AdaSMSet: LLM Orchestration & Combinatorics

• AdaSMSet is a dual-purpose term referring to a specialized LLM orchestration dataset and a family of alternating sum and difference dominated sets in additive combinatorics.
• The Adaptive Scene Manager Dataset is designed to supervise multi-agent role-playing narratives, using explicit actions like init_scene and pick_speaker to enhance decision-level orchestration.
• In additive combinatorics, AdaSMSet offers concrete constructions for sequences that alternate between More Sums Than Differences and More Differences Than Sums, preserving non-filling structural properties.

AdaSMSet refers to two distinct, unrelated technical objects in contemporary research: (1) the "Adaptive Scene Manager Dataset," a large-scale, structured supervision corpus for multi-agent role-playing orchestration in LLMs (Xu et al., 16 Jan 2026), and (2) a designated name for a family of alternating sum and difference dominated sets in additive combinatorics, each with explicit, non-filling-in structural properties (Herrmann et al., 16 Sep 2025). Both usages are authoritative within their respective research areas.

1. AdaSMSet: Adaptive Scene Manager Dataset for Multi-Agent LLM Orchestration

AdaSMSet in the context of LLM researchers refers to the "Adaptive Scene Manager Dataset," a specialized corpus designed to supervise and train LLM-based Scene Managers on decision-level orchestration in multi-character interactive narratives (Xu et al., 16 Jan 2026). Its primary function is to teach neural models to operate at the meta-narrative level, controlling not just utterance generation but the full spectrum of role-playing coordination: scene initiation, speaker selection, narrative transition, dynamic agent introduction, and episode termination.

Motivation: Traditional LLM role-playing frameworks focus on dialogue generation with limited modeling of higher-order narrative structure. AdaSMSet addresses key deficiencies by offering explicit, densely labeled examples for the following discrete orchestration actions:

• init_scene: Initialize a narrative setting.
• pick_speaker: Select the next agent to speak.
• switch_scene: Transition to a new scene.
• add_role: Introduce a new role on demand.
• end: Terminate the episode.

Each annotated action includes arguments (e.g., speaker name, scene description, or rationale), allowing supervised learning of complex orchestration strategies that go beyond local message continuity.

2. Dataset Construction and Format

AdaSMSet is constructed atop 9,900 synthetic dialogue trajectories from AdaRPSet-Synthesis, leveraging LLM outputs for the base narration and scene management. The annotation process involves:

• Inserting pick_speaker actions, determined via a centralized script, at every conversational turn.
• Automatically generating a single-sentence rationale for each pick_speaker decision using GPT-5-Chat, conditioned on character motivations, conversation history, and the pending speaker.
• Representing each episode as a JSON-formatted sequence interleaving:
  • System context (profiles and motivations)
  • User- and actor-role message turns
  • Interleaved scene_manager actions with action labels and structured fields.

Key corpus statistics:

Metric	Value
Convs. (trajectories)	9,900
Total messages	496,493
Avg. messages/conv	50.15
init_scene	9,900
pick_speaker	223,415
switch_scene	10,101
add_role	9,862
end	9,900

This format enables structured action supervision at every decision point, with rationales being critical for teaching turn order, narrative pacing, and adaptive character management.

3. Supervision Structure and Scene Manager Task Definition

At each dialogic step $t$, the Scene Manager observes a global state $G_t = (R_t, H_t)$, where $R_t$ is the set of active roles (with profiles and motivations), and $H_t$ is the full turn-level history. The manager's task is to emit a structured message $m_t$ drawn from the space $\mathcal{M} = \{$init_scene, pick_speaker, switch_scene, add_role, end$\}$, along with structured arguments (attributes such as speaker, new_scene, new_role_name, etc.).

The dataset provides:

• Scalar action targets $m_t^*$
• Action-conditional arguments (e.g., speaker name, rationale, scene text)
• A natural-language rationale at each step explaining the decision in context

All outputs are formatted as JSON-style records suitable for autoregressive LLM conditioning.

4. Training Protocols and Optimization Objectives

The AdaSMSet corpus is used to fine-tune base LLMs (e.g., Qwen2.5-7B, Qwen2.5-14B) via supervised learning, with the following objective per conversational step: $$\mathcal{L}_t(\theta) = -\log p_\theta(m_t^* \mid G_t) - \mathbf{1}[m_t^*=\textrm{pick\_speaker}] \log p_\theta(\textrm{speaker}_t^* \mid G_t, m_t^*) - \cdots$$ Additional terms are included for the other actions as detailed in (Xu et al., 16 Jan 2026). Regularization was not found to be essential. Hyperparameters for optimal performance include a learning rate of $1 \times 10^{-6}$ and up to 16K token context windows over 8 epochs.

At inference, the trained manager receives the full history and responds by emitting a JSON action, with conversation turn control proceeding according to the predicted sequence of scene_manager actions until the episode ends.

5. Evaluation and Empirical Impact

AdaSMSet’s effectiveness is evaluated using AdaptiveBench, a simulation-based testbed which scores orchestration performance across four axes: Scene Understanding, Speaker Discipline (turn order), Role Introduction Judgment, and Overall Assessment, each on a 0–10 scale. Results reported in (Xu et al., 16 Jan 2026) are summarized below:

Model	Scene U	Speaker D	Role Intro J	Overall
Qwen2.5-14B	7.65	8.42	7.34	7.63
Qwen2.5-14B-Ours	8.23	8.25	8.64	8.37
Claude 4.5	8.21	8.62	8.05	8.17

Fine-tuning on AdaSMSet yields a gain of +0.74 on the overall metric for Qwen2.5-14B, exceeding even Claude 4.5 on AdaptiveBench. The result demonstrates the value of explicit, rationale-driven orchestration supervision.

6. Alternate Usage in Additive Combinatorics

Independently, AdaSMSet (in an additive combinatorics context) refers to explicit constructions of sequences of alternating sum and difference-dominated integer sets, as developed in (Herrmann et al., 16 Sep 2025). Here:

• $A_{2\ell}$ is More Differences Than Sums (MDTS)
• $A_{2\ell+1}$ is More Sums Than Differences (MSTD)
• Each $A_{k}$ avoids "filling in" any interior integer gap from prior sets
• Construction is via adjoining $l n$ or $A_1 + l n$ at step $\ell$
• The systematic alternation and size gap between $|A+A|$ and $|A-A|$ is preserved and computable at every stage

The construction proceeds by augmenting a base MSTD set $A_1$ according to residue class and missing sum/difference statistics, achieving infinite strictly alternating chains with non-filling-in growth. A concrete example is the Conway set $A_1 = \{0,2,3,4,7,11,12,14\}$ with $n = 17$, for which the alternation and cardinalities follow precisely (see detailed formulae and table in (Herrmann et al., 16 Sep 2025)).

7. Significance and Research Context

AdaSMSet (as the Adaptive Scene Manager Dataset) establishes a new paradigm for explicit orchestration supervision in multi-agent LLM systems. By densely annotating high-level managerial actions within dialogic narratives, it operationalizes meta-narrative control, yielding empirically validated improvements in scene management, character introduction, speaker selection, and overall simulation coherence.

As a term of art in additive combinatorics, AdaSMSet provides the first non-filling-in solution to the Alexander sequence problem: constructing infinite chains of nested sets with strictly alternating MSTD and MDTS status, each preserving prior “gaps.” The construction has further applications in other algebraic contexts such as finite fields.

Both usages of AdaSMSet represent substantial progress in their respective domains: explicit supervisory datasets for adaptive multi-character LLM narratives (Xu et al., 16 Jan 2026), and combinatorial structural constructions in sumset/difference set theory (Herrmann et al., 16 Sep 2025).