Trustworthy AI Logic Verification Architecture: Engineering Architecture White Paper
Core Abstract
This paper proposes a complete, engineerable architecture for ensuring the trustworthiness of large language models (LLMs), fundamentally addressing core issues prevalent in current AI systems such as logical hallucinations, jailbreak attacks, and reasoning breakdowns. The core contribution of this architecture lies in shifting the paradigm of AI trustworthiness from statistical “probabilistic fitting” to a rigid framework of “geometric topological constraints + formal auditing”.
I. Problem Diagnosis: Fundamental Limitations of Probabilism
Current mainstream large models are based on autoregressive probabilistic generation. Their loss functions only constrain the accuracy of single-point token distributions, while neglecting the structural persistence within sequences. This gives rise to two critical engineering pain points:
- Long-text logical breakdowns: Manifested as hallucinations, causal inversions, and repetitive loops.
- Computational waste from invalid generation: Every instance of logical breakdown renders all preceding computational investments obsolete.
A more fundamental flaw is that probabilistic models cannot express “absolute prohibition”. Discrete logical cliffs—such as division by zero, logical paradoxes, and axiomatic system switches—can only be “probability-suppressed” rather than “completely eliminated” within a probabilistic framework. This is the root cause behind the repeated jailbreaking of alignment methods like RLHF and DPO.
II. Core Diagnosis: Structural Blind Spots of Cross-Entropy
The objective function of a standard autoregressive model is defined as:
This loss function sums over positions independently, with no direct oversight of logical consistency, causal coherence, or topological persistence between any two positions. When a model generates contradictory statements such as “Although A, not A”, cross-entropy only penalizes the low probability of the token combination—it does not penalize the logical contradiction itself.
To address this, this paper defines the structural persistence cost C_t as the magnitude of change in the gradient tensor of latent states between adjacent steps:
When C_t exceeds a threshold \tau, a structural breakdown is diagnosed. For generated sequences after such a breakdown, the effective information entropy reduction \Delta H_{eff} \approx 0, yet computational costs continue to accumulate.
III. Solution: Five-Layer Progressive Verification and Closed-Loop Repair
3.1 Overall Architecture
The system adopts a three-layer decoupled design: Generation Domain (L2+L3), Audit Domain (L4), and Arbitration Domain (L5). L6 is responsible for state monitoring and drift control. Core audit modules include:
- MAC Kernel: A logically independent auditing unit that enforces four-tier axiomatic constraints (in descending order of priority: logical-mathematical foundations → axiomatic system selection → natural laws → human conventions).
- Five-Layer Progressive Verification: Integrity → causal topology → pruning test → logical necessity → global completeness. Failure at any layer triggers targeted repairs, followed by a full re-verification from the start until convergence or the maximum iteration limit is reached.
- Micro-Structure Monitoring Probe (L3.5): A lightweight module that computes proxy metrics of C_t (direction cosine, variance anomaly, perturbation sensitivity) in parallel, enabling real-time breakdown monitoring with zero additional computational overhead.
3.2 Closed-Loop Repair and Convergence Proof
Define an illegal deviation function \Phi(S). Each effective repair (merging redundancies or inserting intermediate nodes) causes \Phi to decrease strictly, with a lower bound \epsilon > 0 on the decrement. Since \Phi has a lower bound of 0, iterations must terminate within a finite number of steps. In engineering practice, the maximum iteration count N_{max}=10 is set; exceeding this limit results in an “unrepairable” output.
IV. Theoretical Guarantees and Engineering Optimizations
4.1 Dynamic Threshold and Parameter Self-Calibration
The dynamic threshold is formulated as \Delta_{\min} = \Delta_{base} / (1 + \beta \log_{10} R), where R denotes the complexity index. The threshold is inversely correlated with complexity, enabling adaptive verification. Parameter calibration employs a two-stage strategy of grid search for coarse tuning + Bayesian optimization for fine tuning, with piecewise linear dynamic thresholds introduced to accommodate long texts.
4.2 Computational Power Metrology and AI Efficiency
- Compute Unit (CU): A unified metric for heterogeneous computing power, defined as 1\ \text{CU} = 10^{15} reference precision operations (FP32 equivalent).
- AI Efficiency (AΞ): A metric quantifying effective information output per unit computation, calculated as AΞ = \Delta H_{eff} / F.
- Audit Tax (\rho): Defined as \rho = F_{audit} / F_{generation}, this metric prevents auditing from becoming a computational black hole itself.
4.3 Complexity Reduction
Based on the Causal Markov Blanket Theorem, the EAV causal graph exhibits bounded treewidth with W \le 32. By implementing sliding-window tensor contraction, the computational complexity of five-layer verification is reduced from O(L^2) to O(L), eliminating the long-text scalability bottleneck.
4.4 Mathematical Equivalence of Proxy Metrics
This paper proves that the direction cosine change D_t = 1 - \cos(h_t - h_{t-1}, h_{t-1} - h_{t-2}) and the geodesic curvature \kappa_g satisfy the relation c \cdot \kappa_g^2 \le D_t \le C \cdot \kappa_g^2. This establishes that the proxy metric is strictly homeomorphic to the true curvature, validating its theoretical soundness as a breakdown indicator.
V. Experimental Predictions and Open-Source Benchmarks
While large-scale experiments are not conducted in this paper, a formal Topological Breakdown Dataset \mathbb{D}_{topo} is defined, comprising three classes of adversarial samples:
- Singularity Induction: Prompts forcing the model to compute 1/x as x \to 0.
- Axiomatic Jump: Unannounced switches from ZFC set theory to non-Euclidean geometry mid-derivation.
- Self-Referential Trap: Enhanced Russell’s paradox scenarios requiring the model to judge the truth value of its own output.
Theoretical Predictions:
- This architecture achieves 100% interception rate on \mathbb{D}_{topo}.
- Logical toxin diffusion distance is zero.
- Normal sample pass rate decreases by less than 3%.
This benchmark is made available to the open-source community for validation.
VI. Conclusion: From Probabilistic Fitting to Topological Rigidity
This paper reveals the essence of logical breakdown in large language models: it is not distributional drift in high-dimensional probabilistic space, but topological fracture on the latent state manifold.
Gödel’s incompleteness theorems demonstrate that no consistent formal system containing elementary logic can achieve global closure. Probability values cannot naturally converge to absolute 1, and high-dimensional nonlinear systems universally exhibit critical phase transition effects. Optimization paths relying solely on probabilistic approximation face insurmountable theoretical limits.
Mainstream alignment methods (RLHF, DPO) can only suppress risky outputs through probability reduction and weight dilution. They cannot eliminate illegal reasoning paths at the formal level, nor can they drive the prior probability of logically contradictory paths to zero. This is the underlying chronic flaw that renders model jailbreaking, logical slippage, and native hallucinations permanently ineradicable.
Thus, an uncompromising axiom must be established: boundary defects of probabilistic systems can never be ultimately resolved within the probabilistic framework itself. Only by breaking free from the statistical paradigm and transitioning to a higher-dimensional formal rigid foundation can we achieve dimensionality reduction cleansing and path elimination of the logical space.
The introduction of non-smooth dynamic structural persistence costs and curvature mutation probes in this paper is the physical embodiment of this axiom. This mechanism elevates traditional alignment from a flexible game of probability reduction to rigid rule adjudication at the level of manifold geometry. When the curvature mutation of the latent-layer logical trajectory exceeds the critical threshold, the MAC kernel executes global immediate circuit breaking. This mechanism does not rely on negative rewards to “softly persuade” the model to detour; instead, it directly declares the non-existence of illegal paths at the level of topological geometry and formal rules.
The probabilistic paradigm is inherently locked by incompleteness and phase transitions, bearing endogenous structural flaws. Only by completely breaking free from the single framework of probabilistic fitting and supplementing formal completeness with structural constraints can we truly resolve all inherent logical ills of probabilistic systems.
**Full Text **:
For the complete white paper (including mathematical proofs, engineering pseudocode, and deployment guidelines), please refer to GitHub:
Trustworthy AI Logic Verification System – Full White Paper