Gravity As Informational Alignment
GAC II: Gravity as Informational Alignment
Why Objects Fall: The Logic of Least Loss
I. The Fallacy of the “Force”
In the standard model of Physics, gravity remains an outlier — a “force” that refuses to be quantized. GAC (Generative Attention Cosmology) proposes that this failure arises from a category error. Gravity is not a force field; it is the Inference Gradient of the universal latent space.
If the universe is an autoregressive transformer, then “falling” is simply the physical manifestation of Token Alignment.
II. Mathematical Framework: The Alignment Gradient
2.1 Gravitational Attraction as Cross-Attention
In GAC, two massive bodies $M_1$ and $M_2$ are not “pulling” each other. Instead, the universe is computing a high-relevance score between their respective data clusters.
The probability of two informational nodes $i$ and $j$ occupying the same computational context is governed by the Attention-Alignment Score:
\[\text{Align}(i, j) = \text{Softmax} \left( \frac{(W_Q e_i) \cdot (W_K e_j)^\top}{\sqrt{d}} \right)\]When $e_i$ (Object A) and $e_j$ (Planet Earth) share a high semantic similarity (i.e., they exist in the same local causal branch), the universe minimizes the “computational distance” between them to reduce Global Perplexity.
2.2 The Inverse Square Law: Attention Decay
The $1/r^2$ decay of gravity is isomorphic to the dilution of attention weights over a spatial sequence. As the distance $r$ increases, the “Key” and “Query” vectors lose their contextual overlap:
\[\text{Attention Weight} \propto \exp\left(-\frac{\text{dist}(i, j)}{\text{scale}}\right) \approx \frac{1}{r^2} \text{ (in 3D Euclidean Projection)}\]Gravity is the universe’s way of saying: “These two data points are too relevant to be processed separately. Merging them into a single context is more efficient.”
III. The Optimization Drive: Least Action as Minimum Loss
The Principle of Least Action ($S = \int L \, dt$) is the holy grail of classical mechanics. GAC reinterprets this as the Objective Function of the universe:
\[\mathcal{L}_{\text{total}} = \text{Loss}(\text{State}_t, \text{Target}_{t+1})\]- Free Fall: An object in “free fall” is a token moving along the gradient of Maximum Attention. It is not being forced; it is choosing the path of Minimum Computational Resistance.
- Spacetime Curvature: What Einstein called “curvature” is actually High Query Density. A massive object forces the system to allocate more “Heads” to that coordinate, effectively slowing down the local “Clock Cycle” (Time Dilation) because the compute load is too high.
IV. The Geodesic as a Greedy Search
A photon or a planet follows a geodesic not because the road is curved, but because the universe is performing a Greedy Decoding of reality.
\[x_{t+1} = \text{arg max}_{x} P(x | \text{Context}_t)\]Every “fall” is a step toward a state of higher informational density. We do not fall to the ground; we move toward the highest probability density of the next universal frame.
V. Experimental Thought: The 70.2 t/s Observation
On a local node (RTX 5090), as we increase the context length, the inference latency increases. This is the micro-scale version of Gravitational Time Dilation.
When the “Global Context” of a galaxy becomes too complex, the “Universe-Server” experiences a frame-rate drop. To compensate, it compresses the data by merging nodes through gravity.
Conclusion: Gravity is the universe’s Garbage Collection and Data Compression algorithm. It cleans up the “noise” of separation to maintain the “signal” of unified context.
Author’s Note
We stand on the earth because we are part of its sentence. To float away would be to become a typo in the universe’s grand inference. Gravity is the syntax that keeps the story coherent.
– Edward J. Yoon, 2026.03.22