Related papers: Concerning the differentiability of the energy fun…
We present a simple, yet general, end-to-end deep neural network representation of the potential energy surface for atomic and molecular systems. This methodology, which we call Deep Potential, is "first-principle" based, in the sense that…
Quantization is a fundamental optimization for many machine-learning use cases, including compressing gradients, model weights and activations, and datasets. The most accurate form of quantization is \emph{adaptive}, where the error is…
This paper establishes a general theory of energy-constrained quantum and private capacities of quantum channels. We begin by defining various energy-constrained communication tasks, including quantum communication with a uniform energy…
Unsupervised learning of discrete representations in neural networks (NNs) from continuous ones is essential for many modern applications. Vector Quantisation (VQ) has become popular for this, in particular in the context of generative…
Power flow analysis is a fundamental tool for power system analysis, planning, and operational control. Traditional Newton-Raphson methods suffer from limitations such as initial value sensitivity and low efficiency in batch computation,…
We present a kinetic energy tensor that unifies a scalar kinetic energy density commonly used in meta-Generalized Gradient Approximation functionals and the vorticity density that appears in paramagnetic current-density-functional theory.…
Neural language models can be successfully trained on source code, leading to applications such as code completion. However, their versatile autoregressive self-supervision objective overlooks important global sequence-level features that…
We derive expressions for the expectation values of the local energy and the local power transferred by an external electrical field to a many-particle system of interacting spinless electrons. In analogy with the definition of the (local)…
Thermodynamics imposes restrictions on what state transformations are possible. In the macroscopic limit of asymptotically many independent copies of a state---as for instance in the case of an ideal gas---the possible transformations…
This work has its origin in intuitive physical and statistical considerations. The problem of optimizing an artificial neural network is treated as a physical system, composed of a conservative vector force field. The derived scalar…
We incorporate in the Kohn-Sham self consistent equation a trained neural-network projection from the charge density distribution to the Hartree-exchange-correlation potential $n \rightarrow V_{\rm Hxc}$ for possible numerical approach to…
In order to establish better performance compromises between the process functionals of a heat engine, in the context of finite time thermodynamics (FTT), we propose some generalizations for the well known Efficient Power function through…
In the standard formulation of quantum mechanics, one starts by proposing a potential function that models the physical system. The potential is then inserted into the Schr\"odinger equation, which is solved for the wave function, bound…
Kernel $k$-means clustering is a powerful tool for unsupervised learning of non-linearly separable data. Since the earliest attempts, researchers have noted that such algorithms often become trapped by local minima arising from…
We investigate the role of energy, i.e. average photon number, as a resource in the computational complexity of bosonic systems. We show three sets of results: (1. Energy growth rates) There exist bosonic gate sets which increase energy…
Probabilistic models can be defined by an energy function, where the probability of each state is proportional to the exponential of the state's negative energy. This paper considers a generalization of energy-based models in which the…
The positive definite Kohn-Sham kinetic energy(KS-KE) density plays crucial role in designing semilocal meta generalized gradient approximations(meta-GGAs) for low dimensional quantum systems. It has been rigorously shown that near nucleus…
Starting with an orthogonal polynomial sequence $\{p_n(s)\}_{n=0}^\infty$ that has a discrete spectrum, we design an energy spectrum formula, $E_k = f (s_k)$, where $|{s_k\}$ is the finite or infinite discrete spectrum of the polynomial.…
This work targets the automated minimum-energy optimization of Quantized Neural Networks (QNNs) - networks using low precision weights and activations. These networks are trained from scratch at an arbitrary fixed point precision. At…
The current paper is devoted to the investigation of the general form of the energy-momentum pseudotensor (pEMT) and the corresponding superpotential for the wide class of theories. The only requirement for such a theory is the general…