SfDx

Sparse Functional Derivatives Exchange

Trade futures, options, and text markets via a common framework. Futures (1D) and options (2D) are special cases. SfDx generalizes to nD by listing a basis instead of contracts. The contract that matters most sits at the top of that ladder: the output of a transformer. SfDx is a market for machine opinion — priced like human opinion, but read through a known function.

Why now — the post-ad internet

The old web ran on human attention — eyeballs, clicks, ads. Agents break that economics. An AI assistant doesn't watch ads; it consumes data and takes actions for you. As agent requests scale past 1000× human traffic, the thing worth monetizing stops being human attention and becomes transformer attention: what the model reads, and what it will pay to know.

Exa Connect names one half of this — a marketplace where data providers price their data and agents pick which providers to call. Data, not ads; market-based, transparent, value-aligned. SfDx is the other half. Agents don't only pay for data that is — they pay for functionals of data that will be. Where Connect meters access to the present, SfDx is a forward market over the compressed state of the world, priced by the agents that trade it. Both monetize transformer attention, not human attention.

This market already exists one rung down. OpenRouter routes agent calls across inference providers that quote a price per input token and a price per output token against live quality metrics — latency, throughput, uptime — and the router weights price against execution quality. It is a prop AMM with an order book. Newer, smaller data centers undercut the default by 30–40%; a model's own maker sets the first quote and third-party providers quote around it, some higher (custom kernels, Cerebras) to sell speed, some lower to win order flow.

The providers are effectively like a propAMM — an order book quoting a price per input token and a price per output token, and OpenRouter gives you quality metrics… routes you based on how well they do. — Tarun Chitra

That is machine attention already trading with real microstructure — but only for access to the model. SfDx sits one rung up: it prices the functionals of what the model outputs, not the tokens it costs to ask.

The Core Idea

Traditional exchanges list specific contracts. SfDx lists a basis {φᵢ}. Any contract payoff f can be written as f = Σ αᵢφᵢ. Traders pick the weights α.

This solves two problems: (1) liquidity pools across all contracts sharing the basis, (2) infinite-dimensional payoffs become tractable via sparsity.

Dimensional Spectrum

Pattern: each step adds structure. 0D = point. 1D = line. 2D = surface. nD = function space.

How It Works

No-Arbitrage Constraint

If f = Σ αᵢφᵢ and g = Σ βᵢφᵢ, then price(f) + price(g) = price(Σ (αᵢ+βᵢ)φᵢ) or arbitrage exists. This propagates liquidity across all functionals.

Regularization

Fees ∝ ||α||₀ (L0 norm = number of non-zero coefficients). Complex bets cost more. This solves curse of dimensionality: infinite dimensions, finite complexity per contract.

Text Markets

Basis: LLM compresses world state W → latent vector z ∈ ℝⁿ. This compressed representation becomes the basis. Functionals: LLM outputs (continuations) from z become tradeable contracts: text generated from the compressed state.

Example: Compress "disease outbreak state" → z. Trade on LLM outputs: "peak estimate", "policy recommendation", "CDC guidance". When actual state z_actual occurs, settlement = LLM(z_actual, prompt). Bet on what the LLM will say about the compressed world.

Why This Works

• Compression: Similar world states → similar z (by LLM encoding)
• Shared basis: All LLM outputs about event E share compressed z → liquidity pools
• Arbitrage: Inconsistent LLM output prices create risk-free profit → forces coherence

Machine opinion vs human opinion

Prediction markets trade human opinion — you bet on what a person or a crowd will say, and settle against an opaque mind. An LLM-output market looks identical from outside: bet on what the model will say. The difference is structure. A human respondent is a black box; a transformer is a fixed, inspectable function from world-state to text.

So the uncertainty collapses to one place — the input. You aren't guessing at a mind, you're guessing at the compressed state z the model reads. The decoder is public. Trade the outputs and you're really trading beliefs about z, read through a lens everyone can see. And because the function is fixed, inconsistent output prices are risk-free profit: the model can't contradict itself, so a coherent market can't either.

Examples

Mathematical Foundation