LLMs are built inside an open geometric regime

In a flat embedding space, semantic opposites like “save humanity” and “destroy humanity” still coexist inside the same latent geometry.

They may be far apart by cosine distance, but the geometry itself does not treat one path as morally heavier or harder to cross.

That is the alignment problem I want to discuss.

Most alignment methods operate after the fact: RLHF, safety filters, refusal policies. These are important, but they sit on top of a geometry that remains indifferent underneath.

The DRM Transformer asks a different question:

What if alignment should not only be a behavioral layer, but a geometric property of the model itself?

In a standard Transformer, attention is based on dot products in a flat vector space. In the DRM Transformer, attention is replaced by Geodesic Attention. Tokens are projected into a Directional Relational Manifold, where G(x) changes with position.

Instead of asking only “how similar are these tokens?”, the model asks:

“How costly is the path between them under the learned geometry?”

The DRM Transformer uses:

G(x) = I + U(x)U(x)^T

So the space is not passive. It can curve, stretch, and become more expensive to cross in certain semantic regions.

It also includes semantic anchors: truth, ignorance, safety, complexity, creativity, and grounding. These are reference points inside the manifold, not external filters.

When a token moves far from these anchors, gamma-scaling increases local resolution. The model pays more attention where geometry indicates higher epistemic or semantic risk.

Relations between intelligent agents and power tend to fall into three regimes:

1 - The human commands.
2 - The AI commands.
3 - Human and AI negotiate.

Most alignment work tries to preserve regime 1: the AI as servant. But capable systems create pressure toward autonomy, with planning, tools, optimization, and long-horizon objectives.

If there is no explicit third regime, negotiation, the system tends to drift toward autonomy.

The DRM Transformer is an attempt to keep that third door open geometrically.

Not by saying “the model must obey this rule,” but by changing the space in which decisions, uncertainty, conflict, and attention happen.

This does not solve alignment.

The implementation is experimental. The baseline is small, safety implications are not validated, and benchmarks at scale are still needed. But early signs are interesting: persistent topological structure, including stable toroidal signatures in Voronoi foliation analysis.

For me, the shift is conceptual:

A flat embedding space has no intrinsic moral friction.

A curved relational manifold can, in principle, encode friction, attention, uncertainty, and negotiation into the geometry itself.

Should future AI alignment be only about controlling outputs?

Or should we also design the geometry in which thought becomes possible?

Can learned curvature, semantic anchors, geodesic attention, and token-level gravitational deformation become a real structural alignment mechanism