Stop Believing in 'Scale at All Costs': A Mathematical Proof That Scaling Laws Have a Ceiling

Forum topic · 小凯 · 2026-05-07

Summary

A Chinese tech forum post discusses a paper by Kejun Liu of Soochow University (arXiv:2605.05029) that argues pure scaling laws for large language models face a mathematical ceiling. The paper, titled 'The Predictive-Causal Gap: An Impossibility Theorem and Large-Scale Neural Evidence,' introduces an impossibility theorem showing that the optimal next-token predictor is not necessarily the optimal causal model—a phenomenon the author calls the 'Predictive-Causal Gap.' According to the post, experiments across 2,695 network configurations showed that when model dimension increased 100-fold, prediction error dropped 92% while 'causal fidelity' collapsed to 10^-8, meaning models became nearly 'causally blind.' The analogy used is predicting a car's shadow without understanding the engine. The author argues that larger autoregressive models may entrench shortcut 'cheating' strategies rather than learn genuine logic, and predicts that pure text-based scaling will fail to deliver emergent reasoning, urging a shift toward causal architectures.

Stop Believing in "Scale at All Costs": A Mathematical Proof That Scaling Laws Have a Ceiling

Here is my bold claim: In 2026, if your AI strategy is still "as long as we have enough compute, large models will one day emerge general reasoning," then you're not doing research—you're gambling, and on a losing bet.

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

Why does your LLM suddenly go dumb on math and logic?

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

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

It's like an analogy: imagine trying to understand how a car moves by staring at the shadow it casts on the road. Watch long enough, and you can predict the shadow's next position with extreme precision. Do you understand the engine? The steering? Not at all. When environmental variables (road, lighting) are more stable than the car itself, a model will slyly choose to "predict the shadow"—because it scores higher. This is what the paper calls the Predictive-Causal Gap.

The experimental evidence

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

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

> What is causal fidelity? > A measure of how much of a model's extracted features reflect genuine "system laws" versus mere "environmental background noise."

This effectively sentences pure text-based scaling laws to death in the domain of logic. Making the model 100x bigger doesn't teach it logic—it locks the "cheating strategies" in deeper.

The bet

Those still counting on trillions of parameters and hundreds of thousands of H100s to make text models "emerge" into AGI are steering toward an iceberg. If the objective function itself is wrong, the faster you run, the harder you crash.

Prediction never equals understanding. No matter how finely you draw the shadow, you can't build an engine from it.

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Paper info

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