Related papers: An Uncertainty Principle for Probabilistic Computa…
This paper is an introduction to the membrane potential equation for neurons. Its properties are described, as well as sample applications. Networks of these equations can be used for modeling neuronal systems, which also process images and…
The first quantum technologies to solve computational problems that are beyond the capabilities of classical computers are likely to be devices that exploit characteristics inherent to a particular physical system, to tackle a bespoke…
Predictive coding is an influential theory of cortical function which posits that the principal computation the brain performs, which underlies both perception and learning, is the minimization of prediction errors. While motivated by…
Quantum mechanics may be formulated as SENSIBLE QUANTUM MECHANICS (SQM) so that it contains nothing probabilistic, except, in a certain frequency sense, conscious perceptions. Sets of these perceptions can be deterministically realized with…
Many real-world problems, e.g. object detection, have outputs that are naturally expressed as sets of entities. This creates a challenge for traditional deep neural networks which naturally deal with structured outputs such as vectors,…
We construct a quantum-inspired classical algorithm for computing the permanent of Hermitian positive semidefinite matrices, by exploiting a connection between these mathematical structures and the boson sampling model. Specifically, the…
In this paper, we introduce elements of probabilistic model that is suitable for modeling of learning algorithms in biologically plausible artificial neural networks framework. Model is based on two of the main concepts in quantum physics -…
We deliver a call to arms for probabilistic numerical methods: algorithms for numerical tasks, including linear algebra, integration, optimization and solving differential equations, that return uncertainties in their calculations. Such…
The uncertainty principle is a fundamental principle in quantum physics. It implies that the measurement outcomes of two incompatible observables can not be predicted simultaneously. In quantum information theory, this principle can be…
Capacity of conscious agents to perform genuine choices among future alternatives is a prerequisite for moral responsibility. Determinism that pervades classical physics, however, forbids free will, undermines the foundations of ethics, and…
While our understanding of the way single neurons process chromatic stimuli in the early visual pathway has advanced significantly in recent years, we do not yet know how these cells interact to form stable representations of hue. Drawing…
It is well known that the problem of divergence in the physical interpretation of quantum mechanics originating from the uncertainty principle has not yet been resolved. Attempting to clear the constraints and confusion of this situation…
The issue of whether we make decisions freely has vexed philosophers for millennia, Resolving this is vital for solving a diverse range of problems, from the physiology of how the brain makes decisions (and how we assign moral…
It is known that the eye's scotopic photodetectors, rhodopsin molecules and their associated phototransduction mechanism leading to light perception, are efficient single photon counters. We here use the photon counting principles of human…
The transition from quantum to classical behavior is a central question in modern physics. How can we rationalize everyday classical observations from an inherently quantum world? For instance, what makes two people, each absorbing an…
Image reconstruction methods based on deep neural networks have shown outstanding performance, equalling or exceeding the state-of-the-art results of conventional approaches, but often do not provide uncertainty information about the…
It has been proposed that populations of neurons process information in terms of probability density functions (PDFs) of analog variables. Such analog variables range, for example, from target luminance and depth on the sensory interface to…
The means by which cortical neural networks are able to efficiently solve inference problems remains an open question in computational neuroscience. Recently, abstract models of Bayesian computation in neural circuits have been proposed,…
Understanding of the phenomena of vision and thought require clarification of the general mechanism of perception. So far, philosophical inquiries and scientific investigations have not been able to address clearly the mysteries surrounding…
We present a detailed physiological model of the retina that includes the biochemistry and electrophysiology of phototransduction, neuronal electrical coupling, and the spherical geometry of the eye. The model is a parabolic-elliptic system…