Why don't current LLMs 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.
The DRM Transformer proposes a structural solution.
In a Directional Relational Manifold, the metric G(x) varies with position. This means that certain regions of space can have high curvature—making geodesics in those regions longer, more computationally expensive, and more difficult to traverse. The geometry can encode that certain transitions are intrinsically more difficult than others.
In practice: if the epistemic anchors (manifold reference points) include a "safety" anchor, tokens approaching dangerous regions encounter gamma > 1—the space expands, the resolution increases, the model is forced to "pay more attention" precisely where the risk is greatest. It's not an external filter. It's the geometry of the space that resists.
More importantly: gravity in the DRM Transformer causes tokens with high confidence and a positive history to deform the space around them, attracting other tokens. Tokens with a negative history do not generate this attraction. Alignment is not imposed by a rule—it emerges from the geometry.
This doesn't 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 not be.
Papers:
Open source:
drm-transformer
First empirical result: a 1M parameter DRM Transformer trained on 10M tokens achieves H1=14 (persistent homology rank) with Voronoi foliation coherence=1.0 and ARI=0.69 — below the best result ever achieved by the 50M aletheion-llm-v2 after dedicated epistemic fine-tuning. The geometry is working.
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