

The fusor is not specially trained. The paper emphasizes that “no special training is needed”: the fusor is a capable instruction-following model used with a carefully designed prompt (Khairi et al., 1 Oct 2025). The prompt is explicitly two-stage. First, it instructs the model to compare the candidate generations with respect to content, language quality, and responsibility. Second, it instructs the model to produce a final answer that fuses the strengths of the candidates while discarding unsafe or weak content (Khairi et al., 1 Oct 2025).

The prescribed output format is also structured. The fusor prompt requests:

• Comparison: ...
• Answer: [[ final fused generation ]]

By contrast, when the same class of model is used as a BoN judge, it is prompted to emit a score from 1 to 5 in the format:

• Analysis: ...
• Answer: [[ SCORE ]]

This contrast is methodologically important. FusioN and BoN may use the same underlying model family as a judge, but one uses it as a generative synthesizer and the other as a scalar scorer (Khairi et al., 1 Oct 2025).

The paper further notes that the fused output may exhibit several behaviors: it may copy a single generation if one candidate is best overall, stitch together spans from multiple candidates, add “glue” or light rephrasing, and discard poor segments (Khairi et al., 1 Oct 2025). It also reports that, in practice, most of the fused answer comes directly from teacher outputs, with only a small amount of unmatched glue text (Khairi et al., 1 Oct 2025). This suggests that the method often acts less as free-form rewriting than as controlled recomposition.

3. Experimental settings

The paper studies FusioN in two distinct regimes: test-time scaling and synthetic data generation (Khairi et al., 1 Oct 2025). These correspond to two different uses of aggregation.

In test-time scaling, the objective is to improve the final answer returned at inference time. The main models are Aya Expanse 8B and Command A 111B, with temperature $N$0 and $N$1 samples in the main experiments. Command A is used as the fusor in the main setting, and ablations also use Gemma-family models and reward-model-based scorers (Khairi et al., 1 Oct 2025). Evaluation includes mArenaHard v2 / Arena, consisting of 498 translated challenging prompts from ArenaHard v2.0 across 11 languages, with pairwise quality judged by GPT-4o and main comparisons against Gemini2.5-Pro (Khairi et al., 1 Oct 2025).

In synthetic data generation, the candidate pool is used to create supervision targets for student fine-tuning rather than direct final answers. The teacher set comprises Gemma3-27B-It, Kimi-K2-Instruct, Qwen3-235B, DeepSeek-V3, and Command A. For each prompt, these teachers produce low-temperature outputs with $N$2, after which either BoN selects one output for SFT or FusioN synthesizes one output for SFT (Khairi et al., 1 Oct 2025). The student models are a 111B instruction-tuned LLM in the main setting and a 7B base LLM in ablations, with no test-time scaling applied after fine-tuning (Khairi et al., 1 Oct 2025).

The multilingual and task breadth are explicit. The main setup spans 11 languages—English, German, French, Spanish, Russian, Japanese, Chinese, Arabic, Korean, Portuguese, and Italian—and three task families: open-ended generation / Arena-style chat, machine translation, and reasoning, including GeoFactX for factual reasoning and MGSM / s1k-X for math reasoning (Khairi et al., 1 Oct 2025).

4. Empirical performance

The paper reports that FusioN “consistently outperforms BoN” across its benchmark suite (Khairi et al., 1 Oct 2025). In test-time scaling, for Aya Expanse 8B, gains on Arena reach up to +10.8% in French. For Command A, FusioN beats BoN in 9 out of 11 languages (Khairi et al., 1 Oct 2025). The paper also states that in some languages FusioN raises Command A above Gemini2.5-Pro, and that on translation it can outperform even an “oracle” selection in some cases, indicating that synthesis can exceed the best single candidate by the task metric (Khairi et al., 1 Oct 2025).

On translation specifically, the reported gain over BoN reaches up to +11.4 XCometXL in Korean, and FusioN is said to beat the oracle in German, Russian, and Chinese (Khairi et al., 1 Oct 2025). These results are central to the paper’s claim that synthesis is not bounded by the best member of the pool in the way BoN is.

In synthetic data generation, fine-tuning on FusioN-produced targets generally yields stronger students than fine-tuning on BoN-produced targets. For the 111B student, the paper reports an average Arena win-rate improvement of +2.5%, an average WMT XCometXL improvement of +0.8, a GeoFactX answer correctness improvement of +1.8%, and a reasoning quality improvement of +1.1% (Khairi et al., 1 Oct 2025). It also states that on GeoFactX FusioN outperforms BoN in 4/5 languages and is especially strong in lower-resource languages such as Swahili and Thai (Khairi et al., 1 Oct 2025).

The main caveat is mathematical reasoning. On MGSM, “BoN can be slightly better,” and the paper suggests that math may be a more specialized domain where classic selection with a good verifier remains difficult to surpass (Khairi et al., 1 Oct 2025). The 7B student ablation introduces a second limitation: FusioN still improves WMT, but BoN is better on Arena and sometimes on reasoning, which the paper interprets as evidence that smaller models may require more tuning for synthetic-data gains to materialize (Khairi et al., 1 Oct 2025).

5. Mechanistic interpretation and analysis

The paper attributes FusioN’s performance to several properties. First, it “uses more of the sample pool,” extracting useful segments from multiple candidates rather than discarding all but one (Khairi et al., 1 Oct 2025). Second, it is described as more sample-efficient: with $N$3, FusioN can already outperform BoN that requires more samples to match it (Khairi et al., 1 Oct 2025). Third, it is robust to weaker teacher pools, though it benefits from diversity and degrades when the pool collapses to a single teacher (Khairi et al., 1 Oct 2025).

A notable claim is that FusioN is “not ceilinged by the fusor’s own performance.” The paper cites GeoFactX as an example in which fused outputs outperform the fusor model itself on answer correctness (Khairi et al., 1 Oct 2025). This is important because a superficial interpretation might assume that the judge merely re-expresses its own latent competence. The reported result suggests instead that the fusor can exploit information distributed across the pool that it would not necessarily generate in a single direct completion.

The paper also includes a contribution analysis based on string matching. The procedure is: find matching blocks between fused output and each teacher output, attribute each character to the teacher with the longest match, and mark unmatched spans as glue or reformulation (Khairi et al., 1 Oct 2025). The reported findings are that a large fraction of FusioN output is copied or adapted from teacher outputs, only a small portion is unmatched glue, the fusor prefers stronger teachers but can still use weaker ones, there is some position bias in favor of earlier samples, and there is “no strong self-bias” when the fusor’s own generation appears in the pool (Khairi et al., 1 Oct 2025).

These observations support a view of FusioN as a structured recombination operator rather than an unconstrained paraphraser. A plausible implication is that its success depends not only on judge quality, but also on the availability of complementary local optima across samples.

6. Scope, limitations, and relation to adjacent notions

The paper identifies the settings in which FusioN is especially strong: diverse candidate pools, sufficiently large fusors, open-ended or translation-like tasks, and situations in which candidates exhibit complementary partial strengths (Khairi et al., 1 Oct 2025). It also identifies failure modes or weaker regimes: tightly constrained domains where verifier-like selection is already strong, especially math; small fusors; homogeneous sample pools; and very small student models under limited fine-tuning budgets (Khairi et al., 1 Oct 2025).

This constrains how the method should be interpreted. FusioN is not presented as a universal replacement for BoN under all task structures. Rather, the paper argues that selection alone leaves quality “on the table” when useful diversity is present (Khairi et al., 1 Oct 2025). This suggests that BoN and FusioN occupy different operating regimes: one is naturally aligned with tasks dominated by global answer correctness under reliable verification, while the other is naturally aligned with tasks in which answer quality decomposes across dimensions or spans.

The term “Fusion-of-$N$4” also appears in unrelated technical literatures, but those uses are conceptually distinct. In multimodal learning, “SFusion” denotes a self-attention-based $N$5-to-one multimodal fusion block for variable-modality inputs (Liu et al., 2022). In mathematical physics, “fusion” denotes algebraic gluing or composition operations, such as the fusion of decoupled 6D SCFTs by gauging a common flavor symmetry and adding a tensor multiplet (Heckman et al., 2018). In quantum computing, “fusion-based quantum computation” refers to architectures built from entangling measurements called fusions on small resource states (Bartolucci et al., 2021). These usages share the broad idea of combining multiple objects into one structured composite, but they are not the LLM generation method introduced in (Khairi et al., 1 Oct 2025).

Within LLM inference, the distinctive content of FusioN is therefore narrow and specific: a general-LLM-judge synthesis framework that replaces sample selection by answer construction (Khairi et al., 1 Oct 2025).

7. Significance

The significance claimed for FusioN is both empirical and conceptual. Empirically, the paper reports broad gains over BoN across multilingual test-time scaling and synthetic-data generation, with especially strong results in open-ended generation and translation (Khairi et al., 1 Oct 2025). Conceptually, it argues for a different view of candidate generations: not as mutually exclusive alternatives to be ranked, but as collaborators whose strengths can be composed (Khairi et al., 1 Oct 2025).

The paper’s closing formulation is that evaluation and utilization of LLM generations should shift “from a monolithic measure of quality, to embracing their polylithic nature” (Khairi et al., 1 Oct 2025). This suggests a broader methodological reorientation in test-time scaling. If accepted, the relevant design question is no longer only how to score samples more accurately, but how to expose and compose their latent complementarities.

In that sense, FusioN is best understood not as a minor variant of BoN, but as a change in the computational role assigned to extra samples. Under BoN, additional samples increase the chance that one of them is already good. Under FusioN, additional samples also enlarge the space of recombinable evidence from which a judge can construct a stronger response (Khairi et al., 1 Oct 2025).