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

arXiv: https://arxiv.org/abs/2603.06333 · HTML: https://mlsanity.com/paper/2603.06333/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 12 references that are in the map.
- First posted on arXiv 6 Mar 2026.

## Builds on (most cited first, 7 of 7)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [TruthfulQA: Measuring How Models Mimic Human Falsehoods](https://mlsanity.com/paper/2109.07958/) (2021)
- [Self-Taught Optimizer (STOP): Recursively Self-Improving Code Generation](https://mlsanity.com/paper/2310.02304/) (2023)
- [SGM: A Statistical Godel Machine for Risk-Controlled Recursive Self-Modification](https://mlsanity.com/paper/2510.10232/) (2025)
- [The Devil Behind Moltbook: Anthropic Safety is Always Vanishing in Self-Evolving AI Societies](https://mlsanity.com/paper/2602.09877/) (2026)
- [Moral Anchor System: A Predictive Framework for AI Value Alignment and Drift Prevention](https://mlsanity.com/paper/2510.04073/) (2025)

## Built on by (most cited first, 2 of 2)

- [Calibration Collapse Under Sycophancy Fine-Tuning: How Reward Hacking Breaks Uncertainty Quantification in LLMs](https://mlsanity.com/paper/2604.10585/) (2026)
- [Testing and Evaluation of Agentic AI Systems In Military Command and Control](https://mlsanity.com/paper/2608.20597/) (2026)

## Abstract (arXiv)

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.