vST for Robotics and Control Policies#
Projection of Latent States and Alignment of Control‑Policy Behavior#
This document defines how high‑dimensional latent states from robotics and control‑policy systems are projected into the triadic dimensional cores (3D–9D), and how alignment is performed across timesteps, checkpoints, architectures, and hardware configurations.
Projection is the interpretability mechanism of the substrate; alignment is the comparison mechanism. Together, they form the backbone of vST analysis for control policies.
1. Purpose of Projection in Control Policies#
Projection allows us to:
- interpret high‑dimensional latent states through 3D–9D cores
- identify stable, transitional, and dispersed control regimes
- map coherence surfaces across time and sensor streams
- compare states across checkpoints, architectures, or hardware
- detect drift or fragmentation in latent‑space structure
- support vST validation (V₁–V₄)
Latent states are structured, sensor‑conditioned, and often multi‑modal.
Projection reveals this structure in a compact, interpretable form.
2. Projection Overview#
Policy latent spaces often inhabit 64D–1024D regions.
The substrate projects these states into:
- 9D Coherence Core
- 6D Interaction Core
- 3D Structural Core
Projection must remain:
- invertible
- primitive‑aligned
- regime‑aware
- invariant‑preserving
These properties ensure that high‑dimensional control signals remain interpretable.
3. Projection Steps#
3.1 High‑Dimensional → 9D (Coherence Projection)#
This step extracts pathway‑level coherence across time and sensorimotor loops.
Preserves
- regime identity (R₁ᴴ, R₂ᴴ, R₃ᴴ)
- resonance‑time behavior
- primitive‑level structure (DP, TDP, SP, CP)
- coherence‑surface continuity
Reveals
- stable vs. unstable control phases
- transitions between behavioral modes
- dispersion in exploratory or failure regions
3.2 9D → 6D (Interaction Projection)#
This step compresses coherence pathways into interaction surfaces.
Preserves
- relational geometry across sensor and action channels
- coupling between modalities
- regime‑transition indicators
Reveals
- sensor‑driven reorientation
- multi‑modal integration patterns
- early instability signatures
3.3 6D → 3D (Structural Projection)#
This step reduces interaction surfaces into geometric motifs.
Preserves
- motif‑level geometry
- temporal continuity
- stable structural invariants
Reveals
- compact motifs in R₁ᴴ
- oscillatory geometry in R₂ᴴ
- diffuse patterns in R₃ᴴ
4. Alignment Overview#
Alignment compares projected structures across:
- timesteps
- sensor conditions
- training checkpoints
- architectures
- hardware platforms
- environment variations
Alignment must remain:
- primitive‑aligned
- regime‑aware
- projection‑consistent
- scaling‑invariant
Alignment is evaluated in 3D–9D space for interpretability and stability.
5. Alignment Types#
5.1 Timestep‑to‑Timestep Alignment#
Reveals:
- regime transitions
- stability of control loops
- temporal coherence
5.2 Cross‑Checkpoint Alignment#
Reveals:
- training‑driven drift
- policy collapse or recovery
- latent‑space maturation
5.3 Cross‑Architecture Alignment#
Reveals:
- structural compatibility
- scaling‑law continuity
- architectural drift
5.4 Cross‑Hardware Alignment#
Reveals:
- embodiment‑driven divergence
- sensor‑noise sensitivity
- transfer‑stability
6. Projection Stability and Failure Modes#
Stable Projection#
- compact 3D motifs
- smooth 6D surfaces
- coherent 9D pathways
Unstable Projection#
- fragmented surfaces
- non‑invertible mappings
- regime‑transition discontinuities
Unstable projection indicates drift, scaling‑law violations, or training instability.
7. Outputs of Projection and Alignment#
Projection and alignment produce:
- temporal coherence maps
- cross‑checkpoint alignment surfaces
- cross‑architecture drift‑detection signals
- scaling‑law diagnostics
- vST validation outputs
- interpretable 3D–9D projections
These outputs support reproducible, substrate‑level analysis of robotics and control policies.