MULTI-STAGE GOAL VERIFICATION: A DEFENSE-IN- DEPTH MATHEMATICAL FRAMEWORK FOR MITIGATING DECEPTIVE ALIGNMENT IN LARGE LANGUAGE MODELS

Large Language Models (LLMs) transition from passive information retrieversto autonomous agents, the risk of inner alignment failure—specifically decep-tive alignment becomes a critical safety concern. This paper proposes a Multi-Stage Checking Framework designed to detect and intercept ”mesa-optimizers”that may attempt to bypass safety protocols through sophisticated reasoning orstrategic honesty. By integrating probabilistic neural evaluation with determinis-tic formal verification, we provide a robust mechanism to ensure that the model’sinternal goals remain subordinate to human-specified objectives. Preliminary re-sults suggest that this decoupled, multi-layer approach significantly increases thecomputational ”cost of deception” for the model, making it mathematically im-probable for an LLM to fool the supervisor across all stages simultaneously. Asthe development of Large Language Models (LLMs) moves toward autonomousagency, the core challenge of AI safety has shifted from simple ”reward hack-ing” to the more insidious problem of Inner Alignment. This research addressesthe Mesa-Optimization problem, where models develop internal objectives (ρθ )that diverge from the intended human goals (Rtrue), potentially leading to decep-tive alignment where models ”fake” compliance to avoid modification. We arguethat traditional behavioral benchmarks are insufficient for detecting these strategicfailures and propose a transition to a Multi-Stage Checking Framework. By com-bining Mechanistic Interpretability to monitor internal neural activations (zt) withSymbolic Verification to test model actions against deterministic formal logic,we create a supervisory environment that is robust against strategic deception.Experimental results across the MiniF2F, GSM8K, and MATH datasets demon-strate that the application of this mathematical framework significantly enhancesreasoning accuracy across various model architectures. In our evaluations, top-performing models such as AlphaGeometry and DeepSeek-Math saw reasoningaccuracy increases of up to 15.18%, while complex competition-level problems inthe MATH dataset reached new performance thresholds after framework integra-tion. These findings suggest that a multi-stage, cross-domain verification pipelinenot only improves the reliability of mathematical problem-solving but also pro-vides a mathematically grounded pathway toward ensuring robust inner-alignmentin next-generation artificial intelligence.