vST for Robotics and Control Policies#
Projection of Latent States and Alignment of Control‑Policy Behavior#
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.