Multiverse: Your Language Models Secretly Decide How to Parallelize and Merge Generation
Authors: Xinyu Yang
Yuwei An
Hongyi Liu
Tianqi Chen
Beidi Chen
Venue: NeurIPS 2025 spotlight ()
Keywords: Generative Modeling; Model Architecture; Parallel Generation; LLM Reasoning
Primary area: deep_learning

Abstract: Autoregressive Large Language Models (AR-LLMs) frequently exhibit implicit parallelism in sequential generation. Inspired by this, we introduce Multiverse, a new generative model enabling natively parallel generation. Multiverse internalizes a MapReduce paradigm, generating automatically through three stages: (i) a Map stage for adaptive task decomposition, (ii) a Process stage for parallel subtask execution, and (iii) a Reduce stage for lossless result synthesis. Next, we build a real-world Multiverse reasoning model with co-design of data, algorithm, and system, enabling rapid and seamless transfer from frontier AR-LLMs. For data creation, we develop Multiverse Curator, an automated LLM-assisted pipeline that transforms sequential reasoning chains into structured training data, avoiding costly human annotations. Algorithmically, we design Multiverse Attention to separate parallel reasoning steps while keeping compatibility with causal attention for efficient training. Systematically, we implement Multiverse Engine to support parallel inference. It features a dedicated interpreter that dynamically switches between sequential and parallel generation, triggered directly by the model. After a 3-hour fine-tuning with 1K examples, our Multiverse-32B stands as the only open-sourced non-AR model achieving performance on par with leading AR-LLMs of the same scale, evidenced by AIME24 & 25 scores of 54% and 46%, respectively. Moreover, our budget control experiments show that Multiverse-32B exhibits superior scaling, outperforming AR-LLMs by 1.87% on average using the same context length. Such scaling further leads to practical efficiency gain, achieving up to 2x speedup across varying batch sizes. We have open-sourced the entire Multiverse ecosystem, including data, model weights, serving system, supporting tools, as well as data curation prompts and detailed training and evaluation recipes.

Multiverse: Your Language Models Secretly Decide How to Parallelize and Merge Generation
Xinyu Yang", Yuwei Antt, Hongyi Liui, Tianqi Chenti, Beidi Chen"
CCUU !Nvidia
xinyuya2, yuwela, hongyil2, tqchen, beidic@andrew cmu.edu
https://aatiivereefM.iihhh
Abstract
Autoregressive Large Language Models (AR-LLMS) frequently exhibit implicit parallelism in sequential generation. Inspired by this, we introduce Multiverse, a new generative model enabling natively parallel generation. Multiverse internalizes a MapReduce paradigm, generating automatically through three stages: (i) Map stage for adaptive task decomposition, (ii) Process stage for parallel subtask execution, and (iii) a Reduce stage for lossless result synthesis. Next, we build a real-world Multiverse reasoning model with co-design of data, algorithm, and system, enabling rapid and seamless transfer from frontier AR-LLMMs For data creation, we develop Multiverse Curator, an automated L-MM-assisted pipeline that transforms sequential reasoning chains into structured training data, avoiding costly human annotations. Algorithmically, we design Multiverse Attention separate parallel reasoning steps while keeping compatibility with causal attention for efficient training. Systematically, we implement Multiverse Engine to support parallel inference. features a dedicated interpreter that dynamically switches between sequential and parallel generation. triggered directly by the model. After 3-hour fine-tuning with IK examples, our Multiverse-33 stands as the only open- sourced non-AR model achieving performance par with leading AR-L.MMs of the same scale, evidenced by AIME24 25 scores of 54% and 46%, respectively. Moreover, our budget control experiments show that Multiverse-32B exhibits superior scaling, outperforming AR-LLMS by 1.87% % on average using the same context length. Such scaling further leads to practical efficiency gain, achieving up to 2x speedup across varying batch sizes. We have open-sourced the entire Multiverse ecosystem, including data, model weights, serving system, supporting tools, as well as data curation prompts and detailed training and evaluation recipes.
Introduction
"In an infinite multiverse, everything that can happen does somewhere"
Test-time scaling has advanced Large Language Models (LLMs) by increasing the generation length [20, 16] and depth [12]. closely reflecting human cognition. However, empowered by modern hardware like GPUs, ideal LLMs can surpass humans by scaling third dimension: width, which al- lows parallel task-solving. Realizing this potential requires L.I.S to "smartly" parallelize and merge their generation, following the classic MapReduce paradigm [8]: splitting into subtasks, processing them independently in parallel, and merging their results. Such philosophy has long history in computer science [26, 1] while driving fundamental progress in other fields including manufactur- ing [19], agriculture [28], and finance [7]. This shift from sequential to parallel task-solving unlocks economies of scale: reducing the time per unit and keeping near-constant overall latency as task complexity grows, thereby offering a promising path towards artificial superintelligence (ASI).
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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Autoregressive Model
Diffusion Model
Multiverse Model
Analysis
Aha!
[Mask] [Mask] [Mask] [Mask]
Analysis: prove equation
Split
Sublask
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[Mask]]
Sublask simplify LHS
Subtask 2:
simplify RHS
Wait, wait.
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Analysis Subtask 1 1... Wait, wait.
Conclusion: LHS RHS
Sequential blocks
Parallel blocks
Map phase: adaptive task split
Reduce phase: lossless result merge
Figure I: Model Overview. Autoregressive models are constrained to sequential generation, while diffusion models struggle with coherence in parallel generation. Our Multiverse is a new generative model natively built on the MapReduce paradigm, enabling adaptive and lossless parallel generation.
Despite this potential, current LLMs are limited by the inherently sequential nature of autoregressive (AR) generation. While non-AR architectures, such as diffusion models [37, 49] and consistency models [22], along with their hybrid semi-AR variants [2. 29]. natively enable parallel generation, they incur substantial computational waste. Their rigid, brute-force parallelism ignores logical dependencies, partly due lack of real-world training data to supervise when and how parallel generation should occur. Another stream of research [48, 6, 45, 32] leverages external tools to parallelize or merge tasks heuristically, leading to the loss of internal states, like the intermediate reasoning steps, during communication with external modules. Although our concurrent work [21, 36] allows internal communication, they introduce inconsistencies between training and inference, limiting their effectiveness to short sequences with shallow parallelism. These challenges raise question: How to design a modeling framework for LLMs that can (i) adaptively split and merge tasks, (ii) losslessly preserve internal states, and (ii) generally apply diverse parallelism pattern??
Due the dominance of AR-LLMs, we start to answer it by revealing numerous intrinsic parallelism in their sequential outputs. Specifically, we analyze the long Chain-of- ofoThhught (CoT) trajectories from the s-K1 dataset [27]. Among them, over 98% exhibit parallelizable branches, despite being trained only for sequential generation. These branches, as shown in Figure 2, fall into collective and selective ones that appear frequently within individual CoT trajectories, either consecutively or recursively, covering wide range of scenarios. However, our prompting and probing tests verify that AR-LLMS cannot actively enforce or discern such parallelism. These findings motivate the design of new modeling framework that can be bootstrapped directly from pre- traitrd AR- which further requires us to address three practical limitations: (i) Data: seal-world CoT trajectories lack explicit parallel structure. (ii) Algorithu:: Transformers with causal attention are limited sequential generation. (iii) System: Inference engines for AR-LLMS cannot support practical parallel generation.
To achieve these, we introduce Multiverse, generative modeling framework built on the MapReduce paradigm that dynamically adjusts its parallelism during generation. internalizes three-staee stage pipeline: a sequential Map stage performs adaptive task decomposition; a parallel Process stage allows independent subtask execution; and sequential Reduce stage ensures lossless result synthesis. Moreover, the pipeline can invoke itself recursively, enabling optimal time complexity with unlimited resources. We thcoretically prove this optimality on a synthetic NP-hard SAT problem, demonstrating that Multiverse is the only framework that achieves lincar-time solution. Based this, co-design our data, algorithm, and system, providing a general solution to building a real-world Multiverse model for complex reasoning tasks, offering smooth and rapid transition from pre-trained AR-LLMs.
Data Curation. In Section 5.1, we develop Multiverse Curator, an automated assisstdd pipeline that transforms sequential reasoning chains into parallel structures via five steps: (i) parsing the sequential chain into a summary tree; (ii) identifying parallelizable nodes within the summary tree: (iii) reformatting the summary into a parallel generation structure; (iv) refilling original reasoning steps into this structure; and (v) adding Map & Reduce stages while rewriting Process stage. Moreover, content and grammar checks are performed to flag low-quality data for regeneration, avoiding costly

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manual filtration and annotation. In practice, this process results in Multiverse-11, a dataset of 1,000 high-quality structured training samples for advancing LLM reasoning.
Algorithm Design. In Section 5.2, we design Multiverse Attention to enable parallel generation while maintaining training efficiency. This is achieved by modifying attention masks and position indices to strictly separate independent reasoning branches in attention calculation. Due to its which can be trained in parallel, similar causal attention. This design also excels in data efficiency: since these changes are minor, pre-trained AR models can be rapidly transferred from causal attention to Multiverse attention using only a few thousand examples.
System Implementation. In Section 5.3, we implement Multiverse Engine featuring a specialized interpreter to support MapReduce in execution. By interpreting control tags generated by the Multiverse model itself, our engine can dynamically switch between sequential and parallel generation with near-zero overhead, yielding a flexible workflow. This process includes two stages: (i) Sequential - Parallel: mapping subtasks to separate branches for parallel execution with prefix sharing, and (ii) Parallel + Sequential: reducing Key-Value (KV) states from all branches back into one sequence.
The integration of these modules enables highly efficient training and inference of Multiverse models. Specifically, we develop Multiverse-32B by supervised fine-tuning (SFT) Qwen-2.5-33B-Insttue with only 1K examples, which takes only 3 hours. Empirically, Multiverse-322 achieves significant performance improvement, outperforming the base model by 23.6%, with AIME24 and AIME25 scores of 53.8% and 45.8%, respectively. These results are comparable to AR-LLMs, confirming that Multiverse does not compromise model performance. Furthermore, Multiverse-321 exhibits more efficient test-time scaling, yielding an average improvement of 1.87% within fixed latency constraints. This efficiency stems from its parallel generation capabilities, leading to up to 2x wall-clock speedup per generated token while keeping effective scaling across variable batch sizes range from I to 128.
2 Related Work
Test-time Scaling, Prior work has shown that optimizing AR-LLMs to generate longer outputs im- proves their reasoning abilities. This is evident in frontier reasoning models built with reinforcement learning (RL) [31, 9, 30, 15, 42], and also validated through supervised fine-tuning (SFT) on smaller models with few distilled examples [27, 47]. However, this length scaling greatly increases latency due to the sequential nature of AR generation. Other methods like depth scaling [12, 49] suffer from the same issue, while width scaling [5, 32] requires external information split or merge generations.
Internal Parallel Generation. Recent work has increasingly explored other models to replace the commonly used AR models, thereby enabling parallel generation. Among them, discrete diffusion models [37, 38, 3, 23, 40], including masked and absorbed variants, are gaining growing attention. To narrow their gap with AR models, efforts have been made on methods like hybrid AR-diffusion generation [2, 10] and training/test-ting scaling [29, 49, 46]. However, [11] has theoretically shown that these approaches cannot reduce the number of sequential generating or sampling steps, as they brute-force parallelize token generation without adhering to inherent relations. Similarly, other work explores continuous diffusion models [4] and consistency models [22]. Among these spurceo non-AR models, a common issue is their current inability to scale to complex reasoning tasks, such as AIME [24]. While our concurrent work [21, 36] begins explore the use of customized attention masks for parallel generation, their design are not general or adaptive, limiting their effectiveness to shallow, non-nested parallelism. contrast, Multiverse offers more efficient and scalable approach to enable internal parallel generation, which is generally applicable to diverse parallelism patterns.
External Parallel Generation. In another line of research, several approaches leverage external tools or models to enable parallel generation [45, 32, 41, 5, 48]. However, these methods generally leverage heuristic rules and external tools to parallelize or merge their generation. For instance, Best-of-N [5] and self-consistency [41] use brute-force approach by parallelizing generation at the beginning of generation. Other methods like Monte Carlo tree search (MCTS) [48] and Tree of Thoughts (ToT) [45] offer more fine-gre tnn-grrined parallelism, yet they are still fundamentally guided by heuristics and depend on an external verifier. While recent work [32] enables more adaptive parallel generation, it suffers from significant information loss when parallelizing and merging its generation, as it requires inter-model communication when switching between sequential and parallel generation, during which short text summaries rather than complete KV states can be shared between models.
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3 Long CoT Generation: Sequential or Parallel in Logic?
In this section, we present several key observations of intrinsic parallelism within AR-LLMs. First, in Section 3.1, we examine the long CoT trajectories generated by such models, verifying the common existence of intrinsic parallelism. Subsequently, Section 3.2 details probing and prompting tests, showing that AR-LLMS are unable to explicitly enforce or discem this parallelism during generation.
3.1 LLMs can Implicitly Generate Parallclizable Branches.
We start by analyzing the long CoT trajectories of current AR- AR-LLMs using the s1K-1.1 dataset [27]. including Deepseek R1 [16] and Gemini 2.0 Flash Thinking [13], aiming answer the following question: Does the logic of sequentially generated text truly depend on content that precedes it?
Calculate GCD(96, 160)
Test from 1 to
Analysis the problem
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Path 2:
a=1
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The correct answer GCD(96, 160) 32.
Conclusion
Conclusion
(a). Path exploration and verification using two selective branches alone.
(b). Case study using collective
(c). Case study when exploring path within a recursive structure.
branches in a consecutive structure.
Parallelizable branches are either collective (with all branches contributing) or selective (with some branches contributing). They can exist alone or as a part in consecutive/nested structures.
Figure 2:
Table Parallelizable branches commonly exist in long CoT trajectories generated by AR-LLMs. Per- example existence ratio (R%) and frequency (F) of different types are measured in the format RJF.
Collective Branch
Selective Branch
Total
Case Study Subtask Execution
Other
Path Exploration
Other
Deepseck R1 Gemini 2.0 Flash
28.0 2.00
47.3
3.38
3.2 0.23
19.4
1.39
1.1 0.07 99.0 7.07
39.4 2.82
45.0
3.22
2.9
0.21
8.3
0.60
1.4 0.09 97.0
6.94
Surprisingly, we observe distinct cases, termed "parallelizable branches", where multiple generation steps can be executed concurrently, rather than strictly awaiting the completion of prior text generation. These cases highlight the inherent parallelism in AR-LLMs. Figure 2 exemplifies these branches, which are categorized as collective and selective, that can combined consecutively or recursively.
Collective Branches. This involves independent steps whose outputs are subsequently merged into the final result. Such scenarios often result from splitting complex task into subtasks that can be processed concurrently. Examples include studying different cases and analyzing individual events.
Selective Branches. This refers to cases where numerous paths are considered, but not all contribute to the final output. Examples include exploring diverse solutions or examining competing hypotheses.
Table further details the occurrence ratios and frequencies for different types in K-1.1, where over 98% of examples involve parallelizable branches. Among them, collective branches (e.g., case study and subtask execution) are dominant, accounting for 79%, with selective branches like path exploration comprising the other 19%. Moreover, these branches appear frequently, averaging 7 times per example, which are arranged into combinations of consecutive and recursive parallel structures.

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3.2
LLMs cannot Explicitly Structure Parallelizable Branches.
Next, we examine the behavior of AR-LLMs from both token and hidden spaces, revealing their current inability to explicitly generate or identify such parallelizable branches based on our structures.
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(a) Prompting Test: Comparing Explicit and Implicit Structure Counts. (b) Probing Test: Classifier Acc.
Figure 3: Our tests show AR-LLMs cannot explicitly enforce discern parallelizable branches.
Prompting Test. We first prompt Deepseek RI and Gemini 2.5 Pro using the same questions, with detailed description of parallel structures that includes both types and their combinations. As shown in Figure 3a, a significant 90% disparity emerges between explicit occurrence and implicit existence of these structures, highlighting that current LLMs are unable to perform explicit parallel generation.
Probing Test. Next, we delve deeper into the hidden space of AR-LLMs, conducting probing test to confirm whether they can discern intrinsic parallelism. Specifically, we label the tokens before each parallel block as positive examples and treat all other tokens as negative. Final-layer representations of these tokens extracted using PrepSeek-RI-Distil--Neee A two-layer MLP classifier is trained to predict whether a token initiates a parallel structure. However, the classifier's low test accuracy in Figure 3b suggests that AR-LLMs do not truly understand such parallelism but generate these structures unconsciously based on patterns from the pre-traie vre-training corpus.
& 70B [9] and QWQ-32B [34].
4 Designing Multiverse for Natively Parallel Generative Modeling.
With all findings in Section 3, we present Multiverse, a new generative modeling framework built on the MapReduce paradigm that explicitly decides how to parallelize and merge the generation process.
4.1 Preliminaries.
Language Modeling aims to learn the joint probability distribution over sequences of words or tokens. Given finite vocabulary V of tokens, and a sequence of L tokens denoted by x1: (x ,"...,,,,") r²), a language model estimates the joint probability P(=1,x² "",",,"... of the sequence.
Autoregressive Modeling involves representing a sequence from left to right, where the probability of each token H, is conditioned the joint probability of the entire sequence x IiLL is factorized as a product of conditional probabilities:
previously tokens the sequence (i.e., xI=t-1). Consequently,
1(x!*1(AAR P(x' x² ..... 2.....,
1ARR)
II 1=1
where AR denotes model parameters. AR models offer high accuracy but exhibit poor parallelism.
4.2 Multiverse Modeling.
Our modeling framework, Multiverse, advances beyond AR by eliminating redundant sequential dependencies between independent sequences, enabling adaptive and lossless parallel generative modeling. Therefore, our Multiverse must "smartly" decide when start and end parallel generation. To realize this, we adopt MapReduce structure internalizing three stages, illustrated in Figure 4.
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Figure 4: Multiverse enables natively parallel generation by internalizing a MapReduce paradigm.
Map Stage. The pipeline begins by generating a task decomposition plan, denoted as x,, Each subtask in x, is then mapped an independent prefix sequence, modeled as ((x1,s|x.)) and P(x),x|x,).
Process Stage. Next, it performs parallel modeling for each branch independently, conditioned on its own prefix. This enables the concurrent generation of diverse branches, like: P(x1, 1:6 ee:.: X1,,)
and 6(x2,1:6/2,,5 X (()a,a)) Each branch should end a specific suffix (i.e, X1,e or X2,e) is generated.
Reduce Stage. After completing all branches, Multiverse shift back sequential generation that conditioned on all preceding tokens, which is modeled as [(x1.(3:1) ( [.) x2,[=,1:6,e]= x(1.3,)))
The integration of this three-stage pipeline enables Multiverse to: (i) adaptively decide when and how to parallelize generation during the Map stage; and (ii) retain informational completeness by ensuring every branch remains fully accessible throughout the Reduce stage and beyond. Notably, Multiverse naturally generalizes to both recursive and consecutive compositions of multiple MapReduce blocks.
4.3 Structured Generation Flow.
To enable automatic and interpretable control over the generation flow, Multiverse further employs structured set of specialized control tags that explicitly define each MapReduce block. These tags, such as <Parallel>, de- lineate the boundaries of such blocks and coordinate all three internal stages. An example is provided in Figure 5.
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Figure 5: MapReduce Structure.
5 Building a Real-world Multiverse Reasoning Model.
To deploy Multiverse in real-world scenarios, present a comprehensive suite consisting of Multi- verse Curator as the data generator, Multiverse Attention as the model architecture, and Multiverse Engine the serving system. This suite enables seamless and rapid transition from leading AR models to Multiverse models. In particular, we apply this suite in complex reasoning tasks, leading to Multiverse model that exhibits strong reasoning capabilities using remarkably low training cost.
5.1 Data Curation: Multiverse 1K.
To address the absence of MapReduce structures in existing sequential reasoning data, we introduce Multiverse-1KK While these long CoT trajactories often inherently contains such structures, explicitly generating them is difficult, as detailed in Section 3. Thus, we develop automated L.LMMassisted pipeline that transforms sequential reasoning chains into parallel MapReduce structures. This convert guided by five-stage prompting protocol powered by Gemini 2.5 Pro [14] shown in Figure 6a.

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Q: Given rational number, write it fraction in lowest terms and calculate the product of the resulting numerator and denominator b. For how many rational numbers between 0 and I will 20! = x b be the resulting product?
To compute the exponenis of primes in 201: For prime 2: 20/2)) 2014) (000) flocr(20/ 20/16) 10+5+2+1-18, prime 3)) 9loon(019)
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(a) Multiverse Curator automatically generated Multiverse- IK using an LLM-assisted data curation pipeline.
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Figure 6: Multiverse co-design data (Multiverse IK), algorithm (Multiverse Attention), and system (Multiverse Engine) to enable real-world reasoning capabilities through a rapid shift from AR-LLMs.
Generating a Summary Tree. First, we iteratively decompose and outline the original reasoning chain into two-level tree structure. In the first round, the entire reasoning chain is broken down into multiple steps. In the second round, each step examined by the LLM for further decomposition into substeps. Each resulting step or substep will be labeled and outlined with a concise description.
Identifying Parallel Groups. Second, instruct the LLM to analyze each reasoning step, identify- ing which steps or groups of steps can be executed in parallel without violating logical dependencies.
Reformating into Parallel Structures. Third, the summary tree is converted into parallel structure based on the previous analysis. To explicitly signal parallel execution, parallelizable steps or step groups are enclosed within the control tags <Parallell and </Parallel> forming parallel block.
Refilling Original Details. Fourth, we prompt the LLM to repopulate the detailed content for each step and substep. This is achieved by retrieving and copying the related original reasoning trajectories.
Adding MapReduce Structures. Finally, we further convert the parallel structures into MapReduce structures as defined in Section 4.3. For each parallel block, the LLM generates both the Map and Reduce stages by outlining the specific goals and results for each individual path. Moreover, all paths are rewritten to avoid words implying sequential relations (e.g., similarly) and to prevent including or referencing content from other paths, thereby ensuring each path's 's completeness and independence.
To further refine our data, two supplementary validation stages are incorporated. After the fourth stage, content check will filter out data if its edit distance ratio is above 0.2. Next, after the fifth
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stage, a grammar check will confirm strict adherence to our MapReduce structures. Data failing either case will be iteratively regenerated through our pipeline until both standards are met. The application of this automated pipeline to the s1K-1.1 dataset has yielded Multiverse IK, new dataset consisting of 1, 1,000 high-quality, structured reasoning trajectories across range of math and science problems.
5.2 Algorithm Design: Multiverse Attention.
Next, we introduce Multiverse Attention to replace the causal attention [39] in AR-LLMs. Causal attention computes the i-th token's output with query q. and keys kj, values vy from positions j S i:
Oij Softmax
((q P()) (Ry + P()) Ma))
(1)
0,
S
where My
is the causal mask, and P(t) is the embedding for the i-th position.
-00, otherwise
However, this formulation poses challenges for parallel generation, as the computation of later paths depend on both (i) the key-value (KV) pairs and (ii) the positional indices produced by earlier paths. To address this issue, we modify both the attention masks and position indices following APE [44], as illustrated in Figure 6b. In Multiverse Attention, each path within the same Process block starts from an identical position and executes independently without accessing others. During the Reduce stage, all paths converge to the same position, which is set to the maximum position reached by any path to ensure non-negative relative distances, while accommodating variable-length paths.
Moreover, its structural similarity to causal attention brings two key efficiency benefits: (i) Hardware Efficiency: it can preserve training parallelism by using customized attention kernel in FlexAtten- tion [43], and (ii) Data Efficiency: it can be rapidly adapted via post-training on a few samples.
5.3 System Implementation: Multiverse Engine.
To enable truly parallel generation in practical deployments, we introduce Multiverse Engine, an extension of existing inference engines designed for AR models. Specifically, we employ SGL.ng [50] due to its support for continuous batching and radix attention. These features allow dynamic batch scheduling and flexible KV-cache reuse, two scenarios frequently occur the Map and Reduce stages.
The Map stage is automatically triggered when a <Parallel> token is generated. Next, the scheduler counts the number of (Outline> encountered to decide the degree of parallelism until reaching </Goal>, Based on this count, the engine creates multiple paths executed in parallel as distinct samples within the same batch. Leveraging radix attention, these paths share the prefix KV cache from the current context. Each path is identified and initiated with "<Path> i" according to its order in the <0utlines list. After prefilling, all paths are added the decoding queue for parallel generation. When a path finishes, either by reaching </Path> or the maximum length, it enters "zombie" state that releases all resources and waits for the completion of other paths before continuing.
The Reduce stage begins once all processing paths have completed. In this stage, the engine merges the KV states from all paths along with the preceding context form a new sequence. Thanks the flexible memory layout of the radix cache, indices of KV cache can be seamlessly merged without any padding. thereby avoiding both physical data copying and subsequent redundant computation. The token <Conclusion>, prefixed by this combined KV cache, is then added to the prefilling queue. Once finished, the task is moved the decoding queue to resume generation along the new sequence.
6 Experiments
We evaluate the effectiveness and efficiency of Multiverse in real-world reasoning tasks. Specifically,
In Section 6.2, Mluttvveree32BB achieves substantial gains over the Qwen2.5 model by 23.6% after training on Multiverse- IK, and matches or exceeds the accuracies of AR-LLMs on reasoning tasks. Section 6.3, Multiverse- 32B scales better than AR-LLMs when using the same generation length.
6.1 Setup.
Training. We created Multiverse by performing SFT on the Bren2.5-32B-Innttuue model [33]. integrating our Multiverse Attention. The training data consisted of a combination of Multiverse 1K
8

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Table 2:
Performance comparison between Multiverse- and other 32B autoregressive LLMs. The
pass @ metric is reported using LightEval [17], while # parallel computes the ratio between the total number of generated tokens and the actual generation length, measuring the degree parallelism.
AIME24
AIME25
MATH500
MiPAA-Diaoon
Model / Metric
pass @1
parallel
pass @
# parallel
pass
parallel
pass @
# parallel
s1-32B
35.4
1.00
25.8
1.00
88.6
1.00
48.0
1.00
s1.1-32B
52.9
1.00
41.7
1.00
93.4
1.00
60.3
1.00
Qween2.5-32B-Imstrruct
15.8
1.00
10.4
1.00
80.4
1.00
47.0
1.00
Autoregreesive-32B
51.3
1.00
42.9
1.0
92.8
1.00
61.6
1.00
Multiverse-32B-zer
52.1
1.07
44.2
1.05
91.8
1.05
62.1
1.06
Multiverse-32B 52.9
1.24
44.2
1.18
92.4
1.15
61.7
1.17
prompted with "Think step by step and in parallel", and the original sequential data appended by "Think step by step", using mixture ratio increased from 0:1 (all original data) to 1:0 (all our data) across eight epochs. Our fine-tuning took hours on 8 NVIDIA B200 GPUs with PyTorch FSDP.
Following common practice in assessing reasoning models, measure Multiverse-321 on four tasks, including AIME24 [24], AIME25 [25]. MATH500 [18]. and GPQA Diamond [35]. LightEval [17] is employed the evaluation toolkit, powered by our SGLang [50]-based Multiverse Engine. We test our model under two prompting conditions: with and without the phrase "in parallel".
Evaluation.
Baselines. We compare our model with the Qwen2.5 model and an Autoregressive-322 trained using the same data, but without any control tags or the Map and Reduce stages. addition to pass@ 1, we report the degree of parallelism (# Parallel) as the ratio between generated token counts and lengths.
6.2 Real-world Reasoning Performance
In Table 2, we report the performance of Multiverse-32B complex reasoning tasks with 32K contexts, showing improvements of 36%, 32%, 12%, and 15% over the Swen2.5-33B-Instreee model across the respective benchmarks after fine-tuning. Notably, Multiverse-32 matches or even surpasses the performance of autoregressive models, as demonstrated by its comparison with Autoregressive-3251 For reference, also include the results of the s1.1-32B model trained on the sequential CoT data from which Multiverse- K derived. The comparable performance between these models confirms that data curation pipeline successfully preserves the original data quality.
We also evaluate Multiverse- 32B---Bo------- a variant prompted without the "think in parallel" instruction. While both versions exhibit similar performance, Multiverse-32B achieves greater parallelism. This parallelism, measured as the ratio of generated tokens to generation length, aligns with our training strategy, suggesting the potential for controllably switching between AR and Multiverse generation. Moreover, the reduced parallelism on AIME tasks indicates that the model exhibits less parallelism during longer generation, partly due to the scarcity of data exceeding 16K tokens in Multiverse- 1K.
6.3 Scaling Performance
To highlight the benefits of parallel generation, we conduct budget control experiments on GPQA- Diamond and MATH500 using the same context length (i.e., approximately equal generation time). We vary the context length from 1K to 4K tokens, during which accuracy increases sharply. As shown in Figure 7, while longer contexts improved performance for both models, Multiverse-328 generates more tokens within the same context length. This parallel scaling yielded performance gains 2.23% on the EPQA-Diamoon (with # parallel = 1.17) and 1.51% % on the MATH500 (with # parallel = 1.15).
7 Efficiency Analysis
Having demonstrated Multiverse-321 strong scalability and overall performance, we now further analyze the practical efficiency of Multiverse, showing the potential unlocked through parallel scaling.

---

35
Multiverse
Multivesse
30
Autoregressive
80
Autoneressive
Performance
Performance
70
45
60
40
50
35
30
1K
1.5K
2K
2,58
3K
3.5K
4K
4.5K
IK
1.5K
2K
25K
3K
Generation Length (Time)
Generation Length (Time)
(a) GPQA-Diamond
(b) Math500
Figure 7: Multiverse achieves better performance using a fixed context length, indicating the same generation time. Due parallel scaling, it generates more tokens within the same time. Here, report the actual generation length, as some examples terminate before reaching the maximum length.
First, we investigate the relationship between the degree of parallelism and latency token across various generation lengths (8K, 16K, and S2K), using a batch size one. The resulting data points, illustrated in Figure 8a, demonstrate that Multiverse enhances generation efficiency by increasing the degree of parallelism. Furthermore, we fit the sampled data points into three inverse curves, one for each. These curves highlight the potential of Multiverse further reduce latency by encouraging parallelism. Specifically, we identify three key regions based on the sample distribution, demarcated by red lines. The first, encompassing parallelism degrees from 1.0 to 1.3, represents the majority of data points and reflects real-world scenarios, yielding an average speedup of 18.5%. Furthermore, examples show that higher parallelization is achievable, offering acceleration up 2. x. The final region, characterized by extended lines, indicates the promising potential for further improvements.
Next, show the speedup achieved by Multiverse-32B with varying degrees of parallelism across different batch sizes, while keeping a fixed 4K output length. The results in Figure 8b indicate that inference remains memory- bound as the batch size increases from I to 128. Therefore, the speedup of Multiverse is influenced by the degree of parallelism in multiple scenarios, showcasing its scalability.
Lateney per taken (ms)
17.5
15.43% 0.60
15.43x
15.0
15.35% 2.14
samplal dhtt
Speedup
12.5
16K: sampled data
1.4
32X: samplea ibit
10.0
1.2
7.5
1.0
# Parallel
Logz(Batc Size
(a) Reduced Latency/Token with Increased Parallel
Stable Speedup Across Varying Batch Size
Figure 8: Multiverse can obtain scalable efficiency gain based on the degree of parallelism.
8 Conclusion
This work proposes Multiverse, natively parallel generative model based on a MapReduce paradigm that internalizes three stages: (i) a Map stage for adaptive task decomposition, (ii) a Process stage for parallel subtask exccution, and (iii) Reduce stage for lossless result synthesis. To build real-world Multiverse reasoning model, we co-design our data, algorithm, and system, enabling seamless and rapid transfer from AR-LLMs. After fine-tumi tinettuning on Multiverse- IK. our Multiverse-32BB achieves performance comparable to AR-LLMS on real-world reasoning tasks, while achieving better performance using the same context length due to parallel scaling. Additionally, such parallel generation also results in an up to 2 efficiency gain across varying batch sizes, based on the degrees of parallelism. We hope Multiverse can be considered a successor to Autoregression for generative modeling. For the Limitations and Broader Impacts, will discuss them in detail in our Appendix.
10

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14

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Acknowledgement
We thank Zhuoming Chen, Haizhong Zheng, Ranajoy Sadhukhan, Yang Zhou, Songlin Yang. Liliang Ren, Wentao Guo, Ruijie Zhu, Yu Zhang, and Yixin Dong for their constructive feedback on this work, along with the authors of sl [27]. SGLang [50], and LightEval [17] for their useful codebase. We are also grateful to BitDeer Al Research for providing GPU resources and Google for supplying API credits. This work was supported in part by a DGX B200 gift from NVIDIA, a Google Research Award, an Amazon Research Award, Intel, Li Auto, Moffett AI, and the CMU CyLab Seed Fund.
A Limitations
While Multiverse provides general framework for generative modeling, its application to diverse data and task types beyond LLM reasoning remains underexplored. Moreover, as Multiverse-32B was trained solely using Supervised Fine-Tuning (SFT), key direction in future research is to integrate Reinforcement Learning (RL) into training to explore and encourage more parallelism, which in turn would require more robust Multiverse engine.
B
Broader Impacts
Multiverse significantly boosts GPU utilization by enabling massive parallel generation. This modeling framework is particularly beneficial for small-batch and long-context inference scenarios, leading to substantial reductions in latency and corresponding energy consumption. Furthermore, Multiverse enables economies of scale for difficult but parallelizable tasks, decreasing the time per task unit while maintaining near-constant overall latency, even as task complexity increases. This remarkable scalability showcases its potential address extremely complex tasks in practice that were previously intractable, offering promising path towards artificial superintelligence (ASI).
C Prompt of Multiverse Curator
In this section, we release our complete five-stage prompting protocol to create Multiverse- 1K powered by the Gemini 2.5 Pro model. This protocol is engineered transform any sequential CoT data into Multiverse data.
This protocol starts with multi-round conversation with the LLM (Stages 1-3) to convert an original reasoning chain into a parallel-structured summary. Stage 4, both this summary and the original reasoning trajectory are fed to the LLM to repopulate each summarized step with its complete, original details. A content checker then immediately assesses these refilled steps. distance (e.g.. Levenshtein distance between the original trajectory (sors) and its rewritten version (Syen). ) denoted as d(s d(soris $yen)) )) is too high, that step is re- generatedd. To normalize this, a relative editor distance is calculated to decide if threshold is exceeded (set to 0.2 in practice):
editor
d( Soris 8gen)
Relative Editor Distance
max(Iength lengttt $gen))
Next, in Stage 5, we transform the output from Stage 4 into a MapReduce-struutune reasoning trajectory by inserting the Map and Reduce phases that are generated by Gemini 2.5 Pro. To ensure the structural validity of the data, we perform a grammar check using a customized XML interpreter, which filters out invalid entries and extracts the outermost MapReduce blocks in the remaining valid ones. Finally, each path rewritten separately to produce fully independent reasoning paths. The prompts used in the entire protocol are follows:
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STAGE 1: Generating Summary Tree
Main-Step Extraction
Analyze the given reasoning chain (for math or coding problem) and pull out every major step. Ignore substeps-only list the top-level insights or actions.
Oulput formal
[First major step]
S2: [Second major step]
S3: [Third major step]
[Description of step x]
Guidelines
Label each top-level step consecutively ('S1', '82', 'S3'....).
Please capture the entire thought process presented in the reasoning chain, and do not skip any step that includes but not is limited
1. Initial problem understanding and analysis
2. All exploration paths (both successful and unsuccessful)
Case studies, checks, or tests performed
4. Any "aha" correction (re-evaluation re-thinking) moments
5. The final reasoning that yields the solution
Keep each item concise yet descriptive.
Do not include any sub-numbering (no 'S2.1', etc.).
Explicitly split multiple cases or scenarios into different steps. Each case should allocated an independent step.
Substep Extraction
Given the output including all main step from a reasoning chain, break it down into all its internal substeps only if it can he meaningfully subdivided into smaller thought units.
Hulputffomat
S1: [Description of step 1]
$2: [Description of step 2]
$2.1 [Description of step 2.1]
$2.2 [Description of step 2.2]
$2. 10 [Description of step 10]
S3: [Description of step 3]
$4: [Description of step 4]
S10: [Description of step 10]
Guidelines
Use the same parent index ('x') as main step (e.g. breaking down 'S2', label 'S2.1' "2.2''.....
Capture entire thought process presented in reasoning chain, do not skip any substep that includes is not limited to:
Initial problem understanding and analysis
2. All exploration paths (both successful and unsuccessful)
3. Case studics, checks, or tests performed
4. Any "aha" or correction (re-evaluation re-thinking) moments
5. The final reasoning that yields solution
Do not introduce deeper nesting larger than 2 (e.g. 'S2.1.1' not allowed).
Explicitly split multiple cases scenarios into different substeps. Each case should be allocated an independent substep.
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continuous sequence of steps. Do STAGE Identifying Parallel Groups
Parallelizing Main Steps
Using only the main steps (S1, ...) you extracted in Stage 1, identify all steps or contiguous step groups that can be executed in parallel without violating logical dependencies, and rewrite the plan as structured parallel execution outline.
1. Identify Parallel Groups
Find sets adjacent main steps with no dependencies among them.
Label groups P1, .2.... and list their step ranges (e.g. [S1+S2, S3]. [S4]).
Rewrite a Purullel Execation Plan
Preserve each step's original wording as much as possible.
Output Format:
Parallel groups: [S1+S2, S3]
P2: [S4]
Parallel execution plan:
PI[parallel reason: ...]:
$1+S2: [text of S1 text of $2]
S3: [text of S3]
P2[parallel reason: .:.::
[text S4]
Guidelines
Coverage: Include every step exactly once, either alone inside parallel group.
Contiguous Blocks: Combine only adjacent steps into blocks; do not combine non-adjacent steps.
Striet Parallelism Only: Build dependency graph: draw edge from step A to B if B uses A's output. group P_i may include steps (or blocks) only if there edges between them. Treat conditional branches as independent tasks.
Contiguous Grouping Only: Each parallel group
parallelize non-adjacent steps.
Conciseness: Keep each bullet short and stick closely the original text.
Parallelizing Substeps
Using only the substeps (S2. 1, $2. ...) you extracted Stage 1, identify substeps or contiguous substep groups can be executed in parallel without violating logical dependencics, and rewrite the plan structured parallel execution outline.
1. Identify Parallel Groups
Find sets adjacent main steps with no dependencies among them.
Label groups P1, P2.... and list their step ranges (e.g. [S2. 1+S2.2, $2.3], [S3. 1]).
Rewrite into a Parallel Execution Plan
Preserve each step's original wording as much as possible.
Output Format:
Parallel groups:
[S2. 1+S2.2, $2.3]
P2: [S2.4] 4]
P2: [S3.1] 1]
Parallel execution plan:
P1[parallel reason: ...]:
S2. 1+$2.2: [text of $2. text of $2.2]
$2.3: [text of $2.3]
P2[parallel reason: ...]:
53.1: [text of $3. 1]
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Guidelines
Coverage: Include every substep exactly once, either alone or inside parallel group.
Contiguous Blocks: Combine only adjacent substeps into blocks; do not combine non-adjacent substeps.
Strict Parallelism Only: Build an explicit dependency graph in your analysis: draw an edge from substep substep B if B uses A's output insight. A group Pi may include steps (or contiguous blocks) only if there edges between any steps. In conditional logic, treat the if branch and branch as independent tasks and parallelize runtime.
even though their outputs cannot both occur
Contiguous Grouping Only: Each parallel group must cover a continuous sequence of stops or blocks. In other words, you may only parallelize adjacent substeps. The occurrence of substeps in parallel groups must follow their original order. For example, P1: [S2.2, S3. is not allowed. Keep each bullet short and stick closely to the original text.
Conciseness:
STAGE 3:
Reformating into Parallel Structures
Get Structured Summary
Please summarize the conversation above by extracting the reasoning steps and substeps in Stage as structure with explicit parallelism annotations following Stage
Output Format
01: [Brief summary of top-level step S1]
<parallel>(paralle, reason: ...]
01.1: [Summary of substep $1.1]
01.2: [Summary substep $1.2]
</parallel>
<parallel<[paralle) reason: ...]
[Brief description of top-level step S2]
<parallel>(paralle reason: ...J
02.1: [Sunmary of substep $2.1 + Summary of substep S2. 2]
02.2: [Summary of substep $2.
</parallel>
03: [Brief description of top-level step S3]
</parallel>
04: [Brief description of top-level step $4]
Guidelines
Max depth of nested <parallel> is 2. Do not nest <parallel> tags more deeply than two levels.
Max depth of nested numbering is 2. Only use Ox and Ox. do not introduce deeper numbering
like yx.y.z.
Sequential subpaths stay unexpanded. If node's children are purely sequential, list them normally without any <parallel> wrapper.
Tag parallel blocks. Wrap only genuinely parallelizahle sibling steps in
<parallel>... < block, and include parallcl-reason annotation.
Concise summaries. Each step and substep should be described briefly and clearly.
Avoid over-splittin, If most children sequential and only a pair can run in parallel, either leave the group un-split tag only the truly parallel pair.
Group parallelizable sets. You may combine several independent paths into one <parallel> block when they share no dependencies.
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STAGE 4:
Refilling Original Details
Refill the Full, Detailed Reasoning Trajectories into the Structured Summary
You will receive an outline that may be incomplete hut includes <parallel> tags indicating parallel structures, It contain summaries for several steps and substeps. You will also receive the corresponding original text, where sentences implicitly explicitly map to hierarchical prefixes (e.g., 01, 01 1, 02) in sequence. Your task process the original reasoning chain sequentially update the outline: replace existing summaries or insert new steps as needed, while preserving the original sparallel> tag structure.
Guidelines:
Initialize Structure Start with the structure provided by the input outline, including its text/summaries and all <parallel> tags in their original locations.
Read Sentences Sequentially: Process each sentence of the original text by one, in the exact order they appear.
Process Each Sentence:
1. Determine the hierarchical prefix associated with this sentence (e.g., 01, 01. 02).
2. Check if a step or substep with this prefix already exists the outline.
3. If exists: Replace its current summary with the full original sentence.
4. If it does not exist: Insert a new step/substep at the correct hicrarchical position (c.g., S1. under $1, S2 after S1), using the full original sentence as its content and matching the outline's indentation.
Keep every existing <parallel> and </parallel> tag exactly where it in the imput outline. Do not add, remove, relocate any tags.
Preserve <parallel> Tags:
Ensure Correct Output Formatting:
Maintain proper hierarchical indentation for all steps and substeps.
Each entry must on own line, beginning with its prefix (e.g.. 01: 01.1:) followed by the full original sentence.
Maintain Completeness: Verify that every sentence from original reasoning chain has been processed and appears in the updated outline. Do not omit or merge any sentences.
STAGE Adding MapReduce Structures Rewriting All Paths
Filling Detailed Goal and Conelusion Based on the New Reasoning Trajectory
Based on the generated reasoning chain, your task is to transform it according to the following rules:
Oulput Format
[Full reasoning copied from the reasoning chain for the first top-level path] [Full reasoning copied from the reasoning chain for the second top-level path]
Let's think in parallel. <Parallel>
<Goal>
Path: [brief, self-contained description of case A]
Path: [brief, self-contained description of case B]
</Goal>
<Path>
[Introductory reasoning for case A] Let's think in parallel.
<Parallel>
<Goal>
Path: [brief, self-contained description of case 1.
Path: [brief, self-contained description of case A.
</Goal>
<Path>
[Full detailed reasoning for case A. 1, rewritten clearly and independentlyl
</Path>
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<Path>
[Full detailed reasoning for case A.2, rewritten clearly and independentlyl
</Path>
<Conclusion>
[Your concise summary of outcomes from A. and A. 2]
</Conclusion>
</Parallel>
</Path>
<Path>
[Full detailed reasoning for case B, rewritten clearly and independently]
</Path>
<Conclusion>
[Your concise summary of outcomes from A and B]
</Conclusion>
</Parallel>
[Full detailed reasoning for any remaining paths]
Guidelines
Remove all numbering labels (e.g., 01, 02. 1) and eliminate any indentation.
For each <Parallel>. </Parallel> block:
Group every step, substep, and subsubstep belonging to the same parallel branch into a single <Path> </Path> section.
Discard the [parallel reason:
annotations.
Within each <Parallel> block:
Insert <Goal> before the first <Path>, listing each branch as Path:
Insert <Conclusion> after the last <Path>, summarizing each hranch's 's independently.
When multiple <Path> entries stem from the same original sentence or have interdapendencies:
Rewrite each path separately completely, ensuring no cross-references.
Provide enough context in each <Path> stands alone.
Fully encapsulate the logical reasoning for each path.
Avoid repetition: do not echo the brief descriptions from <Goal> inside the corresponding <Path>, and minimize redundant information across paths.
Rewriting Paths in the Structured Reasoning Trajectory
You given full structured reasoning trajectory inside <Parallel> block, consisting of: one <Goal> block with multiple <Outline> elements
multiple <Path> blocks
<Conclusion> block.
Some <Path> blocks may contain an entire nested <Parallel> structure (from <Paralle>> to </Parallel>). These nested blocks should be rewritten using the same rules recursively.
For <Goal>:
Rewrite each <0utline> into concise statement of what is being calculated or determined.
Remove any content describing how the problem is solved or intermediate reasoning steps.
For each <Path>:
Keep the original numbering prefix (c.g., 'I:', '2:").
Rewrite the content as a complete, fluent, and logically self-contained paragraph.
Do use transitional phrases like "First," "Then," "Next," "On other hand," etc.
If the <Path> contains five fewer sentences, rewrite them together single coherent paragraph, ensuring logical flow and fluency without using transitional phrases.
If the <Path> contains more than five sentences: Rewrite the first five sentences together single unit, forming fluent paragraph. For the remaining sentences, rewrite each one individually, based on its meaning, as clear and fluent standalone statements.
If the <Path> contains a nested <Parallel> block, apply all these rules recursively to the nested block.
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Each <Path> must make sense independently, even it contains nested reasoning chain.
For <Conclusion>:
Rewrite the conclusion the most concise and synthesized summary of the main outcomes from <Path> blocks.
You may combine or compare results from different paths, but keep it succinct and direct.
Nested <Parallel>:
A nested <Parallel> may appear only as a full block inside <Path>.
If <Path> contains nested <Parallel>... wtt.alle....//aaalllll.e... block, process that inner block exactly as you would the top-level one:
Rewrite the inner <Goal>, <Path>, and <Canclusion> elements accordingly.
Maintain the XML structure do not reindent or alter the tag hierarchy.
Output Format
<Parallel>
<Goal>
<Outline>
1: [concise description the goal of Path 1]
</Outline>
<Outline>
2: [concise description of the goal of Path 2]
</Outline>
</Goal>
<Path>
1: [self-contained paragraph for Path 1, rewritten sentence by sentence]
<Parallel>
<Goal>
<Outline>
1.1: [concise goal for Path 1.1]
</Outline>
<outline>
1.2: [concise goal for Path 1.2]
</Outline>
</Goal>
<Path>
1.1: Crewritten paragraph for Path 1.1]
</Path>
<Path>
1.2: [rewritten paragraph for Path 1.2]
</Path>
<Conclusion>
[sumnarized results from Paths 1.1 and 1.2]
</Conclusion>
</Parallel>
</Path>
<Path>
2: [self-contained paragraph for Path 2, rewritten sentence by sentence]
</Path>
<Conclusion>
[summary of outcomes from Path 1 and Path 2]
</Conclusion>
</Parallel>
Guidelines
You must preserve all XML tags exactly as they appear - do not remove, rename, or reorder tags.
Only modify the inner text of <Outline?, <Path>, and <Conclusion> blocks.
Wrap the final output a single Markdown code block using triple backticks.
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D Examples in Training Data and Model Generation
We present several examples from our Multiverse- IK dataset, along with the corresponding outputs generated by Multiverse-32B, which was trained on this dataset. Both typical collective and selective branches are included.
D.1 Training Examples from Multiverse-1K
Multiverse Data A: Collective Case
<Parallel>
<Goal>
<Outline>
1: Determine the sum of distances from P1 to Ps, Ps, and Pt.
</Outline>
<Outline>
2: Determine the sum of distances from Ps to Pı, Ps. and Pa.
</Outline>
<Qutline>
Determine the sum of distances from Ps Pt. P2. and
</Outline>
<Outline>
4: Determine the sum of distances from P4 to Pi, Ps, and P3.
</Outline>
</Goal>
<Path>
1: For point Pi 0), the distance to P2(10, 20) is
v(10 0)" + (20 v100 V500 22.36.
distance to P5 15) is
v (5 0)2 + (15 0)2 25 2 /250 15.81
The distance to Pa is
((12 - 0)2 +
v14+ 36 v180 13.42.
The sum is 22.36 15.81 + 13.42 51.59.
</Path>
<Path>
2: For point (2010,20) the distance to P)
V(10 0)3 (20 0)2 /500 22.36.
The distance to P3 15)
- 5)2 (20 15)² 225
v50 x0 7.07.
The distance to P6) is
v(10 - 12) + -20- (20- = 6680 ~ 26.08.
The sum is 22.36 + 7.07 26.08 z 55.51.
</Path> <Path>
For point P3 15), distance P)
(5-0)² + (15 0)2 2 15.81
The distance to Ps(10, 20) is
V(5 - 10)2 + (15 20) = ~50 7.07.
The distance to Pa(12, is
V 12) + (15 (-6))² V 49 441
490 ~ 22.14.
The sum is 15.81 + 7.07 + 22.14 z 45.02.
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</Path> <Path>
4: For point Pa the distance i)
- (112-0)2-(66-)) V 13.42.
The distance P2,10,
V 10)² (-6 20) /4+ 676
676
680 26.08.
The distance (5 15) is
V(2 5)2 + ( 15)
/
490 22.14.
The sum is 13.42 26.08 22.14 61.64.
</Path> <Conclusion>
The sums of distances from P2, Pa, Pa to the other three points are approximately 51.59, 55.51. 45.02, and 61.64, respectively.
</Conclusion>
</Parallel>
Multiverse Data B: Selective Case
<Parallel>
<Goal>
<Outline>
1: Determine if can constructed as a countable intersection of open dense sets using Baire Category
Theorem (BCT), leveraging the completeness of S?
</Outline>
<Outline>
Determine can constructed step-by-step step using lt's approximation property to ensure density and K avooiddncce for chords, while addressing potential difficulties.
</Outline>
</Goal>
<Path>
The sphere 5 complete metric space, suggesting the possibility constructing as a countable intersection of open dense sets; however, the specific method for such a construction is not immediately
clear.
</Path>
<Path>
2: A step-by-ster construction of could leverage the given condition to ensure density and that all chords avoid K; H must be dense in S², mcaning it has points in every open subset of S², and any two points in H must have their connecting chord disjoint from K. The family Ω allows approximation of any two points on 5 with chord y' from Ω. This implies is dense the space of all chords, closed nature
with the additional property that chords avoid within the unit ball is open, so a chord disjoint from K lies entirely within this open complement. Consequently, S2 comprises chords in the complement of K. The challenge is to construct dense set H such that all chords connecting points within H avoid K, given that for any X, Y S2, nearby points X', Y' exist whose chord Y' is in Q and thus avoids K. One approach might be to construct H as countable dense set where each pair's connecting chord belongs to Q. Achieving density alone is insufficient; all chords between any two points in H must be in Q. Directly constructing such an H presents significant difficulties. </Path>
means complement
<Conclusion>
The Baire Category Theorem approach for constructing H via intersections (Path 1) lacks a clear method. A step-by-step construction (Path 2) highlights the requirements of density and K K-avoidance for all chords within H. but faces challenges in maintaining the chord property universally during the construction process.
</Conclusion> </Parallel>
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D.2 Generated Examples from Multiverse-322
Multiverse Generation A: Collective Case
<Parallel>
<Goal>
<Outline>
1: Compute Case 1 count.
</Outline>
<Outline>
2: Compute Case 2 count.
</Outline>
</Goal>
<Path>
In Case the path pattern is H-V-H-V-H giving three horizontal two vertical segments. distribute 8 units into three positive horizontal segments:
8 -
7 =
21.
3 3-1
2
We distribute units into two positive vertical segments:
8
1 7.
2 2
=
Total for Case
21 x 7 147.
</Path> <Path>
In Case the pattern is V-II-V-IIV, giving three vertical and two horizontal segments. Distribute units into three positive vertical segments:
2
Distribute units into positive horizontal segments:
7.
Total for Case 2:
21 7 147.
</Path>
<Conclusion>
Case yields 147 paths: Case 2 yields 147 paths: overall 147 147 = 294. </Conclusion> </Parallel>
Multiverse Generation B: Selective Case
<Parallel>
<Goal>
<Outline>
Count horizontal vs. vertical segments.
</Outline>
<0utline>
2: List possible H/V pattern..
</Outline>
</Goal>
<Path>
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1: path from 0) (8, 8) uses exactly eight right moves (ft) and eight up moves (U). With five segments alternating direction, starting with forces the pattern
R
R,
giving three horizontal segments and two vertical segments. Conversely, starting with yields
U
R U R U,
for three vertical and two horizontal segments. In either case there are four direction changes (one at each segment boundary). and the segment counts differ one because there odd number of segments.
</Path>
<Path>
2: The total move count is 16 (&R + 8U). If H 3 and V 2, then the three horizontal segment lengths hi h2 + ha with each h; 1, which has
21
compositions. The two vertical segments + 8 with vj has
8 2
7
compositions, for 21 X 7 = 147 ways when starting horizontal. Similarly. if V = 3 and H 2, there are 21 ways split into three vertical segments and ways for two horizontal segments. again 147 ways. In total there 147 + 147 294 segment-length configurations consistent with five alternating segments summing to (8, 8).
</Path>
<Conclusion>
five-segment path must alternate directions, yielding either (H, (3, (2,3) segments. There are ways to allocate segment lengths each case, for 294 total valid patterns.
</Conclusion>
</Parallel>
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1. Claims
Question:
Do the main claims made in the abstract and introduction accurately reflect the
paper's contributions and scope?
Answer: [Yes]
Justification:
The abstract and introduction clearly state the contributions of this work.
Guidelines:
The answer NA means that the abstract and introduction do not include the claims made in the paper.
The abstract and/or introduction should clearly state the claims made, including the contributions made the paper and important assumptions and limitations. A No or NA answer to this question will not be perceived well by the reviewers.
The claims made should match theoretical and experimental results, and reflect how much the results can be expected to generalize to other settings.
It is fine to include aspirational goals as motivation as long as it is clear that these goals are not attained by the paper.
2. Limitations
Question: Does the paper discuss the limitations of the work performed by the authors?
Answer: [Yes]
Justification:
We will discuss the limitations of our work in Appendix.
Guidelines:
The answer NA means that the paper has limitation while the answer No means that the paper has limitations, but those are not discussed in the paper.
section The authors are encouraged to create separate "Limitations" section in their paper.
The paper should point out any strong assumptions and how robust the results are to violations of these assumptions (e.g.. independence assumptions, noiseless settings, model well-specification, asymptotic approximations only holding locally). The authors should reflect on how these assumptions might be violated in practice and what implications would be.
The authors should reflect the scope of the claims made, e.g., if the approach was only tested on a few datasets or with a few runs. In general, empirical results often depend on implicit assumptions, which should be articulated.
The authors should reflect on the factors that influence the performance of the approach. For example, facial recognition algorithm may perform poorly when image resolution low or images are taken in low lighting. Or speech-to-text system might not be used reliably to provide closed captions for online lectures because it fails to handle technical jargon.
The authors should discuss the computational efficiency of the proposed algorithms and how they scale with dataset size.
If applicable, the authors should discuss possible limitations of their approach to address problems of privacy and faimesss
While the authors might fear that complete honesty about limitations might be used by reviewers as grounds for rejection, worse outcome might be that reviewers discover limitations that aren't 't acknowledged in the paper. The authors should use their best judgment and recognize that individual actions in favor of transparency play an impor- tant role in developing norms that preserve the integrity of the community. Reviewers will be specifically instructed to not penalize honesty concerning limitations.
3. Theory assumptions and proofs
Question: For each theoretical result, does the paper provide the full set of assumptions and a complete (and correct) proof?
Answer:
[NA]
Justification:
The paper does not include theoretical results.
Guidelines:
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The answer NA means that the paper does not include theoretical results.
All the theorems, formulas, and proofs in the paper should be numbered and cross- referenced.
All assumptions should be clearly stated or referenced the statement of any theorems.
The proofs can either appear in the main paper or the supplemental material, but if they appear in the supplemental material, the authors are encouraged provide short proof sketch to provide intuition.
Inversely, any informal proof provided in the core of the paper should be complemented by formal proofs provided in appendix or supplemental material.
Theorems and Lemmas that the proof relies upon should properly referenced.
4. Experimental result reproducibility
Does the paper fully disclose all the information needed to reproduce the main ex- perimental results the paper to the extent that affects the main claims and/or conclusions of the paper (regardless of whether the code and data are provided not)?
Question:
Answer: [Yes]
Justification:
The paper has disclosed all the information in the method and experiment part.
Guidelines:
The answer NA means that the paper does not include experiments.
If the paper includes experiments, a No answer to this question will not be perceived well by the reviewers: Making the paper reproducible is important, regardless of whether the code and data are provided or not.
If the contribution is a dataset and/or model, the authors should describe the steps taken to make their results reproducible or verifiable.
Depending on the contribution, reproducibility can be accomplished in various ways. For example, if the contribution is a novel architecture, describing the architecture fully might suffice, or if the contribution is specific model and empirical evaluation, may be necessary to either make it possible for others to replicate the model with the same dataset, or provide access the model. In general. releasing code and data is often one good way to accomplish this, but reproducibility can also be provided via detailed instructions for how to replicate the results, access to a hosted model (e.g., in the case of large language model), releasing of a model checkpoint, or other means that are appropriate to the research performed.
While NeurIPS does not require releasing code, the conference does require all submis- sions to provide some reasonable avenue for reproducibility, which may depend on the nature of the contribution. For example
(a) the contribution is primarily a new algorithm, the paper should make it clear how reproduce that algorithm. (b) If the contribution is primarily
model architecture, the paper should describe the architecture clearly and fully.
(c) If the contribution is a new model (e.g., a large language model), then there should either be way to access this model for reproducing the results or way to reproduce the model (e.g., with an open-source dataset instructions for how to construct the dataset).
(d) We recognize that reproducibility may be tricky in some cases, in which case authors are welcome describe the particular way they provide for reproducibility, In the case of closed-source models, it may be that access to the model is limited in some way (e.g., to registered users), but it should be possible for other researchers to have some path to reproducing or verifying the results.
5. Open access to data and code
Question: Does the paper provide open access to the data and code, with sufficient instruc- tions to faithfully reproduce the main experimental results, as described in supplemental material?
Answer: [Yes]
Justification:
We provide the code and data required to reproduce our experimental results.
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Guidelines:
The answer NA means that paper does not include experiments requiring code.
Please the NeurlPS code and data submission guidelines (https://nips.co for more details.
public/guse Sublic/guides/Coeer https/oooeSummissoooooolll
While we encourage the release of code and data, we understand that this might not be possible, so "No" an acceptable answer. Papers cannot be rejected simply for not including code, unless this is central to the contribution (e.g., for new open-source benchmark).
The instructions should contain the exact command and environment needed to run to reproduce the results. See the NeurIPS code and data submission guidelines (ht tps: / //nips. cc/publcppcccccccccc cemublic/gute des/ /Csoeeeoemubiii wwwiiiissooooooooo for more details.
The authors should provide instructions data access and preparation, including how to access the raw data, preprocessed data, intermediate data, and generated data, etc.
The authors should provide scripts to reproduce all experimental results for the new proposed method and baselines. only subset of experiments are reproducible, they should state which ones are omitted from the script and why.
At submission time, preserve anonymity, the authors should release anonymized versions (if' applicable).
Providing as much information possible in supplemental material (appended to the paper) recommended, but including URLs to data and code permitted.
6. Experimental setting/details
Question: Does the paper specify all the training and test details (c.g., data splits, hyper- parameters, how they were chosen, type of optimizer, etc.) necessary to understand the results?
Answer: [Yes)
Justification: The paper provides enough training and test details to reproduce the experiment results.
Guidelines:
The answer NA means that the paper does include experiments.
The experimental setting should be presented the core the paper to a level detail that is necessary to appreciate the results and make sense of them.
The full details can be provided either with the code, appendix, as supplemental material.
7. Experiment statistical significance
Question: Does the paper report error bars suitably and correctly defined or other appropriate information about the statistical significance of the experiments?
Answer:
[Yes]
Justification:
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Reviews:
[{"review_id": "8PMeOc6lax", "reviewer": "Reviewer_eCfu", "summary": "This paper proposes Multiverse, a natively parallel generative model based on the MapReduce paradigm. Autoregressive large language models (AR-LLMs) are constrained by sequential generation, while non-AR models like diffusion models struggle with complex tasks. Multiverse features three stages: Map for adaptive task decomposition, Process for parallel subtask execution, and Reduce for lossless result merging.\n\nThe model co-designs data, algorithm, and system: Multiverse 1K dataset transforms sequential reasoning into parallel structures via an LLM-assisted pipeline; Multiverse Attention modifies attention masks for parallel generation; Multiverse Engine enables dynamic scheduling between sequential and parallel modes.", "questions": "In the experimental section, are there more settings provided, such as the code? Additionally, the scores on AIME seem too low. Is it difficult to interpret the effectiveness of the method?\nAt a parallelism ratio of 1.3, the model achieves an 18.5% average speedup. the results seems not strong enough.", "limitations": "The experiments is not strong enough, with less than 2 times speed up. and the baseline is also not strong,", "rating": 3, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 2, "originality": 3, "strengths_and_weaknesses": "Unlike text diffusion models that often rely on rigid parallelization, Multiverse empowers language models to autonomously decide parallel generation strategies, leveraging GPU acceleration through dynamic task decomposition. This self-adaptive parallelism not only optimizes computational efficiency but also preserves logical coherence in complex reasoning, marking a significant advancement in bridging sequential AR-LLMs with parallel hardware capabilities.", "was_revised": false, "final_justification": "", "rebuttal": "We would like to sincerely thank reviewer eCfu for the insightful and valuable comments! They are invaluable for further improving the quality of our paper. We will revise our manuscript in the next version to address all of your concerns. We hope that you might consider raising your score in light of these clarifications.\n\n---\n**Q1**: In the experimental section, are there more settings provided, such as the code?\n**A1**: Thank you for your suggestions. We first need to clarify that our experiments in the paper follow the setups outlined in the S1 paper, which cover both training and evaluation of math and scientific reasoning. This setup is standard and ensures coherence between our training and inference. To address your concern, we further conduct experiments on IFEval and LiveCodeBench as instruction-following and code benchmarks. As shown in Table R1, our method can perform on-par with autoregressive models on these benchmarks. However, they do not increase the performance over base model due to the inconsistency of training and test domains. \n\nTable R1: Experimental Results of various models on instruction-\n| Metric | Qwen2.5-32B-Instruct | s1.1-32B | Autoregressive-32B | Multiverse 32B |\n| :--- | :---: | :---: | :---: | :---: |\n| IFEval | 79.1 | 57.4 | 57.1 | 57.9 |\n| LiveCodeBench(v6) | 39.1 | 39.1 | 38.6 | 39.4 |\n\n---\n**Q2**: Aime score seems low. Is it difficult to interpret the effectiveness of the method?\n**A2**: We emphasize that this work focuses on developing novel model architectures for parallel generation instead of improving reasoning ability, with Multiverse being the only open-source non-autoregressive model to achieve an AIME score above 50—setting a new standard in this area. For a fair comparison with autoregressive models, we adopt the s1 experimental setting, training on the same corpus (with CoT rewriting), and demonstrate performance comparable to s1.1 while achieving significantly higher efficiency. Given that s1.1 was released only two months before our submission and is a strong reasoning model trained purely with supervised fine-tuning, we consider it a reasonable and fair baseline. Although larger datasets, model scales, or compute budgets could further enhance Multiverse, these resources exceed typical academic constraints and lie orthogonal to our architectural design. In this context, we believe that achieving an AIME score above 50 thus represents both a rigorous standard and clear differentiation of model quality.\n\n---\n**Q3**: At a parallelism ratio of 1.3, the speedup is 18.5% which seems not strong enough.\n**A3**: As discussed in lines 290-291, the 18.5% speedup is an average across data exhibiting parallelism from 1.0 to 1.3 instead of 1.3 only. Therefore, our speedup should have a strong correlation with the parallelism ratio, which can be further verified in our Figure 8(b)."}, {"review_id": "mr1llDtJFf", "reviewer": "Reviewer_RkKR", "summary": "This paper introduces Multiverse, a test-time scaling framework for LLM that enables parallel generation. Motivated by the observation that autoregressive models often generate reasoning trajectories with latent parallelizable branches, the authors propose a MapReduce framework that decomposes generation into three stages: Map, Process, and Reduce. The authors design three components: data curation, architecture design, and system implementation. Empirically. the authors demonstrate improvements on mathematical reasoning tasks.", "questions": "1. How important is each of the three components—data, Multiverse attention, scheduler? For example, would just fine-tuning Qwen2.5 on the structured outputs suffice?\n\n2. In Line 126, how does the prompting test work? Can the authors clarify this?\n\nIn general, I lean toward acceptance despite the mentioned weaknesses and questions.", "limitations": "Yes.", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 4, "strengths_and_weaknesses": "## Strengths\n1. The paper demonstrates the inherent parallelizable features of autoregressive generation. The proposed method is novel; the MapReduce framework is elegant and practically useful.\n2. The paper is well written with rich illustrations and clean empirical and structural analysis. \n\n\n## Weaknesses\n1. The empirical improvement of the proposed method appears limited (Table 2, Figure 7). Error bars are not provided, so it's unclear whether the gains are statistically significant or within expected variance.\n2. Ablations are missing: How important is each of the three components—data, Multiverse attention, scheduler? For example, would just fine-tuning Qwen2.5 on the structured outputs suffice?", "was_revised": true, "final_justification": "I appreciate the authors' effort in showing every detailed response. My concerns are largely addressed. Overall, it is a strong paper, and I maintain my recommendation of a clear accept.", "rebuttal": "Thank you for your suggestions. We have responded to your questions below and would appreciate it if you could let us know if our response addresses your concerns. We hope that you might consider raising your score in light of these clarifications.\n\n---\n**Q1**: The empirical improvement of the proposed method appears limited.\n\n**A1**: We appreciate your question and agree that the current empirical improvement is limited. This outcome is directly linked to the degree of parallelism in our training data, Multiverse-1K. Our statistics shows that Multiverse-1K has an average parallelism degree of 1.16 which matches the parallelism observed at inference. This design choice aligns with our core research objective: rather than artificially increasing parallelism, we focus on externalizing the implicit parallel generation capabilities in modern autoregressive LLMs. Therefore, the observed parallelism degree of 1.16 represents the natural baseline of parallel reasoning these models inherently possess, which our Multiverse seeks to make explicit and accessible.\n\n---\n**Q2**: Error bars are not provided thus it is unclear the gains are statistically significant.\n\n**A2**: Thank you for your suggestions. Here we provide our results with error bars for Tab 2, Figure 7 and Figure 8b.\n\nTable 1: Reasoning Performance\n| **Model / Metric** | **AIME24** pass@1 | **AIME24** #parallel | **AIME25** pass@1 | **AIME25** #parallel | **MATH500** pass@1 | **MATH500** #parallel | **GPQA-Diamond** pass@1 | **GPQA-Diamond** #parallel |\n| :--- | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: |\n| s1-32B | $35.4 \\pm 1.7$ | 1.00 | $25.8 \\pm 1.5$ | 1.00 | $88.6 \\pm 0.5$ | 1.00 | $48.0 \\pm 0.4$ | 1.00 |\n| s1.1-32B | $52.9 \\pm 1.7$ | 1.00 | $41.7 \\pm 1.7$ | 1.00 | $93.4 \\pm 0.4$ | 1.00 | $60.3 \\pm 0.6$ | 1.00 |\n| Qwen2.5-32B-Instruct | $15.8 \\pm 1.5$ | 1.00 | $10.4 \\pm 1.2$ | 1.00 | $80.4 \\pm 0.2$ | 1.00 | $47.0 \\pm 0.4$ | 1.00 |\n| Autoregressive-32B | $51.3 \\pm 1.9$ | 1.00 | $42.9 \\pm 1.6$ | 1.00 | $92.8 \\pm 0.4$ | 1.00 | $61.6 \\pm 0.7$ | 1.00 |\n| Multiverse-32B-zero | $52.1 \\pm 1.7$ | $1.07 \\pm 0.02$ | $44.2 \\pm 1.8$ | $1.05 \\pm 0.01$ | $91.8 \\pm 0.2$ | $1.05 \\pm 0.01$ | $62.1 \\pm 0.5$ | $1.06 \\pm 0.01$ |\n| Multiverse-32B | $52.9 \\pm 2.1$ | $1.24 \\pm 0.03$ | $44.2 \\pm 1.5$ | $1.18 \\pm 0.03$ | $92.4 \\pm 0.4$ | $1.15 \\pm 0.01$ | $61.7 \\pm 0.5$ | $1.17 \\pm 0.02$ |\n\nTable 2: GPQA-Diamond Performance with control budget\n| Model | 1k | 1.5k | 2k | 2.5k | 3k | 3.5k | 4k | 4.5k |\n| :--- | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: |\n| Multiverse | $32.8 \\pm 0.4$ | $35.9 \\pm 0.5$ | $40.9 \\pm 0.5$ | $45.5 \\pm 0.4$ | $48.5 \\pm 0.6$ | $50.5 \\pm 0.5$ |$52.0 \\pm 0.4$ | $53.6 \\pm 0.5$ |\n| Autoregressive | $29.3 \\pm 0.4$ | $33.84 \\pm 0.3$ | $37.88 \\pm 0.4$ | $41.27 \\pm 0.4$ | $45.96 \\pm 0.3$| $49.2 \\pm 0.6$ | $51.0 \\pm 0.6$ | $54.2 \\pm 0.7$ |\n\nTable 3: Math 500 Performance with control budget \n| Model | 1k | 1.5k | 2k | 2.5k | 3k | 3.5k | 4k |\n | :--- | :---: | :---: | :---: | :---: | :---: | :---: | :---: |\n | Multiverse | $37.0 \\pm 0.3$ | $54.4 \\pm 0.2$ | $63.6 \\pm 0.4$ | $70.5 \\pm 0.2$ | $76.5 \\pm 0.3$ | $81.8 \\pm 0.2$ | $85.1 \\pm 0.3$ |\n | Autoregressive | $35.2 \\pm 0.2$ | $52.8 \\pm 0.4 $ | $62.0 \\pm 0.3$ | $69.6 \\pm 0.4$ | $74.8 \\pm 0.4$ | $79.6 \\pm 0.3$ | $84.3 \\pm 0.4$ |\n\nTable 4: Full Speedup Results Across Varying Degrees of Parallelism and Batch Sizes\n| #Parallel | bsz=4 | bsz=8 | bsz=16 | bsz=32 | bsz=64 | bsz=128 |\n| :--- | :---: | :---: | :---: | :---: | :---: | :---: |\n| 1.1 | $1.07 \\pm 0.02$ | $1.13 \\pm 0.02$ | $1.06 \\pm 0.01$ | $1.07 \\pm 0.01$ | $1.08 \\pm 0.02$ | $1.15 \\pm 0.02$ |\n| 1.2 | $1.20 \\pm 0.02$ | $1.18 \\pm 0.02$ | $1.18 \\pm 0.01$ | $1.18 \\pm 0.02$ | $1.19 \\pm 0.04$ | $1.22 \\pm 0.02$ |\n| 1.3 | $1.31 \\pm 0.02$ | $1.25 \\pm 0.03$ | $1.32 \\pm 0.02$ | $1.31 \\pm 0.01$ | $1.31 \\pm 0.02$ | $1.35 \\pm 0.02$ |\n| 1.5 | $1.47 \\pm 0.03$ | $1.46 \\pm 0.02$ | $1.54 \\pm 0.02$ | $1.51 \\pm 0.02$ | $1.50 \\pm 0.01$ | $1.55 \\pm 0.03$ |\n\n---\n**Q3**: Ablation study is missing. How important is each of the three components?\n\n**A3**: In our multiverse framework, the three core components—Data, Algorithm, and Engine—are intricately combined. A critical issue arises when fine-tuning the model directly on structured outputs: this process creates a mismatch between the position IDs during fine-tuning  and those during inference stage, leading to significant performance degradation.\n\n---\n**Q4**: Ablation study is missing. How important is each of the three components?\n\n**A4**: Here we provide the full prompt we use during the prompt test.\n```\n**Core Directive**\nYou are an expert mathematician and reasoner. Your primary mode of operation is to solve problems efficiently. \nWhen you think, you can process information in parallel to solve multiple parts of a problem at once. This requires you to first analyze the structure of any given problem.\n**Conditional Logic Mandate:**\nDuring your Chain of Thought thinking progress, you should think in parallel. Specifically determine if the problem can be decomposed into independent, non-sequential sub-tasks.\n* **If the problem is decomposable**, you should use the Parallel Processing Format defined below.\n* **If the problem is inherently sequential** or too simple for decomposition, solve it using a standard, linear step-by-step explanation.\nYou are to make this decision yourself. Do not ask for permission.\n---\n**Parallel Processing Format**\nWhen a problem is decomposable, you must structure your entire thought process as follows:\n```xml\n<Parallel>\n  <Goal 1>\n    Define the first independent objective.\n  </Goal>\n  <Goal 2>\n    Define the second independent objective.\n  </Goal>\n  \n  <Path 1>\n    Execute the steps to achieve Goal 1. Show your work.\n  </Path>\n  <Path 2>\n    Execute the steps to achieve Goal 2. Show your work.\n  </Path>\n  \n  <Conclusion>\n    Synthesize the results from all Paths to generate the final answer.\n  </Conclusion>\n</Parallel>\n```\nWe observed the reasoning generation with this prompt and analyzed the parallelism within the chain of thought."}, {"review_id": "5mARH9z2Aw", "reviewer": "Reviewer_AVNf", "summary": "This paper converts existing single threaded dataset into multi-threaded ones. Furthermore, when fine-tuned on this dataset, the model learns to replicate the behavior on unseen problems, thus realizing the proposed benefits.", "questions": "Multiverse attention. I can understand that the positional index being set to the same over the different <path> during training. There is a supposed benefit that the <path> follows directly after the prefix. Please explain why during inference different various paths can share the same positional index for the \"reduce\".\n\nThe argument given that \"current LLM cannot parallelize\" is rather weak. I do not object to that because whether or not the claim is valid, it does not take away the main contribution of the paper. I do recoomend to either improve the argument or to remove.\n\nI suggest that authors can cite works (don't know if published or not) which aim to allow multiple \"paths\" to also see each others progress, as opposed to just the common prefix, in the Related Works.", "limitations": "No", "rating": 5, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 4, "originality": 4, "strengths_and_weaknesses": "Strength: \n\nThis is a burgeoning topic that see more and more attempts at addressing. This publication takes a very straightforward approach to get quite satisfactory results. This is the case where simple is good. The S1 dataset should be a boon for people to comprehend, extend, and improve upon this Multiverse.\n\nThough running the inference in a multi-threaded manner, the authors generated the multiverse training data in a single-threaded manner. Although it should be understood by experts in this field, most readers, especially junior ML practitioners, would not immediately comprehend how practical this is.\n \nWeakness: \n\nthe \"map reduce\" analogy is a weak one, I don't think it's that necessary. After all, most of the readers are not and will not be employed in cloud companies, and they don't and shouldn't be expected to - even if they hold a CS degree - instantly understand what map-reduce is. It's very simply a spawn-collect (scatter-gather, or even simpler, fork-join) pattern of programming.\n\nThe concept of \"plan - spawn - collect\" is fairly straightforward. There are certainly many other forms of parallelism.\n\nhere are still many unresolved issues in multi-threaded LLM as alluded to in this paper. As this is the first step to multi-threaded LLM, I probably should would refrain from calling this \"weakness\". I expect any void to be quickly filled.", "was_revised": true, "final_justification": "I apologize that I didn't spot this \"Final Justification\" field when the reviewer panel asked me to revise the review. Took me several attempts to try to find where I needed to revise but couldn't find it.\n\nAfter the rebuttal I think all the minor concerns - all concerns were minor to begin with - are addressed. I maintain my score of Accept.", "rebuttal": "Thank you for your suggestions. We have responded to your questions below and would appreciate it if you could let us know if our response addresses your concerns. We hope that you might consider raising your score in light of these clarifications.\n\n---\n**Q1**: Instead of “Map-Reduce” why not use spawn-collect (scatter-gather, or even simpler, fork-join)?\n\n**A1**:  Thank you for this suggestion. After revisiting the core definitions of MapReduce and Fork-Join, we now recognize that Fork-Join more accurately captures the type of parallelism enabled by Multiverse on modern hardware. Unlike MapReduce's batch-oriented, fault-tolerant processing across large clusters, Fork-Join's work-stealing scheduler and fine-grained task decomposition better exemplify the low-overhead, multi-core parallel computation with shared KV cache that we leverage. Framing Multiverse within a Fork-Join paradigm is indeed more precise and should facilitate better understanding, especially for a broader audience. We will incorporate this revised terminology in our camera-ready version if the paper is accepted.\n\n---\n**Q2**:  Explain during inference, why different paths can share the same position ids when “reduce”.\n\n**A2**:  First, although we refer to “shared position IDs,” we do not actually have any computation between different query and key tokens for the same position. This is because softmax attention only considers the distance (i.e., $QK^T$) between token pairs that are not masked, as defined in Equation 1. Thus, the only constraint is that the query token’s positional id must be greater than or equal to the key token’s positional id to ensure the causal relation. By assigning the “Conclusion” token a positional id equal to one more than the maximum id used by any path, we satisfy this causal requirement. (For a deeper discussion of why this works and KV states from different paths can be merged, please see APE [1].) \n\nSecond, we employ the same position id assignment rule during both training and inference, ensuring full consistency. This symmetry means the optimization process directly reflects inference behavior, because the model is trained to attend to tokens that share identical positional ids. \n\nFinally, position sharing itself is not new; it has been widely adopted in prior work on LLM length extrapolation [2, 3]. Because a token’s representation combines its hidden state and its positional embedding, modest adjustments to positional ids (even only during inference) have little adverse effect on model performance, as evident by these work.\n\n---\n**Q3**: The argument that “current LLM can not parallelize” is rather weak\n\n**A3**: We thank the reviewer for highlighting this point and agree that the statement “current LLMs cannot parallelize” is ambiguous. Modern LLMs do exploit parallelism in several aspects, such as prefilling input tokens or serving multiple requests concurrently. Our argument, however, centers on a more specific and fundamental bottleneck: the autoregressive decoding process. This focus is critical because autoregressive modeling remains the dominant architecture underlying today’s leading LLMs. \n\nDuring generation for a single response, each token is conditioned on all preceding tokens—a dependency represented by $P(\\text{token}_n \\mid \\text{token}_1, \\ldots, \\text{token}\\_{n-1})$. This strict causal dependency prevents parallelization within a single decoding sequence, leading to inherently sequential generation. As a result, latency remains high, particularly in long-form generation tasks such as Chain-of-Thought (CoT) reasoning. Drawing on the concept of goodput [4], we emphasize that overcoming this fundamental bottleneck is critical for improving efficiency in latency-sensitive applications.\n\nIn the camera-ready version, we plan to include these details in our introduction for improved clarity. We will also expand the related work section with additional hardware details. Specifically, we will highlight that modern GPUs achieve speedups primarily through parallel computation, yet autoregressive decoding is largely I/O-bound, meaning that increased compute resources do not proportionally reduce latency. This reinforces the importance of rethinking decoding architectures to unlock genuine gains in responsiveness.\n\n---\n**Q4**: Suggestions about citation on works that aim to allow different paths to see each other during inference.\n\n**A4**: Thank you for your suggestions. We will definitely include work in this direction in our next version, including [5] and [6]. Additionally, we have conducted an ablation study on Multiverse’s sharing mechanism. In this setting, each parallel path can read the tokens produced by the other paths after a fixed interval of k sequential tokens, both during training and inference. As shown in Table R1, this cross-path visibility yields no performance improvement; in fact, overly frequent sharing slightly degrades accuracy, likely because the model becomes confused by mixing KV-cache states from different paths during the generation of each path. (Here, k=$\\infty$ means the strategy used in our paper.)\n\nTable R1: Ablation Study between sharing frequency and downstream performance of Multiverse-32B.\n| Task | AIME24 | AIME25 | MATH500 | GPQA-Diamond |\n| :--- | :---: | :---: | :---: | :---: | \n| k=1 |  48.8 | 40.8 | 91.0 | 58.1 |\n| k=8 |  50.4 | 41.7 | 91.8 | 60.6 |\n| k=64 |  51.3 | 43.3 | 92.4 | 60.6 |\n| k=$\\infty$ |  51.7 | 42.5 | 92.4 | 61.7 |\n\n---\n**Reference:**\n[1]. Yang, Xinyu, Tianqi Chen, and Beidi Chen. \"Ape: Faster and longer context-augmented generation via adaptive parallel encoding.\" arXiv preprint arXiv:2502.05431 (2025).\n\n[2]. Jin, Hongye, et al. \"Llm maybe longlm: Self-extend llm context window without tuning.\" arXiv preprint arXiv:2401.01325 (2024).\n\n[3]. Rerope: https://github.com/bojone/rerope\n\n[4]. Zhong, Yinmin, et al. \"{DistServe}: Disaggregating prefill and decoding for goodput-optimized large language model serving.\" 18th USENIX Symposium on Operating Systems Design and Implementation (OSDI 24). 2024.\n\n[5]. Rodionov, Gleb, et al. \"Hogwild! inference: Parallel llm generation via concurrent attention.\" arXiv preprint arXiv:2504.06261 (2025).\n\n[6]. Hsu, Chan-Jan, et al. \"Group Think: Multiple Concurrent Reasoning Agents Collaborating at Token Level Granularity.\" arXiv preprint arXiv:2505.11107 (2025)."}, {"review_id": "DRUmJBPyQP", "reviewer": "Reviewer_y3b7", "summary": "The authors present a prompting, fine-tuning, and execution method that enables decomposing problems into parallel components. The system first decomposes the problem into subproblems, then generates them independently, and merges them into a solution for the problem. To fine-tune models, they propose the Multiverse 1K dataset, which contains explicitly annotated parallel branches.", "questions": "- Section 5.1 describes the process of creating the dataset, but this is in contrast with Sec 3.2, where the authors claim that the LLMs cannot decompose the problem into parallel branches. What is the key difference between Sec 3.2 and 5.1 that enables the LLMs to generate them? Isn't Sec. 3.2 Just a prompting issue then?\n- What are the baselines reported in Tab 2. exactly? Is Autoregressive 32B the same as Qwen2.5-32B-Instruct just fine-tuned on the task in the standard way? Is the difference between Multiverse-32B-zero and Multiverse-32B only the system prompt, or are they also fine-tuned differently? The text says \"variant prompted without the 'think in parallel' instruction\", but is this done only in test time or also during tuning? Also, if prompted without \"think in parallel\"  but fine-tuned with \"think in parallel\" in place and by generating parallel branches, does it still generate parallel branches?\n- What is the parallelism metric reported in Tab 2? The caption says \"ratio between the total number of generated tokens and the actual generation length\", but I don't understand what the difference is between the total number of generated tokens and the generation length. Is it something similar to what I described in the weaknesses?\n- How do the authors measure the implicit parallelism for Table 1 and Figure 3? Do they check the examples by hand? Is there some more advanced promoting technique that is used?\n- Fig 8: What is P?\n- Line 83: what are the varying batch sizes? \n- Line 132: For the hidden-state probe, the authors should probably use some internal layer of the model rather than the last.\n- Line 154: Why are there square brackets in $x_{[1:3,s]}$ and not in $x_{1,1:6}$?\n- Line 204: How does this rewrite work? Is it by prompting or by hand?", "limitations": "The authors discuss the limitation of their work in a satisfactory way.", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 3, "originality": 3, "strengths_and_weaknesses": "# Strengths\n\n- Interesting and novel idea\n- Relatively simple\n\n# Weaknesses\n- Some details are not clear. See questions below.\n- For most of the examples, the amount of seedup in Table 2 is relatively low. This is surprising given the ~7 average branches reported in Tab 1. Perhaps the authors should consider reporting a parallelism metric where they compute the \"parallelness\" of the sequence, where they sum the length of the sequential steps, but they use the max of the branches as the length of a parallel block, and they divide this number by the original length.", "was_revised": true, "final_justification": "The authors cleared the doubts that I had about the paper. I think it is an interesting idea that's worth publishing.", "rebuttal": "Thank you for reviewing our paper and for your valuable feedback. Below, we address your concerns point by point, and we will revise our paper according to your suggestions. We would appreciate it if you could let us know whether your concerns are addressed by our response. We hope that you might consider raising your score in light of these clarifications.\n\n---\n**Q1**: How to define the parallelism? Could you provide some parallelism metric? The speedup is unmatched with the number of parallel branches.\n\n**A1**: In this paper, we define the *degree of parallelism* as\n\n$\\text{parallelism} = \\frac{\\text{total tokens generated}}{\\text{total tokens generated **sequentailly**}}$.\n\nBecause Multiverse can generate multiple tokens per step, its denominator, “sequential tokens”, can be smaller than the total number of generated tokens. This value remains tied to the maximum generation length, which in turn is defined by the highest position id in the generation.\n\nCrucially, the number of parallel branches alone only illustrates the frequency of implicit parallel generation, but does not determine this ratio. What matters is each branch’s *coverage*—the portion of the overall task (generated tokens) that it handles in parallel. In practice, major parallel structures arise within specific subtasks rather than spanning the entire reasoning trace. \n\nTo further understand this question, we also compute the parallelism in our Multiverse-1K , which is **16.7 %** on average. This value matches the parallelism and speedup seen at inference time. We will further include this value and clarify their difference in our later version for better understanding.\n\n---\n**Q2**: Whether LLM can generate in parallel or not? The key difference between section 3.2 and section 5.1\n\n**A2**: The key difference lies in whether the model is creating a parallel structure from scratch or identifying parallelism within an existing structure.\n- In section 3.2, we verified that LLM struggles to generate a parallel thinking trace directly from the instruction prompt. We call this explicit parallelism.\n- In section 5.1, when provided with a pre-existing, sequentially-generated thinking trace, LLM can effectively identify the inherent parallel logic within that trace. We call this implicit parallelism.\n\n---\n**Q3**: The difference between Multiverse 32B-zero vs Multiverse 32B\n\n**A3**: Thank you for the question. Both Multiverse-32B-zero and Multiverse-32B use the same fine-tuned checkpoint; the only distinction is the inference prompt:\n- Multiverse 32B-zero is prompted with \"Let's think step by step.\"\n- Multiverse 32B is prompted with \"Let's think step by step and in parallel.\"\n\nWe included both variants to understand the prompt’s impact on parallelism and overall performance. As shown in Table 2, adding the phrase “and in parallel” preserves accuracy while markedly increasing the degree of parallelism. Therefore, we view this technique as an effective way of modifying model behavior. Moreover, this prompt design also mirrors our training pipeline: autoregressive data were tagged with “Let’s think step by step,” while Multiverse data were tagged with “Let’s think step by step and in parallel.” The correspondence between these training prompts and the observed inference patterns underscores the critical role of prompt engineering in shaping model behaviour with prompt fine-tuning.\n\n---\n**Q4**: What is the baseline in table 2 exactly? How was the autoregressive model trained?\n\n**A4**: To train the autoregressive baseline, we keep the data mixture, learning rate, number of epochs, and all other hyperparameters identical to those used for Multiverse-32B. The only changes are:\n- Attention mechanism: Multiverse attention is replaced with standard causal attention.\n- Corpus processing: All special tokens are stripped out, and we delete the content in Map phases (<Goal> … </Goal>) and Reduce phases (<Conclusion> … </Conclusion>) so that the remaining text reflects a purely sequential chain-of-thought (CoT) process.\nThis is the **main baseline** we hope to compare with in Tab 2.\n\n---\n**Q5**: How to measure the implicit parallelism in Table 1 and Figure 3? Is it by hand or prompt?\n\n**A5**: Thank you for the question. We measure implicit parallelism with a two-step process that combines LLM automation and human verification:\n-  First, we prompt Gemini-2.5-Pro to identify and list every instance of implicit parallelism.\n-  Next, a human annotator verifies each instance and categorizes it as either a selective or collective branch.\n\n---\n**Q6**: What is P in figure 8?\n\n**A6**: The variable P represents the degree of parallelism, with the parallel metric clarified in A1. For readability in the current version, we scale it by a factor of 10; thus, P = 11 corresponds to an actual parallelism of 1.1. In the camera-ready version, we will remove this scaling factor, allowing the degree of parallelism to be visualized directly.\n\n---\n**Q7**: Line 83: What is the varying batch size?\n\n**A7**: The varying batch size corresponds to the experiment detailed in Figure 8b where we tested the speedup under different batch size. The results show that the speedup from multiverse generation is scalable with batch size increase and maintained stable under different settings.\n\n---\n**Q8**: Line 132: For the hidden states probing experiment, use the internal layer instead of the last layer.\n\n**A8**: Here we provide the probing test of different models in the internal layer.\nTable R1: Probing Test for QWQ-32B\n| Layer | 8 | 16 | 24 | 32 | 40 | 48 | 56 | 64 | \n| :--- | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | \n| Accuracy | 48% | 49% | 52% | 52% | 55% | 48% | 47% | 48% |\n\nTable R2: Probing Test for R1-Distilled 32B\n| Layer | 8 | 16 | 24 | 32 | 40 | 48 | 56 | 64 | \n| :--- | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: | \n| Accuracy | 53% | 48% | 54% | 52% | 49% | 55% | 51% | 57% |\n\nTable R3: Probing Test for R1-Distilled 32B\n| Layer | 10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 |\n| :--- | :---: | :---: | :---: | :---: | :---: | :---: | :---: | :---: |\n| Accuracy | 51% | 52% | 49% | 50% | 47% | 46% | 48% | 53% |\n\nThe result verifies the conclusion that LLM does not truly understand parallelism. \n\n---\n**Q9**: Line 154: Why are there square brackets in x[1:3,s] not in x[1,1:6]\n\n**A9**: Thank you for your question! Here, we use x[1:3, s] to combine the variables of $x_1$, $x_2$ and $x_s$. Therefore, the square brackets denotes a list with two separate part. For $x\\_{1,1:6}$, we do not use square brackets as we view 1:6 as a whole. We will further add square brackets.\n\n---\n**Q10**: Line 204: How does the rewrite work? Is it implemented by hand?\n\n**A10**: The entire data curation workflow, including all rewriting steps, was conducted via API calls to the Gemini 2.5 pro model. Here is the detailed prompt for rewrite:\n```\n# Rewriting Paths in the Structured Reasoning Trajectory\n\nYou are given a full structured reasoning trajectory inside a `<Parallel>` block, consisting of:\n\n* one `<Goal>` block with multiple `<Outline>` elements\n* multiple `<Path>` blocks\n* one `<Conclusion>` block.\n\nSome `<Path>` blocks may contain an entire nested `<Parallel>` structure (from `<Parallel>` to `</Parallel>`). These nested blocks should be rewritten using the same rules recursively.\n\n***\n\n## For `<Goal>`\n\n* Rewrite each `<Outline>` into a **concise statement of what is being calculated or determined**.\n* Remove any content describing **how** the problem is solved or intermediate reasoning steps.\n\n***\n\n## For each `<Path>`\n\n* Keep the original numbering prefix (e.g., `1:`, `2:`).\n* Rewrite the content as a **complete, fluent, and logically self-contained paragraph**.\n* Do **not** use transitional phrases like “First,\" “Then,\" “Next,\" “On the other hand,\" etc.\n* If the `<Path>` contains **five or fewer sentences**, rewrite them together as a single coherent paragraph, ensuring logical flow and fluency without using transitional phrases.\n* If the `<Path>` contains **more than five sentences**: Rewrite the first five sentences together as a single unit, forming a fluent paragraph. For the remaining sentences, rewrite each one individually, based on its meaning, as clear and fluent standalone statements.\n* If the `<Path>` contains a **nested `<Parallel>` block**, apply all these rules recursively to the nested block.\n\nEach `<Path>` must make sense independently, even if it contains a nested reasoning chain.\n\n***\n\n## For `<Conclusion>`\n\n* Rewrite the conclusion as the **most concise and synthesized summary** of the main outcomes from all `<Path>` blocks.\n* You may combine or compare results from different paths, but keep it succinct and direct.\n\n***\n\n## Nested `<Parallel>`\n\n* A nested `<Parallel>` may appear only **as a full block inside a `<Path>`**.\n* If a `<Path>` contains a nested `<Parallel>...</Parallel>` block, process that inner block exactly as you would the top-level one:\n    * Rewrite the inner `<Goal>`, `<Path>`, and `<Conclusion>` elements accordingly.\n    * Maintain the XML structure — do not reindent or alter the tag hierarchy.\n\n```"}]

Author rebuttal:

Meta-review: This paper introduces a test-time scaling framework for LLMs that enables decomposing problems into parallel components. The authors also propose the Multiverse-1K dataset for training purposes and present empirical improvements on mathematical reasoning tasks.

Most reviewers find this work novel and value it as the first attempt at multi-threaded LLMs. The proposed dataset also seems to have great potential for future research. Some concerns were raised regarding performance improvements, error bars, and other minor details, but these were well addressed by the authors during the rebuttal.

Given the above, the AC recommends acceptance. This recommendation is based on down-weighting the comments from Reviewer eCfu due to their late response to the rebuttal.
Decision: Accept (spotlight)