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Decentralized Master-Mind: Joint Action Refinement through Iterative Intent Denoising in Multi-Agent Pathfinding
Valeriy Vyaltsev, Anton Andreychuk, Taisia Zlotnikova, Konstantin Yakovlev, Aleksandr Panov, Alexey Skrynnik
TL;DR
Independent final-action sampling can turn locally plausible choices into incompatible joint actions in decentralized MAPF. DMM refines communicated action intents before commitment and is fine-tuned with MICPO; it achieves strong benchmark results and scales to very large teams. Its refinement does not itself enforce joint-action feasibility as a hard constraint.
Problem
In decentralized MAPF, independently sampling per-agent actions can recombine locally valid choices into incompatible joint actions, even when the distributions are correctly learned.
Source: §1 · pp. 1–2Method
DMM iteratively refines decentralized action intents through local communication before commitment, and MICPO fine-tunes the multi-round process using critic-free rollout comparisons.
Source: §1 · p. 2, §7 · p. 13Results
Across POGEMA, DMM generally achieves higher success rates and lower solution costs; DMM-MICPO-3M solves 1,598 of 1,600 MovingAI tasks, the highest evaluated coverage.
Source: §7 · p. 13Takeaways & Limitations
Coupling agents’ evolving action choices before commitment can improve decentralized MAPF beyond independent one-shot sampling.
Source: §7 · p. 13DMM does not hard-enforce joint-action feasibility, so collision-free execution in the reported MovingAI and large-scale experiments uses centralized CS–PIBT shielding.
Source: §7 · p. 13
Abstract
from arXiv · showhide
Decentralized multi-agent path finding (MAPF) with communication requires agents to reach individual goals without collisions under partial observability. Learnable policies trained on expert data provide an effective approach to this problem. However, when several coordinated joint actions are valid in the same context, independently sampling from per-agent distributions can recombine locally valid choices into incompatible joint actions. This failure can arise from the final sampling mechanism even when the per-agent action distributions are learned correctly. DMM (Decentralized Master-Mind) addresses this by replacing one-shot action sampling with discrete, iterative refinement of action intents across communication rounds, inspired by denoising in diffusion models. Agents initialize random action intents and refine them through local communication, coupling their choices before commitment. DMM is pretrained with imitation learning on expert MAPF solutions and further optimized with MICPO, a critic-free group-relative reinforcement-learning method designed for multi-agent, multi-round action refinement. DMM generally achieves higher success rates and lower solution costs than the evaluated learnable baselines. On 1,600 MovingAI tasks, DMM fine-tuned with MICPO solves 1,598, the highest coverage among the evaluated methods, while achieving solution costs close to those of the strongest baselines. DMM also scales to over one million simultaneously acting agents in obstacle-rich environments. These results show that round-level intent refinement can improve joint-action coordination while preserving decentralized execution.
1 Introduction
Decentralized MAPF must coordinate agents navigating shared graphs despite partial observability and the combinatorial growth of joint configurations. DMM refines agents’ action intents before commitment, and the paper reports stronger learned-policy results across benchmarks and large teams.
1 Introduction
- Independent final-action sampling can recombine locally valid choices into incompatible joint actions, even when agents communicate and their action distributions are correctly learned.In the corridor example, only two of four joint outcomes coordinate the agents; the others stall or collide.Source: §1 · p. 2
- DMM replaces one-shot action sampling with iterative refinement of decentralized action intents through neighboring agents’ messages before commitment.Agents’ intermediate intents are part of communication, coupling their choices while preserving decentralized execution.Source: §1 · p. 2
- MICPO fine-tunes DMM on complete rollouts using critic-free, group-relative optimization adapted to multi-agent, multi-round refinement.The method addresses challenges of using centralized or decentralized critics for shared team outcomes.Source: §1 · p. 2
- 1,598 of 1,600 MovingAI tasks are solved by the DMM solver; POGEMA results show generally higher success and lower costs, and DMM solves tested instances above one million agents.The MovingAI evaluation uses post-sampling action processing; the large-scale instances include obstacles.Source: §1 · p. 2
2 Related Work
Classical MAPF methods trade solution quality, computational cost, and scalability. Learning-based approaches acquire coordination from data, but DMM differs by communicating evolving action intents during decentralized refinement.
Classical MAPF Approaches
- Classical MAPF spans search and optimization methods with solution guarantees, alongside reactive and prioritized methods that favor scalability but may sacrifice optimality.CBS and variants search the joint state space; reductions use flow or SAT solvers, while PIBT, LaCAM [23], MAPF-LNS2, and prioritized planning [26] offer other trade-offs.Source: Classical MAPF Approaches · pp. 2–3
Learning-Based MAPF Approaches
- Learned direct-commitment policies sample each agent’s final action independently, so communication does not prevent locally valid choices from forming infeasible joint actions.Examples include policies without communication such as PRIMAL [27] and MAPF-GPT [9], and communication-based methods including DHC [11], DCC [12], MAGAT [13], and LC-MAPF [34].Source: Learning-Based MAPF Approaches · p. 3
- DMM communicates intermediate intents during decentralized, per-timestep refinement, unlike DiffLNS [38], which centrally refines a joint-action tensor into a full-horizon plan.Other multi-robot approaches typically coordinate separately from refinement, such as by simulating teammates or exchanging already planned trajectories [42] [43] [45].Source: Learning-Based MAPF Approaches · p. 3
3 Background
The background defines MAPF goals and feasibility, then describes decentralized communication and the learning objectives used to train policies. Agents exchange local information before simultaneous action commitment.
MAPF Preliminaries
- A MAPF instance uses a four-connected grid, agents with distinct starts and goals, and a shared action set; feasible joint actions avoid vertex conflicts and opposite-direction edge conflicts.A solution is a sequence of feasible joint actions that reaches every agent’s goal within the execution horizon.Source: MAPF Preliminaries · pp. 3–4
- Solution quality is measured by sum of costs and makespan, while success rate is the fraction of instances in which all agents reach their goals within the horizon.Sum of costs aggregates agents’ earliest goal-arrival times; makespan measures the last arrival.Source: MAPF Preliminaries · p. 4
Decentralized MAPF with communication
- Each agent receives an egocentric local observation and communicates over a dynamic graph with its nearest agents within observation range, including itself.Communication proceeds through synchronous rounds before the agents select actions simultaneously.Source: Decentralized MAPF with communication · p. 4
- Decentralized execution restricts decisions to local information: agents do not observe others’ committed actions, impose no ordering, or encode and aggregate the global state or joint action.Per-agent computation is independent of team size under these restrictions.Source: Decentralized MAPF with communication · p. 4
Training Objectives
- Imitation learning trains a shared policy to match each agent’s expert action distribution given its local context at commitment.The expert demonstrations contain timestep samples with local observations, expert actions, and communication graphs.Source: Training Objectives · p. 4
- Independent final-action sampling makes the joint-action distribution factorize across agents, whereas reinforcement learning optimizes expected team return over decentralized rollouts.The rollout return is a shared terminal team outcome.Source: Training Objectives · p. 4
4 Method
Independent per-agent action distributions can fail to reproduce coordinated joint actions, even when each local distribution is learned optimally. DMM refines communicated action intents before local commitment, with imitation pretraining followed by MICPO fine-tuning.
The Decentralized Factorization Gap
- When expert actions remain dependent given the full context, even an optimal product executor has a positive distribution-matching gap; missing local information can also make the gap positive.The gap includes both discarded residual action dependence and action-relevant information unavailable in an agent’s local context.Source: The Decentralized Factorization Gap · p. 5
DMM: Decentralized Iterative Intent Refinement
- DMM couples agents’ choices by exchanging and refining their evolving action intents across communication rounds, then each agent selects its final action locally.The observation-derived latent stays fixed while the communicated intent changes across rounds.Source: DMM: Decentralized Iterative Intent… · pp. 5–6
Imitation Pretraining
- Teacher forcing supplies expert-informed initial intents and replaces sampled votes with expert actions during pretraining, with both probabilities annealed to a nonzero floor.This keeps the communicated intent trajectory informative for neighboring agents while reducing teacher forcing over training.Source: Imitation Pretraining · p. 6
MICPO: Critic-Free Multi-Agent Fine-Tuning
- MICPO removes the critic and compares matched rollouts sharing each step’s initial intent, using a shared group-relative advantage and per-agent, per-round importance ratios.The reference-policy penalty anchors each round to imitation-pretrained behavior while leaving the communication pathway trainable.Source: MICPO: Critic-Free Multi-Agent… · p. 7
- MICPO’s team return combines off-goal duration and blocked non-wait actions, normalizes the components separately within matched groups, and retains high- and low-return trajectories for replay.Replay selection does not change the group used to compute advantages.Source: MICPO: Critic-Free Multi-Agent… · p. 7
5 Experimental Setup
The evaluation combines standalone learned-policy benchmarks, solver-level tests with action processing, a large-scale execution study, and a targeted corridor experiment. The setup varies model size, map domains, agent counts, and decoding or shielding choices.
DMM configurations and training
- DMM-3M retains the LC-MAPF Transformer backbone, while DMM-0.8M reuses observation-dependent computation across refinement rounds and has 763,296 parameters, approximately 4.25× fewer than DMM-3M.Both implementations preserve the same intent representation, local communication semantics, and final action rule.Source: §5 · p. 8
- Both DMM variants receive one million imitation-pretraining iterations followed by MICPO fine-tuning; the training data derive from mazes, random, and house maps with up to 32 agents.The retained teacher-forcing floor is β0 = βr = 0.8; MICPO uses 500 outer iterations and group size G = 24 for each variant.Source: §5 · p. 8
POGEMA benchmark
- POGEMA compares standalone learned policies across Random, Mazes, Warehouse, and Cities-Tiles, with Figure 3 showing success rate versus agent count and SoC ratio to LaCAM* on solved instances.The comparison excludes collision shielding, search, and other action-repair mechanisms.Source: §5 · p. 8, Figure 3 · p. 9
MovingAI benchmark
- MovingAI evaluates maximum-agent scenarios across 32 maps and 1,600 tasks, comparing search-based, hybrid, and learned methods under method-specific time or step budgets.The main comparison uses sampling with RSE for HMAGAT and argmax with RSE for both DMM variants; no method performs post-solution refinement.Source: §5 · p. 8
Large-scale scalability experiment
- The scalability study tests DMM-MICPO-0.8M on 2304 × 2304 maze maps with 131,072 to 1,048,576 agents, four layouts, and approximately 29.1% obstacles.CS–PIBT shields execution; the GPU implementation processes independent conflict groups in parallel, though a single large conflict group can limit parallelism.Source: §5 · pp. 8–9
Corridor experiment
- The corridor experiment trains policies on two expert trajectories and samples 1,000 joint actions per seed at their shared ambiguous state, including a DMM variant with zero retained teacher forcing.The scenario distinguishes coordinated resolutions from mutual-wait stalls and simultaneous-movement collisions.Source: §5 · p. 9
6 Experimental Results
Across POGEMA, MovingAI, million-agent, and corridor-conflict evaluations, DMM shows strong coverage and solution quality while refining action intents to coordinate agents. Its performance and computational trade-offs vary by model size and evaluation setting.
POGEMA Benchmark
- DMM-3M generally outperforms matched LC-MAPF-3M; MICPO improves both model sizes, while the lighter 0.8M variant remains competitive.At maximum team sizes, DMM-MICPO-3M reaches 1.000 success on Warehouse (192 agents) and 0.922 on Cities-Tiles (256), versus 0.938 and 0.805 for LC-MAPF-3M. DMM-MICPO-3M has per-domain median SoC ratios from 1.006 to 1.102, versus 1.063 to 1.892 for MAGAT+ and HMAGAT.Source: POGEMA Benchmark · p. 10
MovingAI Benchmark
- 1,598/1,600 tasks: DMM-MICPO-3M achieves the highest MovingAI coverage among evaluated methods.DMM-MICPO-0.8M solves 1,593 tasks, ahead of HMAGAT (1,576), LG-LaCAM (1,569), LaGAT (1,543), and MAPF-LNS2 (1,411).Source: Figure 4 · p. 10, MovingAI Benchmark · p. 11
- DMM-MICPO-3M matches the virtual-best SoC on 736 tasks and has mean/median SoC ratios of 101.8/100.1%; its q95 ratio is 107.3%.It solves all 50 tasks on 31 of 32 maps and 48 on the remaining map; its map-wise mean virtual-best ratio never exceeds 108.9%.Source: MovingAI Benchmark · p. 11
- 2.33 seconds: DMM-MICPO-0.8M has the lowest median MovingAI runtime, while the 3M variant provides best coverage and solution quality at runtime comparable to MAPF-LNS2.The runtime distributions reflect actual configurations rather than equalized inference budgets: search-based and hybrid methods are time-limited, whereas HMAGAT and DMM are step-limited.Source: MovingAI Benchmark · p. 11
Scaling DMM to One Million Agents
- An 8× increase in agent count raises DMM’s mean per-step cost 1.73×, from 440.3 to 763.1 milliseconds; DMM solves all 16 instances.For a 1,048,576-agent rollout, all agents reach their goals after 16,345 steps, with total runtime of 4.40 hours. Central congestion clears as agents reach goals, while shielding remains a substantial runtime cost.Source: Scaling DMM to One Million Agents · pp. 11–12, Figure 5 · p. 12
Corridor Conflict
- With teacher-forcing floor β0 = βr = 0.8, DMM places 94.8% of samples on the two valid corridor resolutions, versus about 50% for LC-MAPF, MAGAT+, and HMAGAT.More refinement rounds increase valid-action frequency; removing the nonzero teacher-forcing floor makes DMM approach the baselines’ near-uniform action frequencies.Source: Corridor Conflict · pp. 12–13, Table 2 · p. 12
7 Conclusion
DMM refines action intents through local communication before commitment, and MICPO fine-tunes this multi-round process from shared task-level outcomes. Across the reported evaluations, DMM improves on learned-policy baselines and scales to more than one million agents, but does not hard-enforce joint-action feasibility.
7 Conclusion
- DMM refines stochastic action intents through local communication before simultaneous commitment, while MICPO fine-tunes the multi-round process using shared task-level outcomes.This preserves decentralized execution while letting agents' evolving choices influence one another.Source: §7 · p. 13
- Across POGEMA, DMM generally achieves higher success rates and lower solution costs than evaluated learned policies; DMM-MICPO-3M solves 1,598 of 1,600 MovingAI tasks.The compact DMM-MICPO-0.8M solves every tested large-scale instance up to 1,048,576 simultaneously acting agents.Source: §7 · p. 13
- DMM does not enforce joint-action feasibility as a hard constraint, so incompatible intermediate choices remain possible during refinement.The MovingAI and large-scale experiments use CS–PIBT for collision-free execution, making those systems centralized.Source: §7 · p. 13
Appendix Contents
- The appendices cover the factorization-gap proof, architecture variants, MICPO training, hyperparameters, MovingAI evaluation, GPU execution, and refinement and communication ablations.They also include corridor ablations and reactive-policy results with and without Repeat-State Escape.Source: Appendix Contents · p. 16
A Decentralized Factorization Gap Proof
The proof decomposes expected joint KL divergence for a product executor into error components. Under sufficient capacity and ideal cross-entropy optimization, learning error vanishes, leaving an irreducible error at the stated minimum.
A Decentralized Factorization Gap Proof
- For a product executor, the expected joint KL divergence decomposes into local cross-entropy and entropy terms; the remaining irreducible error is the minimum in Eq. (6).The proof substitutes the local cross-entropy identity and collects entropy terms.Source: A Decentralized Factorization Gap Proof · p. 16
- With sufficient capacity and ideal cross-entropy optimization, each local policy reaches its Bayes-optimal conditional, while all three terms in Eq. (20) are nonnegative.The terms are labeled action coupling, missing local information, and learning error.Source: A Decentralized Factorization Gap Proof · p. 16
B DMM Architecture Variants
DMM-3M and DMM-0.8M implement the same intent-refinement process with different observation encoders and computation reuse. The accompanying MICPO procedure describes scenario generation, rollout collection, trajectory selection, replay, and the training configurations.
B DMM Architecture Variants
- DMM-3M compresses its observation into 32 latent tokens and processes them with current neighbor messages at every refinement round.Its observation representation remains unchanged across rounds while intent and communication state evolve.Source: B DMM Architecture Variants · p. 16
- DMM-3M retains an LC-MAPF-style Transformer encoder–decoder, while DMM-0.8M uses a structured observation encoder and reuses observation key/value projections across refinement rounds.Both variants preserve the same intent-refinement process; 0.8M contains 763,296 trainable parameters, about 4.25× fewer than DMM-3M.Source: B DMM Architecture Variants · pp. 16–17, Figure 6 · p. 17
- DMM-0.8M separately processes spatial and agent-record inputs into a 38-token representation, then reuses precomputed observation projections while updating with round-specific messages.Its structured encoder uses an 11 × 11 spatial field and 13 local agent records.Source: B DMM Architecture Variants · p. 17
C MICPO Training Procedure
- MICPO training generates maze and randomly obstructed maps online, then collects rollouts in which agents complete all refinement rounds before each environment action.Trajectories end when all agents occupy their goals or the rollout horizon is reached; agents are not absorbed at goals.Source: C MICPO Training Procedure · pp. 17–18
- MICPO retains the lowest- and highest-return trajectories in each matched group, samples valid environment timesteps, and replays all refinement rounds from stored initial intents and votes.Replay recomputes message features and action distributions sequentially; the reference policy remains fixed at the imitation-pretrained checkpoint.Source: C MICPO Training Procedure · p. 18
D Training Hyperparameters
- Table 3 summarizes the imitation-pretraining and MICPO configurations used for DMM-3M and DMM-0.8M.The supplied passage points to Appendix B for architecture details and Appendix C for rollout and replay procedures.Source: D Training Hyperparameters · p. 18
E MovingAI Benchmark Protocol
The MovingAI protocol evaluates maximum-agent tasks using specified solver budgets, collision processing, and outcome measures. The GPU pipeline keeps environment dynamics and observation construction on-device, with chunking to bound memory use at large agent counts.
E MovingAI Benchmark Protocol
- The MovingAI benchmark uses 1,600 maximum-agent tasks from 32 maps, with populations ranging from 32 to 8,000 agents; unsolved tasks count as failures.The omitted maze map was excluded because preliminary runs found no evaluated method solved any maximum-agent task on it.Source: E MovingAI Benchmark Protocol · p. 18
- Search and hybrid solvers receive 600 seconds, while reactive learned solvers receive 5,000 environment steps and share the CS–PIBT collision shield.The main reactive comparison also uses Repeat-State Escape to prevent cycling among previously visited joint configurations.Source: E MovingAI Benchmark Protocol · p. 18
- Reported measures include solved tasks, per-task virtual-best SoC wins, relative SoC distributions, and runtime; runtime does not reflect equalized compute budgets.Search and hybrid methods are time-limited, whereas reactive policies are step-limited.Source: E MovingAI Benchmark Protocol · p. 19
F GPU-Accelerated Environment and Observation Pipeline
- The GPU implementation keeps environment state and observation tensors on-device, processing moves and collision resolution without host transfers during rollouts.It also constructs observations with batched GPU breadth-first search, cached distance windows, and on-device neighbor assembly.Source: F GPU-Accelerated Environment and… · p. 19
- BFS and agent chunking bound peak memory for large agent counts while preserving the computation and sparse communication graph.Each agent attends only to its precomputed top-k neighbors.Source: F GPU-Accelerated Environment and… · p. 19
G Inference-Time Refinement Depth
At the largest evaluated team size in each POGEMA domain, four refinement rounds capture most observed gains, and fixed checkpoints often improve further when unrolled beyond training depth. MICPO fine-tuning generally reaches comparable performance with fewer test-time rounds.
G Inference-Time Refinement Depth
- At Ktest = 4, success rises substantially while makespan and collisions fall; further rounds add smaller gains, with most benefit reached at the Ktrain = 4 depth.The comparison spans four domains and both DMM-3M and DMM-MICPO-3M checkpoints.Source: G Inference-Time Refinement Depth · p. 20, Figure 7 · p. 20
- Fixed checkpoints trained with Ktrain = 4 generally match or improve on their Ktest = 4 performance at Ktest = 8 and 12, without retraining.Changes beyond the training depth are smaller and occasionally non-monotonic, though additional rounds often reduce collisions.Source: G Inference-Time Refinement Depth · p. 20, Figure 7 · p. 20
- At the same test-time depth, DMM-MICPO-3M generally achieves higher success and lower makespan and collision counts than DMM-3M.On Warehouse with 192 agents, MICPO at Ktest = 2 achieves lower makespan than DMM-3M at Ktest = 12.Source: G Inference-Time Refinement Depth · p. 20
H Intent-State Communication Ablation
Fixed-checkpoint communication perturbations show that DMM's coordination relies more on broadcasting evolving intents than on learned features alone. This qualitative ordering persists after MICPO fine-tuning, while the experiments measure reliance of trained policies rather than retrained alternatives.
H Intent-State Communication Ablation
- Removing h while retaining evolving intent z causes only a limited success-rate drop, whereas removing z causes sharp deterioration as team size grows.The fixed checkpoints are evaluated at K = 4 on Mazes; the interventions change communicated information, not the intent-update or final-action rules.Source: H Intent-State Communication Ablation · pp. 20–21, Figure 8 · p. 21
- Replacing evolving z with initial z0 degrades performance to a level similar to removing z, indicating that the changing intent trajectory matters beyond its initialization.Each agent continues updating its own intent normally in the z0-only intervention.Source: H Intent-State Communication Ablation · p. 21
- Shuffling full messages across agents reduces success, showing that message content alone is insufficient when its correspondence to local context is disrupted.The intervention preserves message structure but permutes assembled messages before decoding.Source: H Intent-State Communication Ablation · p. 21
- After MICPO, Full and no-h remain stronger at large team sizes than no-z, z0-only, and shuffled variants; the qualitative ordering persists.MICPO improves robustness to the perturbations without removing dependence on evolving-intent communication.Source: H Intent-State Communication Ablation · p. 21
- These post-training interventions measure what fixed learned policies rely on, not how architectures retrained without h or z would perform.They do not evaluate alternative message parameterizations trained from scratch.Source: H Intent-State Communication Ablation · p. 21
I Corridor Refinement and Teacher-Forcing Ablations
In the ambiguous corridor, deeper test-time refinement continues to increase valid joint-action frequency beyond the training depth. Among training choices, round-level teacher forcing supplies most of the coordination benefit, while a retained floor matters more than annealing versus a constant schedule.
I Corridor Refinement and Teacher-Forcing Ablations
- Valid joint-action frequency rises from 83.7 ± 2.7% at Ktest = 2 to 94.8 ± 1.1% at Ktest = 4, then reaches 99.6 ± 0.4% at Ktest = 8 and 99.9 ± 0.1% at Ktest = 12.The checkpoints use Ktrain = 4; both valid resolutions remain represented, while stall and collision frequency falls from 0.16 at Ktest = 2 to below 0.01 at Ktest = 12.Source: I Corridor Refinement and… · p. 21, Table 4 · p. 21
- With only βr active, valid frequency is 0.930 (annealed) or 0.926 (disabled from the start), versus 0.807 or 0.794 with only β0 active.Removing both mechanisms yields 0.501 or 0.502, while the standard configuration reaches 0.948; βr incorporates expert action into each evolving intent update.Source: I Corridor Refinement and… · pp. 21–22
- With shared floor β0 = βr = β, valid frequency peaks at 0.948 for β = 0.8 and falls to 0.931 at β = 1.0.At matched floors, annealed versus constant schedules yield 0.845 versus 0.831 at β = 0.4 and 0.948 versus 0.939 at β = 0.8; the retained floor has the larger effect.Source: I Corridor Refinement and… · p. 22, Figure 9 · p. 22
- Overall, corridor ablations show that test-time refinement improves coordination beyond training depth, while round-level teacher forcing provides most training-time coordination benefit.The valid-action measure sums frequencies of the two coordinated resolutions, WL and RW.Source: I Corridor Refinement and… · pp. 21–22
J Decoding and Repeat-State Escape
On the same 1,600 MovingAI task keys, the inference configurations show little effect from adding RSE to DMM sampling, while historical argmax-with-RSE packages have lower matched sum of costs. Those package comparisons do not isolate argmax as the cause.
J Decoding and Repeat-State Escape
- Adding RSE to sampling barely changes DMM coverage or matched quality, while historical argmax-with-RSE configurations have lower matched SoC than sampling with RSE.DMM-MICPO-0.8M changes from 1,593 to 1,592 solved tasks with matched SoC changing by less than 0.2%; DMM-MICPO-3M stays at 1,599 solved, with matched SoCs of 311,768 versus 336,001 for argmax-with-RSE and sampling-with-RSE, respectively.Source: J Decoding and Repeat-State Escape · p. 22, Table 5 · p. 22
- The observed differences compare complete inference configurations, not a single-factor causal effect of argmax.Historical DMM argmax-with-RSE uses zero initial intent, whereas sampled-round runs use a Dirichlet initial intent; implementations also differ.Source: J Decoding and Repeat-State Escape · p. 22