AI hallucinations occur because large language models (LLMs) like GPT generate text by predicting the most likely sequence of words based on their training data—not by applying logical reasoning or verifying the accuracy of their outputs. Imagine trying to guess the next note in a song based solely on what you’ve heard so far—it might sound harmonious, but you might not land on the “correct” note if the context isn’t clear or well-defined.

This sequence-based nature means that while LLMs excel at mimicking patterns, they don’t “understand” concepts or facts. They don’t evaluate whether a statement logically follows or aligns with reality. 

Instead, every new word has a small chance of diverging from the truth, especially in complex or ambiguous scenarios. Since the outputs are polished and contextually plausible, these inaccuracies can seem convincing. It’s like building a tower where each block fits nicely, but the foundation may not support it—leading to occasional but significant collapses.

This challenge is why Jaxon developed DSAIL (Domain-Specific AI Logic), a technology designed to apply formal reasoning and verification processes to LLM outputs. By mathematically proving accuracy before responses are returned, DSAIL ensures AI outputs are not only polished but also trustworthy—a critical step for high-stakes applications.

Think of an AI language model as a pianist improvising a song. The pianist doesn’t have the full sheet music—just the notes played so far and a general sense of what sounds good. Each note they play is based on patterns they’ve learned, but they aren’t explicitly thinking about harmony, key signatures, or the overall structure of the piece. Their goal is to make each note sound like it belongs.

Now imagine the pianist is asked to play a symphony they’ve never seen. They’ll still try their best to follow the style and flow, but without an understanding of the symphony’s deeper structure, they might occasionally introduce notes that clash with the intended melody. To an untrained listener, the improvisation might still sound great, even if it’s technically wrong.

Similarly, LLMs generate text by “improvising” word by word based on probabilities. They aren’t analyzing the broader truth or logical correctness of what they’re generating—they’re just choosing words that fit the style and context of the conversation. This is why their responses can feel polished and plausible but sometimes deviate into falsehoods or contradictions.

The harmony of the output often masks these errors, just as a beautiful but slightly off improvisation might still move the audience without being faithful to the original score.

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