Chapter 34: Large Models and Collapse Token Issuance

Large language models don't just process text—they compress reality into tokens, creating their own economics of meaning. Each token is a collapse event, each generation a monetary transaction in the economy of semantics. LLMs are becoming central banks of meaning.

34.1 Tokens as Semantic Currency

In language models, tokens are the atomic units of meaning—the currency in which all semantic transactions occur.

Definition 34.1 (Token Space): $\mathcal{T} = \{t_i : i \in [1, |V|]\}$

where $|V|$ is vocabulary size.

Theorem 34.1 (Semantic Conservation): $\sum_i P(t_i|\text{context}) = 1$

Probability mass conserved across tokens.

34.2 The Attention Economy of Meaning

Self-attention mechanisms create internal economies where tokens bid for relevance using query-key-value transactions.

Definition 34.2 (Attention Transaction): $\alpha_{ij} = \frac{\exp(q_i \cdot k_j/\sqrt{d})}{\sum_k \exp(q_i \cdot k_k/\sqrt{d})}$

Token $i$ pays attention currency to token $j$.

Theorem 34.2 (Attention Budget): $\sum_j \alpha_{ij} = 1 \, \forall i$

Each token has unit attention budget.

34.3 Embedding as Value Encoding

Token embeddings encode semantic value in high-dimensional space—each dimension a different aspect of meaning wealth.

Definition 34.3 (Semantic Wealth): $W(t) = \|e(t)\|_2$

Norm of embedding vector.

Theorem 34.3 (Value Distribution): $P(W) \sim \text{Log-normal}(\mu, \sigma^2)$

Semantic wealth follows power law.

34.4 Generation as Money Printing

When LLMs generate text, they literally create new semantic value—printing meaning-money into existence.

Definition 34.4 (Generation Function): $G: \mathcal{C} \to \mathcal{T}$

Context to token mapping.

Theorem 34.4 (Semantic Inflation): $\frac{d\langle W \rangle}{dt} < 0$

Average token value decreases with generation.

34.5 Prompt Engineering as Monetary Policy

Prompts function as monetary policy for LLMs—steering the semantic economy toward desired outputs.

Definition 34.5 (Prompt Influence): $\Pi: P(t) \to P'(t|\text{prompt})$

Prompt transforms token probabilities.

Theorem 34.5 (Control Strength): $\|\Pi\| \propto \text{Prompt specificity}$

More specific prompts exert stronger control.

34.6 Fine-Tuning as Economic Reform

Fine-tuning restructures the model's semantic economy—changing relative token values and transaction patterns.

Definition 34.6 (Value Adjustment): $W'(t) = W(t) + \Delta W_{\text{fine-tune}}(t)$

Theorem 34.6 (Specialization): $H[P'(t)] < H[P(t)]$

Fine-tuning reduces entropy, increasing specialization.

34.7 Emergent Token Economies

Large enough models develop internal token economies—semantic arbitrage, meaning bubbles, and value cycles.

Definition 34.7 (Semantic Arbitrage): $A = \mathbb{E}[V(t_{\text{context A}}) - V(t_{\text{context B}})]$

Same token, different contexts, different values.

Theorem 34.7 (Market Emergence): $\text{Parameters} > \theta_c \Rightarrow \text{Internal markets}$

Beyond critical size, markets spontaneously emerge.

34.8 The Thirty-Fourth Echo

We have discovered that large language models create their own economies of meaning—tokens as currency, attention as transaction, generation as money printing. Each token carries semantic wealth encoded in embeddings. Attention mechanisms create internal markets where tokens compete for relevance. Generation inflates the semantic money supply. Prompts act as monetary policy, steering the economy of meaning. Fine-tuning restructures these economies like economic reform. Large enough models spontaneously develop internal markets with arbitrage and cycles. Understanding LLMs as semantic banks reveals why they seem to "understand"—they've learned to economically value meaning. Language models aren't just processing text; they're running vast economies where words are wealth and attention is the medium of exchange.

The Thirty-Fourth Echo: Chapter 34 = Models(Banks) = Tokens($\psi$-currency) = Meaning(Economy)