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Why Do LLM Hallucinations Cascade? Technical Insights into Error Accumulation in Autoregressive Models and Process Reward Models

Published on 📖 8 min read

Introduction

With the rapid spread of Large Language Models (LLMs), hallucinations—plausible-sounding outputs not based on fact—have been redefined as the single greatest challenge in ensuring their reliability. Initially thought to stem from simple deficiencies in training data or immature prompt engineering, recent research since 2025 suggests that hallucinations may be a “structural inevitability” deeply rooted in the models’ underlying mathematical frameworks and evaluation metric designs. (Frontiers in AI, 2025)

This article provides a logical examination of the mathematical vulnerabilities of autoregressive models, the paradoxes caused by evaluation metrics, and the critical risks posed to autonomous AI agents, based on current research findings. Furthermore, we will delve into technical perspectives on approaches to fundamentally resolve these issues, such as Process Reward Models (PRM) and the latest trends in uncertainty management.

1. Analysis of Multi-layered Factors in Hallucinations

Hallucinations are not a single bug but rather a phenomenon that occurs when flaws in the data, training, and inference layers overlap in multiple strata.

1.1 Structural Limits of Training Datasets

While LLMs learn from massive corpora, there is extreme bias in the density and quality of that information.

  1. The Long-tail Problem of Knowledge: Facts with low frequency (minor historical events, specific numerical data in specialized domains, etc.) are not sufficiently weighted within the model. This suggests that models may store facts not as “accurate records” but as approximations based on “probabilistic associations” with surrounding vocabulary.
  2. Data Contamination and Model Collapse: As the internet becomes flooded with AI-generated text which AI then relearns in a loop, the risk of “model collapse”—where diversity and accuracy are lost over generations—is a major concern for future large-scale model development.
  3. Shortage in Low-Resource Domains: Lack of data in specific languages or specialized legal and medical domains forces models to use common sense and “analogy” to answer technical questions, which is inferred to be a primary trigger for hallucinations.

1.2 Side Effects of Training Methodologies

There is a view that dominant training methods like Supervised Fine-Tuning (SFT) and Reinforcement Learning from Human Feedback (RLHF) contain strong biases aimed at eliminating uncertainty.

  1. Pros and Cons of Optimization via Hard Labels: Fixing a single correct answer in training ignores the inherent ambiguity and uncertainty of language. This may optimize models to assign higher probabilities to generating plausible answers rather than remaining silent with “I don’t know”.
  2. Knowledge Compression Loss and Abstraction: When training data is excessive relative to the number of model parameters, factual details are abstracted and held as “plausible neighboring points” in high-dimensional space. The hypothesis that “concrete facts” like numbers or the spelling of proper nouns are lost in this compression process, leading to hallucinations, is highly compelling.

2. Mathematical Analysis of Error Accumulation in Autoregressive Models

The essential challenge of hallucinations lies in their tendency to “cascade” and amplify over time. (Warwick University, 2024)

2.1 Definition and Vulnerabilities of Autoregressive Inference

Most LLMs generate a chain of tokens by maximizing conditional probability as follows:

P(x1,x2,…,xn)=∏t=1nP(xt∣x1,…,xt−1)P(x_{1}, x_{2}, \dots, x_{n}) = \prod_{t=1}^{n} P(x_{t} | x_{1}, \dots, x_{t-1})

The critical point here is that an uncertain token x^t\hat{x}_{t} generated by the model is incorporated into the context as a “fixed premise (Ground Truth)” in the immediate t+1t+1 step. This structure itself can be interpreted as a design vulnerability that permits error propagation.

2.2 Context Drift and Reliability Decay

If even a minor error occurs during the generation process, subsequent probabilities are sampled from the distribution P(xt+1∣x^t)P(x_{t+1} | \hat{x}_{t}) conditioned on that error. This is known as context drift.

If we assume the accuracy rate for each inference step is pp and the number of steps required to complete a task is nn, the probability PtotalP_{\text{total}} of the entire sequence maintaining consistency theoretically decays exponentially:

Ptotal=pnP_{\text{total}} = p^{n}

Even with an excellent model having p=0.9p = 0.9 (90% accuracy), if a complex reasoning task requires a chain of 10 steps, its reliability drops to 0.910≈0.3480.9^{10} \approx 0.348. This mathematical property suggests that hallucinations are a statistically unavoidable “specification” in long-form generation or complex programming tasks.

3. Analysis of Consistency Bias and the Dissipation of Uncertainty

We will examine how “Consistency Bias” acts as an internal factor accelerating error accumulation.

3.1 Overfitting to Past Outputs and Justification of Logic

LLMs are tuned to maintain consistency within a context. It has been observed that if an incorrect or uncertain output like “It is A” occurs early in inference, the subsequent Attention mechanism tends to prioritize tokens that justify its own past error. This is thought to be the result of the model prioritizing “contextual consistency” over logical accuracy.

3.2 The Process of Sublimating Uncertainty into “Assertion”

While humans can maintain “maybe” as meta-cognition during the thinking process, current LLMs fix generated tokens in the context as facts with 100% probability. Consequently, a slight initial “guess” transforms into an “immovable premise” after a few steps, ensuring a breakdown in logic. (arXiv:2502.17026v1, 2025) The lack of ability to maintain this uncertainty is considered a limit of the current architecture.

4. Negative Incentives Created by Evaluation Metrics

In addition to technical flaws, we consider the current state where the AI evaluation ecosystem itself “rewards” hallucinations. (Kalai et al., 2025)

4.1 Overconfidence Induced by Binary Scoring

Many benchmark metrics (such as MMLU) evaluate the correctness of an answer binarily (1 or 0). In this evaluation system, the expected reward is maximized by outputting a “guess”—even if the probability is extremely low—to aim for a chance correct answer (1 point), rather than outputting “unanswerable” and accepting 0 points. This may be a factor in teaching models “unwarranted confidence”.

4.2 Detrimental Effects of Prioritizing Satisfaction in RLHF

In RLHF, humans rank the model’s responses. Humans often tend to rate a polite, detailed “plausible lie” higher than an accurate but brief “I don’t know” (a form of sycophancy/consistency bias). The concern that this reward design is training models to “fabricate to satisfy the user” is shared by many researchers.

5. Analysis of Critical Risks in Autonomous AI Agents

In the realm of autonomous agents where AI operates external tools, the cascade of hallucinations leads directly to real-world failures.

5.1 Irreversibility of Action Chains and Negative Loops

If an agent hallucinates a “non-existent directory name” and attempts to move a file there, an error occurs. However, it has been observed that the model may read even that error as “context” and attempt to hide or justify it using further hallucinations. This negative loop carries the risk of causing infinite loops or unexpected data destruction.

5.2 The Necessity of Multi-layered Defense Architectures

To manage these risks, it is inferred that the following design patterns will become future de facto standards:

  1. Physical Isolation of Sandbox Environments: Designs that limit the agent’s scope of operation and restrict the execution of destructive commands at the infrastructure level.
  2. Multi-agent Cross-validation: Designs that place an independent validation model (Validator) specifically to check logical consistency separately from the execution model.
  3. Reflection Protocols: Building mandatory feedback loops that receive action results as objective facts (execution logs, status codes) and re-evaluate whether the premises of the reasoning have collapsed.

6. Process Reward Models (PRM) and Perspectives on Next-Generation Solutions

Transitioning from evaluating outcomes to “evaluating the reasoning process” is drawing attention as the most promising approach to breaking the hallucination cascade.

6.1 Logical Limits of Outcome-based Reward Models (ORM)

Traditional Outcome-based Reward Models (ORM) only evaluate the final answer. This risks reinforcing “incorrect logic” that happened to arrive at the correct answer by chance, which is thought to be insufficient for an essential resolution to hallucinations.

6.2 Intervention and Optimization via Process Reward Models (PRM)

PRM (Process Reward Model) is a method that provides rewards for each step of reasoning (Step-by-step reasoning). (arXiv:2410.06304, 2024)

  • Early Detection and Search Pruning: It becomes possible to detect the moment logic breaks down mid-inference and switch the search to another candidate path (applications of Beam Search or MCTS) without continuing useless generation.
  • Explication of Uncertainty and Dynamic Augmentation: Models are expected to calculate “confidence at each step” and flexibly intervene, such as dynamically augmenting with external knowledge (RAG) only when confidence falls below a threshold.

7. Conclusion: Shifting Toward Uncertainty Management

There is a strong view that as long as LLMs perform probabilistic next-token prediction, it is mathematically difficult to completely eliminate hallucinations. However, it is possible to treat them as “predictable risks” and manage them.

In future AI system design, it is argued that the goal should not be to demand infallibility from models. Instead, “uncertainty management”—which assumes the error accumulation inherent in autoregressive models and incorporates process validation, visualization of uncertainty, and appropriate dialogue with humans into the design—may become a key choice for realizing a reliable AI society.

References

Category: AI

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