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Martingale Neural Operators: Learning Stochastic Marginals via Doob-Meyer Factorization

arXiv:2605.15806v2 Announce Type: replace Abstract: Neural operators excel as deterministic surrogates, but inevitably collapse to the conditional mean when applied to stochastic PDEs, discarding the variance and tail structure upon which uncertainty quantification depends. Recovering this structure typically requires Monte Carlo rollouts or grafted generative models, both of which surrender the one-shot efficiency and resolution invariance that define the operator paradigm. To resolve this,...

arXiv CS 7d ago

Free energy Estimation on Any State Space

arXiv:2605.31063v1 Announce Type: cross Abstract: Free energy estimation is a fundamental yet challenging problem, from physics to statistics. Classical approaches rely on thermodynamic transformations, ranging from direct estimation, quasistatic integration, to finite-time averaging. [He and Du et al., 2025] learns neural transports to significantly accelerate the efficiency in the finite-time regime.

arXiv Physics 9d ago

Are we really tilting? The mechanics of reward guidance in flow and diffusion models

Announce Type: new Abstract: Reward guidance algorithms steer a learned generative process toward the reward-tilted measure at inference time. While empirically powerful, these methods are prone to reward hacking: the guided model over-optimizes the reward at the cost of fidelity to the learned distribution. Prior work has attributed this to the complexity of neural reward functions or implicit biases in diffusion training, but its fundamental origins remain poorly understood.

arXiv CS 7d ago

Free energy Estimation on Any State Space

arXiv:2605.31063v1 Announce Type: cross Abstract: Free energy estimation is a fundamental yet challenging problem, from physics to statistics. Classical approaches rely on thermodynamic transformations, ranging from direct estimation, quasistatic integration, to finite-time averaging. [He and Du et al., 2025] learns neural transports to significantly accelerate the efficiency in the finite-time regime.

arXiv CS 9d ago