Why Geometry Is the Hard Problem in AI — and What Solving It Unlocks for Manufacturing

Every major AI breakthrough of the last decade has been built on a common pattern: find a way to represent the target domain as discrete tokens or regular arrays, then apply statistical learning at scale. Text → tokens → transformers. Images → pixels → convolutional networks → vision transformers. Proteins → amino acid sequences → AlphaFold.

Geometry has resisted this pattern. Three-dimensional shapes — the foundational data type of engineering and manufacturing — lack the discrete, regular structure that makes statistical learning tractable. A B-rep surface has a variable number of faces, edges, and vertices, with topology that encodes design intent in ways that a pixel grid does not.

This is the hard problem our guests Elissa Ross (Metafold) and Rui Aguiar (Cosmon) are working on — and the breakthrough they are building toward has significant implications for what AI can do in manufacturing.

Why Geometry Doesn't Have Tokens

Language models work because sentences can be represented as sequences of tokens with learnable statistical relationships. The model learns that "the engine overheats when..." predicts certain engineering context words based on co-occurrence across millions of documents.

Try that with 3D geometry. A CAD model of a turbine blade has no natural sequential structure. Its B-rep representation — surfaces, edges, vertices — depends on how the modeler chose to construct it. The same physical shape modeled in two different CAD tools will have different topology, different parameterization, and different vertex count. A statistical model trained to learn from B-rep topology will fail to generalize because topology is not a stable representation of shape.

Three partial solutions exist:

Voxelization discretizes the 3D space around the shape into a regular grid (like pixels, but in 3D). Computationally expensive at any resolution that preserves fine detail.

Point cloud sampling samples points on the surface at random. Stable but loses connectivity — the model doesn't know which points are adjacent.

Mathematical feature extraction converts the geometry into numerical features derived from mathematical analysis: curvature, wall thickness, medial axis transform, accessibility maps. This is Metafold's approach — and it is the one most directly useful for manufacturing AI.

Metafold's Insight: Geometry as Manufacturing-Relevant Features

Metafold's core technical insight is that the relevant signal for manufacturing AI is not the raw topology of the shape — it's the manufacturing-relevant properties of the shape, which can be derived from mathematical analysis.

A CNC machinist looking at a part doesn't reason about B-rep faces. They reason about accessible features, wall thicknesses, internal radii, and reach distances relative to their tooling. A DfM screening AI that reasons from the same mathematical properties — encoded from the geometry directly — can classify manufacturability without requiring the model to learn raw shape topology.

This connects naturally to implicit geometry representation. TPMS (Triply Periodic Minimal Surfaces) and SDF-based designs are already expressed as continuous mathematical functions. Metafold can analyze those functions directly — compute their curvature distributions, evaluate their wall thicknesses, check their feature accessibility — without first converting them to a mesh. The AI pipeline is geometry-function → mathematical feature extraction → manufacturing prediction.

For additive manufacturing in particular, this matters enormously. Complex internal structures — gyroid lattices, topology-optimized internals, conformal cooling channels — are routinely designed as implicit geometry. AI that can reason about those structures mathematically rather than topologically closes the design-to-production loop in ways that mesh-based AI cannot.

Cosmon's Insight: Task Specificity Over Generality

Where Metafold focuses on the geometry representation problem, Cosmon approaches from the other direction: rather than build general geometry AI, build narrow, task-specific agents trained to make one manufacturing decision well.

This is a practical bet on a real phenomenon: a deep learning model trained on 50,000 examples of "is this CNC feature machinable with standard tooling?" outperforms a general geometry model on that specific question. The training distribution exactly matches the deployment distribution. The model's uncertainty is calibrated against real manufacturing outcomes, not synthetic examples.

Cosmon's architecture composes multiple narrow agents to handle the breadth of manufacturing decisions that any single general model would struggle with. The result is an agentic system for design-to-production conversion — not a single geometry model, but a coordinated pipeline of specialists.

What the Breakthrough Unlocks

These approaches converge on a set of manufacturing workflows that were previously inaccessible:

Automated DfM screening at design stage. Geometry AI that can evaluate a CAD model for process-specific manufacturability — before the design leaves engineering — shifts DfM from a manufacturing bottleneck to a continuous design check. Issues that currently cause two-week rework cycles when caught at first article are caught in minutes at the design stage.

AI-assisted lattice design for additive. Implicit TPMS lattice parameters (cell size, wall thickness, orientation) can be optimized by AI against structural and manufacturing constraints — producing lightweighted designs that are analytically characterized before the first powder bed is loaded.

Toolpath classification from geometry features. Feature recognition for CAM programming — the first step toward the 80/20 automation of CAM — requires reliable classification of machined feature types from 3D geometry. Mathematical feature extraction makes that classification tractable for the standard feature families that represent 80% of machining volume.

The geometry problem is not solved. But it is more tractable than it was three years ago, and the companies building the foundational infrastructure are already producing value in production manufacturing environments. The engineering AI stack is not complete without geometry intelligence — and the teams closest to cracking it are building from mathematics up, not from general AI down.