arXiv:2606. 23838v1 Announce Type: new Abstract: When two or more parameters or labels produce similar data, they are degenerate, or hard to distinguish.
arXiv:2607. 06252v1 Announce Type: cross Abstract: Many problems in science and engineering are difficult to model accurately, either due to unknown physical mechanisms, poorly quantified measurement uncertainty, or prohibitive computational costs of high-fidelity simulations.
arXiv:2407. 12288v5 Announce Type: replace-cross Abstract: The progress of machine learning over the past decade is undeniable.
arXiv:2510. 12744v2 Announce Type: replace-cross Abstract: We develop a unified statistical framework for softmax-gated Gaussian mixture of experts (SGMoE) that addresses three long-standing obstacles in parameter estimation and model selection: (i) non-identifiability of gating parameters up to common translations, (ii) intrinsic gate-expert interactions that induce coupled differential relations in the likelihood, and (iii) the tight numerator-denominator coupling in the softmax-induced conditional density.
arXiv:2606. 09856v1 Announce Type: cross Abstract: Post-training Large Language Models (LLMs) for reasoning typically focuses on deductive tasks such as mathematics and coding where correctness is verifiable.
arXiv:2509. 23385v5 Announce Type: replace-cross Abstract: Simulation-based inference (SBI) is transforming experimental sciences by enabling parameter estimation in complex non-linear models from simulated data.
arXiv:2608. 00852v1 Announce Type: new Abstract: Understanding and controlling complex dynamical systems often requires executing thousands of numerical simulations across vast parametric landscapes, which is time-consuming.
arXiv:2410. 14843v4 Announce Type: replace-cross Abstract: Vanilla variational inference finds an optimal approximation to the Bayesian posterior distribution, but even the exact Bayesian posterior is often not meaningful under model misspecification.
arXiv:2606. 25188v1 Announce Type: new Abstract: Efficient uncertainty quantification (UQ) is essential for trustworthy large-scale learning.
arXiv:2606. 09949v1 Announce Type: cross Abstract: Data-driven PDE surrogates are trained with data produced by numerical PDE solvers.
arXiv:2607. 10546v1 Announce Type: new Abstract: Discovering governing partial differential equations (PDEs) from noisy observational data is a fundamental challenge in scientific machine learning.
arXiv:2605. 27991v2 Announce Type: replace-cross Abstract: Gradient-flow optimization is usually viewed as an algorithmic procedure for minimizing empirical loss, with training duration selected by validation or heuristic early-stopping rules.
arXiv:2606. 16923v1 Announce Type: new Abstract: Simulation-based inference (SBI) of latent parameters is often hindered by simulator misspecification, the mismatch between simulated and real-world observations caused by inherent modeling simplifications.