neural controlled differential equations

**Neural CDEs** are a **neural network architecture that parameterizes the response function of a controlled differential equation with a neural network** — $dz_t = f_ heta(z_t) , dX_t$, providing a continuous-time, theoretically grounded model for irregular time series classification and regression. **How Neural CDEs Work** - **Input Processing**: Interpolate the irregular time series ${(t_i, x_i)}$ into a continuous path $X_t$. - **Neural Response**: $f_ heta$ is a neural network mapping the hidden state to a matrix that interacts with $dX_t$. - **ODE Solver**: Solve the CDE using standard adaptive ODE solvers (Dormand-Prince, etc.). - **Output**: Read out the prediction from the terminal hidden state $z_T$. **Why It Matters** - **Irregular Time Series**: Purpose-built for irregularly sampled data — outperforms RNNs, LSTMs, and Transformers on irregular benchmarks. - **Missing Data**: Naturally handles missing channels and variable-length sequences. - **Memory Efficient**: Adjoint method enables constant-memory training regardless of sequence length. **Neural CDEs** are **continuous RNNs for irregular data** — using controlled differential equations to process time series with arbitrary sampling patterns.