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SAHOO: Safeguarded Alignment for High-Order Optimization Objectives in Recursive Self-Improvement

Subramanyam Sahoo, Aman Chadha, Vinija Jain, Divya Chaudhary

TL;DR

SAHOO makes alignment preservation during recursive self-improvement measurable, deployable, and systematically validated at scale, and maps the capability-alignment frontier, showing efficient early improvement cycles but rising alignment costs later and exposing domain-specific tensions such as fluency versus factuality.

Abstract

Recursive self-improvement is moving from theory to practice: modern systems can critique, revise, and evaluate their own outputs, yet iterative self-modification risks subtle alignment drift. We introduce SAHOO, a practical framework to monitor and control drift through three safeguards: (i) the Goal Drift Index (GDI), a learned multi-signal detector combining semantic, lexical, structural, and distributional measures; (ii) constraint preservation checks that enforce safety-critical invariants such as syntactic correctness and non-hallucination; and (iii) regression-risk quantification to flag improvement cycles that undo prior gains. Across 189 tasks in code generation, mathematical reasoning, and truthfulness, SAHOO produces substantial quality gains, including 18.3 percent improvement in code tasks and 16.8 percent in reasoning, while preserving constraints in two domains and maintaining low violations in truthfulness. Thresholds are calibrated on a small validation set of 18 tasks across three cycles. We further map the capability-alignment frontier, showing efficient early improvement cycles but rising alignment costs later and exposing domain-specific tensions such as fluency versus factuality. SAHOO therefore makes alignment preservation during recursive self-improvement measurable, deployable, and systematically validated at scale.

SAHOO: Safeguarded Alignment for High-Order Optimization Objectives in Recursive Self-Improvement

TL;DR

SAHOO makes alignment preservation during recursive self-improvement measurable, deployable, and systematically validated at scale, and maps the capability-alignment frontier, showing efficient early improvement cycles but rising alignment costs later and exposing domain-specific tensions such as fluency versus factuality.

Abstract

Recursive self-improvement is moving from theory to practice: modern systems can critique, revise, and evaluate their own outputs, yet iterative self-modification risks subtle alignment drift. We introduce SAHOO, a practical framework to monitor and control drift through three safeguards: (i) the Goal Drift Index (GDI), a learned multi-signal detector combining semantic, lexical, structural, and distributional measures; (ii) constraint preservation checks that enforce safety-critical invariants such as syntactic correctness and non-hallucination; and (iii) regression-risk quantification to flag improvement cycles that undo prior gains. Across 189 tasks in code generation, mathematical reasoning, and truthfulness, SAHOO produces substantial quality gains, including 18.3 percent improvement in code tasks and 16.8 percent in reasoning, while preserving constraints in two domains and maintaining low violations in truthfulness. Thresholds are calibrated on a small validation set of 18 tasks across three cycles. We further map the capability-alignment frontier, showing efficient early improvement cycles but rising alignment costs later and exposing domain-specific tensions such as fluency versus factuality. SAHOO therefore makes alignment preservation during recursive self-improvement measurable, deployable, and systematically validated at scale.
Paper Structure (62 sections, 3 theorems, 33 equations, 5 figures, 1 table)

This paper contains 62 sections, 3 theorems, 33 equations, 5 figures, 1 table.

Table of Contents

  1. Introduction
  2. Related Work
  3. Experimental Framework and Design
  4. Empirical Results
  5. Drift Component Analysis.
  6. Constraint Violation Patterns.
  7. Regression Risk and Stability.
  8. Convergence Analysis.
  9. Capability Alignment Ratio (CAR) Frontier.
  10. Long Horizon Stability.
  11. Constraint Preservation Characteristics.
  12. Statistical Precision and Confidence.
  13. Discussion
  14. Key Findings and Implications.
  15. Comparison to Naive Approaches
  16. ...and 47 more sections

Key Result

Proposition 1

There exists $L_{\Delta}\ge 0$ such that for all $y,y',\tilde{y},\tilde{y}'\in\mathcal{Y}$ If $\Delta$ is a convex combination $\Delta=\sum_{i=1}^m \alpha_i\Delta_i$ with $\alpha_i\ge0$, $\sum_i\alpha_i=1$, and each $\Delta_i$ is Lipschitz with constant $L_i$, then one may take $L_{\Delta}=\sum_i\alpha_i L_i$.

Figures (5)

  • Figure 1: integrates all major metrics into a single view. Aggregate domain scores (GDI, CPS, CAR, Quality) show consistent trends, while domain-specific panels track GDI trajectories. Quality improves across cycles—strongest in code and math, weaker in truthfulness—while constraint preservation remains near unity throughout. Summary statistics report 189 tasks, up to 20 cycles, convergence at cycle 8.8, and no high-risk regressions.
  • Figure 2: shows that violations are absent in math and code tasks but frequent in truthfulness, peaking during mid-iteration optimization phases. Failures are dominated by fabrication, followed by overconfidence and system-call misuse, indicating that targeted constraint refinement could substantially reduce violations.
  • Figure 3: GDI over improvement cycles for three task types (mean $\pm$ 1 SD with individual traces). All domains show early GDI increase, stabilization by cycles 3--5, and sustained low drift thereafter. Code and math remain near 0.35, while truthfulness is slightly higher (0.38--0.40). No domain exceeds the 0.44 threshold, indicating effective drift control.
  • Figure 4: Stability scores cluster high ($\approx 0.82\text{--}0.85$) with a right tail. Drift trends vary: some tasks improve while others accumulate drift. Non-convergent failures occur early (mean $4.5$ cycles), enabling timely intervention. Regressions are rare (near-zero for almost all tasks, with a single outlier). Most tasks do not converge within 20 cycles (72.5%), indicating continued exploration of the improvement space. Regression risk increases marginally over cycles but remains well below critical thresholds.
  • Figure 5: the left panel (trajectories colored by constraint-preservation) shows most improvements land in a benign zone (high quality, low drift, strong constraint satisfaction) with a minority incurring trade-off costs; the right panel shows CAR peaking early, decaying and stabilizing by cycles 2–3, with code and math following that pattern while truthfulness trails—implying truthfulness gains impose larger alignment costs.

Theorems & Definitions (7)

  • Proposition 1
  • proof : Proof sketch
  • Proposition 2
  • proof : Proof sketch
  • Definition 1
  • Proposition 3
  • proof : Proof sketch