Understanding language models through state-space dynamics rather than semantics.
Latent space is not a "vector cloud" or "embedding library." It is a high‑dimensional dynamical landscape shaped by the model's weights, attention topology, and training distribution. Navigation through this landscape follows structural constraints — not meaning.
1. Latent states as points in a constrained manifold
Each token sequence encodes into a point on a manifold defined by the model's internal geometry. Key properties:
- Dimensionality: Typically thousands of dimensions.
- Topology: Not Euclidean in practice due to nonlinearities, attention routing, and residual pathways.
- Manifold constraints: The model tends to project inputs into specific "basins" — regions reflecting stable patterns.
Implication
Two different prompts land in the same basin if they share structural patterns, not semantics. This explains why unrelated tasks sometimes interact.
2. Navigation = controlled drift under repeated transformations
Each layer applies a transformation:
stateₜ₊₁ = f(stateₜ, attentionₜ, weights)
This creates a discrete dynamical system.
- Residual connections act as integrators.
- Attention acts as a context‑dependent routing mechanism.
- Layer norms act as stabilizers.
LLMs are not selecting answers — they are following a trajectory.
3. Attractor regions
The latent space contains attractors: regions that trajectories fall into. Attractors arise from:
- repeated gradient reinforcement during training,
- frequency‑dominated token patterns,
- structural templates (lists, explanations, plans),
- safety tuning and reward shaping.
Once the model enters an attractor, the output tends to follow a predictable pattern.
Example
When an input resembles "step‑by‑step," the trajectory moves toward the chain‑of‑thought basin.
4. Why domain mismatch causes incorrect trajectories
If the input is structurally ambiguous, the encoded state may:
- fall into the wrong basin,
- drift toward a statistically dominant attractor,
- trigger patterns unrelated to the intended domain.
This is the latent‑space origin of hallucination.
The model isn't wrong — it is following the only stable trajectory available from the representation you forced it into.
5. State‑space navigation with constrained domains
If the domain is fixed before encoding, navigation becomes reliable.
Example structure:
raw_input → domain_extractor → canonical_form → encode → latent_trajectory
The trajectory becomes reproducible because the manifold region is fixed.
This is the foundation of:
- 0‑context (forcing isolation),
- domain intelligence (rewriting inputs),
- verifiable agent loops (stabilizing outputs).
6. Representation shaping
You can influence navigation by controlling the input representation:
- enforcing schemas,
- using structural cues,
- flattening ambiguity,
- removing irrelevant entropy,
- collapsing multi‑domain prompts into one resolved domain.
This is the equivalent of placing the system into the correct coordinate frame before simulation.
Stability analysis for multi‑LLM pipelines.