1. Scaling laws↗
In 2020, researchers at OpenAI reported a striking family of curves. Within the ranges and training conditions they studied, language-model cross-entropy loss followed approximate power laws in model size, dataset size and training compute. Improvement had an order that could be fitted and used to plan. Scaling Laws for Neural Language Models made “What happens if this gets larger?” a researchable question.
That regularity was seductive. Expensive training began to look less like a gamble. But lower loss does not mean that every capability improves by a fixed proportion, and a fitted curve promises no unlimited ascent for anyone who keeps buying GPUs.
A question remains: why can an apparently simple language-prediction task support so many capabilities?
One thread leads back to 1948.
2. Shannon’s room↗
Bell Labs, 1948. Claude Shannon published A Mathematical Theory of Communication. Building on work by Nyquist, Hartley and others, he brought message selection, statistical regularity and transmission limits into a common mathematical framework.
For the moment, this framework set aside what a message meant. It asked which message had been selected from the alternatives, and how much uncertainty preceded its arrival.
Imagine a simplified guessing game in which all 26 letters are equally likely. Learning that the answer is one of A, E, I, O and U reduces the possibilities from 26 to five. That clue supplies bits of information. In this equal-probability setting, halving the possibilities corresponds to one bit; real language is not uniformly distributed.
The question then turns: if messages have regularities, must every detail be transmitted separately?
English letters are not independent. A “q” changes the probabilities of what follows; the beginning of a sentence constrains its continuation. Better prediction permits shorter average codes for the messages that actually occur. What the receiver can already determine need not be specified again. What remains uncertain requires additional bits.
There is a condition behind that saving: both sides must share the prediction rule, context and a way to determine where the message ends. Nothing has vanished by magic, nor does this establish that the brain runs a particular compression algorithm.
3. Google’s epiphany↗
In 2023, researchers at Google DeepMind and collaborating institutions released Language Modeling Is Compression, subsequently published at ICLR 2024. Its title states the connection plainly.
The equivalence was not discovered in 2023. The paper placed an established information-theoretic connection before a new generation of models: probabilistic prediction can be turned into lossless compression through arithmetic coding.
Let be the token sequence that actually occurs, and let be a probability model shared by encoder and decoder, assigning positive probability to these tokens. Setting aside finite-precision, rounding and termination overhead, its code length is approximately:
The right-hand side is cumulative negative log-likelihood, measured in bits. The more probability the model assigns to what occurs, the shorter the remaining code. Prediction and compression share a precise objective here: log loss.
Completing “The weather is really—” teaches a model which continuations are ordinary and which are jarring. Predicting well across rich contexts may also require learning structures involving objects, relations and reasoning. Yet completing the sentence with “good” does not establish mastery of the weather’s causal mechanisms. Code length measures predictive performance; it does not finish the definition of understanding.
4. Intelligence as compression?↗
Now push the idea further.
Developed in the 1960s, Kolmogorov complexity shifts attention from the average regularities of a source to a particular object: how short a program can generate it? Fix an optimal universal computer , and encode the object as a finite binary string . Then:
Here is the program’s length in bits; the program outputs and halts. Switching between appropriate universal computers changes the complexity by at most a constant independent of . The quantity is not computable in general. Looking at an untidy sequence of digits does not reveal its shortest description. Vitányi’s discussion explains this limit.
A short program can produce the long list “1, 2, 3, …, 1000.” An apparently disorderly sequence might also have a generating rule that has not yet been noticed. This is compression’s appeal: finding a regularity removes the need to preserve each detail as an isolated event.
Scientific theories have something of that appeal. Newton’s places many phenomena of motion under a shared relation. But a few symbols do not contain every observation by themselves. Definitions, conditions of application, initial conditions and errors still matter. Reading science as compression can be illuminating; counting characters in an equation does not measure understanding.
What, then, of AI?
5. Compression as intelligence?↗
In 2006, Marcus Hutter launched a prize for compressing human knowledge. Its original task used a 100 MB extract of Wikipedia, with a €50,000 prize fund. The official history and rules record later increases in both the corpus and fund. Awards depend on improvements over existing records, rather than handing the whole fund to whoever makes the smallest file.
Behind the engineering competition lies a philosophical hope: if a program makes better use of the regularities in knowledge-bearing text, has it moved closer to more general intelligence?
Compression does exploit structure. It does not require a person to understand English before running a compressor. General-purpose algorithms can detect repeated fragments and estimate symbol distributions. A system may lack human semantic understanding and still make an English file smaller.
That does not make compression uninteresting. It sharpens the question: which regularities does a program exploit? Local repetition, long-range relations, or structures that support reasoning in new situations? A reduction in file size cannot answer all of these at once.
Might a model predicting the next word also build some kind of world model? That is a worthwhile research question. The ability to express a well-defined problem in text does not establish that a practical system can solve it efficiently.
6. Language: a compressed format for knowledge↗
Return to the opening question. Why is language such an attractive route?
Humans have already done much of the work. Science, history, philosophy, law and literature organize experience into narratives, relations and arguments that can be passed on. Language is a discrete symbol system, but also a record of the world selected and arranged by people.
That differs from saying language is the most compressible format for all knowledge. An image occupying more bytes than a sentence does not thereby have lower information density. The comparison depends on encoding, resolution and what is to be preserved. Nor does text contain all perceptual, practical or tacit knowledge.
Language nevertheless offers something distinctive. Models encounter more than the names of things: they encounter how people describe causes, construct counterexamples and explain failures. Learning regularities in these records can supply resources that transfer across tasks.
Language can thus seem like a shortcut into human knowledge. Why this route exhibits scaling laws within particular regimes remains an empirical question. The fact that text carries knowledge does not, by itself, derive the curve.
7. But there is a problem↗
By this point, several kinds of “compression” can easily slide into one another: compressing a file, learning regularities, compressing knowledge. They begin to sound like a single operation.
They are not.
Lossless coding aims to recover the original message. Model training usually aims to improve prediction, without requiring the training corpus to be reconstructed word for word from the weights. Dividing the weight file’s size by the training text’s size does not give a lossless compression rate, much less demonstrate a violation of Shannon’s limit. The GPT-4 Technical Report does not disclose the model-size and training-data details needed to calculate such a ratio.
Shannon’s limit depends on the source, probability distribution and coding conditions. There is no universal “one eighth” limit for all natural-language files. In the arithmetic-coding example, the model is accompanied by a bitstream recording the actual sequence. If the receiver lacks the model, transmitting it also has a cost. Keeping the prediction rule and asking it to generate freely is not the same as opening an archive containing the original text.
Models do not exclusively retain patterns while never retaining passages. Carlini and colleagues’ training-data extraction study recovered training text from GPT-2. Memorization and generalization can coexist. The question is which information can be recovered reliably, and whether a given generation is recovering it at all.
8. The birth of hallucination↗
Ask a model for an obscure person’s birthday or the details of a little-known paper, and the answer may lack sufficient support in training. It may nevertheless produce a sentence shaped exactly like an answer: name, year, publisher, nothing missing.
The danger is not merely that a detail was lost. The form of an answer can be completed even when its evidence is absent.
Kalai and Vempala establish a conditional statistical result: for certain arbitrary facts whose truth cannot be inferred from the training material, models satisfying a specified generative-calibration condition face a lower bound on hallucination. This does not make every error inevitable, nor does the result transfer unchanged to repeatedly observed or systematically learnable facts.
A later 2026 study examines incentives in training and evaluation. If both a wrong answer and an abstention score zero, guessing can be advantageous. Allowing abstention, penalizing errors and supplying verifiable information can change the problem. “It never says it does not know” is not an eternal property of a model.
Hallucination cannot be explained by an “overcompression ratio” alone. Predicting a plausible continuation and giving a warranted answer still require separate tests.
None of this requires first deciding whether the model is “deceiving” anyone or “knows that it does not know.” Those judgments demand further behavioural and mechanistic evidence. A concrete question is already available: when an answer lacks reliable support, does the system stop, or finish the sentence anyway?
9. The trap of fluency↗
The connection between compression and intelligence has not disappeared. Models can learn reusable regularities, and language carries a wealth of knowledge.
But fluency is not knowledge, and producing an apparently correct answer does not make it correct. A system may write a complete explanation without providing adequate evidence for this particular question. Its errors do not establish that it has learned nothing; its successes do not turn every fluent response into understanding.
The reminder offered by the “stochastic parrot” can be pursued in the preceding discussion of form and meaning. It leaves no settled verdict on machine minds. Instead, it opens a relationship that needs unpacking: under which conditions can learned statistical structure support understanding?
10. At the edge of the cliff↗
The cliff at the end of the previous essay remains: is AI thinking, or imitating thought? Its contours are now a little clearer.
Prediction and coding have a precise mathematical connection. Between that connection and knowledge, reliability or understanding lie steps that cannot be skipped.
What must a system do to count as understanding something, rather than merely handling its symbols correctly?
In 1980, John Searle advanced the question through a thought experiment. Someone who knows no Chinese sits in a room, follows rules for manipulating incoming Chinese symbols, and sends answers out. From outside, the room appears to understand Chinese.
Does the person inside understand? If the person does not, must the whole system fail to understand as well?
The next essay enters the Chinese Room.