F
Forward problem
Given the process, compute the result
Choose a mechanism, initial state, and evolution rule; then simulate the observations it would produce.
Mathematics asks. Evidence constrains.
Explore the research language behind our work. The diagrams explain concepts and methods; they do not display live trading or performance.
Forward ↔ Inverse
The outcome is visible.The mechanism is not.
AI learning and quantitative inference both work backward from observed effects. AI learns a model from data; quant research infers candidate market mechanisms from price, volume, order flow, and context. Without constraints, the answer is rarely unique or stable.
y = F(θ, x₀) + ε
Several mechanisms can leave the same footprint.
F⁻¹
Inverse problem
Given the result, infer the process
Start with the recorded tape and recover a candidate latent state, operator, or mechanism that could explain it.
λ
Regularization
Discipline makes inference usable
Point-in-time data, simplicity, trading costs, hostile regimes, and forward evidence constrain the many explanations that fit history.
PDE/ODE, state-space models, stochastic processes, and neural networks can define candidate forward operators. None proves that the market obeys one equation; each remains a hypothesis under test.
Signals learn.Risk does not deform.
A fiber bundle with a learned connection. The base manifold is the market. The fibers are feature space. The connection — how signals are transported — is learned. One section of the bundle is never allowed to deform: the veto.
Regimes deform the manifold. The invariants survive.
Measureeverything.
Execution research follows the path from decision to fill: waiting time, slippage, market impact, and tail behavior that averages can hide.
Method illustration · Charts use synthetic data, not measured distributions or coverage.
Latency distribution
Slippage distribution
Evidence Coverage
Decision to fillLinked records
Tail behaviorOutlier analysis
Venue contextMarket and session
Replay stateAssumptions and inputs
Markets cross borders.So does intelligence.
A cross-session research fabric spanning the United States and Hong Kong — learning from one market while the other sleeps.
NEW YORK / SIGNAL ORIGIN
US market structure, execution research, and long- and short-horizon intelligence.
HONG KONG / SESSION MEMORY
Asian session context, cross-market hypotheses, and a laboratory where market behaviour is structured differently.
ONE RESEARCH SURFACE
Different venues and clocks, normalized into evidence the research system can compare.