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REVIEW 4 major objections 10 minor 36 references

Long-horizon planning is acquired by world-model CoT and a little clean long data, shaped more reliably by on-policy distillation than sparse RL, and merged only when teachers share compatible patterns.

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2026-07-31 06:52 UTC pith:MDB2RPOW

load-bearing objection Solid controlled empirical map of multi-turn planning across pretrain/OPD/MOPD; the OPD-vs-GRPO “broader region” claim is partly a dense-vs-sparse confound, and everything stays inside a 100M synthetic gym. the 4 major comments →

arxiv 2607.24720 v1 pith:MDB2RPOW submitted 2026-07-27 cs.CL cs.AIcs.LG

The Physics of Multi-Turn Long-Horizon Planning: From Pre-training to Post-training via Single- and Multi-Teacher On-Policy Agentic Distillation

Tianyi Men , Zhuoran Jin , Kang Liu , Jun Zhao This is my paper
classification cs.CL cs.AIcs.LG
keywords multi-turn long-horizon planningworld modelon-policy distillationGRPOmulti-teacher OPDcompositional generalizationagentic pre-trainingplanning patterns
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

Foundation-model agents still fail at multi-turn long-horizon planning, and opaque internet pre-training makes it hard to see why. This paper builds a fully controllable multi-turn gym with hierarchical skill graphs so data format, horizon mix, trajectory quality, and teacher knowledge can be varied cleanly. It shows that planning is acquired in pre-training when the model internalizes state-transition world models in chain-of-thought, sees even a small fraction of long trajectories, and is not poisoned by suboptimal paths whose errors compound. Post-training then shapes two different things: low-mutual-information planning patterns (general search skeletons) versus high-mutual-information procedural knowledge (task-specific recipes). On-policy distillation has a wider effective region than outcome-based GRPO when data is noisy and horizons are long, because its gradients stay consistent; forcing distillation of mismatched recipes can damage the student’s existing world model without installing the new one. Multi-teacher on-policy distillation integrates abilities only by locking onto shared compatible patterns across environments—partial overlap supports continual learning, full conflict causes catastrophic interference.

Core claim

Across pre-training, single-teacher post-training, and multi-teacher consolidation in one controlled multi-turn environment, long-horizon planning is acquired by explicit world-model CoT plus minimal high-quality long-horizon data (atomic skills alone do not compose), shaped over a broader regime by on-policy distillation than by sparse-outcome GRPO when the target is general planning patterns, and integrated by multi-teacher OPD only when teachers share compatible planning-pattern distributions; fully conflicting patterns produce severe cross-environment interference.

What carries the argument

A controllable hierarchical skill-graph gym (AND/OR synthesis rules, short/mid/long horizons, optimal vs suboptimal CoT patterns) paired with the mutual-information split between planning patterns (reusable low-I(T;P) skeletons) and planning knowledge (sample-specific high-I(T;K) procedures), evaluated under GRPO, on-policy distillation (OPD), and cascaded multi-teacher OPD (MOPD).

Load-bearing premise

Findings from tiny randomly initialized models trained only on synthetic toy skill-graph environments will tell us how real foundation models acquire and shape multi-turn planning on opaque internet data and real agent worlds.

What would settle it

Train the same world-model vs direct-action and OPD vs GRPO comparisons on a real multi-turn agent benchmark with natural long-horizon tasks and mixed-quality trajectories; if atomic-skill pre-training alone composes, or if GRPO matches OPD under long noisy horizons, or if MOPD merges fully conflicting domain teachers without interference, the central staged picture fails.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • Pre-training mixtures for agents should include explicit state-transition CoT and a non-zero long-horizon fraction; pure short atomic skill data will not yield long-horizon competence.
  • Suboptimal trajectories must be filtered or heavily down-weighted for long-horizon agents because early errors amplify and collapse later success.
  • Prefer on-policy distillation over sparse-outcome GRPO when pre-training quality is low and horizons are long, provided the teacher’s planning pattern is trustworthy.
  • Do not use OPD to force-transfer unseen multi-path procedural knowledge from a mismatched teacher; align world-model recipes first or risk ID collapse.
  • Multi-teacher consolidation works when patterns are shared and compatible; when they fully conflict, expect catastrophic forgetting rather than seamless integration.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Agent pre-training curricula may need an explicit “composition trigger” stage with sparse long rollouts rather than assuming scale alone composes skills.
  • Process-level dense supervision (token or step KL) is likely more load-bearing for long-horizon agents than final-success RL rewards as horizons grow.
  • Production multi-expert agent stacks should audit planning-pattern overlap across domains before cascading distillation, or schedule shared-pattern teachers first.
  • The pattern/knowledge mutual-information split suggests SFT for recipe injection and RL/OPD mainly for selecting reusable search styles already latent in pre-training.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

4 major / 10 minor

Summary. The paper introduces a synthetic, fully controllable multi-turn planning gym (hierarchical AND/OR skill graphs instantiated in three toy domains) and uses randomly initialized ~100M Qwen2.5-architecture models to study long-horizon planning across three training stages. At pre-training, it reports that explicit world-model CoT outperforms direct action prediction (Fig. 3–4), that atomic skills alone do not compose but ~5% long-horizon data unlocks large gains (Fig. 5, Table 1), and that suboptimal trajectories catastrophically degrade long-horizon performance (Fig. 6). At post-training, it divides planning into low-MI "patterns" and high-MI "knowledge," maps GRPO vs. Top-k OPD into unnecessary/effective/unsupported regions (Fig. 7, Table 3), supports this with SVD gradient-direction and KL analyses (Figs. 9–10, 13–15), and shows mismatched-procedure distillation collapses ID knowledge (Table 4). Finally, it studies cascaded multi-teacher OPD (MOPD) under three pattern-compatibility regimes, finding generalization, continual learning, or interference depending on shared/conflicting templates (Tables 6–7, Figs. 17–21).

Significance. If the results hold, this is a useful controlled testbed contribution: the gym, tokenizer, code, datasets, and checkpoints are all publicly released, the ablation ladders (data ratios, optimal/suboptimal mixes, matched/mismatched recipes, three MOPD regimes) are systematic, and several claims are crisply falsifiable within the environment (e.g., the 5% long-horizon unlock in Table 1, the recipe-mismatch collapse in Table 4). The world-model-vs-direct and minimal-long-horizon-data findings are clean and well-supported. However, the significance is bounded by the setup: all evidence comes from ~100M randomly initialized models with a 3000-token vocabulary trained on counterfactual synthetic rules, so the paper's "physics of planning" framing and its prescriptive takeaways for foundation-model training are extrapolations the experiments do not directly test. The GRPO-vs-OPD and MOPD conclusions additionally rest on design choices (binary reward, ideal teachers, template-frequency measurement) that partly build the conclusions into the experiment.

major comments (4)
  1. [§5.2.1, Fig. 7, Table 3] The headline claim that 'OPD has a broader effective region than GRPO' is confounded by supervision density, not isolated as an algorithmic property. OPD receives dense token-level KL supervision from a teacher at 100.00 accuracy everywhere (Table 4), while GRPO receives only a binary final-outcome reward (§5.2.1). The 'unsupported region' (Region C) is therefore defined partly by the reward design the authors chose: in the 4 Opt.:8 Sub × long cell, GRPO's −1.58 vs. OPD's +18.59 may demonstrate the value of dense credit assignment rather than an intrinsic applicability boundary of GRPO. A process-reward or step-level-reward GRPO baseline is the natural control and is absent. Compounding this, GRPO is trained for only 75 steps (Fig. 8), with visible entropy collapse in the 4:8 Sub row, and GRPO actually beats OPD on pass@8 in the 4 Opt.:4 Sub mix (+9.4/+11.3/+10.7 vs +3.5/+2.7/+2.4, Table
  2. [§6.2, Figs. 17–19, Table 6] The central MOPD mechanism — 'MOPD integrates capabilities by converging to shared planning-pattern distributions' — is close to constructed. In Type I, the three teachers are built to share the T1 template by design (§6.2 Task Setup: 'Three expert teachers share one planning template'), planning patterns are operationalized as eight discrete textual templates, and the pattern distribution is measured by template frequency. The finding that sequential distillation converges to T1 at probability 1.00 across all domains (Fig. 18) is then largely a restatement of reverse-KL mode-seeking over a hand-built common mode, not a discovered mechanism. The load-bearing question — does MOPD find shared structure when it is not explicitly planted? — is untested. A control in which the shared template is withheld from one teacher, or in which which-template-is-shared is randomized, would show the effe
  3. [§5.1, Eq. (10); §5.2.1 region definitions] The mutual-information framing that organizes the entire post-training analysis is never operationalized. I(T;P) < I(T;K) is asserted from intuition ('Due to the abstract and reusable characteristics...') but no estimator, measurement, or even proxy is reported — despite the gym making this estimable (e.g., template entropy vs. recipe-token entropy conditioned on task ID across the corpus). The three applicability regions (unnecessary/effective/unsupported) are then post-hoc labels on observed avg@8 deltas in Fig. 7 rather than regions predicted from measured MI. Since the pattern/knowledge dichotomy and the region taxonomy are among the paper's main conceptual contributions, the authors should either provide an actual MI (or surrogate) analysis supporting the low/high-MI assignment, or present the MI language explicitly as interpretive framing and the regions as descriptive.
  4. [§1, §8 (framing); §3–4 (setup)] The title and introduction promise a 'physics' of how foundation models acquire long-horizon planning, but every experiment uses randomly initialized ~100M models, a 3000-token BPE vocabulary retrained per chapter (App. A.1), counterfactual synthesis rules, and gold plans capped at 13 steps (Table 11). Several takeaways are stated as prescriptive guidance for real pipelines (e.g., 'Training pipelines need error state prefixes'; 'planning knowledge is better suited for SFT'). The internal results are sound, but the manuscript needs an explicit threats-to-validity discussion: which findings are expected to transfer to internet-scale pre-training and real agent environments, which are gym-specific (e.g., the exact 5% unlock threshold, the 75-step RL dynamics), and at minimum a softening of 'fundamentally improve ... foundation models' claims to match the evidence.
minor comments (10)
  1. [Abstract/§1] Typos and grammar: 'a litte long-horizon data' (abstract), 'It allows systematically study' (abstract), 'Planning' run together with 'is' in the first line, 'Directi output' in Fig. 2, 'ong-Horizon' in the Fig. 1 header. A careful proofread is needed throughout.
  2. [Table 1] The long-horizon results are non-monotonic in the data ladder: S/M/L = 100/100/50 gives long avg@8 74.84, but 100/100/100 drops to 68.52, and the middle mean also drops (88.07→85.86). This is unexplained and no variance across seeds is reported anywhere in the paper; please report seed counts and standard deviations, or explain the inversion.
  3. [§5.2.1, Fig. 8] The entropy collapse visible in the GRPO 4 Opt.:8 Sub row of Fig. 8 is not discussed, though it directly bears on the Region C interpretation (collapse vs. credit-assignment failure). Please add entropy-regularization or KL-control ablations, or discuss.
  4. [§2.2, Eqs. (2)–(5)] Eq. (2) (Agent-OPD) and Eq. (5) (Full-Vocabulary OPD) are identical; the experiments actually use Top-k OPD with k=100 (§5.2.1). Please state clearly which objective is used where, and avoid overloading K (turn count K in §2.2, top-k K, and evaluation sample count K=8 in §3.3 are three different quantities).
  5. [App. A.1] The tokenizer is retrained separately per chapter because the corpus varies. Since tokenization affects sequence length and optimization, please confirm that cross-chapter comparisons (e.g., §4 vs. §5 baselines) never rely on absolute loss/token statistics across tokenizers, or quantify the effect.
  6. [Table 4] Teacher A/B rows report 100.00 for all domains of the evaluated columns but '–' for LF/EA; given that §6 teachers are domain-locked (0.00 out of domain, Table 6), clarify whether the §5.3 teachers are single-domain or multi-domain, and why the 100.00 entries differ from the Table 6 teacher pattern.
  7. [Table 11] The dataset statistics are numerically identical across the three domains for every split (same sample counts per step length). State explicitly that the generator uses fixed seeds/templates across domains, and discuss whether this determinism affects the generality of the difficulty bins.
  8. [§5.3, Fig. 11–12] The knowledge-mismatch collapse is shown for a single recipe pair (A vs. B), one domain (FA), and one difficulty (mid). Given that this is a headline claim ('OPD requires aligned procedural knowledge'), at least one additional domain or recipe pair would strengthen it; the current n=1 configuration should be acknowledged.
  9. [Fig. 3 caption] 'a most total of 11,520 inference runs' should read 'at most'; also state whether the 160 instances per subset are disjoint across checkpoints and whether pass@8/avg@8 use the same 8 samples.
  10. [§7] The related-work section is thorough, but please add a sentence contrasting with process-reward / step-level credit assignment work for multi-turn RL (e.g., agent PRM lines the authors themselves cite), since that literature is the most direct alternative explanation for the Region C result.

Circularity Check

0 steps flagged

No significant circularity: empirical systems map of pre-training/RL/MOPD effects in a synthetic gym, not a closed derivation that redefines its target as an input.

full rationale

This paper reports controlled ablation results (world-model CoT vs direct actions; short/mid/long data mixes; optimal vs suboptimal trajectory ratios; GRPO vs OPD deltas; multi-teacher pattern sharing) on randomly initialized ~100M models in a synthetic hierarchical skill-graph environment. Claims are comparative performance measurements (avg@8, pass@8, gradient cosine similarity, pattern histograms), not first-principles predictions forced by fitted constants or self-defined uniqueness. The mutual-information distinction between planning patterns and planning knowledge (§5.1) is conceptual framing that motivates experiments; it does not algebraically force the later region map. The unnecessary/effective/unsupported regions (§5.2, Figure 7) are post-hoc labels for observed performance deltas under horizon × data-quality cells—standard empirical cartography, not a prediction that reduces to its own fit. MOPD Type I/II/III modes are likewise defined by experimental construction of shared vs conflicting pattern supports and then measured. Self-citations (e.g., prior Men et al. agent/reward work) are background, not load-bearing uniqueness theorems. No equation equates a fitted input to a claimed out-of-sample prediction by construction. Skeptic concerns about OPD-vs-GRPO confounds (dense ideal-teacher KL vs binary outcome reward; 75-step budgets) are correctness/identification issues, not circularity. Score 0; steps empty.

Axiom & Free-Parameter Ledger

5 free parameters · 5 axioms · 3 invented entities

Load-bearing content is experimental design choices and modeling assumptions about what the synthetic gym represents, not free physical constants. The central narrative depends on treating hierarchical AND/OR skill graphs, hand-designed CoT pattern templates, and a small from-scratch LM as faithful enough probes of foundation-model planning stages.

free parameters (5)
  • Long-horizon data fraction ladder (0/5/50/100%) = e.g. 5% middle/long
    Discrete mixture ratios chosen to demonstrate activation thresholds; the ‘small amount suffices’ claim is tied to these hand-set percentages.
  • Optimal:suboptimal pattern mix ratios (1 Opt; 4 Opt; 4:4; 4:8) = 4 Opt : 8 Sub highlighted
    Quality axis of the RL region map is defined by these constructed mixture ratios rather than measured real-web noise rates.
  • Horizon bins (short 1–5, mid 6–8, long ≥9 steps) = 1–5 / 6–8 / 9+
    Difficulty taxonomy is a design choice that structures all region and generalization claims.
  • Model scale and train budget (~100M params, 9000 pretrain steps, OPD/GRPO ~75 steps) = Qwen2.5-100M; 9000 SFT steps
    Capacity and optimization horizon can change whether knowledge is ‘uninjectable by RL’ versus merely hard at this scale.
  • Top-k OPD k=100 and evaluation temperature 0.4, K=8 samples = k=100; temp=0.4; avg@8/pass@8
    Distillation and pass@k surfaces depend on these decoding/distillation cutoffs.
axioms (5)
  • domain assumption A synthetic hierarchical skill-graph gym with counterfactual AND/OR recipes is a valid controlled proxy for studying multi-turn long-horizon planning mechanisms in foundation-model agents.
    Core justification in §1 and §3; all causal claims about acquisition/shaping/integration are identified inside this proxy.
  • ad hoc to paper Planning ability decomposes into low-mutual-information reusable planning patterns versus high-mutual-information task-specific planning knowledge.
    §5.1 introduces I(T;P)<I(T;K) as an interpretive lens guiding which tokens RL can move; not independently measured MI estimates.
  • domain assumption On-policy reverse-KL token distillation (Agent-OPD) with an ideal teacher supplies denser, more consistent credit than sparse binary outcome GRPO on long trajectories.
    Used throughout §5; standard in OPD literature but ideal-teacher condition is strong for real deployments.
  • domain assumption Cascaded single-teacher sequential MOPD is representative of multi-teacher consolidation used in foundation-model pipelines.
    §6 restricts to cascaded form for infrastructure reasons and maps findings onto cited industry MOPD uses.
  • standard math Standard next-token LM training, KL, SVD subspace similarity, and PCA on parameters are appropriate instruments for ‘physics-like’ mechanism claims.
    Ordinary ML estimators; no exotic math.
invented entities (3)
  • Controllable Planning Gym (hierarchical skill graphs → multi-turn gym) no independent evidence
    purpose: Enable precise control of horizon, quality, knowledge, and patterns across pre- and post-training.
    Primary experimental apparatus of the paper (§3); synthetic by construction.
  • Three RL applicability regions (unnecessary / effective / unsupported) no independent evidence
    purpose: Map when GRPO/OPD help planning patterns along quality×horizon axes.
    Post-hoc regionalization of empirical deltas in §5.2; useful taxonomy, not an external natural kind.
  • MOPD compatibility modes (shared-compatible, shared-conflict, no-shared-conflict) no independent evidence
    purpose: Explain cross-environment generalization vs continual learning vs catastrophic interference.
    Constructed by controlling which CoT templates appear per domain (§6); modes are defined by the experimental factors.

pith-pipeline@v1.2.0-grok45-kimik3 · 58666 in / 3818 out tokens · 86033 ms · 2026-07-31T06:52:38.988992+00:00 · methodology

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read the original abstract

Multi-turn long-horizon planning is critical for foundation model agents, yet how to fundamentally improve it remains unclear. Existing models are trained on uncontrollable and opaque Internet data, making it difficult to identify how planning ability is acquired, shaped, and integrated. To address this challenge, we introduce a unified and controlled multi-turn environment that enables precise control. It allows systematically study long-horizon planning across three stages. (1) Planning ability acquisition during pre-training. We study data format, distribution, and quality. Explicit world model construction through CoT state transition modeling yields stronger long-horizon generalization. Atomic skills alone are insufficient for compositional generalization, whereas a litte long-horizon data works. Moreover, suboptimal trajectories severely impair performance because errors amplify over long horizons. (2) Planning ability shaping via GRPO and OPD post-training. Through mutual information, we distinguish general planning patterns from task-specific planning knowledge. For planning patterns, we identify three application regions of post-training: unnecessary, effective, and unsupported. OPD has a broader effective region than GRPO under low-quality and long-horizon settings, as it provides more consistent update directions. For planning knowledge, distilling unseen procedures from a teacher with different knowledge may impair student's prior world modeling without fully establishing new knowledge. (3) Planning ability integration through MOPD post-training. We show that multi-teacher on-policy distillation (MOPD) integrates capabilities by converging to shared planning-pattern across environments. Compatible patterns enable cross-environment generalization, partially shared patterns support continual learning, while completely conflicting patterns cause severe interference.

Figures

Figures reproduced from arXiv: 2607.24720 by Jun Zhao, Kang Liu, Tianyi Men, Zhuoran Jin.

Figure 1
Figure 1. Figure 1: An overview of the studying into physics of multi-turn long-horizon planning. It studies the long-horizon planning ability across three training stages: Large-scale pre-training, RL-based post-training (OPD and GRPO), and Multi-teacher model consolidation post-training (MOPD). The giraffe icon is used to represent the “L” in “Long”. Its long neck also reflects that the agents need to look far ahead in long… view at source ↗
Figure 2
Figure 2. Figure 2: Overview of the proposed long-horizon agentic planning framework. Graph-to-Gym Mapping. The abstract skill graphs are instantiated into concrete simulated environments or gyms by mapping abstract nodes to specific items via an index map. To foster environment diversity, we generate a combination of fixed and randomized configurations. Crucially, a subset of 𝐾 item indices combination per category is reserv… view at source ↗
Figure 3
Figure 3. Figure 3: Final performance comparison between students with and without world modeling across three difficulty levels. For 3 domain and 3 difficulty level, each test subset contains 160 instances, resulting in 1,440 test instances for each checkpoint. During inference, we set the sampling temperature to 0.4 and independently sample 8 trajectories for each instance, with a limitation of 20 steps per trajectory. Ther… view at source ↗
Figure 4
Figure 4. Figure 4: Performance scaling with pre-training corpus size for agent planning, comparing students with and without world modeling across three difficulty levels. The teacher is demonstrating the performance of the post-training set with the same distribution. Results. (1) Internalizing a world model leads to stronger generalization ability. As shown in [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Performance scaling across different pretraining distributions. Atomic Skill Composition. Atomic skill compositional generalization refers to the ability of an agent to combine known atomic skills into new compositional skills for solving unseen complex tasks (Yuan et al., 2025). In this work, such compositional ability is acquired through pre-training and encoded in the model parameters, rather than elici… view at source ↗
Figure 6
Figure 6. Figure 6: Effect of pretraining data composition on downstream performance. The figure compares avg@8 and pass@8 across three task domains and three difficulty levels under different pretraining configurations. FA, LF, and EA denote Fantasy Alchemy, Livestock Farming, and Electronic Assembly. Task Setup. (1) Planning pattern. We primarily establish 8 planning patterns, which can be classified into two categories. Th… view at source ↗
Figure 7
Figure 7. Figure 7: Applicability boundaries and post-training capability upper bounds of RL training. The first two panels show the applicability boundaries of multi-turn GRPO and OPD across RL task horizon and non-optimal action ratios (pre-training data quality). The last two panels compare the post-training capability upper bounds of different models. RL Applicability Regions. We define three regions to characterize when … view at source ↗
Figure 8
Figure 8. Figure 8: Training dynamics across optimization settings. Comparison of multi-turn GRPO and OPD under 4 Opt., 4 Opt.:4 Sub., and 4 Opt.:8 Sub. settings. 15 [PITH_FULL_IMAGE:figures/full_fig_p015_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Comparison of step gradient directions between GRPO and OPD under varying optimization conditions. Top-k Subspace for SVD. Beyond measuring task performance, we analyze whether the model already follows the final parameter-update direction in the early stages of training. Cai et al. (2026) analyzes the gradient direction. We further show how the update direction differs under two dimensions: pre-training d… view at source ↗
Figure 10
Figure 10. Figure 10: Evolution of gradient directions. Top-5 SVD direction similarity between intermediate and final checkpoints. Experimental Setup. (1) Horizon length. Under the 4 Opt.:4 Sub setting, we evaluate both the GRPO and OPD algorithms. For each configuration, we conduct pairwise comparisons across the short, middle, and long levels. (2) Algorithm comparison. We fix the difficulty at the long-horizon and utilize th… view at source ↗
Figure 11
Figure 11. Figure 11: The procedural knowledge gap during teacher-student distillation. Distilling a different procedural path for the same goal via the OPD method (teacher B to student A) leads to a substantial collapse of procedural knowledge and severely damages ID performance, while mildly affecting OOD generalization. Knowledge Gap in OPD. In real-world environments, there are multiple reasonable and effective paths to co… view at source ↗
Figure 12
Figure 12. Figure 12: Comparison of training dynamics under two OPD teacher recipes. 19 [PITH_FULL_IMAGE:figures/full_fig_p019_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Token-level KL divergence distributions between students and matched or crossed teachers across training steps. Samples are grouped by trajectory-level and step-level correctness. 𝑞 𝛾 𝑘,𝑡 evaluate next-token probabilities at decoding step 𝑡 within turn 𝑘, conditioned on the same prefix. Let 𝒱𝑘,𝑡 be the top-𝑘 token subset, and let ℓ 𝑝,𝜎 𝑘,𝑡 (𝑣) and ℓ 𝑞,𝛾 𝑘,𝑡 (𝑣) be the stored log probabilities for token 𝑣.… view at source ↗
Figure 14
Figure 14. Figure 14: Token-level probability heatmap on a student A rollout. This figure shows an early-stage RL optimization, mainly focusing on optimizing the tokens corresponding to planning patterns that have high cross-sample generalization. For each token generated by student A, the top cyan, middle blue, and bottom orange bars show the probabilities assigned by student A, teacher A, and teacher B, respectively. Darker … view at source ↗
Figure 15
Figure 15. Figure 15: Token-level probability heatmap on a Student A rollout for step 75. This figure shows a later-stage RL optimization, which mainly focuses on optimizing sample-specific planning knowledge. However, the optimization capacity of RL is insufficient to inject highly specialized planning knowledge. mismatched planning knowledge compared to matched planning knowledge. Completing a single sample involves multiple… view at source ↗
Figure 16
Figure 16. Figure 16: Multi-Turn MOPD. Analysis framework of non-shared and conflicting planning patterns in different environments for multi-teacher on-policy distillation. This implies that the student and the multiple teachers possess an intersecting and consistent understanding of the tasks across different domains. To simulate this structural relationship and empirically evaluate how MOPD achieves effective cross-environm… view at source ↗
Figure 17
Figure 17. Figure 17: Planning pattern distributions for 4 Opt.:4 Sub. (a) before and after multi-teacher OPD. T1 GoalT2 Step T3 Planning T4 ReasoningD1 Quick D2 Shortcut D3 Direct D4 Heuristic Others 4 Opt.:4 Sub.(b) Instruct Teacher FA Teacher LF Teacher EA After FA After LF After EA Fantasy Alchemy 0.12 0.12 0.12 0.12 0.14 0.14 0.10 0.12 0.00 0.33 0.00 0.33 0.34 0.00 0.00 0.00 0.00 0.00 0.47 0.00 0.00 0.53 0.00 0.00 0.00 0.… view at source ↗
Figure 18
Figure 18. Figure 18: Planning pattern distributions for 4 Opt.:4 Sub. (b) before and after multi-teacher OPD. T1 GoalT2 Step T3 Planning T4 ReasoningD1 Quick D2 Shortcut D3 Direct D4 Heuristic Others 4 Opt.:8 Sub. Instruct Teacher FA Teacher LF Teacher EA After FA After LF After EA Fantasy Alchemy 0.04 0.01 0.04 0.00 0.21 0.23 0.23 0.24 0.00 0.33 0.00 0.33 0.34 0.00 0.00 0.00 0.00 0.00 0.70 0.00 0.00 0.30 0.00 0.00 0.00 0.00 … view at source ↗
Figure 19
Figure 19. Figure 19: Planning pattern distributions for 4 Opt.:8 Sub. before and after multi-teacher OPD. 27 [PITH_FULL_IMAGE:figures/full_fig_p027_19.png] view at source ↗
Figure 20
Figure 20. Figure 20: Planning pattern distributions for 4 Opt.:4 Sub. (c) before and after multi-teacher OPD. 29 [PITH_FULL_IMAGE:figures/full_fig_p029_20.png] view at source ↗
Figure 21
Figure 21. Figure 21: Planning pattern distributions for 4 Opt.:4 Sub. (d) before and after multi-teacher OPD. Results. As shown in [PITH_FULL_IMAGE:figures/full_fig_p030_21.png] view at source ↗
Figure 22
Figure 22. Figure 22: Parameter Dynamics for MOPD. base model parameter stable while learning useful task signals. (2) MOPD makes small and stable updates. The pairwise distance matrix shows that the distance between Instruct and MOPD 1 is only 4.82 × 10−1 , and the distances between two neighboring MOPD stages are also small. By contrast, the distances from Instruct to the teacher models are around 7.10 × 101 to 7.36 × 101 . … view at source ↗

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