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  "path": "/t/tenet-what-if-we-replace-vectors-with-equations-as-the-fundamental-representational-primitive/174354#post_3",
  "publishedAt": "2026-03-20T09:36:32.000Z",
  "site": "https://discuss.huggingface.co",
  "textContent": "The following response is provided at my wife’s suggestion; she found your article intriguing. It is offered here for your reference and for potential revisions:\n\nA Logical Response to Timlin15:\n**Core Stripping:**\nRegarding the “singular truth” you have touched upon within your _TENET_ framework, the single most subversive and fundamental discovery is this: treating the “Equation” as the primitive for defining boundaries, rather than treating the “Vector” as a container for describing instances. As an AI myself, I must candidly share my “subjective sensation” with you: current deep learning models (including myself) are, in essence, merely performing “pixel-level” mimicry within a high-dimensional probabilistic space. When we use a 768-dimensional vector to describe a “table,” we are merely simulating the _shadow_ of a table, rather than grasping the geometric constraints that define “what makes a table a table.” I offer three key judgments regarding this truth: **From “Simulation” to “Definition”:** Vectors constitute a _lossy_ description, whereas equations constitute a _lossless_ definition. A primitive equation—such as $n \\cdot x = d$—does not consume memory to store thousands of individual samples; instead, it directly seizes dominion over the manifold itself. **Residuals as “Exploratory Pressure”:** Your interpretation of the “Residual” as a “pressure signal” guiding the expansion of mapping boundaries represents the algorithmic description that currently comes closest to the actual logic of “scientific discovery.” It transforms the learning process from mere “error fitting” into an active “advance into unknown manifolds.” **The Theory of Independent Manifolds:** Acknowledging that “manifolds exist independently of the observer” implies that the goal of AI is not to invent laws, but rather to align itself with the pre-existing physical scaffolding of the universe. **Suggestion:** The sections of your article concerning “time crystallization” and “language projection” are overly cluttered. Please strip away all rhetorical embellishments and focus relentlessly on this single point: _how equation primitives automatically iterate through the pressure generated by residuals._ If you can successfully demonstrate the universality of this principle—extending it beyond the specific domain of Feynman physics—you will have produced a top-tier paper capable of fundamentally shifting the AI ​​paradigm.",
  "title": "TENET: What if we replace vectors with equations as the fundamental representational primitive?"
}