LLMs are not intelligent entities. They are high‑dimensional operators that transform one domain representation into another. This framing removes the mystique and replaces it with structure — the kind you can reason about, control, and engineer around.
This section unifies the ideas we've been developing: latent spaces, domain mapping, representation changes, state‑space thinking, and control‑theoretic intuition.
Why "Transfer Function" is the Right Mental Model
A transfer function describes how an input representation becomes an output representation under a system's internal dynamics. That is exactly what an LLM does:
- Input domain: tokens, structure, implicit state, task-specific cues.
- Operator: the model weights, attention patterns, and latent geometry.
- Output domain: a new sequence that reflects a transformed representation.
LLMs don't "understand" or "reason." They apply a deterministic operator over a probabilistic latent space.
Domain → Latent → Domain
The internal flow mirrors control theory:
1. Encoding (Domain → State)
Raw text becomes a vector state. This is the model's internal representation of the problem — the equivalent of moving into Laplace or frequency space.
2. Propagation (State → State)
Attention layers act as a cascade of operators, composing multiple transformations.
3. Decoding (State → Domain)
The final latent state is projected back into the token domain.
Each step is a transfer between representations. No step requires intelligence.
The Core Insight
If you change the representation, you change the solvability.
This allows you to solve:
- tasks you haven't explicitly prompted,
- workflows spanning multiple domains,
- problems that look impossible in token space.
This is why prompts that restructure the domain outperform prompts that try to guess instructions.
Operator Perspective vs Intelligence Perspective
Intelligence Perspective:
- LLMs "figure out" answers.
- LLMs "reason" or "understand."
- Wrong outputs imply "lack of intelligence."
Operator Perspective:
- Inputs were in the wrong representation.
- The operator mapped to the wrong domain.
- The latent geometry amplified irrelevant dimensions.
This difference is decisive in building robust systems.
Domain Mismatch
Most LLM failures come from domain mismatch:
- The input domain does not reflect the problem.
- The operator transforms something that doesn't encode the correct structure.
- The output is a valid transform — but of the wrong domain.
This is why reformatting the problem (like moving to Laplace domain) works.
Domain Intelligence
When you craft inputs that align with the latent operator, you bypass domain mismatch entirely. Domain Intelligence systems solve this by:
- Identifying the required representation.
- Rewriting the problem into a solvable transform.
- Passing it through the LLM only after domain alignment.
- Interpreting output through the correct downstream domain.
This produces high reliability without requiring "reasoning." It's engineering.
LLMs as Part of a Control Loop
In large systems, the LLM is just one operator in a feedback loop:
- System state: context, environment data, traces.
- LLM operator: transforms state into an action or new state.
- Environment response: browser, API, user.
- Feedback: error signals, correction.
This mirrors:
- PID loops
- Model-based control
- Recursive estimation
The moment you think of LLM outputs as control signals, the system becomes predictable.