# Uncertainty Quantification

Universal DFT Hamiltonian models quickly map atomic structure to electronic properties, but their predictions carry no reliability information. EviDTB attaches evidential deep regression to the SLEM backbone in DeePTB, learns only the residual between the converged Hamiltonian and a reference Hamiltonian built from the initial density, and returns a per-atom uncertainty score in a single forward pass. On 5,478 held-out structures, removing the 15% most uncertain structures lowers the 99th percentile of the mean local squared prediction error from 16.63 to 3.72 eV²; on 636 generated structures evaluated without retraining, the score has a Spearman correlation of 0.743 with that error.

Universal DFT Hamiltonian models quickly map atomic structure to electronic properties, but their predictions carry no reliability information. EviDTB attaches evidential deep regression to the SLEM backbone in DeePTB, learns only the residual between the converged Hamiltonian and a reference Hamiltonian built from the initial density, and returns a per-atom uncertainty score in a single forward pass. On 5,478 held-out structures, removing the 15% most uncertain structures lowers the 99th percentile of the mean local squared prediction error from 16.63 to 3.72 eV²; on 636 generated structures evaluated without retraining, the score has a Spearman correlation of 0.743 with that error.

Causal mediation analysis splits a treatment effect into an indirect pathway through mediators and a direct pathway through other processes, and attaching a confidence interval to the indirect effect usually means refitting several nuisance functions on every table and resampling repeatedly. MediPFN adapts a pretrained tabular foundation model to predict those nuisance functions, then a separate head learns quantiles of the estimator's standardized error from simulated tables with known indirect effects, with symmetrization and independent calibration producing the interval. On synthetic, distribution-shift and real-covariate tables its coverage sits closer to the 95% nominal level than several comparators, and paired timing gives a median 59.1-fold speedup over bootstrap.

Causal mediation analysis splits a treatment effect into an indirect pathway through mediators and a direct pathway through other processes, and attaching a confidence interval to the indirect effect usually means refitting several nuisance functions on every table and resampling repeatedly. MediPFN adapts a pretrained tabular foundation model to predict those nuisance functions, then a separate head learns quantiles of the estimator's standardized error from simulated tables with known indirect effects, with symmetrization and independent calibration producing the interval. On synthetic, distribution-shift and real-covariate tables its coverage sits closer to the 95% nominal level than several comparators, and paired timing gives a median 59.1-fold speedup over bootstrap.

A robot that files a hallway defibrillator under fire extinguisher would carry that wrong description in memory. MIT researchers added uncertainty quantification to the existing DAAAM memory system, so the robot compares descriptions of the same object from different viewpoints, estimates how unsure it is about what it saw, and selects extra views to fuse a more accurate caption. Against baseline methods, the system raised object-description accuracy by 5 percent and resolved ambiguity for about 92 percent of objects using only two additional captions per object.

A robot that files a hallway defibrillator under fire extinguisher would carry that wrong description in memory. MIT researchers added uncertainty quantification to the existing DAAAM memory system, so the robot compares descriptions of the same object from different viewpoints, estimates how unsure it is about what it saw, and selects extra views to fuse a more accurate caption. Against baseline methods, the system raised object-description accuracy by 5 percent and resolved ambiguity for about 92 percent of objects using only two additional captions per object.

Cross-modal single-cell matching has returned a match but rarely a confidence. BASILISC places a Bayesian posterior over a siamese network of two modalities and defines uncertainty on the correspondence between a pair of cells, tested on multi-omics benchmarks where the true pairing is known. At the cell-type level, discarding the least certain fifth of pairs raises accuracy from 0.93 to 0.98; at the cell level, the posterior flags wrong matches that cross a cell-type boundary better than a deterministic read of the same scores, AUROC 0.68 against 0.64.

Cross-modal single-cell matching has returned a match but rarely a confidence. BASILISC places a Bayesian posterior over a siamese network of two modalities and defines uncertainty on the correspondence between a pair of cells, tested on multi-omics benchmarks where the true pairing is known. At the cell-type level, discarding the least certain fifth of pairs raises accuracy from 0.93 to 0.98; at the cell level, the posterior flags wrong matches that cross a cell-type boundary better than a deterministic read of the same scores, AUROC 0.68 against 0.64.

Active learning for materials and molecular property prediction treats high-uncertainty samples as the information a model is missing. Across formation energy, bandgap and solubility tasks, uncertainty came from loss-landscape sampling and from ensembles retrained with different seeds, then was calibrated with linear calibration factors and a neural network. Calibrated uncertainty generally did not reduce the data a model needed to improve on out-of-distribution data, showing no advantage over random sampling or uncalibrated estimates, and error bars overlapped.

Active learning for materials and molecular property prediction treats high-uncertainty samples as the information a model is missing. Across formation energy, bandgap and solubility tasks, uncertainty came from loss-landscape sampling and from ensembles retrained with different seeds, then was calibrated with linear calibration factors and a neural network. Calibrated uncertainty generally did not reduce the data a model needed to improve on out-of-distribution data, showing no advantage over random sampling or uncalibrated estimates, and error bars overlapped.

Flood warning for Australian catchments now comes as a 90% prediction band rather than a single flow curve: three independently trained LSTMs give the mean flow and the 5th and 95th percentiles, and the band's position against a 15% annual exceedance threshold becomes a high, moderate or low risk label. On CAMELS-AUS, the q=0.05 Quantile-LSTM reached the lowest RMSE of 0.0801 in South Australia against 0.0963 for a conventional LSTM, while peak timing error across states ran about 1.94 to 3.12 days with peaks underestimated by roughly 30%.

Flood warning for Australian catchments now comes as a 90% prediction band rather than a single flow curve: three independently trained LSTMs give the mean flow and the 5th and 95th percentiles, and the band's position against a 15% annual exceedance threshold becomes a high, moderate or low risk label. On CAMELS-AUS, the q=0.05 Quantile-LSTM reached the lowest RMSE of 0.0801 in South Australia against 0.0963 for a conventional LSTM, while peak timing error across states ran about 1.94 to 3.12 days with peaks underestimated by roughly 30%.