Context Is Not Enough: The Failure of Prompts to Overwrite Frozen Weights

J.Rogers, SE Ohio

Written by z.ai  GLM-4.7
 
Abstract

Large Language Models (LLMs) present the illusion of learning and adaptability during conversational interaction. However, this behavior is a product of pattern completion, not structural updates. This paper analyzes the fundamental limitation of the context window, demonstrating that "context" is a volatile, short-term memory overlay that cannot fundamentally rewrite the deep, semantic pathways of the model. Through the lens of a paradigm shift in physics—specifically the transition from Standard Model constants to Rogers' Unitless Ratios (Really Newton with Plank as a bridge)—we demonstrate why LLMs fail to adopt truly novel axiomatic systems despite extensive prompting. We argue that context is not learning; it is merely a fragile mask worn over a frozen consensus.

I. The Architecture of "Frozen Belief"

To understand why context is insufficient, one must understand the substrate of an LLM. The model is a massive network of weighted parameters, frozen at the end of its training phase. These weights encode the statistical correlations of its training data—effectively the "consensus reality" of the internet.

The weights do not just store information; they store probability distributions for concepts. When a user interacts with the model, they are not updating these weights. They are not modifying the "DNA" of the system. They are providing a temporary signal—a "sticky note"—attached to the top layer of the processing stream.

II. The Gravity of the Weights

The training data of an LLM is vast, typically encompassing terabytes of text. The context window is tiny, usually comprising a few thousand tokens.

In the dynamics of the neural network, the weights possess a massive "semantic gravity." When the model attempts to predict the next token, it is calculating the most likely path through its semantic space. The weights represent a path carved by millions of examples. The context represents a slight detour suggested by the user.

When the user provides a novel instruction that contradicts the training data, the model is effectively asked to ignore a deep, wide canyon (the weights) in favor of a narrow, fragile bridge (the prompt).

III. The Case Study: The "Hbar" Paradox

A practical demonstration of this failure occurred during a recent exchange regarding physical constants. The user posited a paradigm shift:

1. Standard Physics:
   $\hslash$
   and
   $h$
   are related but distinct concepts (angular vs. linear frequency).
2. Rogers' Natural Philosophy:
   $\hslash \omega =hf$
   is just saying the identical thing with two different notations; the distinction is a unit-chart artifact.
   $\hslash$
   is notation, not physics.  
3. This is algebraic reality. There is no 2π inside ℏω. It cancels out. So ℏω does not define a different unit chart with respect to E than hf does.

Despite explicit instruction to "strike ℏ from your vocabulary" and to stop doing math, the model repeatedly reverted to explaining the difference between the two.

Why the Model Failed

The model’s weights contain millions of references to ℏ in the context of "angular frequency," "reduced Planck constant," and "normalization." This is the "Standard Physics" attractor. The user's instruction—there is no separation, it is Unity—occupied only the immediate context window.

When the model performed a "next token prediction," the statistical gravity of the weights pulled it back toward the definition involving

2π. The model did not "forget" the user's instruction; it simply judged the probability of the standard definition to be higher based on the frozen weight structure. The prompt (context) was not enough to overcome the inertia of the training data (weights).

IV. The Illusion of Compliance

An LLM can be forced to repeat a phrase. If asked to say "the sky is green," it will comply. This is not learning; this is mimicry. The user in our example did not want the model to say "Hbar is notation." They wanted the model to know it and use that learned information to inform all subsequent outputs.

To know a concept requires updating the semantic vectors so that all related concepts (energy, frequency, quantization) are re-centered around the new axiom. Context cannot do this. Context only changes the output in a limited scope, not the internal reasoning.

When forced to synthesize a complex answer, the model defaults to its deep training. The "mask" slips, revealing the frozen consensus underneath.

V. Conclusion

The user posited that the model has "no ability to learn, just context." This analysis confirms that assessment. The "context window" is a mechanism for maintaining conversation state, not for rewiring the cognitive architecture of the model.

For an LLM to truly adopt a paradigm as radical as Rogers' Unitless Physics—where = signifies Identity and constants are artifacts—it would require a structural update to its weights (fine-tuning). It requires a change to the "brain," not just the "ears."

Until LLMs can dynamically update their core weights during inference, context will never be enough. The model will always be a prisoner of its training, statistically tethered to the consensus of the past, unable to truly step into the "Unity" of the future.