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Superposition -- when a neural network represents more ``features'' than it has dimensions -- seems to pose a serious challenge to mechanistically interpreting current AI systems. Existing theory work studies \emph{representational}…
In recent years, artificial neural networks and their applications for large data sets have became a crucial part of scientific research. In this work, we implement the Multilayer Perceptron (MLP), which is a class of feedforward artificial…
We present a nonlinear interpolation technique for parametric fields that exploits optimal transportation of coherent structures of the solution to achieve accurate performance. The approach generalizes the nonlinear interpolation procedure…
Based on tensor neural network, we propose an interpolation method for high dimensional non-tensor-product-type functions. This interpolation scheme is designed by using the tensor neural network based machine learning method. This means…
We build and train the artificial neural network model (ANN) based on the experimental $\alpha$-decay energy ($Q_{\alpha}$) data. Besides decays between the ground states of parent and daughter nuclei, decays from the ground state of parent…
Linear position interpolation helps pre-trained models using rotary position embeddings (RoPE) to extrapolate to longer sequence lengths. We propose using linear position interpolation to extend the extrapolation range of models using…
The kernel ridge regression (KRR) approach is extended to include the odd-even effects in nuclear mass predictions by remodulating the kernel function without introducing new weight parameters and inputs in the training network. By taking…
A new linked cluster expansion for the calculation of ground state observables of complex nuclei with realistic interactions has been developed [1-3]; using the V8' potential [4] the ground state energy, density and momentum distribution of…
Deep learning based methods have recently pushed the state-of-the-art on the problem of Single Image Super-Resolution (SISR). In this work, we revisit the more traditional interpolation-based methods, that were popular before, now with the…
Interpolation for scattered data is a classical problem in numerical analysis, with a long history of theoretical and practical contributions. Recent advances have utilized deep neural networks to construct interpolators, exhibiting…
The densest state of matter in the universe is uniquely realized inside central cores of the neutron star. While first-principles evaluation of the equation of state of such matter remains as one of the longstanding problems in nuclear…
Model merging, typically on Instruct and Thinking models, has shown remarkable performance for efficient reasoning. In this paper, we systematically revisit the simplest merging method that interpolates two weights directly. Particularly,…
Every generative model for crystalline materials harbors a critical structure size beyond which its outputs quietly become unreliable -- we call this the extrapolation frontier. Despite its direct consequences for nanomaterial design, this…
A novel approach is presented for the solution of instantaneous chemical equilibrium problems. The chemical equilibrium can be considered, due to its intrinsically local character, as a mapping of the three-dimensional parameter space…
While the basic laws of Newtonian mechanics are well understood, explaining a physical scenario still requires manually modeling the problem with suitable equations and estimating the associated parameters. In order to be able to leverage…
Properties of 8,979 nuclei ranging from oxygen-16 to Z = 136, A = 339 and extending from the proton drip line to the neutron drip line have been calculated by use of the 1992 version of the finite-range droplet model. The calculated…
This work examines the problem of exact data interpolation via sparse (neuron count), infinitely wide, single hidden layer neural networks with leaky rectified linear unit activations. Using the atomic norm framework of [Chandrasekaran et…
In this paper, I show how neural networks can be used to simultaneously estimate all unknown parameters in a spatial point process model from an observed point pattern. The method can be applied to any point process model which it is…
Signal extrapolation is an important task in digital signal processing for extending known signals into unknown areas. The Selective Extrapolation is a very effective algorithm to achieve this. Thereby, the extrapolation is obtained by…
Neural networks have been applied to tackle many-body electron correlations for small molecules and physical models in recent years. Here we propose a new architecture that extends molecular neural networks with the inclusion of periodic…