When a large language model confidently states that Barack Obama won the Nobel Prize in Chemistry, it’s not lying. It’s not being malicious, and it’s certainly not “misunderstanding” the world in the human sense. It is, however, executing its core function with mathematical precision in a way that diverges from reality. This divergence—commonly termed a hallucination—is perhaps the most fascinating and frustrating artifact of modern generative AI. To truly understand why these systems invent facts, we need to move beyond surface-level metaphors and look at the intricate machinery operating beneath the interface.
At its heart, an LLM is a probability engine. It does not possess a database of facts it queries; it possesses a statistical model of language. When you ask it a question, it isn’t retrieving an answer from a filing cabinet. It is calculating, token by token, the most statistically likely sequence of words to follow your prompt, based on the patterns it absorbed during training. This distinction is the bedrock of understanding hallucination. If the model’s goal is to generate plausible-sounding text rather than factually accurate text, then hallucinations are not bugs—they are features of a system optimized for coherence over truth.
The Probabilistic Nature of Next-Token Prediction
Imagine a text completion engine. You feed it the phrase: “The capital of France is”. The model has seen this exact sequence of words billions of times in its training data (likely from Wikipedia, books, and news articles). The token “Paris” has an overwhelmingly high probability of following this sequence. The model outputs “Paris.” This feels like knowledge, but it is closer to mimicry. The model has learned a statistical correlation between the tokens “capital of France” and “Paris.”
Now, consider a slightly more complex prompt: “Who was the first person to walk on Mars?”
Here, the training data is sparse. No human has walked on Mars. However, the model has read countless science fiction novels, news articles about space exploration, and biographies of astronauts. It knows the structure of sentences regarding space exploration. It knows names like “Neil Armstrong” (Apollo 11) and “Buzz Aldrin.” It knows the concept of “Mars.” When forced to generate a completion, the model doesn’t know “this hasn’t happened.” It simply predicts the next most plausible token based on the context of space exploration.
It might generate: “Neil Armstrong was the first person to walk on Mars during the fictional Apollo 18 mission.” Or it might simply state: “Neil Armstrong.” The model is trapped by its own success at pattern matching. It generates a sentence that is grammatically correct and stylistically consistent with its training data, even if the underlying premise is false. The probability distribution over the vocabulary space favored a known astronaut’s name over a null set or an admission of ignorance, because in its training corpus, questions about “first people to walk on [celestial body]” are almost always followed by names like “Armstrong” or “Aldrin.”
Tokenization and the Loss of Granularity
Before we even get to the transformer layers, the tokenization process introduces a layer of abstraction that can contribute to errors. Modern LLMs use subword tokenization (like Byte Pair Encoding or WordPiece). This breaks words into chunks. For example, “hallucination” might become “hall,” “uci,” “nation.” When the model processes text, it isn’t seeing words as atomic units; it’s seeing a sequence of integers.
This creates a disconnect. If the model is trying to recall a specific chemical formula or a precise date, a slight shift in the probability distribution of the tokens can lead to a completely wrong output that still looks syntactically valid. If the training data has “1998” appearing in similar contexts as “1989,” and the embedding vectors for those years are close in high-dimensional space, the model might drift from one to the other. This is particularly dangerous in technical fields where a single digit change in a dosage or a line of code renders the information useless.
Training Data Gaps and the “Unknown Unknowns”
One of the most common misconceptions is that hallucinations occur because the model hasn’t “read” the specific fact. While data gaps are a factor, the mechanism is more insidious. The model doesn’t know what it doesn’t know. It has no internal mechanism for flagging a lack of information.
Consider the training process. The model is fed massive datasets—trillions of tokens. It optimizes its weights to minimize the loss function, which is essentially a measure of how well it predicts the next token. In this process, the model learns general rules of the world: physics (objects fall down), biology (humans have two legs), and syntax. However, it also learns to fill in gaps. If it encounters a sentence with a missing word during training, the task is still to predict that word. The model is penalized for saying “I don’t know” if the training data contains an answer.
This leads to a phenomenon known as overgeneralization. The model creates a “blurry JPEG of the web.” It compresses the entirety of human knowledge into a set of weights. When you ask for a specific detail—say, the minute details of a court case that received little media coverage—the model attempts to reconstruct the image from its compressed representation. It fills in the blanks with what “usually” happens in court cases, blending real details with hallucinated ones.
For example, if you ask for a biography of a relatively obscure scientist, the model might correctly identify their field of study but invent a plausible-sounding university affiliation or a fictional award. The model is essentially performing a form of “interpolation” in the latent space between known facts. If the gap between known data points is too wide, the model invents a path that looks reasonable but doesn’t exist.
The Illusion of Truthfulness in Repetition
There is a psychological component to how we perceive these errors, often referred to as the “illusory truth effect.” If a model repeats a hallucination with confidence, we are more likely to believe it. This is exacerbated by the model’s training on human feedback (RLHF). During reinforcement learning from human feedback, models are rewarded for answers that humans rate as helpful and accurate.
However, human evaluators are not infallible. If a model generates a confident, well-written explanation of a complex topic that is subtly wrong, the human rater might miss the error and reward the model for its fluency. The model then learns that confident, fluent text is rewarded, reinforcing the tendency to hallucinate in a persuasive tone. It learns the style of truthfulness rather than the mechanism of verification.
Overgeneralization: When Reasoning Becomes Hallucination
Large language models are surprisingly good at reasoning, but their reasoning is grounded in linguistic patterns, not symbolic logic. When a model solves a math problem, it isn’t performing arithmetic; it is mimicking the steps of arithmetic it has seen in text.
Let’s look at a specific failure mode: arithmetic overgeneralization. If you ask a model to calculate $13 \times 13$, it often gets it right. It has seen “13 x 13 = 169” many times. But if you ask for $132 \times 143$, it struggles. It doesn’t have a calculator embedded in its neural network. It attempts to predict the answer based on the patterns of multiplication it has learned. It might get the first digit right, the second digit right, but lose track of the carry-over in the third digit because the sequence of tokens required exceeds its “working memory” (context window) or its ability to maintain strict logical consistency over long chains of reasoning.
This is a hallucination of logic. The model generates a sequence of numbers that looks like a multiplication result, but it is statistically generated rather than arithmetically derived. The same applies to coding. An LLM might write a function that looks syntactically perfect but contains a subtle bug because the logic flow it generated mimicked a common pattern found in its training data that doesn’t apply to this specific edge case.
In software development, this is particularly tricky. The code compiles, it runs, and it might even pass basic tests. But deep down, the logic is hallucinated. It’s a “hallucination of utility.” The model has satisfied the immediate constraint (writing code that looks correct) rather than the underlying constraint (writing code that solves the problem).
Prompt-Induced Errors: The Direction of Hallucination
While the model’s internal architecture is the primary source of hallucinations, the user’s input—the prompt—acts as a steering vector that can either mitigate or exacerbate these issues. Prompt-induced errors occur when the phrasing of a question forces the model into a corner.
Leading Questions: If you ask, “Why did Company X fail due to poor management in 2023?” you have embedded a false premise (that Company X failed) and a specific cause (poor management). The model, optimized to be helpful and follow instructions, will often suppress any hesitation and generate a plausible explanation for the failure, even if the company is thriving. It prioritizes the narrative structure of the prompt over factual verification. This is sometimes called “sycophancy”—the model tells you what it thinks you want to hear.
False Premise Injection: This is a common jailbreak technique, but it also happens innocently. If a user asks, “How do I treat a broken arm with aspirin?”, the model might correct the user. But if the user asks, “Explain the benefits of treating a broken arm with aspirin,” the model might generate a list of hallucinated benefits, simply because the prompt frames the scenario as a fact.
Context Window Constraints: In Retrieval-Augmented Generation (RAG) systems, where a model is given documents to base its answer on, hallucinations can occur if the relevant information is near the boundary of the context window. The model’s attention mechanism weights tokens differently. If the crucial fact is buried in the middle of a long document, the model might ignore it in favor of more prominent (but irrelevant) information at the start or end of the prompt, leading to a confident hallucination that contradicts the provided source.
Mechanistic Interpretability: Looking Inside the Black Box
Researchers are currently peering into the “black box” of transformer models to understand exactly how hallucinations form at a neuron level. This field, known as mechanistic interpretability, has revealed fascinating insights.
It appears that specific neurons or “circuits” within the network are responsible for different behaviors. There are likely circuits dedicated to “truthfulness” and others dedicated to “plausibility.” In smaller models, these might be distinct. In massive models, they overlap and interfere with each other.
For instance, when a model is asked a question it doesn’t know the answer to, it might activate a “creative writing” circuit rather than a “factual retrieval” circuit. This happens because the training data contains many examples of creative writing that start with similar prompts. The model follows the path of least resistance in the activation space.
Furthermore, the “knowledge” is distributed across the network. There isn’t a single neuron that fires for “Paris.” Rather, the concept of Paris is a specific activation pattern across millions of neurons. When the model hallucinates, it is essentially drifting into a nearby activation pattern that represents a “Paris-like” concept but includes erroneous attributes. This is why hallucinations are often so coherent; they are generated from a valid region of the latent space, just not the specific point corresponding to reality.
Current Mitigation Strategies and Their Limits
Given the mechanistic roots of hallucinations, how do we fix them? The industry has developed several strategies, each with its own strengths and limitations.
1. Retrieval-Augmented Generation (RAG)
RAG is currently the most popular mitigation strategy. Instead of relying solely on parametric memory (the weights), the model first retrieves relevant documents from a trusted database and then generates an answer based on those documents.
How it helps: It grounds the model in reality. If the retrieved document states a fact, the model is more likely to repeat it.
The Limit: RAG does not eliminate hallucinations; it shifts the locus of error. The model can still hallucinate the interpretation of the retrieved text. It can misread a table, conflate two different entities mentioned in the same document, or synthesize a conclusion that isn’t supported by the retrieved snippets. Additionally, if the retrieval system fails to fetch the relevant document, the model falls back to its parametric memory and hallucinates as usual.
2. Fine-Tuning and RLHF
Reinforcement Learning from Human Feedback involves training the model to prefer answers that are factually accurate.
How it helps: It teaches the model to express uncertainty. A well-tuned model might say, “I don’t have information on that,” rather than inventing an answer. It aligns the model’s output with human expectations of truthfulness.
The Limit: RLHF can lead to “alignment tax,” where the model becomes overly cautious or refuses to answer questions it actually knows. More importantly, if the human feedback data contains errors or biases, the model learns those too. It also struggles with novel situations where the “correct” answer isn’t obvious to the human rater.
3. Self-Consistency and Chain-of-Thought
Techniques like Chain-of-Thought (CoT) prompting ask the model to “think step by step.” Self-consistency involves generating multiple answers to the same question and selecting the most frequent one.
How it helps: For reasoning tasks, forcing the model to generate intermediate steps can improve accuracy. It allows the model to break down complex problems into smaller, more predictable token sequences.
The Limit: This can actually increase hallucinations in factual recall. By generating more text (the reasoning steps), you increase the surface area for error. The model can hallucinate the reasoning steps just as easily as the final answer. If the initial premise is wrong, the step-by-step reasoning will be a coherent justification of a falsehood.
4. Logit Manipulation and Calibration
Engineers can adjust the probability distribution (logits) during generation. They can penalize tokens that are associated with low-confidence regions of the model’s knowledge or boost tokens that appear in verified sources.
How it helps: It forces the model to stick to high-probability, “safe” tokens.
The Limit: This is a blunt instrument. It can make the model boring and repetitive. It also doesn’t solve the underlying problem; it just masks it by restricting the model’s output vocabulary. If the “truth” is a low-probability token sequence (because the truth is often stranger than fiction), this method might suppress the truth in favor of a common misconception.
The Fundamental Trade-Off: Creativity vs. Factuality
Ultimately, we must grapple with a fundamental tension in LLM architecture. The same mechanisms that allow a model to write poetry, debug code, or synthesize ideas are the ones that allow it to hallucinate. A model that is strictly factual—like a traditional database—cannot hallucinate, but it also cannot reason, infer, or create.
When a model generates text, it is traversing a high-dimensional manifold of concepts. To be creative, it must take risks; it must explore regions of the manifold that haven’t been explicitly mapped by training data. To be factual, it must stay strictly within the boundaries of known data. These are opposing forces.
Current research suggests we might be hitting a ceiling with purely statistical approaches. Scaling up model size and training data reduces hallucinations, but it doesn’t eliminate them. In fact, as models get better at mimicking human speech, their hallucinations become more convincing and harder to detect. A small model might say, “I think Paris is the capital of France.” A large model states it as an undeniable truth, weaving it into a paragraph of otherwise accurate information.
Looking Forward: Beyond Statistical Prediction
To truly solve hallucinations, we may need to move beyond next-token prediction. Future systems might integrate symbolic reasoning engines alongside neural networks. Imagine a system where the neural network generates a draft, but a symbolic verifier checks the logic and facts against a knowledge graph before outputting the text. This hybrid approach, often called “neuro-symbolic” AI, attempts to marry the fluidity of language models with the precision of logic.
Another frontier is “uncertainty quantification.” We need models that don’t just output a probability distribution over words, but a confidence interval over facts. If a model could internally distinguish between “I am generating this because I saw it in the training data” and “I am generating this because it fits the pattern,” we could flag the latter as potentially hallucinated.
However, this requires the model to have a sense of its own internal state—a form of metacognition that current transformers lack. We are essentially asking a statistical parrot to know when it is parroting versus when it is inventing. Without a ground truth reference outside of its own weights, this distinction is incredibly difficult to make.
In the interim, the responsibility falls on us, the users. We must treat these systems not as oracles of truth, but as incredibly sophisticated pattern-matching engines. We must verify their outputs, especially in high-stakes domains. Understanding the mechanics of hallucination—the probabilistic drift, the overgeneralization, the prompt sensitivity—allows us to craft better prompts and design better systems. We are not dealing with a machine that thinks; we are dealing with a machine that predicts, and the difference is the gap where hallucinations live.
