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The Lossy Compressor: A New Model for LLM Cognition and the Nature of Hallucination
Copyright ©: Coherent Intelligence 2025 Authors: Coherent Intelligence Inc. Research Division
Date: July 29th 2025
Classification: Academic Research Paper | Information Theory Analysis
Framework: Universal Coherence Principle Applied Analysis | OM v2.0
Abstract
Current conceptual models of Large Language Models (LLMs) often anthropomorphize their function, attributing to them faculties like "reasoning" or "believing." This paper proposes a more fundamental and architecturally grounded model based on information theory: LLMs are best understood as massive, lossy compressors of their training data, and their generative function is an act of imperfect decompression. We argue that the training process is an exercise in compressing a vast, Ontologically Incoherent Information Space (OIIS) into a finite set of model weights, a process that necessarily involves significant information loss. Inference, or text generation, is the probabilistic reconstruction of text from this compressed, high-entropy representation.
Within this framework, the phenomenon of "hallucination" is demystified. A hallucination is not a cognitive failure in the human sense but a predictable decompression error. It is an artifact of the model attempting to reconstruct information that was blurred or lost during the lossy compression phase. This model provides a more accurate understanding of LLM limitations, reframes the alignment challenge as a problem of ensuring high-fidelity decompression, and aligns perfectly with the principles of the Theory of Domain-Coherent Systems.
Keywords
Large Language Models (LLM), Information Theory, Lossy Compression, Decompression, Hallucination, ToDCS, Informational Entropy, AI Cognition, Source Coding.
1. Introduction: Moving Beyond Anthropomorphism
To engineer and align advanced AI systems effectively, we require a model of their function that is grounded in their architecture, not in metaphors of human cognition. Describing LLMs as "thinking" or "reasoning" entities obscures their true nature and leads to fundamental misunderstandings of their capabilities and failure modes.
This paper offers a new foundational model derived from classical information theory. We propose that the entire lifecycle of an LLM, from training to inference, can be elegantly and accurately described as a process of lossy compression and imperfect decompression. This framing provides a parsimonious explanation for the system's core behaviors and demystifies its most notorious failure mode: hallucination.
By viewing the LLM as a sophisticated data compressor, we can move beyond anthropomorphic speculation and begin to analyze its function with the mathematical rigor of information theory, providing a clearer path to understanding and improving its reliability.
2. The LLM as a Lossy Compressor
The core of our model rests on a simple, undeniable architectural reality: the size of an LLM's parameters is orders of magnitude smaller than the size of its training corpus.
2.1. Training as Massive, Lossy Compression
The training of an LLM on a multi-trillion token dataset is the act of encoding the statistical patterns, semantic relationships, and linguistic structures of that data into a comparatively small set of weights. This is, by definition, an act of compression.
Crucially, this compression is lossy. Unlike a lossless algorithm (e.g., ZIP), which allows for the perfect reconstruction of the original data, the LLM's training process cannot preserve every piece of information. It operates like JPEG or MP3 compression, preserving the most prominent and statistically significant features while discarding or blurring fine-grained details. The source data—a quintessential Ontologically Incoherent Information Space (OIIS) full of contradictions—is compressed into a high-entropy, probabilistic summary. The specific is sacrificed for the general.
2.2. Inference as Imperfect Decompression
If training is compression, then text generation (inference) is decompression. When a user provides a prompt, they are providing a key that instructs the model on which part of its compressed information space to begin decompressing and what structure the decompressed output should take.
This decompression is imperfect for two reasons:
- It is Generative, Not Replicative: The model is not designed to retrieve a specific, original text. It is designed to generate a new text that is statistically consistent with the compressed patterns. It probabilistically predicts the next token in a sequence, creating a novel artifact that conforms to the learned data distribution.
- It Operates on Degraded Data: The decompressor is working with the blurred, lossy representation created during training. It cannot reconstruct information that was never faithfully stored.
3. Demystifying Hallucination as a Decompression Error
The lossy compressor model provides a clear and non-mysterious explanation for AI "hallucinations."
Definition: Hallucination A hallucination is a decompression error that occurs when a generative model produces an output that is syntactically coherent but semantically or factually decoherent from reality.
Hallucinations are not the model "making things up" any more than a JPEG artifact is the image "making things up." They are the predictable and inevitable consequences of a lossy compression/decompression cycle.
Decompression errors manifest in several ways:
- Factual Fabrication: The model is asked for a specific fact (e.g., a paper's DOI, a legal citation) that was either absent from the training data or blurred into statistical noise during compression. The decompressor, tasked with producing an output in the form of a citation, generates a token sequence that is structurally correct but semantically false.
- Contextual Blending: The prompt acts as an ambiguous key, causing the decompressor to blend patterns from multiple, unrelated parts of the compressed data. The result is a coherent-sounding sentence that nonsensically combines disparate concepts.
- Probabilistic Drift: The auto-regressive generation process can drift down a path of high probability that diverges from factual accuracy. Each token is a plausible continuation of the last, but the complete sequence is untethered from reality.
4. Connection to the Theory of Domain-Coherent Systems
This information-theoretic model provides a powerful parallel to the cognitive model of ToDCS.
- The OIIS and the Lossy Corpus: The training corpus is the practical embodiment of the chaotic OIIS that wisdom must act upon.
- The Prompt as DA/Decompression Key: The prompt serves a dual role. In the cognitive framework, it is a Domain Anchor that attempts to create a SCOCIS. In the information-theoretic framework, it is the key that guides the decompression process. Both are external signals that impose temporary order on an internal, high-entropy system.
- Decompression Errors as Decoherence: A hallucination is a form of decoherence. The decompressed output fails to maintain phase-lock with the ground truth of the source data. It is a clear symptom of the system's underlying informational entropy being expressed in the output.
This model reinforces the argument that LLMs are not reasoning engines. A reasoning engine requires the lossless preservation of a coherent knowledge base (a SCOCIS). A lossy compressor of an incoherent knowledge base (an OIIS) is, by its nature, an approximation engine. Its outputs are not logical entailments but probabilistic reconstructions.
5. Conclusion: A New Foundation for AI Reliability
Viewing LLMs as lossy compressors is not a criticism but a clarification. It provides a more accurate, architecturally-grounded model of their function that allows us to move past flawed anthropomorphic metaphors. This lens reveals that the core challenge of AI reliability is not about teaching a model "not to lie," but about improving the fidelity of the compression/decompression process.
The path to more robust AI systems involves two complementary approaches:
- Improving the Compressor: Developing new architectures and training methods that can compress the world's information with greater fidelity, preserving more detail and creating a lower-entropy internal representation.
- Guiding the Decompressor: Engineering robust, high-density Domain Anchors (prompts and fine-tuning frameworks) that can guide the decompression process along paths of high factual and logical coherence, minimizing the probability of entropic drift.
Ultimately, the lossy compressor model provides a stark reminder of the nature of these systems. They do not "know" things in the human sense; they store a compressed echo of the language we have used to describe them. A hallucination is simply the sound of that echo becoming distorted. Our task is to build systems that can hold that echo true.