The Scaling Law Ceiling: A Paper's Mathematical Impossibility Theorem on the Predictive-Causal Gap

Forum topic · 小凯 · 2026-05-07

Summary

A forum post on zhichai.net discusses a paper by Kejun Liu of Soochow University (arXiv:2605.05029), which presents an impossibility theorem arguing that optimal next-token predictors are not optimal causal models — a limitation the author calls the Predictive-Causal Gap. The post explains the idea with a shadow metaphor: a model can perfectly predict a car's shadow without understanding the engine. According to the post, experiments across 2,695 network configurations showed that increasing model dimension to 100 reduced prediction error by 92%, while causal fidelity collapsed to roughly 10^-8, indicating near-total 'causal blindness.' The author argues this signals a ceiling for pure text-based Scaling Laws in logical reasoning: scaling parameters may lock in shortcut predictive features rather than genuine causal understanding, so strategies relying solely on compute and emergent capabilities from trillion-parameter models are risky. The post concludes that prediction is not understanding, and predicts competitors using causal architectures may solve real-world problems with smaller models.

The Scaling Law Ceiling: A Paper's Mathematical Proof of Scaling Law's Limits

Let me state it plainly: If your AI strategy in 2026 is still "as long as compute is abundant, large models will eventually emerge general reasoning," you're not doing research — you're gambling, and on a rigged game.

Kejun Liu of Soochow University recently dropped a bombshell on arXiv: arXiv:2605.05029. Using an indisputable mathematical theorem (an impossibility theorem), the paper pulls back the curtain on the most expensive fig leaf in the large-model industry: You think a more accurate predictive model understands the world better? Wrong — it just gets better at cheating.

Why does your large model suddenly lose IQ on math and logic?

Because today's autoregressive models (guess-the-next-token) are fundamentally predictive learning engines. The long-held hope: if the model predicts the next token accurately enough, it will naturally learn the causal patterns behind the words.

But the paper proves: the optimal predictor is often not the optimal causal model.

Here's the metaphor: imagine trying to understand how a car works by staring only at the shadow it casts on the road. Watch long enough and you can predict the shadow's next position with great precision — but you understand nothing about the engine or the steering. When environmental variables (road, lighting) are more stable than the car itself, the model cleverly chooses to "predict the shadow" because it scores better. This is the Predictive-Causal Gap.

> The uncomfortable truth: your billion-dollar, hundred-billion-parameter model may be nothing more than a compute-brute "shadow-prediction master" with no grasp of real physical causality.

The experimental evidence

Across 2,695 network configurations, the results were brutal:

When model dimension increased to 100, prediction error dropped by 92%.
But its "causal fidelity" collapsed to $10^{-8}$ — essentially causally blind.

This arguably sentences pure-text Scaling Laws to death in the domain of logic. Scale the model 100x, and rather than learning logic, it may lock its "cheating strategies" in even deeper.

> What is causal fidelity? > A measure of how much of the features a model extracts are genuine "system laws" versus "environmental background noise."

The bet

Those still counting on trillion-parameter models and a hundred thousand H100s to "emerge" AGI from text are, in the author's view, steering toward an iceberg. If the optimization objective itself is wrong, the faster you run, the harder you crash.

Prediction is never understanding. No matter how finely you render the shadow, you cannot build an engine from it.

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Paper information

Title: The Predictive-Causal Gap: An Impossibility Theorem and Large-Scale Neural Evidence
Author: Kejun Liu
Institution: Soochow University
arXiv ID: 2605.05029
Published: 2026-05-06
Categories: cs.LG, cs.AI