4,303 research outputs found
Combinatorial representations of token sequences
This paper presents new representations of token sequences, with and without associated quantities, in Euclidean space. The representations are free of assumptions about the nature of the sequences or the processes that generate them. Algorithms and applications from the domains of structured interviews and life histories are discussed. © Springer Science+Business Media Inc. 2005
Training neural networks to encode symbols enables combinatorial generalization
Combinatorial generalization - the ability to understand and produce novel
combinations of already familiar elements - is considered to be a core capacity
of the human mind and a major challenge to neural network models. A significant
body of research suggests that conventional neural networks can't solve this
problem unless they are endowed with mechanisms specifically engineered for the
purpose of representing symbols. In this paper we introduce a novel way of
representing symbolic structures in connectionist terms - the vectors approach
to representing symbols (VARS), which allows training standard neural
architectures to encode symbolic knowledge explicitly at their output layers.
In two simulations, we show that neural networks not only can learn to produce
VARS representations, but in doing so they achieve combinatorial generalization
in their symbolic and non-symbolic output. This adds to other recent work that
has shown improved combinatorial generalization under specific training
conditions, and raises the question of whether specific mechanisms or training
routines are needed to support symbolic processing
Design for a Darwinian Brain: Part 1. Philosophy and Neuroscience
Physical symbol systems are needed for open-ended cognition. A good way to
understand physical symbol systems is by comparison of thought to chemistry.
Both have systematicity, productivity and compositionality. The state of the
art in cognitive architectures for open-ended cognition is critically assessed.
I conclude that a cognitive architecture that evolves symbol structures in the
brain is a promising candidate to explain open-ended cognition. Part 2 of the
paper presents such a cognitive architecture.Comment: Darwinian Neurodynamics. Submitted as a two part paper to Living
Machines 2013 Natural History Museum, Londo
Monomiality principle, Sheffer-type polynomials and the normal ordering problem
We solve the boson normal ordering problem for
with arbitrary functions and and integer , where and
are boson annihilation and creation operators, satisfying
. This consequently provides the solution for the exponential
generalizing the shift operator. In the
course of these considerations we define and explore the monomiality principle
and find its representations. We exploit the properties of Sheffer-type
polynomials which constitute the inherent structure of this problem. In the end
we give some examples illustrating the utility of the method and point out the
relation to combinatorial structures.Comment: Presented at the 8'th International School of Theoretical Physics
"Symmetry and Structural Properties of Condensed Matter " (SSPCM 2005),
Myczkowce, Poland. 13 pages, 31 reference
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