pith. sign in

arxiv: 2511.00413 · v5 · submitted 2025-11-01 · 💻 cs.LG

Tree Training: Accelerating Agentic LLMs Training via Shared Prefix Reuse

Jinghui Wang , Shaojie Wang , Yinghan Cui , Xuxing Chen , Chao Wang , Liang Huang , Can Tang , Xiaojiang Zhang
show 4 more authors
Junyi Peng Li Wan Haotian Zhang Bin Chen
This is my paper

Pith reviewed 2026-05-18 02:00 UTC · model grok-4.3

classification 💻 cs.LG
keywords agentic LLMstree-structured trajectoriesshared prefix reuseper-token weighted lossDFS serializationredundancy-free partitioningsupervised fine-tuningreinforcement learning
0
0 comments X

The pith

Averaging the loss over all branches in a tree trajectory is algebraically identical to a per-token weighted loss where each token's weight equals the fraction of branches passing through it.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Agentic LLM training produces tree-structured token trajectories from branching interactions such as tool use and sub-agents. Treating each branch as an independent linear sequence repeats forward and backward computation on every shared prefix. The paper shows that averaging losses across branches equals a single weighted loss computation with weights set by branch fractions through each token. DFS serialization visits every token exactly once while adapted full-attention and SSM layers preserve the exact log-probabilities that independent branches would produce. Redundancy-Free Tree Partitioning extends the approach to cases where the full tree exceeds memory, bounding peak usage to one root-to-leaf path and eliminating all redundant work.

Core claim

Averaging the loss over all branches independently is algebraically identical to a per-token weighted loss, where each token's weight equals the fraction of branches passing through it. The problem therefore reduces to computing the log-probability of every token in the prefix tree exactly once, with no repeated computation across shared prefixes: DFS serialization of the tree visits every token exactly once, and full-attention and SSM layers are adapted to ensure the resulting log-probabilities match independent per-branch calculation exactly. Redundancy-Free Tree Partitioning handles memory-constrained settings with zero redundant computation and peak memory bounded by a single root-to-toe

What carries the argument

DFS serialization of the tree, which visits every token exactly once, with adaptations to full-attention and SSM layers to match independent per-branch log-probabilities, plus Redundancy-Free Tree Partitioning that bounds peak memory to one root-to-leaf path.

Load-bearing premise

Adapting full-attention and SSM layers to the DFS-serialized tree must produce log-probabilities that exactly match independent per-branch calculation, and Redundancy-Free Tree Partitioning must incur zero redundant computation while bounding peak memory to a single root-to-leaf path.

What would settle it

Run both standard per-branch training and the proposed tree method on the same small trajectory tree and verify that the total loss and per-token gradients match exactly; any numerical difference would falsify the claimed algebraic identity.

Figures

Figures reproduced from arXiv: 2511.00413 by Bin Chen, Can Tang, Chao Wang, Haotian Zhang, Jinghui Wang, Junyi Peng, Liang Huang, Li Wan, Shaojie Wang, Xiaojiang Zhang, Xuxing Chen, Yinghan Cui.

Figure 1
Figure 1. Figure 1: Illustration of shared prefixes. Left: Multiple trajectories share common prefix segments (e.g., all trajectories share r→u), while smaller subsets may share longer prefixes (e.g., trajectories 1–3 share r→u→v1). Right: Merging these overlapping prefixes forms a hierarchical tree, where shared computation is explicitly represented by internal nodes, and unique continuations correspond to leaf branches. Thi… view at source ↗
Figure 2
Figure 2. Figure 2: Schematic of the preprocess (sequence packing), forward pass, and backward pass in a tree-structured dataset. Pink blocks represent the (X, Q, K, V, O, dO, dV ) for the prefix, while yellow blocks correspond to those of the suffix parts. shared prefix are identical across both sequences. There￾fore, in the forward pass, the causal mask ensures that the outputs O1 and O′ 1 are identical, thus eliminating th… view at source ↗
Figure 3
Figure 3. Figure 3: Comparison between single-path and multi-path tree packing. Step 1 packs the shared prefix r→u→v1, and Step 2 packs r→u→v5 separately. The optimal strategy instead treats r→u→ {v1, v5} as a hierarchical shared prefix, enabling greater computation reuse, as discussed in section 2.2.2. into subtrees under a total trajectory-length budget C, ensur￾ing that each batch stays within capacity while maximizing reu… view at source ↗
Figure 4
Figure 4. Figure 4: A Comparative Illustration of Backward V-Gradient Computation Tree-Packing and Original Packing. Pink blocks represent the (Q, K, dO, dV ) for the prefix parts, while yellow blocks correspond to those of the suffix parts. The orange blocks signify that their corresponding (S or P) values are active in the attention computation, whereas the white blocks indicate that their (S or P) values are masked out, th… view at source ↗
Figure 5
Figure 5. Figure 5: Implementation of flattened tree trajectory. Each flattened tree trajectory requires (1) a gradient scale tensor for prefix reuse, (2) a position embedding tensor that restores original token positions, and (3) a shared-prefix attention mask that enables proper computation reuse across overlapping prefixes during both forward and backward passes. Linear Operation The linear operation is ubiquitous in the T… view at source ↗
Figure 6
Figure 6. Figure 6: Backward computation with gradient scaling in Tree Training. After the first gradient of the flattened tree trajectory (dY ) is computed, the gradient scaler is applied to scale the gradients of shared prefixes by their reuse counts. For example, the shared prefix r→u is used by five trajectories (scale = 5), and v1 is used by three trajectories (scale = 3), ensuring correct gradient accumulation. dXi = dY… view at source ↗
Figure 7
Figure 7. Figure 7: Real agentic trajectory trees and their overlap characteristics. The upper row visualizes representative trajectory trees extracted from multi-turn agentic RL rollouts, exhibiting different degrees of prefix sharing: Low Overlap (POR = 28.0%), Medium Overlap (POR = 70.5%), and High Overlap (POR = 88.7%). The lower row plots the corresponding active trajectory counts over trajectory length for both the base… view at source ↗
Figure 8
Figure 8. Figure 8: End-to-end training speedup of Tree Training across datasets with varying Potential Overlap Ratios (POR). Each subfigure reports the relative reduction in total training time of Tree Training compared to the baseline Sequence Packing. From left to right: (a) synthetic datasets where the full tree fits in GPU memory, (b) synthetic datasets requiring tree packing under memory constraints, and (c) real agenti… view at source ↗
read the original abstract

Agentic large language model (LLM) training often involves multi-turn interaction trajectories that branch into multiple execution paths due to concurrent tool use, think-mode, sub-agent, context management and other runtime designs. As a result, the tokens produced by a single task naturally form a tree-structured token trajectory with shared prefixes, rather than a linear sequence. Existing training pipelines linearize such trajectories and treat each branch independently, leading to substantial redundant computation in both forward and backward passes. We derive that averaging the loss over all branches independently is algebraically identical to a per-token weighted loss, where each token's weight equals the fraction of branches passing through it. The problem therefore reduces to computing the log-probability of every token in the prefix tree exactly once, with no repeated computation across shared prefixes: we propose DFS serialization of the tree, which visits every token exactly once, and adapt full-attention and SSM layers to ensure the resulting log-probabilities match independent per-branch calculation exactly. In practice, a single trajectory tree can be too large to fit in GPU memory; we therefore propose Redundancy-Free Tree Partitioning, which handles memory-constrained settings with zero redundant computation and peak memory bounded by a single root-to-leaf path. Together, these contributions form Tree Training, an efficient framework for training LLMs on tree-structured trajectories, achieving up to 6.2x end-to-end training speedup on dense and MoE models for both supervised fine-tuning and reinforcement learning.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper claims that averaging the loss over all branches of a tree-structured token trajectory is algebraically identical to a per-token weighted loss (with each token weighted by the fraction of branches passing through it). It proposes DFS serialization of the tree together with adaptations to full-attention masks and SSM state handling so that log-probabilities are computed exactly once and match independent per-branch calculations. A Redundancy-Free Tree Partitioning scheme is introduced to handle large trees under memory constraints with zero redundant computation and peak memory bounded by a single root-to-leaf path. The resulting Tree Training framework is reported to deliver up to 6.2x end-to-end speedup for supervised fine-tuning and reinforcement learning on both dense and MoE models.

Significance. If the layer adaptations are shown to produce exactly matching log-probabilities and the partitioning incurs no hidden redundancy, the work offers a practical and theoretically grounded route to eliminate redundant forward/backward computation on branched trajectories that arise naturally in agentic LLM training. The algebraic identity is a clean, parameter-free derivation that directly reduces the problem to single-pass tree traversal; this is a genuine strength. The extension to both dense and MoE architectures and to both SFT and RL settings broadens potential impact.

major comments (2)
  1. [DFS Serialization and Layer Adaptations] DFS Serialization and Layer Adaptations section: the assertion that modified full-attention masks and SSM state save/restore produce log-probabilities that exactly equal those from independent per-branch forward passes is load-bearing for the claimed equivalence. No explicit proof, edge-case verification (e.g., multi-branch trees with shared prefixes of varying depth), or small-scale numerical comparison against a baseline of separate branch computations is provided; any cross-branch leakage in the attention mask or incorrect recurrent-state reset would invalidate the weighted-loss reduction.
  2. [Experimental Evaluation] Experimental Evaluation section: the 6.2x end-to-end speedup figure is presented without sufficient controls. Details are missing on model sizes and types, dataset characteristics, exact baseline implementation (linearized independent branches), batching strategy, hardware, and whether the reported time includes partitioning overhead or only the core forward/backward passes.
minor comments (2)
  1. [Abstract] Abstract: the phrase 'up to 6.2x' should be qualified with the specific model, task, and memory regime in which it was measured.
  2. [Notation and Preliminaries] Notation: ensure that 'prefix tree', 'trajectory tree', and 'branch' are defined once and used consistently; the transition from per-branch loss to per-token weighting would benefit from an explicit equation linking the two formulations.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive feedback and for recognizing the potential impact of our work on accelerating training for agentic LLMs. We address each of the major comments below and will update the manuscript accordingly to strengthen the presentation.

read point-by-point responses

  1. Referee: [DFS Serialization and Layer Adaptations] DFS Serialization and Layer Adaptations section: the assertion that modified full-attention masks and SSM state save/restore produce log-probabilities that exactly equal those from independent per-branch forward passes is load-bearing for the claimed equivalence. No explicit proof, edge-case verification (e.g., multi-branch trees with shared prefixes of varying depth), or small-scale numerical comparison against a baseline of separate branch computations is provided; any cross-branch leakage in the attention mask or incorrect recurrent-state reset would invalidate the weighted-loss reduction.

    Authors: We appreciate this observation. The algebraic equivalence between averaging losses over branches and the per-token weighted loss is derived in Section 3.1 of the manuscript. To address the concern, we will include an explicit formal proof of the equivalence in the appendix of the revised manuscript. Additionally, we will add a small-scale numerical verification experiment comparing the log-probabilities from our DFS serialization with modified attention masks and SSM handling against independent per-branch computations on multi-branch trees with varying shared prefix depths. This will confirm the absence of cross-branch leakage and correct state resets. revision: yes

  2. Referee: [Experimental Evaluation] Experimental Evaluation section: the 6.2x end-to-end speedup figure is presented without sufficient controls. Details are missing on model sizes and types, dataset characteristics, exact baseline implementation (linearized independent branches), batching strategy, hardware, and whether the reported time includes partitioning overhead or only the core forward/backward passes.

    Authors: We agree that more experimental details are necessary for reproducibility and to substantiate the speedup claims. In the revised manuscript, we will expand the Experimental Evaluation section to include: specific model sizes and architectures (e.g., 7B dense and MoE models), dataset characteristics (number of trajectories, branching factors, etc.), a detailed description of the baseline implementation (linearized independent branches with standard attention), batching strategy used, hardware specifications (GPU types and counts), and clarification on timing measurements (confirming inclusion of partitioning overhead in end-to-end times). We will also report additional metrics such as memory usage and per-component timings. revision: yes

Circularity Check

0 steps flagged

No significant circularity; central equivalence is a direct algebraic identity

full rationale

The paper's key derivation states that averaging loss over independent branches is algebraically identical to a per-token weighted loss with weights as branch fractions through each token. This identity follows immediately from the definition of averaging and does not reduce to any fitted parameter, self-referential equation, or prior result by the same authors. The DFS serialization, attention/SSM adaptations, and Redundancy-Free Tree Partitioning are presented as new algorithmic mechanisms to realize the exact per-token log-probabilities without repetition; these steps are constructive proposals rather than re-expressions of inputs. No load-bearing claim relies on self-citation chains, uniqueness theorems imported from prior work, or ansatzes smuggled via citation. The derivation chain is self-contained against external benchmarks and introduces independent content.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The approach rests on standard assumptions about tree traversals and transformer attention semantics with no new free parameters or invented physical entities; the algebraic identity is treated as a direct consequence of loss averaging.

axioms (2)
  • domain assumption DFS serialization of the prefix tree visits every token exactly once while preserving the causal structure needed for exact log-probability computation.
    Invoked when proposing DFS serialization to replace independent branch processing.
  • domain assumption Full-attention and SSM layers can be adapted to the serialized tree such that per-token log-probabilities remain identical to those computed on independent branches.
    Central to the claim that the weighted loss can be realized without repeated computation.

pith-pipeline@v0.9.0 · 5829 in / 1395 out tokens · 37149 ms · 2026-05-18T02:00:27.660747+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

20 extracted references · 20 canonical work pages · 5 internal anchors

  1. [1]

    Abdelaziz, I., Basu, K., Agarwal, M., Kumaravel, S., Stal- lone, M., Panda, R., Rizk, Y ., Bhargav, G. P. S., Crouse, M., Gunasekara, C., Ikbal, S., Joshi, S., Karanam, H., Kumar, V ., Munawar, A., Neelam, S., Raghu, D., Sharma, U., Soria, A. M., Sreedhar, D., Venkateswaran, P., Un- uvar, M., Cox, D. D., Roukos, S., Lastras, L. A., and Kapanipathi, P. Gra...

    work page 2024

  2. [2]

    Axelrod, R

    Association for Computational Linguistics. doi: 10.18653/v1/2024. emnlp-industry.85. URL https://aclanthology. org/2024.emnlp-industry.85/. Goru, R., Mehta, S., and Jain, P. One-pass to reason: To- ken duplication and block-sparse mask for efficient fine- tuning on multi-turn reasoning,

    work page doi:10.18653/v1/2024 2024

  3. [3]

    Hou, Z., Hu, Z., Li, Y ., Lu, R., Tang, J., and Dong, Y

    URL https: //arxiv.org/abs/2504.18246. Hou, Z., Hu, Z., Li, Y ., Lu, R., Tang, J., and Dong, Y . Treerl: Llm reinforcement learning with on-policy tree search,

    work page arXiv

  4. [4]

    Ji, Y ., Ma, Z., Wang, Y ., Chen, G., Chu, X., and Wu, L

    URL https://arxiv.org/abs/ 2506.11902. Ji, Y ., Ma, Z., Wang, Y ., Chen, G., Chu, X., and Wu, L. Tree search for llm agent reinforcement learning,

    work page arXiv

  5. [5]

    Tree search for llm agent reinforcement learning.arXiv preprint arXiv:2509.21240, 2025

    URL https://arxiv.org/abs/2509.21240. Kim, S., Moon, S., Tabrizi, R., Lee, N., Mahoney, M. W., Keutzer, K., and Gholami, A. An llm compiler for parallel function calling,

    work page arXiv

  6. [6]

    Li, Y ., Gu, Q., Wen, Z., Li, Z., Xing, T., Guo, S., Zheng, T., Zhou, X., Qu, X., Zhou, W., Zhang, Z., Shen, W., Liu, Q., Lin, C., Yang, J., Zhang, G., and Huang, W

    URL https://arxiv.org/ abs/2312.04511. Li, Y ., Gu, Q., Wen, Z., Li, Z., Xing, T., Guo, S., Zheng, T., Zhou, X., Qu, X., Zhou, W., Zhang, Z., Shen, W., Liu, Q., Lin, C., Yang, J., Zhang, G., and Huang, W. Treepo: Bridging the gap of policy optimization and ef- ficacy and inference efficiency with heuristic tree-based modeling,

    work page arXiv

  7. [7]

    Treepo: Bridging the gap of policy optimization and efficacy and inference efficiency with heuristic tree-based modeling.arXiv preprint arXiv:2508.17445, 2025

    URL https://arxiv.org/abs/ 2508.17445. Liu, Z., Yue, T., Tang, Y ., Guo, L., Cai, J., Liu, Q., Chen, X., and Liu, J. Prefix grouper: Efficient grpo training through shared-prefix forward,

    work page arXiv

  8. [8]

    Prefix grouper: Efficient GRPO training through shared-prefix forward

    URL https://arxiv. org/abs/2506.05433. Luo, X., Zhang, Y ., He, Z., Wang, Z., Zhao, S., Li, D., Qiu, L. K., and Yang, Y . Agent lightning: Train any ai agents with reinforcement learning,

    work page arXiv

  9. [9]

    Packer, C., Wooders, S., Lin, K., Fang, V ., Patil, S

    URL https: //arxiv.org/abs/2508.03680. Packer, C., Wooders, S., Lin, K., Fang, V ., Patil, S. G., Stoica, I., and Gonzalez, J. E. Memgpt: Towards llms as operating systems,

    work page arXiv

  10. [10]

    MemGPT: Towards LLMs as Operating Systems

    URL https://arxiv. org/abs/2310.08560. Pope, R., Douglas, S., Chowdhery, A., Devlin, J., Bradbury, J., Levskaya, A., Heek, J., Xiao, K., Agrawal, S., and Dean, J. Efficiently scaling transformer inference,

    work page internal anchor Pith review Pith/arXiv arXiv

  11. [11]

    Raha, A., Mathaikutty, D

    URLhttps://arxiv.org/abs/2211.05102. Qin, R., Li, Z., He, W., Zhang, M., Wu, Y ., Zheng, W., and Xu, X. Mooncake: A kvcache-centric disaggregated architecture for llm serving,

    work page arXiv

  12. [12]

    Mooncake: A kvcache-centric disaggregated architecture for llm serving, 2024

    URL https:// arxiv.org/abs/2407.00079. Shah, J., Bikshandi, G., Zhang, Y ., Thakkar, V ., Ramani, P., and Dao, T. Flashattention-3: Fast and accurate attention with asynchrony and low-precision,

    work page arXiv

  13. [13]

    FlashAttention-3: Fast and Accurate Attention with Asynchrony and Low-precision

    URL https: //arxiv.org/abs/2407.08608. Shoeybi, M., Patwary, M., Puri, R., LeGresley, P., Casper, J., and Catanzaro, B. Megatron-lm: Training multi- billion parameter language models using model par- allelism,

    work page internal anchor Pith review arXiv

  14. [14]

    URL https://arxiv.org/abs/ 1909.08053. Wang, F. and Hegde, S. Accelerating direct preference optimization with prefix sharing,

    work page internal anchor Pith review Pith/arXiv arXiv 1909

  15. [15]

    Wang, G., Zeng, J., Xiao, X., Wu, S., Yang, J., Zheng, L., Chen, Z., Bian, J., Yu, D., and Wang, H

    URL https: //arxiv.org/abs/2410.20305. Wang, G., Zeng, J., Xiao, X., Wu, S., Yang, J., Zheng, L., Chen, Z., Bian, J., Yu, D., and Wang, H. Flashmask: Efficient and rich mask extension of flashattention,

    work page arXiv

  16. [16]

    Xu, W., Mei, K., Gao, H., Tan, J., Liang, Z., and Zhang, Y

    URLhttps://arxiv.org/abs/2410.01359. Xu, W., Mei, K., Gao, H., Tan, J., Liang, Z., and Zhang, Y . A-mem: Agentic memory for llm agents.arXiv preprint arXiv:2502.12110,

    work page arXiv

  17. [17]

    Qwen3 Technical Report

    URL https: //arxiv.org/abs/2505.09388. Yao, S., Yu, D., Zhao, J., Shafran, I., Griffiths, T., Cao, Y ., and Narasimhan, K. Tree of thoughts: Deliberate problem solving with large language models.Advances in neural information processing systems, 36:11809–11822,

    work page internal anchor Pith review Pith/arXiv arXiv

  18. [18]

    Agentrl: Scaling agentic reinforcement learning with a multi-turn, multi-task framework, 2025

    URLhttps://arxiv.org/abs/2510.04206. Zhong, W., Guo, L., Gao, Q., Ye, H., and Wang, Y . Memory- bank: Enhancing large language models with long-term memory,

    work page arXiv

  19. [19]

    MemoryBank: Enhancing Large Language Models with Long-Term Memory

    URL https://arxiv.org/abs/ 2305.10250. Zhou, Y ., Jiang, S., Tian, Y ., Weston, J., Levine, S., Sukhbaatar, S., and Li, X. Sweet-rl: Training multi-turn llm agents on collaborative reasoning tasks,

    work page internal anchor Pith review Pith/arXiv arXiv

  20. [20]

    URL https://arxiv.org/abs/2503.15478

    work page arXiv