Flow matching SetTransformer. We indicate with d̃ both the observation (d) and the intermediate output of the attention blocks. To embed each of the stars in the observation (d) the parameter state θ_t at the ODE time t, we used a simple MLP with 128 neurons with a SiLU activation function. We then passed d̃ through three stacked SABs with a skip connection (dashed line) to encode the correlations between the particles while modulating the output of each block on t using FiLM. Then we used a CAB with a FiLM modulation to focus the attention mechanism on finding the relevant feature in d̃ to regress the parameters θ. The vector field v_φ was obtained by compressing the output of the CAB through an MLP with output dimensions equal to the dimensionality of θ, in our case 13 dimensions.