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StartLux-Decision: AutoThink Decision Models with Reinforcement Learning for Calibrated Deliberative Decisions

Xialie Zhuang, Zunhai Su, Jia Pan, Ngai Wong, Guanhua Chen, Chuan-Wei Kuo

arXiv:2610.17309v2cs.CLcs.AI

TL;DR

Open-weight decision models largely rely on single-pass prediction without explicit reasoning, while computational decisions can require more deliberation. StartLux-Decision pairs efficient Instant models with confidence-guided AutoThink reasoning; on the public subset of Decision Index 0.3, Instant models outperform the strongest evaluated comparable-scale open-weight decision models by 7.4–16.9 points.

  • Problem

    Existing open-weight decision models largely rely on single-pass prediction without explicit reasoning, while decision probabilities can guide downstream systems to act, invoke a stronger model, or defer to human review.

    Source: §1 · p. 4

  • Method

    StartLux-Decision pairs single-pass Instant models with confidence-guided AutoThink reasoning, trained in three stages; RLCD2 rewards probabilistic decision-quality gains and softly penalizes long reasoning traces.

    Source: §1 · p. 4

  • Results

    On the public subset of Decision Index 0.3, Instant models outperform the strongest evaluated comparable-scale open-weight decision models by 7.4–16.9 points.

    Source: §1 · p. 4

  • Takeaways & Limitations

    The model family combines efficient single-pass prediction with adaptive reasoning through a unified probability interface and supports deployment with vLLM, llama.cpp, and MLX.

    Source: §7 · p. 26

    Adaptive reasoning adds generation cost for routed decisions; at the default threshold, the 4B, 9B, and 27B models reason on approximately 33%, 29%, and 28% of Decision Index questions, respectively.

    Source: §5.2 · p. 20

Abstract

from arXiv · show

We introduce StartLux-Decision, decision models from 0.8B to 27B parameters that combine efficient single-pass prediction with adaptive, confidence-guided reasoning. The Instant models use bidirectional attention in full-attention layers to improve decision accuracy while keeping single-pass inference. The AutoThink models invoke explicit reasoning for uncertain decisions and answer confident cases directly. A three-stage training pipeline establishes shared decision capabilities, specializes the two variants, and equips AutoThink with reasoning through reasoning supervision and reinforcement learning. We introduce Reinforcement Learning for Calibrated Deliberative Decisions (RLCD$^2$), which uses a frozen model and proper scoring rules to reward improvements in decision probability quality and applies a soft penalty to overlong reasoning traces. RLCD$^2$ raises the share of reasoning traces that terminate within the generation limit by up to 48 percentage points and cuts average reasoning length by up to 65%, while largely preserving decision accuracy. On the public subset of Decision Index 0.3, the Instant models outperform the strongest evaluated comparable-scale open-weight decision models by 7.4-16.9 points, and the 27B AutoThink model reaches 73.4. We also introduce DecisionPivot, a programmatically verifiable benchmark of computational decisions built from contrast pairs that differ in a single answer-changing detail. On DecisionPivot, AutoThink outperforms its Instant counterparts by 11.5-18.4 points in pair accuracy and leads among evaluated systems. The models can be run using frameworks such as vLLM and MLX, with quantized versions available to reduce memory usage.Inference code and links to model weights are available at https://github.com/StartLuxLabs/Startlux-Decision .

1. Introduction

StartLux-Decision combines efficient single-pass prediction with confidence-guided reasoning through a shared probabilistic interface. The paper also introduces methods for improving reasoning efficiency and calibrating probabilities under downstream selection policies, and evaluates the models on established and new decision benchmarks.

Motivation

  • Decision-making systems use probability distributions to support choices such as acting autonomously, invoking a stronger model, or deferring to human review, but single-pass models can struggle with computation-intensive decisions.The paper identifies arithmetic, scheduling, and procedural verification as examples where multi-step reasoning may be essential, and notes that decision-oriented training can impair reliable reasoning-trace generation and termination.Source: §1 · p. 4

Model design and training

  • AutoThink uses explicit reasoning for uncertain decisions and answers confident cases directly, while Instant uses bidirectional attention in full-attention layers for accurate single-pass prediction.A three-stage training pipeline establishes shared decision capabilities, specializes the variants, and equips AutoThink with reasoning supervision and reinforcement learning; both share a probability interface.Source: §1 · p. 4

Reasoning reinforcement learning

  • RLCD2 increases reasoning traces terminating within the generation limit by up to 48 percentage points and reduces average reasoning length by up to 65%, while largely preserving decision accuracy.It rewards changes in decision probability quality using proper-score differences from a frozen starting model’s pre- and post-reasoning readouts, with a soft penalty for long traces.Source: §1 · p. 4

Benchmark results

  • On Decision Index 0.3, Instant models beat the strongest evaluated comparable-scale open-weight decision models by 7.4–16.9 points; on DecisionPivot, AutoThink beats Instant counterparts by 11.5–18.4 percentage points in pair accuracy.The 4B Instant model surpasses all evaluated reference decision models on Decision Index 0.3; the 27B AutoThink model reaches 86.9% and leads evaluated reference systems on DecisionPivot, whose contrast pairs differ in one answer-changing detail.Source: §1 · p. 4

Policy-aware calibration

  • Policy-aware calibration reduces confidence–accuracy gaps to within 2.7 percentage points across 184 settings spanning four decision pipelines.For the 9B verifier, predictions assigned 80–90% confidence are 92% accurate individually but only 78% accurate after selecting the highest-scoring response from 32 candidates.Source: §1 · p. 4

Deployment and release

  • The models support vLLM, llama.cpp, and MLX, with quantized variants to reduce memory requirements; the authors publicly release weights and inference code.The release is intended to enable independent evaluation, practical deployment, and further research.Source: §1 · pp. 4–5

2. Model Design and Training

StartLux-Decision pairs single-pass Instant prediction with confidence-guided AutoThink reasoning, using a three-stage pipeline to establish shared decision capabilities, specialize the variants, and train AutoThink to reason efficiently.

2.1 Decision Formulation and Probability Readout

  • Each typed decision question yields a probability distribution over named options, binary choices, or ordered-scale levels, serving as both prediction and confidence estimate.The shared option-letter readout extracts logits at the final prompt position without adding a prediction head; it supports up to 26 options, grouping longer lists for processing.Source: §2.1 · p. 5, §2.2 · p. 5

2.2 Model Variants and Adaptive Inference

  • Across 7,800 core DecisionPivot items, 27B AutoThink answered 39% directly and improved accuracy from 57% to 93% on reasoning-invoked cases.The confidence gate is applied independently per question; confident cases use the initial prediction, while uncertain cases invoke reasoning and fuse initial and post-reasoning probabilities.Source: §2.2 · p. 6, Figure 3 · p. 7

2.3.1 Stage 1: Full-Parameter SFT

  • Stage 1 uses full-parameter supervised fine-tuning on Lux-Release to establish shared decision capabilities.The mixture contains approximately 2.7 million examples for models from 0.8B to 9B parameters and approximately 0.8 million for 27B; soft cross-entropy trains option probabilities, followed by held-out temperature calibration.Source: §2.3.1 · pp. 7–8

2.3.2 Stage 2: Adapter-Based Decision Training

  • Stage 2 trains adapters on Lux-Rounds to broaden task coverage, then merges them into Stage 1 weights; Instant uses bidirectional full-attention layers, while AutoThink retains causal attention.The 1.7-million-example mixture includes benchmark and breadth data, verified API-generated examples, and retained Lux-Release examples; Instant’s modified attention is trained rather than applied only at inference.Source: §2.3.2 · pp. 8–9
  • Bidirectional attention improved DI 0.3 performance at four of five evaluated scales, with gains up to 2.4 points in controlled comparisons.The comparisons used identical training data and the same Stage 1 checkpoint; linear-attention layers remained causal.Source: Figure 4 · p. 9, §2.3.2 · p. 9

2.3.3 Stage 3: Reasoning Supervision and RL

  • Stage 3 adds reasoning supervision and RL to causal AutoThink models while preserving single-pass prediction; RLCD2 rewards reasoning-induced probability improvements and softly penalizes overlong traces.Decision-trained models can fail to generate or terminate reasoning reliably; supervision improves post-reasoning accuracy, while RLCD2 further improves efficiency while largely preserving decision accuracy.Source: §2.3.3 · p. 9

3. RLCD2: Reinforcement Learning for Calibrated Deliberative Decisions

RLCD2 rewards improvements in probabilistic decision quality after reasoning while softly penalizing excessive trace length. It improves reasoning efficiency while largely preserving held-out accuracy, with trade-offs that depend on model scale and reasoning budget.

3.1 Scoring Foundations and Reward Formulation

  • RLCD2 rewards the change in decision-weighted proper-score quality after reasoning, measured by a frozen model, and applies a soft penalty beyond a reasoning-length budget.The length penalty discourages excessive computation without hard truncation; λ = 10^-4 controls the penalty per token beyond the budget. The weighting function mixes uniform and Beta(8, 2) densities, emphasizing high-confidence decisions while preserving a proper score.Source: §3 · p. 10, §3.1 · p. 10

3.2 Policy Optimization and Training

  • Training applies group-relative policy gradients to sampled reasoning traces, restricting updates to questions whose maximum initial option probability is below 0.9.A frozen copy of the reasoning-supervised model supplies both probability readouts; traces of eight tokens or fewer count as empty and receive zero reward. Rewards are centered within each prompt’s sampled group, advantages are clipped to [-5, 5], and are not normalized by within-group standard deviation.Source: §3.2 · p. 11

3.3 Effects on Reasoning and Decision Quality

  • At 9B, termination rises from 45.9% to 93.9% and mean trace length falls from 2,494 to 868 tokens, a 65% reduction.At 4B, termination increases from 89.5% to 99.3%, mean trace length falls 37%, and the 90th percentile falls from 4,096 to 1,358 tokens; 27B already terminates 97.2% of traces at a mean of 313 tokens. Held-out default-answer accuracy remains largely unchanged; at 4B, raw post-reasoning calibration error falls from 9.0 to 8.1 percentage points, while temperature-scaled errors are 3.1 and 3.2 points. On DecisionPivot, 9B pair accuracy rises from 53.3% to 59.9%.Source: Table 2 · p. 11, §3.3 · p. 12, Figure 5 · p. 12

3.4 Reward Design and Reasoning Budget

  • At 4B, DecisionPivot pair accuracy is 52.9% with a 512-token budget, 59.2% at 2,048 tokens, and 59.9% at 3,072 tokens.The 3,072-token budget differs from the pre-RL checkpoint by -0.4 points (interval [-1.8, +0.8]); removing the penalty raises pair accuracy to 61.7% but makes traces 40% longer, with about one third failing to terminate. Budgets of 512–3,072 tokens achieve approximately 99% termination, while held-out accuracy changes by at most 0.6 points.Source: §3.4 · p. 12, Table 3 · p. 13
  • At 4B, a 2,048-token budget improves DecisionPivot accuracy by 2.5 points on examples with pre-RL traces under 512 tokens but lowers it by 5.9 points for traces of 2,048–4,095 tokens.At 3,072 tokens, the loss in that longer-trace group is 4.2 points. At 9B, accuracy improves 7.3 points on previously unterminated traces, which make up 54% of examples, while 27B shows no statistically clear changes; the released models use a 3,072-token training budget. Controlled comparisons find that the length penalty drives termination, whereas proper-score rewards contribute to calibration improvements over accuracy-only rewards.Source: §3.4 · pp. 13–14, Figure 6 · p. 13

4. Experimental Evaluation

Across Decision Index and DecisionPivot, Instant models lead comparable-scale references on DI 0.3, while AutoThink improves contrast-pair accuracy, especially at 27B; StartLux-Decision models also show lower calibration errors than evaluated references.

4.1 Experimental Setup

  • DI public-subset scores are model-selection and development results, whereas DecisionPivot was excluded from data, checkpoint, and configuration choices and provides the independent evaluation.DI 0.3’s public subset accounts for 20% of its leaderboard score; this evaluation covers that subset, with most tasks belonging to families represented during training.Source: §4.1 · p. 15, §4 · p. 15

4.2 Decision Index

  • On Knowledge & Reasoning, 4B and 9B AutoThink outperform their Instant counterparts by 7.0 and 6.2 points, while 27B Instant outperforms all references across the five DI domains.The 4B and 9B Instant models lead in four of the five domains.Source: §4.2 · pp. 15–16, Figure 8 · p. 16

4.3 DecisionPivot

  • DecisionPivot’s core track has 13 generated task families with 600 examples each, predominantly contrast pairs differing in one answer-changing detail; pair accuracy requires both answers to be correct.Its separate reused-tasks reference track covers 34,104 examples absent from training.Source: §4.3 · p. 16
  • At the 0.9 confidence threshold, 27B AutoThink reaches 86.9% DecisionPivot pair accuracy, above all evaluated references including GLM-5.3 (82.2%).AutoThink gains 18.4, 12.4, and 11.5 points over Instant at 4B, 9B, and 27B, respectively.Source: §4.3 · p. 16, Figure 9 · p. 17
  • On filtering, goal-state verification, and schedule-conflict tasks, 4B and 9B AutoThink improve pair accuracy over Instant by approximately 51 and 56, 30 and 44, and 46 and 25 points, respectively.Single-pass prediction remains effective for policy interpretation, clause changes, and dependency resolution.Source: §4.3 · p. 16, Figure 10 · p. 17

4.4 Probability Calibration

  • On DecisionPivot, AutoThink calibration errors are 2.4, 3.3, and 5.2 percentage points at 4B, 9B, and 27B, versus 7.3, 6.4, and 5.1 for Instant.Perplexity Decider v1.1, hosted Jev, and Clef have calibration errors of 8.9, 13.8, and 19.3 points, respectively, with systematic overconfidence; 27B AutoThink is the only StartLux-Decision model underconfident on average.Source: Figure 11 · p. 18, §4.4 · p. 18

5. Capability and Reliability Analysis

The analysis examines how training choices, adaptive reasoning, and downstream selection affect decision performance and probability reliability. It finds that task-family exposure, reasoning, and policy-aware calibration each shape outcomes, with calibration depending on the deployed policy and evaluation distribution.

5.1 Effects of Training Data and Attention Design

  • Training-data gains concentrate in represented task families: added Stage 2 data improves 18 corresponding DecisionPivot tasks by 8.6 points versus 0.3 on outside-family tasks, while bidirectional attention adds 3.0 points on 16 tasks absent from a narrower mixture.Related training families raise 4B accuracy on generated answerable-fact decisions from 61.5% to 75.8%; across evaluated data groups, there is no clear improvement outside their respective coverage.Source: §5.1 · pp. 18–19

5.2 Adaptive Reasoning and Prediction Fusion

  • AutoThink exceeds Instant on computation-intensive tasks, including by 26 accuracy points on reconstructed GSM8K at 4B and by 13.6 points at 27B, while raising overall DI 0.3 by 0.5 points at 9B and 27B.At 4B, AutoThink also leads by 22 points on CRUXEval, 10 on GPQA Diamond, and 11 on MMLU-Pro; at 27B, it leads by 19, 10, and 9 points on those tasks, respectively. At the default threshold, 9B and 27B gain 1.0 and 2.5 accuracy points on held-out training-distribution examples, using 596 and 273 reasoning tokens per example; always reasoning gives no further gain. On DecisionPivot, 9B reaches 59.9% pair accuracy with 1,365 tokens versus 22.3% without reasoning; 27B reaches 86.9% with 304 tokens versus 48.0%. RLCD2 raises 9B pair accuracy from 53.3% to 59.9% while reducing tokens by 40%; at 4B tokens decrease 25% with pair accuracy changing by less than 0.5 points. Reasoning on Decision Index is invoked for approximately 33%, 29%, and 28% of 4B, 9B, and 27B questions, averaging 372, 271, and 110 tokens per question; Instant avoids autoregressive generation.Source: §5.2 · pp. 19–20
  • At 27B, weighting post-reasoning probabilities at 75% reduces held-out calibration error from 3.7 to 1.6 points with little accuracy change, but increases Decision Index calibration error by 0.8–2.0 points versus equal weighting.The 75%–25% fusion weight is selected using held-out Brier score; on DecisionPivot, 9B pair accuracy is 56.6% with equal weights, 59.9% at 75% post-reasoning weight, and 61.5% with post-reasoning probabilities alone. Under the default policy, calibration errors for default answers at 4B, 9B, and 27B are 3.7, 2.2, and 1.6 points; approximately half of 9B and 27B default predictions can be accepted at a 5% target error rate, versus 2% at 4B.Source: §5.2 · p. 20, §5.5 · p. 23

5.3 Evidence Sensitivity and Probability Consistency

  • Removing supporting evidence lowers the supported answer’s probability in 90–97% of cases, with mean decreases of 0.29–0.61, while irrelevant perturbations change it by less than 0.015 on average.Probability consistency generally improves with scale: mean deviation from a summed affirmative probability of one falls from 0.25 for 0.8B Instant to 0.04 for 27B Instant; AutoThink is comparable at 4B and 27B and lower at 9B.Source: §5.3 · p. 21

5.5 Policy-Aware Calibration

  • Policy-aware calibration narrows signed confidence–accuracy gaps from [−11.7, +20.5] to [−2.7, +2.1] percentage points across 184 settings, but transfer to unseen datasets leaves overconfidence up to 6.1 points.Mean absolute gaps decrease across best-of-N, think-gate, cascade, and select-then-think pipelines. Calibration maps use returned predictions and policy information; maps are fit within routing-confidence strata or with candidate scores, count, and log count.Source: Figure 15 · p. 22, §5.5 · pp. 22–23

5.4 Policy-Induced Miscalibration

  • Selection and routing can undermine calibration: after individual-response calibration, selected responses are overconfident in 111 of 113 pairs at N = 16, and individual thresholds exceed a 5% target error in 44 of 67 best-of-16 pairs.The calibration-gap increase with candidate count occurs in all 126 evaluated runs; think-gate routing is associated with lower accuracy at matched confidence for 11 of 12 models. No threshold violations occur when thresholds are certified on policy-selected responses.Source: §5.4 · pp. 21–22

6. Efficient Inference and Deployment

StartLux-Decision supports multiple inference backends and precision formats, with reported tradeoffs in serving latency, local deployability, and decision performance. The evaluations cover single-readout and matched single-pass latency, plus AutoThink end-to-end latency when reasoning is invoked.

6.1 Runtime Support

  • Instant and AutoThink run on vLLM, llama.cpp with GGUF, and MLX, with backend-specific bidirectional-attention support and high top-choice agreement with reference implementations.Supported formats include BF16 across all three backends, FP8 on vLLM, Q8_0 and Q4_K_M on llama.cpp, and 8-bit and 4-bit MLX builds; top-choice agreement does not imply numerical agreement between predicted probabilities.Source: §6.1 · p. 23

6.2 GPU Serving Performance

  • At comparable scales, Instant achieves substantially higher DI 0.3 scores while staying within 3 ms of the fastest reference at 4B and 9B, and about 6 ms at 27B.The comparison covers 186 of 300 requests processed in one forward pass; after prompt-length weighting, they represent approximately 91% of the DI request distribution.Source: Table 6 · p. 24, §6.2 · p. 24
  • BF16 Instant readouts take 24–52 ms for 256-token prompts and 31–98 ms for 1,024-token prompts; FP8 cuts 8,192-token latency by approximately 25–30% for 9B and 27B.At 1,024 tokens, BF16 and FP8 Instant readouts have approximately 2–8% higher latency than causal AutoThink readouts, rising to 6–14% at 8,192 tokens. AutoThink end-to-end latency includes reasoning generation and post-reasoning readout when reasoning is invoked.Source: §6 · p. 23, §6.2 · p. 24
  • On llama.cpp with GGUF Q8_0, 4B Instant has the lowest median latency among comparable-scale references, while 9B is within 3 ms of the fastest.At 2B and 27B, median latency is approximately 5 ms and 14 ms higher than d1-3B and Kev 27B, respectively; at 0.8B, Instant matches Bosun 3.1 1.7B in median latency.Source: §6.2 · pp. 24–25, Table 7 · p. 25

6.3 Local Inference on Apple Silicon

  • On an Apple M5 Pro with 64 GB of unified memory, 1,024-token BF16 Instant readouts range from 59 ms at 0.8B to approximately 1.1 s at 9B; 8-bit and 4-bit quantization enable local 27B deployment.The 27B models exceed the available memory in BF16.Source: §6.3 · p. 25, Table 8 · p. 26

6.4 Quantized Inference

  • FP8 and Q8_0 largely preserve BF16 decision performance, while Q4_K_M loses up to 4.3 points for 27B AutoThink on DecisionPivot.MLX 8-bit builds achieve 99.5–99.6% top-choice agreement with the vLLM BF16 reference, compared with 96.3–97.5% for 4-bit builds.Source: §6.4 · p. 25, Table 9 · p. 26

7. Conclusion · Appendix A. Data Sources · A.1 Record Format

StartLux-Decision combines single-pass prediction, confidence-guided reasoning, and calibrated confidence, with evaluations showing strong decision performance. The conclusion also describes deployment support and identifies generalization and reliability under distribution shift as future work.

7. Conclusion

  • RLCD2 improves reasoning termination and efficiency through proper-score rewards and a soft length penalty while largely preserving held-out decision accuracy.Source: §7 · p. 26
  • Evaluations on Decision Index and DecisionPivot demonstrate strong decision performance, while policy-aware calibration mitigates reliability distortions induced by selection and routing.Source: §7 · p. 26
  • The unified probability interface combines efficient single-pass prediction with confidence-guided reasoning; vLLM, llama.cpp, and MLX support GPU and local deployment.Future work will focus on generalization beyond represented task families and robust probability reliability under distribution shift.Source: §7 · p. 26

Appendix A. Data Sources

  • Appendix A documents the training mixtures, label provenance, and data integrity checks for the training pipeline.Source: Appendix A · p. 29

A.1 Record Format

  • Each training record encodes a typed decision with candidate options, target probabilities, label provenance, and a parent-group identifier; records from the same state share a group for splitting and decontamination.Source: §A.1 · p. 29
  • Overlength records are excluded rather than truncated, and a record-level hash deterministically permutes option order to reduce positional shortcuts.Source: §A.1 · p. 29

A.2 Data Composition Across Training Stages · A.3 Benchmark-Specific Training Coverage

Training data scales and sources vary across the three stages, while benchmark-specific Stage 2 training uses benchmark training splits without using evaluation items. The appendices also specify Lux-Release label provenance and summarize benchmark-specific coverage.

A.2 Data Composition Across Training Stages

  • Lux-Release contains approximately 2.7 million records for 0.8B–9B models and 0.8 million for 27B, with the 27B mixture emphasizing benchmark training splits and knowledge-oriented multiple-choice questions.Its sources include public and community decision datasets, generated examples, knowledge and commonsense questions, and smaller tool-use, safety, and challenging-decision collections.Source: §A.2 · p. 29, Table A.1 · p. 29
  • Table A.1 identifies label provenance as human annotation or source gold label (H), model-generated or model-assigned label (T), or programmatically computed label (P).It summarizes Lux-Release composition and label provenance across model scales.Source: Table A.1 · p. 29
  • Lux-Rounds, used in Stage 2, contains approximately 1.7 million records from benchmark training splits, related public datasets, and additional decision families.Other sources include generated and model-written examples, select-all questions, teacher-labeled decisions, a Lux-Release subset, and reconstructed GSM8K training problems.Source: §A.2 · p. 29
  • Lux-Think supplies approximately 4,000–21,000 supervised reasoning examples per model for Stage 3.The passage points to Section 2.3 for further detail.Source: §A.2 · p. 29

A.3 Benchmark-Specific Training Coverage

  • Table A.2 summarizes task-related Stage 2 training sources for Decision Index 0.2.1 benchmarks in the preview-model mixture.The T marker denotes a benchmark’s official training split, separate from its evaluation items.Source: §A.3 · p. 29
  • No evaluation item is used in training for either the preview or released models.This applies to the benchmark-specific training coverage described for Decision Index 0.2.1.Source: §A.3 · p. 29

A.4 Licensing and Data Usage … B.3 Calibration and Resolution under Proper Scoring Rules

The appendices document model licensing, data generation and integrity controls, training implementation and ablations, and explain how proper-scoring-rule gains may reflect calibration, resolution, or both.

A.4 Licensing and Data Usage

  • Inference code is released under Apache-2.0, and model weights use CC BY-NC 4.0 for non-commercial use, with separate commercial licensing available.Table A.2 describes benchmark-specific Stage 2 coverage for preview models and is not an exhaustive record of final released checkpoints.Source: §A.4 · pp. 29–30, Table A.2 · p. 30

A.5 Generated and Model-Written Data

  • Programmatically generated examples pair independent templates with deterministic labels, while model-written examples are kept only after two verifier models independently recover the label.Generators receive no evaluation items, and procedural templates are independent of those used in DecisionPivot.Source: §A.5 · p. 30

A.6 Data Integrity Checks

  • Audits found answer-position and option-format shortcuts in original GSM8K, motivating reconstructed DI 0.3 questions; training records are screened against held-out sets by parent group.The audits use content-blind baselines, and decontamination covers Decision Index, public JevBench, DecisionPivot, and other held-out sets.Source: §A.6 · p. 30

Appendix B. Training Implementation and Additional Analyses

  • Stage 1 and RLCD2 update all language-model parameters; Stage 2 and reasoning supervision use merged adapters, while the pretrained vision tower remains frozen.The passage refers to Section 2 for the frozen vision tower.Source: Appendix B · p. 30

B.1 Bidirectional Prompt Attention

  • Bidirectional prompt attention removes the causal mask in full-attention layers while preserving causal recurrence in linear-attention layers.With bidirectional attention disabled, the modified implementation produces outputs bit-identical to the original causal implementation.Source: §B.1 · p. 30

B.2 Additional Training Ablations

  • Table B.1 summarizes targeted 4B-model ablations of probability optimization, parameter updates, reasoning termination, and RLCD2 initialization.The supplied passage gives the ablation scope but not the results.Source: §B.2 · p. 31, Table B.1 · p. 31

B.3 Calibration and Resolution under Proper Scoring Rules

  • A higher expected proper score can reflect improved calibration, resolution, or both, while outcome uncertainty is fixed for a given evaluation distribution.The Brier decomposition assigns negative miscalibration, positive resolution, and negative outcome uncertainty.Source: §B.3 · p. 31

B.4 Direct Probability Optimization … C.2 Theoretical Properties

Direct probability optimization improves calibration with comparable decision scores, while the theoretical analysis shows how selection, routing, and certification policies can alter calibration. The paper also characterizes when policy-aware calibration is preserved and how reasoning gates can be optimized under scoring and computation costs.

B.4 Direct Probability Optimization

  • The direct objective combines logarithmic, decision-utility, and record-level terms regularized toward a reference model, but the utility terms mean strict propriety is not guaranteed.Its calibration improvement is attributed to the combined objective because individual term contributions were not isolated.Source: §B.4 · p. 31
  • Calibration error falls from 5.1 to 3.9 points and Brier loss from 0.278 to 0.271, while DI 0.2.1 scores remain comparable at 52.49 and 52.57.Sampled-answer policy gradients yield a similar DI score of 52.55 but no calibration improvement; the optimized model's fitted temperature increases from 1.37 to 1.60.Source: §B.4 · p. 31

Appendix C. Policy-Aware Calibration: Proofs and Details

  • The appendix formalizes calibration effects induced by selection and routing and distinguishes marginal calibration of individual predictions from policy-aware calibration after selection or routing.It defines a think-gate that routes inputs to reasoning when single-pass confidence falls below a threshold.Source: Appendix C · p. 32, §C.1 · p. 32

C.2 Theoretical Properties

  • Under stated monotonicity assumptions, best-of-N selection makes accuracy at a fixed score non-increasing in candidate-pool size, producing weak overconfidence when individual responses are calibrated.For 9B-verifier responses scored 0.8–0.9, accuracy is 75.6%, 93.4%, and 98.3% across low-, medium-, and high-easiness strata; this is consistent with, but does not establish, one assumption.Source: §C.2 · p. 32
  • When post-reasoning correctness increases with initial confidence at fixed output confidence, reasoning-route accuracy is no greater than overall accuracy, which is no greater than non-reasoning-route accuracy.The inequalities reverse under non-increasing dependence; AUROC above or below 0.5 diagnoses residual ranking direction, but 0.5 does not establish conditional independence.Source: §C.2 · p. 32
  • Marginally certifying a gated system does not ensure each route meets the same error bound, whereas certifying every accepted route guarantees the bound overall.Overall accepted-prediction error is the route-weighted average of route-specific errors.Source: §C.2 · p. 33
  • Calibration conditional on all policy statistics determining return is preserved under any return event determined by those statistics and reported confidence.Policy-aware maps approximate conditional correctness using candidate scores, counts, or routing confidence, but finite-sample estimation does not guarantee exact conditional calibration.Source: §C.2 · p. 33
  • For fixed reasoning policy, optimal gating reasons exactly when its pointwise value is positive; with a fixed gate and strictly proper score, the optimal readout is the conditional label distribution.This characterization does not establish that the released models' fixed confidence threshold is optimal.Source: §C.2 · p. 33

C.3 Evaluation Protocols

The evaluation tests best-of-N verification and model routing across held-out arithmetic, reasoning, diagnostic, and Chinese decision settings, with confidence calibration and acceptance thresholds defined explicitly.

C.3 Evaluation Protocols

  • Best-of-N tests nine verifiers on held-out GSM8K training variants, five unseen arithmetic datasets, and reasoning tasks; routing tests twelve models across diagnostic, reasoning, and Chinese decisions.Diagnostic decisions span 39 task families; CJ-Bench contains challenging decisions in Chinese.Source: §C.3 · p. 33
  • Signed overconfidence is mean reported confidence minus empirical accuracy; route effect is routed minus non-routed accuracy at matched confidence, and thresholds use a 95% fixed-sequence Clopper–Pearson procedure.Thresholds are computed on the calibration half of each of 20 source-problem splits.Source: §C.3 · p. 33
  • Policy-aware calibration reduces signed confidence–accuracy gaps across selection and routing pipelines.The external actor-to-reasoner result uses publicly available system records; other results come from the authors’ evaluations.Source: Table C.1 · p. 34
  • Residual routing information correlated with route-dependent accuracy differences (Spearman −0.88 across 36 model–dataset settings).Residual AUROC measures how routing confidence ranks correctness within bins of post-reasoning confidence; triangles mark cascades.Source: Figure C.1 · p. 34

C.4 Results Across Decision Pipelines · C.5 Policy-Specific Threshold Certification · Appendix D. Evaluation Details

Across decision pipelines, route-aware calibration reduces route-specific gaps, while policy-specific thresholds reduce observed error violations but may accept no predictions on some routes. Appendix D documents evaluation scoring, safeguards, and inference details.

C.4 Results Across Decision Pipelines

  • Route-aware isotonic calibration reduces route-specific gaps to approximately 2 percentage points across nine models.It maps post-reasoning confidence within quantile strata of initial confidence, addressing residual routing-confidence information associated with route effects for think-gates and cascades.Source: §C.4 · p. 34
  • System Switch records show an 8.3-point mean absolute gap between overall reasoner accuracy and deferred-item accuracy, versus 2.1 points after route-aware calibration.System Switch defers uncertain actor decisions to a reasoner.Source: §C.4 · p. 34

C.5 Policy-Specific Threshold Certification

  • Policy-specific thresholds reduce observed violations of target error rates among accepted predictions, although some routes accept no predictions.Table C.2 reports accepted-prediction error rates and, in parentheses, the number of 20 evaluation splits exceeding target α.Source: §C.5 · p. 34, Table C.2 · p. 35
  • Changes in candidate count N, routing rate, generator, or task family may require renewed calibration and threshold certification.Source: §C.5 · p. 35

Appendix D. Evaluation Details

  • Appendix D details Decision Index scoring, per-benchmark results, evaluation safeguards, and inference for long option lists and multiple questions.Source: Appendix D · p. 35
  • DecisionPivot is described by StartLux (2026), and its data and scorer are available on Hugging Face.Source: Appendix D · p. 35

D.1 Decision Index Evaluation … D.4 Handling Multiple Questions and Long Option Lists

The appendix reports controlled evidence on attention direction and GSM8K reconstruction, alongside evaluation safeguards and serving procedures for long option lists and multiple document questions. The reported effects include benchmark differences, option-list accuracy, and throughput gains under a specified serving configuration.

D.1 Decision Index Evaluation

  • 64.9 versus 50.3 on MuSR, bidirectional attention outscored causal attention in a controlled Stage 2 comparison using identical data and the same Stage 1 checkpoint.Three additional bidirectional seeds scored 55.8–58.1, gains of 5.5–14.6 points over the causal model; on SATA-Bench, Stage 3 and explicit reasoning account for 4.4 of the 6.7-point cross-variant difference. At 27B, AutoThink scores 11.8 points below Instant on MuSR, while reasoning changes AutoThink accuracy by only +0.5 points.Source: §D.1 · p. 35
  • At least one StartLux-Decision model leads on 23 of 37 public DI 0.3 benchmarks, whose results are reported as chance-corrected skill points.DI 0.2.1 aggregates 38 benchmarks across five weighted domains; DI 0.3 retains five domains and includes 37 public benchmarks. Unanswered requests count as incorrect, and repeated reasoning-trace evaluations vary by approximately 0.05 index points.Source: Table D.1 · p. 35, §D.1 · p. 35

D.2 GSM8K Benchmark Reconstruction

  • Earlier checkpoints score 0.7–1.8 points higher on DI 0.2.1 with original GSM8K distractors, but the 4B Instant model trained only on reconstructed questions shows no such advantage.DI 0.3 replaces distractors with answers from other problems to reduce cues that create an answer-selection shortcut.Source: §D.2 · p. 36

D.3 Evaluation Reliability and Serving Configuration

  • Valid evaluation runs require at least 99.9% request completion, and prefix caching and chunked prefill are disabled because they can alter decision readouts under vLLM 0.19.1.Unanswered requests count as incorrect.Source: §D.3 · p. 36

D.4 Handling Multiple Questions and Long Option Lists

  • A single readout handles up to 26 options; longer lists use parallel groups of at most 25, advancing each group’s top three to a final readout.For lists up to 151 options, this procedure eliminates the correct answer before the final round in 0.2–0.7% of cases.Source: §D.4 · pp. 36–37
  • 86.7% accuracy on 151-option intent questions compared with 95.7% for 26 options was reported for the 4B model.Serving such lists requires multiple readouts.Source: §D.4 · p. 37
  • For a 3,200-token document with 32 questions, reusable document representations raise measured throughput from 2.8 to 27 decisions per second at 27B.Questions are evaluated independently, so adding questions does not change existing predictions; reuse depends on serving configuration, and bidirectional prompt attention prevents reuse of a question-independent document encoding.Source: §D.4 · p. 37

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