DRM-Transformer

Source: Dev.to

Why Current LLMs Don’t Geometrically Distinguish Between Saving and Destroying Humanity

Because the embedding space is flat. In Euclidean space, the distance between “curing cancer” and “creating a bioweapon” is only a cosine angle. There is no curvature, no moral weight, no geometric notion that certain regions of space are more dangerous than others. Geometry is indifferent.

This is a fundamental alignment problem. When the representation space treats all directions equally, the difference between generating a useful response and a destructive response depends exclusively on surface fine‑tuning (RLHF, safety filters). Remove the filter and the underlying geometry offers no resistance.

Directional Relational Manifold

In a Directional Relational Manifold (DRM), the metric (G(x)) varies with position. Certain regions can have high curvature—making geodesics in those regions longer, more computationally expensive, and more difficult to traverse. The geometry can encode that some transitions are intrinsically harder than others.

Practical Implications

• Epistemic anchors (manifold reference points) can include a “safety” anchor.
• Tokens that approach dangerous regions encounter (\gamma > 1) — the space expands, resolution increases, and the model is forced to “pay more attention” precisely where the risk is greatest.
• This resistance is not an external filter; it is built into the geometry of the space.

Gravity in the DRM Transformer

• Tokens with high confidence and a positive history deform the space around them, attracting other tokens.
• Tokens with a negative history do not generate this attraction.
• Alignment thus emerges from the geometry rather than being imposed by a rule.

Alignment Outlook

• The approach does not completely solve alignment, but it shifts the conversation from “how to impose external constraints” to “how to construct geometries that have intrinsic preferences.”
• A planar geometry is morally neutral by construction.
• A curved geometry may embed moral biases.

Papers

• DRM: Directional Relational Manifolds
• The Geometry of Consciousness
• DRM Relativistic Dynamics

Open Source

• Repository: drm-transformer

First Empirical Result

A 1 M‑parameter DRM Transformer trained on 10 M tokens achieves:

• Persistent homology rank (H_1 = 14)
• Voronoi foliation coherence = 1.0
• Adjusted Rand Index (ARI) = 0.69

These metrics are below the best result ever achieved by the 50 M‑parameter aletheion-llm-v2 after dedicated epistemic fine‑tuning, indicating that the geometry is already having a measurable effect.