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Though modern neural networks have achieved impressive performance in both vision and language tasks, we know little about the functions that they implement. One possibility is that neural networks implicitly break down complex tasks into…

This paper is to derive a mathematical model for neuron by imposing only a principle of symmetry that two modelers must come up with the same model when one is approaching the problem by modeling the conductances of ion channels and the…

Our understanding of neural computation is founded on the assumption that neurons fire in response to a linear summation of inputs. Yet experiments demonstrate that some neurons are capable of complex functions that require interactions…

Biological cortical neurons are remarkably sophisticated computational devices, temporally integrating their vast synaptic input over an intricate dendritic tree, subject to complex, nonlinearly interacting internal biological processes. A…

Neuronal circuits of the cerebral cortex are the structural basis of mammalian cognition. The same qualitative components and connectivity motifs are repeated across functionally specialized cortical areas and mammalian species, suggesting…

Monte Carlo methods provide detailed and accurate results for radiation transport simulations. Unfortunately, the high computational cost of these methods limits its usage in real-time applications. Moreover, existing computer codes do not…

The multiple-valued quantum logic is formulated systematically such that the truth values are represented naturally as unique roots of unity placed on the unit circle. Consequently, multi-valued quantum neuron (MVQN) is based on the…

The predictive power of neural networks often costs model interpretability. Several techniques have been developed for explaining model outputs in terms of input features; however, it is difficult to translate such interpretations into…

Neurons in the brain are complex machines with distinct functional compartments that interact nonlinearly. In contrast, neurons in artificial neural networks abstract away this complexity, typically down to a scalar activation function of a…

The conductance through a finite quantum dot network is studied as a function of inter-dot coupling. As the coupling is reduced, the system undergoes a transition from the antidot regime to the tight binding limit, where Coulomb resonances…

Some neurons in deep networks specialize in recognizing highly specific perceptual, structural, or semantic features of inputs. In computer vision, techniques exist for identifying neurons that respond to individual concept categories like…

Despite the success of neural networks at solving concrete physics problems, their use as a general-purpose tool for scientific discovery is still in its infancy. Here, we approach this problem by modelling a neural network architecture…

Capsule networks are a recently developed class of neural networks that potentially address some of the deficiencies with traditional convolutional neural networks. By replacing the standard scalar activations with vectors, and by…

This paper suggests a statistical framework for describing the relations between the physical and conceptual entities of a brain-like model. Features and concept instances are put into context, where the paper suggests that features may be…

The principles of neural encoding and computations are inherently collective and usually involve large populations of interacting neurons with highly correlated activities. While theories of neural function have long recognized the…

We show that cellular automata can classify data by inducing a form of dynamical phase coexistence. We use Monte Carlo methods to search for general two-dimensional deterministic automata that classify images on the basis of activity, the…

Fabricating powerful neuromorphic chips the size of a thumb requires miniaturizing their basic units: synapses and neurons. The challenge for neurons is to scale them down to submicrometer diameters while maintaining the properties that…

A Path Integral Monte Carlo method is used to investigate the thermodynamics of nuclear like systems. Systems composed of bosons or fermions interracting via a Lennard-Jones potential with periodic boundary conditions were simulated and the…

We investigate whether a neural network approach can reproduce and predict the electron-nucleus cross sections in the kinematical domain of present and future accelerator-based neutrino oscillation experiments. For this purpose, we consider…

Compositional Explanations is a method for identifying logical formulas of concepts that approximate the neurons' behavior. However, these explanations are linked to the small spectrum of neuron activations (i.e., the highest ones) used to…