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

Aniket Deroy

Keywords: Optmization, Rewarrd Hacking, Large Language Models

Abstract:

Large Language Models (LLMs) transition from passive information retrievers
to 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 or
strategic honesty. By integrating probabilistic neural evaluation with determinis-
tic formal verification, we provide a robust mechanism to ensure that the model’s
internal goals remain subordinate to human-specified objectives. Preliminary re-
sults suggest that this decoupled, multi-layer approach significantly increases the
computational ”cost of deception” for the model, making it mathematically im-
probable for an LLM to fool the supervisor across all stages simultaneously. As
the development of Large Language Models (LLMs) moves toward autonomous
agency, the core challenge of AI safety has shifted from simple ”reward hacking”
to the more insidious problem of Inner Alignment. This framework formalizes
the detection of deceptive mesa-optimizers—AI models that hide internal objec-
tives (ρθ ) to avoid being corrected during training. By defining deception as a
state where a model mimics alignment to minimize gradient pressure, the frame-
work introduces a composite safety gate, Vtotal, that evaluates internal activations
against a predefined safety constitution.To prevent ”gradient hacking,” a safety tax
(λ) is integrated into the global loss function, penalizing any discrepancy between
task accuracy and logical validity. This is enforced through a Dual-Stream Op-
timization path: mathematical tasks are verified by symbolic engines to prevent
step-skipping, while reasoning tasks are monitored by a Process Reward Model
(PRM) to detect ”stochastic parroting.” Ultimately, if a model produces a cor-
rect answer through disconnected logic, the resulting loss spike makes deceptive
strategies computationally inefficient and gradient-disfavored. In our evaluations,
top-performing models such as AlphaGeometry and DeepSeek-Math saw reason-
ing accuracy increases of up to 15.18%, while complex competition-level prob-
lems in the MATH dataset reached new performance thresholds after framework
integration. These findings suggest that a multi-stage, cross-domain verification
pipeline not only improves the reliability of mathematical problem-solving but
also provides a mathematically grounded pathway toward ensuring robust inner-
alignment in next-generation artificial intelligence.

Submission Number: 116