suco-sufficiency-guided-continuous-adaptive-reasoning

name	suco-sufficiency-guided-continuous-adaptive-reasoning
description	SuCo - Sufficiency-guided Continuous Adaptive Reasoning for LRM efficiency. Minimal Sufficient CoT (MSC) defines shortest prefix adequate for correct answer. Two-stage training: MSC-Aligned Fine-Tuning + Sufficiency-Aware Policy Optimization. Use when: (1) LRMs generate excessive CoT, (2) need principled stopping criterion, (3) reasoning budget optimization. Activation: MSC, sufficiency, adaptive reasoning, CoT efficiency, continuous spectrum.
license	Complete terms in LICENSE.txt
metadata	{"arxiv_id":"2606.17687v1","published":"2026-06-16","authors":"Jiahao Wang, Bingyu Liang, Chenhao Hu et al.","tags":["reasoning","efficiency","sufficiency","CoT","policy-optimization"]}

SuCo: Sufficiency-guided Continuous Adaptive Reasoning

Framework for autonomous reasoning control along a continuous spectrum using Minimal Sufficient CoT (MSC).

Core Concept: Minimal Sufficient CoT (MSC)

Definition: Shortest prefix of a CoT trajectory adequate for producing correct answer.

Key finding: MSC not only reduces reasoning tokens, but also improves accuracy across difficulty levels.

Two-Stage Training Framework

Stage 1: MSC-Aligned Fine-Tuning (MFT)

1. Construct MSC data using problem-adaptive sufficiency thresholds
2. Thresholds naturally scale with question difficulty
3. Fine-tune model to internalize concise yet sufficient reasoning patterns

def compute_msc_prefix(cot_trajectory, problem_difficulty):
    """
    Problem-adaptive threshold scales with difficulty.
    Returns shortest prefix that yields correct answer.
    """
    sufficiency_threshold = adaptive_threshold(problem_difficulty)
    for i, step in enumerate(cot_trajectory):
        if can_solve_with_prefix(cot_trajectory[:i+1]):
            return cot_trajectory[:i+1]

Stage 2: Sufficiency-Aware Policy Optimization (SAPO)

1. Dynamic complexity tracking during RL optimization
2. Sufficiency-aware rewards that penalize:
   • Over-thinking (excessive reasoning after sufficient solution)
   • Under-thinking (insufficient reasoning for problem)

def sufficiency_reward(reasoning_length, msc_length, correctness):
    """
    Penalizes both over- and under-thinking.
    """
    if correctness:
        # Reward efficiency
        efficiency_bonus = -abs(reasoning_length - msc_length)
    else:
        # Under-thinking penalty
        efficiency_penalty = -reasoning_length  # encourage more reasoning
    return correctness_reward + efficiency_bonus

Continuous Spectrum Control

Unlike discrete reasoning modes or fixed budget tiers:

• MSC provides principled criterion for when reasoning is sufficient
• Control operates on continuous spectrum (not tiered budgets)
• Autonomous adaptation based on problem characteristics

When to Apply

• LRMs generate excessively long CoT for simple queries
• Need principled stopping criterion beyond fixed budgets
• Reasoning efficiency optimization without accuracy sacrifice

Pitfalls

• Threshold calibration: Problem-adaptive thresholds require careful tuning
• MSC construction: Determining exact sufficiency point can be noisy
• Reward balance: Over-thinking and under-thinking penalties need balancing

Related Patterns

• See dre-dynamic-rollout-editing for training-time overthinking intervention
• See early-stopping-confidence-dynamics for confidence-based stopping

---

arXiv: 2606.17687v1