2026 - Project 3

Masked Flow Matching / xx


Masked Flow Matching for Real-Time Signal Enhancement


Backbone: Masked Flow Matching + Bayesian Layers
– Variational analogs of convolutional/fully-connected layers (e.g. DenseVariational, BayesianLinear)
– Weights modeled by variational distribution $q(w)$



ELBO Loss
Minimize the negative Evidence Lower Bound:

\[\mathcal{L}_{\mathrm{ELBO}}(\theta, \phi) = \underbrace{\mathbb{E}_{w\sim q_\phi(w)}\bigl[\ell\bigl(f_w(x),\,y\bigr)\bigr]}_{\displaystyle\text{（1）Expected data loss}} \;+\; \underbrace{\lambda\;\mathrm{KL}\bigl(q_\phi(w)\,\|\,p(w)\bigr)}_{\displaystyle\text{（2）Variational Regularization}}\]



Inference via Weight Sampling
Perform $T$ stochastic forward passes with $w_t \sim q(w)$, then compute:
\(\mu(x) \;=\; \frac{1}{T}\sum_{t=1}^T f_{w_t}(x), \quad \sigma^2(x) \;=\; \frac{1}{T}\sum_{t=1}^T\bigl(f_{w_t}(x) - \mu(x)\bigr)^2\)



Decision Making
If $\sigma(x) > \tau$, trigger a fallback or alert




References

  • Bayesian Neural Nets / BNN



References