GLIDE: Generalized Layer-wise Intrinsic Distributional Evaluation for Heterogeneous LLM Agents

1 Introduction

• Because a locally plausible but unhelpful step can redirect sequential reasoning, reliable branch comparison is central to allocating search computation.Inaccurate or poorly calibrated signals may repeatedly favor misleading trajectories.Source: §1 · p. 1
• Heterogeneous agents can assign incompatible confidence scales to comparable candidates, making raw scores unreliable for cross-agent comparison.External evaluators can provide a shared scoring basis but are costly at every candidate step.Source: §1 · p. 2
• Useful steps tend to show stable alignment between local layer updates and the global update induced by the step, unlike failure-specific transitions.This coherence is proposed as intrinsic step-level evidence computable from the generator’s forward pass without task-specific supervision or judge calls.Source: §1 · p. 2
• GLIDE calibrates intrinsic layer-wise residual-coherence evidence against each agent’s recent score distribution and converts it into a cross-agent reward for MCTS.The reward combines absolute residual evidence with agent-relative standing and supports adaptive branching using predictive uncertainty.Source: §1 · p. 2
• Experiments show that GLIDE improves performance-cost trade-offs and step-level preference quality.Source: §1 · p. 2

2 Related Work

• Search and planning systems still require reliable value estimation, while judge-based scoring costs inference and heterogeneous agents have non-comparable score scales.This motivates intrinsic, calibrated search-control signals that do not use external verifiers.Source: §2 · p. 2
• Process reward models provide dense step-level feedback but require task-specific data, additional training, and inference.Source: §2 · p. 2
• Token-level intrinsic scores avoid some verifier costs but mainly reflect local confidence, while hidden-state methods often target full-chain analysis or local smoothness rather than online heterogeneous step ranking.These limitations motivate a supervision-free intrinsic signal tailored to step-wise heterogeneous search.Source: §2 · p. 3

3.1 Layer-wise Intrinsic Stability Evaluation

• Layer-wise residual coherence measures whether local updates support a candidate step’s global residual change, with high ISLE scores also requiring sufficient token-level decisiveness.The decisiveness gate downweights diffuse predictive distributions; Figure 2 shows successful transitions concentrated in high-coherence, high-decisiveness regions, while failed-only transitions are more diffuse.Source: §3.1 · pp. 3–4, Figure 2 · p. 4

3.2 Distributional Calibration for Heterogeneous Agents

• GLIDE rank-normalizes each step’s ISLE score within the generating agent’s recent score window, then harmonically combines that standing with the raw score to preserve absolute evidence.The pessimistic fusion gives high reward only when both intrinsic evidence and agent-relative standing are strong.Source: §3.2 · p. 5

3 GLIDE: Generalized Layer-wise Intrinsic Distributional Evaluation

• GLIDE combines intrinsic layer-wise evidence with agent-wise distributional calibration to provide a pessimistic cross-agent reward for MCTS value estimation and adaptive branching.The reward requires both strong intrinsic evidence and high standing within the generating agent’s recent score distribution.Source: §3 · p. 3, §3.2 · p. 5

3.3 Adaptive Branching with Calibrated Rewards

• GLIDE uses calibrated reward as the MCTS transition value and couples agent-relative predictive uncertainty with reward saturation to set successor branching width.The rule favors uncertain, insufficiently supported successors while suppressing redundant expansion near high-reward regions; generators are sampled uniformly to preserve diversity without a learned router.Source: §3.3 · pp. 5–6

4.1 Experimental Settings

• Experiments average performance over three runs and use a heterogeneous open-source pool of Qwen2.5-7B-Instruct-1M, Mistral-7B-Instruct-v0.3, and Llama-3.1-8B-Instruct.GLIDE uses a calibration window of 50 and branching bounds of 1 to 4, matching SYMPHONY-S’s maximum fixed expansion width.Source: §4.1 · p. 6

4.3 Preference Quality of Calibrated Rewards

• RGLIDE achieves the strongest overall ranking quality against intrinsic metrics, hidden-state baselines, PRMs, and heterogeneous judges, without task-specific supervision or additional verifier calls.Its gains over raw or uncalibrated signals indicate that distributional calibration makes SISLE a more reliable heterogeneous candidate-comparison signal.Source: Table 4 · p. 7, §4.3 · p. 7

4.4 Controlled Comparison and Ablation Study

• Across single-agent, dual-agent, and full heterogeneous pools, GLIDE improves task performance and token efficiency; adding agents alone is insufficient without calibrated score alignment.Ablations find that raw SISLE weakens performance, removing adaptive branching reduces the benefit of uncertainty-aware allocation, and calibration alone is insufficient when the signal comes from external judgment.Source: Table 5 · p. 7, §4.4 · p. 8, Table 6 · p. 8

4.2 Main Results

• GLIDE consistently improves over SYMPHONY-S with the same heterogeneous agent configuration, across multi-hop reasoning, long-horizon interaction, and symbolic arithmetic.The results attribute the gains to candidate evaluation and computation allocation rather than a stronger model pool; GLIDE also remains competitive with broader task-specific baselines using lightweight intrinsic evaluation.Source: §4.2 · pp. 6–7

4.5 Cross-Task Outcome Separability

• SISLE maintains clear separation between successful and failed generations across MGSM, GPQA, and HumanEval, complementing its role in calibrated agent control.The evaluation reports average AUROC, FPR95, and AUPR across tasks and models; higher AUROC/AUPR and lower FPR95 indicate stronger separation.Source: Figure 4 · p. 8, §4.5 · p. 8

• GLIDE transforms layer-wise residual coherence into a cross-agent calibrated reward for heterogeneous LLM-agent search, enabling verifier-free value estimation and adaptive branching.The conclusion reports improved task performance and step-level preference quality with low overhead.Source: §5 · p. 8

Limitations

• GLIDE requires hidden-state access, which may be unavailable for closed-source models, and its calibration targets repeatedly contributing heterogeneous model pools rather than single black-box deployments.Future work should study approximations using partial traces or API-level confidence signals.Source: Limitations · p. 9

A Algorithm Pseudocode

• Algorithm 1 presents the pseudocode for the GLIDE framework.Source: A Algorithm Pseudocode · p. 12

B.1 Markov Decision Processes and LLM Agents

• The MDP formulation represents sequential decision making with states, actions, transition dynamics, rewards, and a discount factor; LLM agents can act as policies, value functions, or world models.LLM agents use language-based state representations and can operate in open-ended environments with minimal task-specific engineering.Source: §B.1 · p. 12

B.2 Monte Carlo Tree Search (MCTS)

• MCTS builds a partial search tree and balances exploration with exploitation through selection, expansion, simulation, and backpropagation.Rollouts estimate a newly expanded node’s potential value, though recent LLM reasoning frameworks sometimes substitute a learned value function or heuristic.Source: §B.2 · pp. 12–13

C.2 Analysis of Assumption 1

• Under Assumption 1, layer-wise residual updates lie near a shared low-dimensional subspace and can accumulate through a stable dominant component.The two implications yield an approximate low-rank bound and a positive local-to-global coherence margin.Source: §C.2 · p. 13, §C.2.1 · p. 14, §C.2.2 · p. 15

C.2.1 Low-dimensional residual subspace

• With bounded perturbations around a shared residual subspace, the layer-wise update matrix remains close to low rank.In the noiseless case, its rank is at most k.Source: §C.2.1 · p. 14

C.2.2 Positive local-to-global coherence margin

• When a stable residual component dominates perturbations, local updates have positive average agreement with the global update, supporting Φcoh and SISLE.The analysis also invokes the decisiveness gate Φdec in the SISLE stability score.Source: §C.2.2 · pp. 14–15

C.3 Proof of Proposition 1

• Within one agent and search state, the probability that SISLE reverses the ordering of two candidate steps decreases exponentially with their latent utility gap.The proposition assumes an order-preserving noisy surrogate with mean-zero sub-Gaussian noise.Source: §C.4 · pp. 15–16, §C.3 · p. 15

D.1 Infrastructure and Model Configuration

• The main experiments use Qwen2.5-7B-Instruct-1M, Mistral-7B-Instruct-v0.3, and Llama-3.1-8B-Instruct on a local server with three RTX 4090 GPUs.The same model pool is used for GLIDE and reproduced SYMPHONY-S.Source: §D.1 · p. 16, D Main Experimental Details · p. 16

D.2 MCTS and GLIDE Hyperparameters

• Across HotpotQA, WebShop, and Game of 24, MCTS uses K = 10 iterations; GLIDE uses 50-item score and entropy windows and branching bounds nmin = 1, nmax = 4.The maximum width matches SYMPHONY’s fixed expansion width; generation uses temperature 0.2, top-p = 0.9, and a 200-token step limit.Source: §D.2 · p. 16

D.3 Task-Specific Prompting and Settings

• Task prompts use 3-shot Chain-of-Thought for HotpotQA, 1-shot interaction examples for WebShop, and 2-shot atomic arithmetic steps for Game of 24.The Game of 24 prompt specifies explicit state transitions for MCTS expansion.Source: §D.3 · p. 16

D.4 Main Benchmark Baselines

• The baseline suite spans prompting, feedback-driven reasoning, structured search, MCTS agents, multi-agent frameworks, and WebShop-specific supervised or task-native methods.SYMPHONY-S is the primary controlled baseline because it shares GLIDE’s open-weight model pool and has comparable search budget.Source: §D.4 · pp. 16–17

E.1 Test-Time Compute Scaling

• At K = 10, GLIDE improves over SYMPHONY-S while using fewer tokens than SYMPHONY-L; at K = 50, it outperforms ToT, RAP, and LATS while using far fewer tokens.The comparison reports Exact Match, expanded nodes, and token consumption per question.Source: Table 7 · p. 17, §E.1 · p. 19

E.2.1 Search Budget and Adaptive Branching

• GLIDE adapts branching within nmin = 1 and nmax = 4, so its maximum width matches SYMPHONY while average width can be lower.Branching is adjusted using predictive uncertainty and calibrated reward saturation; Figure 5(a) reports generally stable performance across bounds, with moderate gains for a slightly larger search space.Source: Figure 5 · p. 18, §E.2.1 · p. 19

E.2.2 Calibration Horizon and Stability

• The agent-specific calibration windows are online profiles that adapt to score and entropy shifts during inference rather than relying on held-out-set statistics.Figure 5(b) indicates a broad performance plateau around |W| = 50 and a stable trade-off between sensitivity and robustness.Source: Figure 5 · p. 18, §E.2.2 · pp. 19–20

E.3 MCTS Evaluation Baselines under Fixed Search

• GLIDE achieves the best performance across HotpotQA, WebShop, and Game of 24 under the same fixed MCTS framework.Table 8 compares probability-based, hidden-state, uncalibrated intrinsic, heterogeneous-agent, and process-reward evaluation baselines.Source: Table 8 · p. 20, §E.3 · p. 20, §E.4.1 · p. 21

E.4.1 Scoring Baselines

• GLIDE’s calibrated reward is computed from the generation pass and requires neither task-specific process supervision nor additional verifier forward passes.The fixed-search comparison includes probability-based metrics, hidden-state metrics, and process reward models such as GenPRM-7B.Source: §E.4.1 · pp. 20–21, §E.3 · p. 20

E.4.2 Ranking Metrics

• P@1, MRR, and NDCG@3 evaluate step-level preferences by whether successful child nodes rank highly among expanded children.P@1 checks the top-ranked child, MRR tracks the first successful child’s rank, and NDCG@3 measures the quality of the top three.Source: §E.4.2 · p. 21
• Inference latency and peak GPU memory quantify the efficiency of each scoring method.Source: §E.4.2 · p. 21

E.5 Failure Case Analysis

• Internally coherent steps can receive high SISLE scores despite violating external task constraints, because intrinsic coherence does not directly verify grounding or task-specific requirements.MCTS may recover if later observations expose the mismatch, but recovery is not guaranteed when the branch remains plausible or the search budget is limited.Source: §E.5 · pp. 21–22
• The WebShop example’s clicked “Smoked Bacon Sea Salt 3-Pack” matches salient wording but is seasoning rather than a vegetarian bacon substitute.Source: §E.5 · pp. 21–22

F Cross-Task Outcome Separability

• The auxiliary outcome-separability analysis uses one direct generation per input, without search traces, tree expansion, or adaptive branching.It tests whether SISLE remains associated with final outcomes outside the main MCTS control pipeline.Source: F Cross-Task Outcome Separability · p. 22

F.1 Datasets and Models

• The analysis covers 11-language MGSM averages, GPQA Diamond, and HumanEval, using open-source models from multiple model families and scales.Decoding is greedy with bounded output lengths; HumanEval receives a larger token budget for full Python implementations.Source: §F.1 · p. 22, §F.2 · p. 22

F.3 Outcome-Separability Results

• The evaluation scores complete generated solutions labeled by final task outcome, using AUROC, AUPR, and FPR95 to measure separation.Higher AUROC/AUPR and lower FPR95 indicate stronger separation.Source: §F.3 · p. 23

F.4 Layer-Subset Analysis

• Partial layer subsets retain useful residual-coherence signals and remain competitive with several scoring baselines, while all layers remain the default under the cumulative residual-stream assumption.The analysis compares First 50%, Last 50%, Odd, and Even layer subsets on MGSM while holding outputs and labels fixed.Source: §F.4 · p. 23

F.5 Memory Overhead of Hidden-State Scoring

• GLIDE computes hidden-state scores during generation, discards the states immediately, and stores only scalar scores in the search tree.On GPQA Diamond, Table 11 reports negligible additional peak memory across models from 8B to 70B.Source: §F.5 · pp. 23–24, Table 11 · p. 24

F.3 Outcome-Separability Results

• Across datasets and model families, SISLE consistently separates successful from failed generations, supporting outcome relevance beyond the main MCTS control pipeline.Table 10 reports AUROC/AUPR/FPR95; MGSM results average 11 language versions.Source: §F.3 · p. 23, Table 10 · p. 24

G Use of AI Assistants

• AI assistants helped with language editing and writing refinement; the authors state that they verified the technical content, results, and scientific claims.Source: G Use of AI Assistants · p. 24

H.1 Model Artifacts

• The evaluated model artifacts came from public releases or repositories, were used under their licenses and terms, and were not redistributed as modified checkpoints.The paper identifies configuration details in Sections F.1, E.4.1, and 4.1.Source: §H.1 · p. 24

H.2 Data Artifacts

• The evaluation uses HotpotQA, WebShop, Game of 24, MGSM, GPQA, and HumanEval for non-commercial research under the benchmarks’ terms and licenses.Source: §H.2 · p. 24
• Figures 6–10 and Figure 10 compare scoring methods’ successful-versus-failed outcome separation across 11 MGSM language versions, with higher AUROC/AUPR and lower FPR95 indicating better separation.Source: Figure 6 · p. 25, Figure 7 · p. 26, Figure 8 · p. 27
• Figures 11–15 show MGSM layer-subset analyses for Mistral, Gemma, Phi, InternLM2, and Qwen models.Source: Figure 11 · p. 30, Figure 12 · p. 30, Figure 13 · p. 30
• Task-specific prompt templates standardize answer extraction across mathematical reasoning, scientific multiple-choice reasoning, and code generation.Source: Figure 16 · p. 31