Understanding the behavior of deep networks is crucial to increase our confidence in their results. Despite an extensive body of work for explaining their predictions, researchers have faced reliability issues, which can be attributed to insufficient formalism. In our research, we adopt novel probabilistic and spectral perspectives to formally analyze explanation methods. Our study reveals a pervasive spectral bias stemming from the use of gradient, and sheds light on some common design choices that have been discovered experimentally, in particular, the use of squared gradient and input perturbation. We further characterize how the choice of perturbation hyperparameters in explanation methods, such as SmoothGrad, can lead to inconsistent explanations and introduce two remedies based on our proposed formalism: (i) a mechanism to determine a standard perturbation scale, and (ii) an aggregation method which we call SpectralLens. Finally, we substantiate our theoretical results through quantitative evaluations.

Carbon materials possess active sites and functionalities on the surface that can attract prominent interest as solid adsorbents for diverse gas adsorption. This study aimed to predict the optimized methane uptake, adsorption energy (E ad), and adsorbent rediscovery through multitechniques of neural, regression, classifier ML-DFT, and Uniform Manifold Approximation and Projection (UMAP). Nitrogen and oxygen (N/O) functionalities and graphene, graphene oxide (GO), and N-doped GO were applied to the methane storage medium. Multi-ML algorithms were employed for the adsorption energy of CH4 uptake on (i) N/O functionalities such as pyridinic (N-py), carboxyl (O-II), oxidized (N-x), hydroxyl (O-h), Nitroso (N-ni), and Amine (primary, secondary, and tertiary). (ii) The graphene surfaces are decorated with N/O heteroatoms to construct graphene oxide (GO) and N-doped GO. The DFT calculations were applied by PW91 and the Dmol3 package. N/O-functionalities in the distance of similar to 2.0 to 3.1 & Aring; groups obtained E ad of approximately -2.0 to -4 eV. Further, ML models accomplished the forthcoming rediscovery of CH4 physisorption by using the multiadsorptive features of optimized adsorbents with an R 2 of 0.99. ML-derived sensitivity analysis approach was applied to specifications such as deformation adsorption energy, N/O functionality type, and optimized structure. CH4 adsorption specifications indicate sensitivity levels of -0.03 to 0.02 eV. The synergetic DFT/ML approaches distinguished the modeled and rediscovered phases of CH4 adsorption on N/O functional groups and graphene structures. UMAP is employed as a new adsorbent screening approach to play a complementary role in the ML modeling process.

A natural way of estimating heteroscedastic label noise in regression is to model the observed (potentially noisy) target as a sample from a normal distribution, whose parameters can be learned by minimizing the negative log-likelihood. This formulation has desirable loss attenuation properties, as it reduces the contribution of high-error examples. Intuitively, this behavior can improve robustness against label noise by reducing overfitting. We propose an extension of this simple and probabilistic approach to classification that has the same desirable loss attenuation properties. Furthermore, we discuss and address some practical challenges of this extension. We evaluate the effectiveness of the method by measuring its robustness against label noise in classification. We perform enlightening experiments exploring the inner workings of the method, including sensitivity to hyperparameters, ablation studies, and other insightful analyses.