25,375 research outputs found
A mathematical theory of semantic development in deep neural networks
An extensive body of empirical research has revealed remarkable regularities
in the acquisition, organization, deployment, and neural representation of
human semantic knowledge, thereby raising a fundamental conceptual question:
what are the theoretical principles governing the ability of neural networks to
acquire, organize, and deploy abstract knowledge by integrating across many
individual experiences? We address this question by mathematically analyzing
the nonlinear dynamics of learning in deep linear networks. We find exact
solutions to this learning dynamics that yield a conceptual explanation for the
prevalence of many disparate phenomena in semantic cognition, including the
hierarchical differentiation of concepts through rapid developmental
transitions, the ubiquity of semantic illusions between such transitions, the
emergence of item typicality and category coherence as factors controlling the
speed of semantic processing, changing patterns of inductive projection over
development, and the conservation of semantic similarity in neural
representations across species. Thus, surprisingly, our simple neural model
qualitatively recapitulates many diverse regularities underlying semantic
development, while providing analytic insight into how the statistical
structure of an environment can interact with nonlinear deep learning dynamics
to give rise to these regularities
Synthetic Quantum Systems
So far proposed quantum computers use fragile and environmentally sensitive
natural quantum systems. Here we explore the new notion that synthetic quantum
systems suitable for quantum computation may be fabricated from smart
nanostructures using topological excitations of a stochastic neural-type
network that can mimic natural quantum systems. These developments are a
technological application of process physics which is an information theory of
reality in which space and quantum phenomena are emergent, and so indicates the
deep origins of quantum phenomena. Analogous complex stochastic dynamical
systems have recently been proposed within neurobiology to deal with the
emergent complexity of biosystems, particularly the biodynamics of higher brain
function. The reasons for analogous discoveries in fundamental physics and
neurobiology are discussed.Comment: 16 pages, Latex, 1 eps figure fil
Smart Nanostructures and Synthetic Quantum Systems
So far proposed quantum computers use fragile and environmentally sensitive
natural quantum systems. Here we explore the notion that synthetic quantum
systems suitable for quantum computation may be fabricated from smart
nanostructures using topological excitations of a neural-type network that can
mimic natural quantum systems. These developments are a technological
application of process physics which is a semantic information theory of
reality in which space and quantum phenomena are emergent.Comment: LaTex,14 pages 1 eps file. To be published in BioMEMS and Smart
Nanostructures, Proceedings of SPIE Conference #4590, ed. L. B. Kis
Task adapted reconstruction for inverse problems
The paper considers the problem of performing a task defined on a model
parameter that is only observed indirectly through noisy data in an ill-posed
inverse problem. A key aspect is to formalize the steps of reconstruction and
task as appropriate estimators (non-randomized decision rules) in statistical
estimation problems. The implementation makes use of (deep) neural networks to
provide a differentiable parametrization of the family of estimators for both
steps. These networks are combined and jointly trained against suitable
supervised training data in order to minimize a joint differentiable loss
function, resulting in an end-to-end task adapted reconstruction method. The
suggested framework is generic, yet adaptable, with a plug-and-play structure
for adjusting both the inverse problem and the task at hand. More precisely,
the data model (forward operator and statistical model of the noise) associated
with the inverse problem is exchangeable, e.g., by using neural network
architecture given by a learned iterative method. Furthermore, any task that is
encodable as a trainable neural network can be used. The approach is
demonstrated on joint tomographic image reconstruction, classification and
joint tomographic image reconstruction segmentation
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