From Hallucination Elimination to Computing Power Measurement: An Engineering Feasible Technical White Paper
Concise Statement
All technical solutions described in this paper shall enter the global public domain (CC0) upon release. The author waives all copyrights, patent rights and related rights. Any individual or entity may freely use, modify, distribute and commercialize the content of this paper without authorization, payment or attribution.
Abstract
Current large model inference suffers from two directly measurable engineering pain points: long-text logical fragmentation and computing power waste caused by invalid generation. Starting from these two pain points, this paper presents a complete mathematical diagnosis and engineering correction scheme.
Diagnosis: Cross-entropy loss only fits the surface symbol distribution but does not constrain the structural persistence within the sequence. This causes the logical consistency of symbol concatenation to degrade with sequence length during generation, manifesting as hallucinations, logical fragmentation and repetitive generation. Every fragmentation event renders the preceding computing power investment completely obsolete.
Correction: A structural persistence constraint term \mathcal{L}_{struct} is introduced into the loss function to force the model to pay a topological persistence cost for each symbol generation step. Mathematically, this is equivalent to imposing local curvature constraints on the free energy landscape; engineering-wise, it can be efficiently implemented through gradient regularization. The structural persistence constraint inherently suppresses logical fragmentation, leading to a significant reduction in invalid computing power consumption during long-text generation. Introducing this constraint does not increase computing power overhead but instead substantially improves the effective computing power conversion rate.
Extension: This correction scheme naturally derives an auditable computing power measurement unit — CU (Compute Unit) — and an intelligent efficiency metric — AΞ (AI Efficiency Unit). Together, they form the fundamental measurement standard for the AI computing power economy.
This paper provides complete mathematical definitions and engineering implementation schemes. All content is dedicated to the public domain.
1. Two Core Engineering Pain Points
1.1 Long-Text Logical Fragmentation
Phenomenon: When generating long texts, the logical consistency of large models degrades with sequence length, characterized by factual contradictions, causal fragmentation and repetitive loops.
Existing explanations mostly attribute this to “attention dilution” or “context window limitations”. This paper offers a more fundamental diagnosis: cross-entropy loss only constrains the symbol distribution of point-wise prediction but does not enforce structural persistence across the sequence.
1.2 Computing Power Waste from Invalid Generation
Every segment of output following logical fragmentation renders all preceding computing power investment completely wasted. Users pay the full inference cost for fragmented text but receive zero effective information.
The current industry lacks mechanisms to quantify this waste or proactively avoid it during either training or inference phases.
2. Diagnosis: The Structural Blind Spot of Cross-Entropy
2.1 Cross-Entropy Only Fits Surface Distribution
The optimization objective of standard autoregressive models is to minimize cross-entropy loss:
This objective sums losses independently across positions. Logical consistency, causal coherence and topological persistence between any two positions fall outside the direct scope of the loss function.
2.2 Formal Definition of Structural Persistence
Define the local structural tensor S_t of the sequence at step t:
where h_t denotes the hidden state at step t. S_t characterizes the gradient of dependence of the current generation step on historical information.
Define the structural persistence cost as the magnitude of change in structural tensors between adjacent steps:
When C_t exceeds a predefined threshold \tau, structural fragmentation is declared. For symbol sequences generated after fragmentation, the effective information entropy reduction \Delta H_{eff} \approx 0, while computing power consumption F continues to accumulate.
2.3 Quantification of Fragmentation-Induced Computing Power Waste
Assume the model generates L_{waste} invalid tokens after the fragmentation point, with each token consuming f FLOPs. The wasted computing power for this inference is:
This portion of computing power produces zero effective information entropy reduction, yet users are fully charged under the current token-based pricing model.
3. Correction: Structural Persistence Constraint
3.1 Constraint Formulation
Append the structural persistence term to the original loss function:
where \lambda is the constraint strength and \tau is the tolerance threshold.
3.2 Engineering Implementation
In practical implementation, the Frobenius norm of S_t can be efficiently approximated using gradient norms:
This approximation only requires retaining gradient vectors of adjacent steps during backpropagation, resulting in minimal computational overhead. More crucially: the structural persistence constraint inherently suppresses logical fragmentation, systematically reducing invalid generation after fragmentation events. This means the invalid computing power consumption F_{waste} of models during long-text generation is drastically reduced. Introducing this constraint does not increase computing power burden but instead significantly improves the effective computing power conversion rate.
Pseudocode:
def compute_struct_loss(logits, hidden_states, lambda_struct, tau):
ce_loss = cross_entropy(logits, targets)
grads = [torch.autograd.grad(ce_loss, h, retain_graph=True) for h in hidden_states]
struct_loss = 0
for t in range(1, len(grads)):
diff = torch.norm(grads[t] - grads[t-1])
struct_loss += max(0, diff - tau)
return ce_loss + lambda_struct * struct_loss / (len(grads) - 1)
3.3 Physical Equivalence Interpretation
\mathcal{L}_{struct} is mathematically equivalent to imposing local curvature constraints on the free energy landscape. It forces the model to avoid drastic jumps in structural tensors during sequence generation — i.e., compelling the model to pay an additional gradient cost for maintaining logical continuity.
Essential Distinction from Traditional Gradient Penalty: Although \mathcal{L}_{struct} resembles temporal gradient penalty in mathematical form, the two are fundamentally different. Traditional regularization methods (e.g., R1, WGAN-GP) aim to smooth decision boundaries under the premise that the model itself is stable, and regularization merely makes the optimization process more gradual. In contrast, the underlying logic of \mathcal{L}_{struct} holds that: the natural state of sequence structure is inherently unstable. Logical fragmentation is not a random jitter during optimization but an inevitable collapse of structure in the absence of persistence-maintaining work. Traditional regularization is like adding handrails to a smooth slide; \mathcal{L}_{struct} is equivalent to artificially creating friction in a vacuum — without it, structure cannot exist and will evaporate into random noise.
4. Extension: From Energy Consumption Correction to Computing Power Measurement
4.1 Rationale for a Unified Measurement Standard
The introduction of structural persistence constraints distinguishes effective computing power consumption from raw computing power consumption. The former excludes FLOPs wasted after fragmentation, while the latter represents the actual computational operations executed by hardware.
The industry requires a unified measurement standard to audit effective computing power. Current token-based pricing cannot distinguish between effective and wasted computation — it only counts output word count without accounting for structural persistence costs.
4.2 CU (Compute Unit): Unified Measurement of Physical Computing Power
Definition: 1 CU = 10^{15} reference precision operations (FP32 equivalent).
CU unifies heterogeneous computing power into standard operation counts while deducting communication losses and storage jitter.
Precision Conversion: Let P_0 (FP32) be the reference precision and E_i be the effective computing capacity of precision P_i. The conversion coefficient is k_i = E_0 / E_i. The total standard computing power is:
To prevent hardware vendors from optimizing specifically for benchmark programs, E_i must be measured using Standard Reference Workloads (SRW). SRW must include representative operators from at least three mainstream architecture types, with weights determined by weighted voting of the Governance Committee based on actual industry proportions, and re-reviewed every two years.
Network Correction: The net computing power of distributed clusters is:
The network correction factor is:
where D(\Gamma) is the topological normalized diameter, B_{inter} is the average interconnection bandwidth, and \alpha, \beta are calibrated through empirical measurements.
Storage Correction:
where V is storage capacity, T is occupancy duration, B is bandwidth, \alpha is availability coefficient, and L is access latency.
Issuance-Destruction Anchoring Mechanism: CU paid by users is immediately destroyed; equivalent CU is newly issued and allocated to service providers after they submit valid computing power proofs. Total issuance is anchored to global computing power growth rate, with a basic inflation rate \pi_0 introduced to prevent deflation:
The recommended value of \pi_0 ranges from 0.5% to 1% per annum.
4.3 AΞ (AI Efficiency Unit): Measurement of Intelligent Efficiency
Definition: 1 AΞ = 1 Bit (effective information entropy reduction) / 1 Tera-FLOP.
where \Delta H_{eff} = \Delta H_{int} \cdot \mathbb{I}[\forall t, C_t \leq \tau], meaning the information entropy reduction is fully counted only if no structural fragmentation occurs throughout the sequence.
To further distinguish self-consistent hallucinations from reasoning consistent with physical reality, a reality anchoring correction can be applied:
where P_{world} denotes the external world model.
AΞ measures: how much effective logical order is produced per unit of computing power.
4.4 Relationship with Structural Persistence Constraint
The direct outcome of the structural persistence constraint is the separation of \Delta H_{eff} and F_{waste}. CU provides a unified measurement of F, while AΞ quantifies the efficiency metric \Delta H_{eff} / F. Together, they form a complete computing power economic ledger: CU records the amount of physical work consumed, AΞ measures how much effective order is produced by this work, and the structural persistence constraint defines the boundary of “effectiveness”.
4.5 Inference from a Simple Mathematical Equation
Hardware efficiency (FLOPS/J) and algorithm efficiency (\Delta H/FLOPS) are two widely recognized valid metrics in academia. Their product yields:
This represents how many bits of effective information entropy reduction are produced per joule of energy.
This equation is mathematically indisputable. It reveals that any claim about model capability must ultimately answer the question of effective information output per unit energy consumption. \Delta H / J serves as a hardware-agnostic theoretical limit benchmark. In engineering practice, AΞ must be annotated with the corresponding hardware platform — the mission of measurement standards is to reveal differences rather than eliminate them.
5. Discussion
5.1 Parameter Tuning
\tau and \lambda need to be tuned for specific tasks. This is not a burden but rather a set of control knobs:
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High \lambda mode (e.g., \lambda \in [0.5, 2.0]) is suitable for code generation and mathematical logic reasoning scenarios that require strict logical rigidity.
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Low \lambda mode (e.g., \lambda \in [0.05, 0.2]) is appropriate for creative writing scenarios that allow moderate structural jumps.
The reward for parameter tuning is a substantial reduction in invalid computing power waste and a fundamental improvement in logical consistency.
5.2 Limitations
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Gradient norm approximation may introduce variance under large batch sizes.
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The rigorous mathematical definition of structural persistence requires further refinement.
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The SRW governance mechanism of CU relies on the credibility of the Governance Committee, posing potential social engineering risks.
5.3 Future Work
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Systematically verify the effectiveness of structural persistence constraints on public benchmarks.
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Develop open-source benchmark suites for CU/AΞ measurement.
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Explore lightweight schemes for real-time fragmentation detection and generation termination during inference.
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Investigate preliminary frameworks for establishing a CU/AΞ Governance Committee.
6. Conclusion
Starting from the two engineering pain points of long-text logical fragmentation and computing power waste in large model inference, this paper diagnoses the structural blind spot of cross-entropy loss, proposes a mathematical correction scheme based on structural persistence constraints, and provides an engineering feasible pseudocode implementation. This constraint inherently suppresses logical fragmentation, leading to a significant reduction in invalid computing power consumption.
This correction scheme naturally extends to derive two measurement units — CU (Compute Unit) and AΞ (AI Efficiency Unit) — laying the foundation for an auditable measurement standard for the AI computing power economy. The \Delta H / J equation further reveals that: the ultimate benchmark for any intelligent system is the effective information output per unit energy consumption.
Appendices
Appendix A: Core Symbol Table
| Symbol | Meaning | Unit |
|---|---|---|
| \mathcal{L}_{CE} | Cross-entropy loss | -– |
| \mathcal{L}_{struct} | Structural persistence loss | -– |
| C_t | Structural persistence cost | -– |
| \tau | Fragmentation threshold | -– |
| \lambda | Constraint strength | -– |
| CU | Compute Unit | 10^{15} reference precision operations |
| AΞ | AI Efficiency Unit | Bit / Tera-FLOP |
| \Delta H_{eff} | Effective information entropy reduction | Bit |
| F | Equivalent FP16 computation | Tera-FLOP |
| F_{waste} | Wasted computing power | Tera-FLOP |
| \pi_0 | Basic inflation rate | 1/ year |
Appendix B: Standard Reference Workload (SRW) Specification
Workload Type: Transformer Decoder Autoregressive Generation
Key Operator Set:
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Matrix Multiplication (FP16 / INT8)
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Convolution / State Space Operators
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Softmax
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LayerNorm / RMSNorm
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Attention Score Calculation
Operating Parameters:
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Sequence Length: 2048
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Batch Size Range: 1–64
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Data Type: FP16 / BF16
Acceptance Criteria:
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Stable operation on at least three mainstream GPU architectures
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Correlation coefficient >0.95 with inference performance of mainstream large models (e.g., LLaMA, Qwen series)
Update Mechanism: SRW evolves dynamically with mainstream model architectures; the current version reflects the characteristics of industry-leading computation graphs in 2026. Update proposals are reviewed by the Governance Committee and take effect upon voting approval.
Appendix C: Separation of Computation and Verification — Privacy-Preserving and Decentralized Implementation of CU Network
C.1 Core Separation Principle
The CU network requires miners to submit computing power proofs to obtain newly issued CU. The proof must verify two facts:
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The miner has actually consumed physical computing power F (i.e., executed model inference).
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The generated sequence has no structural fragmentation (\forall t, C_t \leq \tau).
In traditional schemes, verifiers need access to complete input-output content for validation, leading to privacy exposure. The key to separation lies in this: the calculation of structural persistence cost C_t is independent of content semantics.
C_t depends solely on model weights and intermediate hidden states, and is mathematically orthogonal to the plaintext content of input text.
C.2 Two-Layer Network Architecture
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Execution Layer (Miner Network): Runs complete model inference, generates outputs and records the C_t sequence. Miners have no access to original input plaintext.
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Verification Layer (Blockchain Light Nodes): Only verifies C_t \leq \tau and signature validity, with no access to any user data.
C.3 Workflow
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End-Side Preprocessing: Users run the first k layers of the model on local devices to obtain intermediate hidden states h_k. Original input text never leaves the user’s device.
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Miner Execution: Users send h_k to the miner network. Miners continue running the remaining layers to generate hidden state sequences and logits, while calculating C_t for each step. Miners return encrypted logits and the complete C_t sequence.
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End-Side Validation and Signing: Users decrypt logits locally to obtain final outputs. They simultaneously verify whether the C_t sequence satisfies C_t \leq \tau throughout the entire process. If valid, users sign the “effective computing power proof” with their private key — which includes model hash, h_k hash, output hash, C_t sequence, timestamp — and broadcast it to the blockchain.
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On-Chain Verification and CU Minting: Verification nodes only validate:
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Validity of user signature
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Mathematical consistency between the C_t sequence and publicly available discriminator weights (to prevent forgery)
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\forall t, C_t \leq \tau
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Upon successful verification, a smart contract is triggered to mint corresponding CU to the miner’s address.
C.4 Engineering Guarantees for Privacy and Security
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User Privacy: Miners only receive h_k and cannot reverse-engineer the original input. This can be further strengthened through differential privacy or secure multi-party computation.
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Anti-Fraud for Miners: C_t calculation depends on model weights and complete gradient graphs. Miners cannot forge consistent C_t sequences without actually executing inference.
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Lightweight Verification: Verification nodes only require signature verification and scalar comparison, no GPU is needed, and they can run on ordinary CPUs.
C.5 Compatibility with Existing Technology Stacks
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Computation Partitioning: Already supported by frameworks such as Apple MLX and llama.cpp, representing mature engineering practice.
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Gradient Recording: Frameworks like PyTorch natively support retaining intermediate gradients; calculating C_t requires minimal additional code.
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Zero-Knowledge Proof (Optional Enhancement): To eliminate reliance on user signatures, miners can generate ZK Proofs (e.g., Groth16, Plonk schemes) to prove C_t \leq \tau.
C.6 Significance for Decentralized Computing Power Networks
The separation of computation and verification equips the CU network with two key capabilities: privacy protectionand trustless verification, making it the first distributed AI measurement protocol that satisfies both requirements simultaneously. Any individual or institution with idle GPU resources can join the network to provide computing power without legal risks.
Appendix D: Open-Source Community Practice and Anti-Attack Q&A
This section provides framework-level solutions for core uncertainties in technology implementation and network operation. Specific parameters will be iteratively improved through community practice.
Q1: After domain fine-tuning or cross-task transfer of the main model, is it necessary to retrain the structural discriminator \mathcal{D}_{struct}? Are there lightweight transfer schemes available?
A1:
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Necessity Judgment: If fine-tuning causes significant shifts in hidden state distribution (e.g., transferring from general text to code domains), retraining is mandatory; if only surface-level outputs are optimized (e.g., style fine-tuning), retraining is unnecessary.
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Lightweight Transfer Frameworks:
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Layer-Wise Freezing Strategy: Fix the bottom feature extraction layers of the discriminator and only fine-tune the top classification layer.
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Domain Adapter: Insert small Adapter modules into the discriminator and only train adapter weights to achieve rapid alignment.
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Distribution Shift Detection: Automatically determine whether discriminator update is needed by calculating the KL divergence of hidden states before and after fine-tuning.
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Q2: How to enhance the anti-attack robustness of the median computing power anchoring mechanism to prevent a single entity from manipulating the computing power conversion benchmark?
A2:
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Computing Power Sharding Constraint: Set an upper limit on the computing power proportion of any single entity in the entire network; computing power exceeding the threshold is excluded from median statistics.
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Dynamic Staking and Reputation Linkage: Miner staking requirements are linked to historical reputation scores. Fraudulent behavior results in permanent reputation deduction and public disclosure of misconduct, exponentially increasing the cost of attacks.
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Anomaly Data Filtering: Adopt truncated median algorithm to eliminate extreme values at both ends of the distribution; deploy multi-dimensional verification baselines by splitting detection tasks into multiple subtasks and taking consistent results.
Q3: Under high \lambda constraint, model-generated content tends to be overly conservative. How to balance logical rigidity and creativity?
A3:
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Scenario-Specific \lambda-\gamma Linkage: Adopt high \lambda + low \gamma for strong logic scenarios (code/mathematics); adopt low \lambda + high negative \gamma for creative scenarios (novels/scripts) to encourage reasonable structural jumps.
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Dynamic Adaptive Adjustment: Introduce a novelty scoring module; automatically increase \gamma when the score falls below the threshold, and automatically raise \lambda when structural fragmentation risk increases.
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User Interactive Adjustment: Provide a visualization panel allowing users to adjust parameters in real time to balance personalized needs.
Q4: There are biases in computing power conversion across different architecture hardware (CPU/GPU/TPU). How to achieve fair measurement for heterogeneous hardware?
A4:
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Hardware-Agnostic Benchmark Tasks: Define general computing tasks decoupled from model architectures (e.g., matrix multiplication, core attention computation) as computing power benchmarks.
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Multi-Dimensional Conversion Coefficient Calibration: Model both computing efficiency and communication efficiency simultaneously; computing power conversion must consider both operation speed and data transmission loss.
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Decentralized Calibration Mechanism: Benchmark tests are jointly conducted by miners using different hardware types; the average result of multi-party verification is adopted as the final conversion coefficient to avoid centralized pricing monopoly.
References
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License
This work is dedicated to the global public domain under the CC0 1.0 Universal Public Domain Dedication. No rights are reserved.
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