149,197 research outputs found
A Combinatorial Bit Bang Leading to Quaternions
This paper describes in detail how (discrete) quaternions - ie. the abstract
structure of 3-D space - emerge from, first, the Void, and thence from
primitive combinatorial structures, using only the exclusion and co-occurrence
of otherwise unspecified events. We show how this computational view
supplements and provides an interpretation for the mathematical structures, and
derive quark structure. The build-up is emergently hierarchical, compatible
with both quantum mechanics and relativity, and can be extended upwards to the
macroscopic. The mathematics is that of Clifford algebras emplaced in the
homology-cohomology structure pioneered by Kron. Interestingly, the ideas
presented here were originally developed by the author to resolve fundamental
limitations of existing AI paradigms. As such, the approach can be used for
learning, planning, vision, NLP, pattern recognition; and as well, for
modelling, simulation, and implementation of complex systems, eg. biological.Comment: 23 pages, 4 figure
Predictive Coding for Dynamic Visual Processing: Development of Functional Hierarchy in a Multiple Spatio-Temporal Scales RNN Model
The current paper proposes a novel predictive coding type neural network
model, the predictive multiple spatio-temporal scales recurrent neural network
(P-MSTRNN). The P-MSTRNN learns to predict visually perceived human whole-body
cyclic movement patterns by exploiting multiscale spatio-temporal constraints
imposed on network dynamics by using differently sized receptive fields as well
as different time constant values for each layer. After learning, the network
becomes able to proactively imitate target movement patterns by inferring or
recognizing corresponding intentions by means of the regression of prediction
error. Results show that the network can develop a functional hierarchy by
developing a different type of dynamic structure at each layer. The paper
examines how model performance during pattern generation as well as predictive
imitation varies depending on the stage of learning. The number of limit cycle
attractors corresponding to target movement patterns increases as learning
proceeds. And, transient dynamics developing early in the learning process
successfully perform pattern generation and predictive imitation tasks. The
paper concludes that exploitation of transient dynamics facilitates successful
task performance during early learning periods.Comment: Accepted in Neural Computation (MIT press
A Novel Predictive-Coding-Inspired Variational RNN Model for Online Prediction and Recognition
This study introduces PV-RNN, a novel variational RNN inspired by the
predictive-coding ideas. The model learns to extract the probabilistic
structures hidden in fluctuating temporal patterns by dynamically changing the
stochasticity of its latent states. Its architecture attempts to address two
major concerns of variational Bayes RNNs: how can latent variables learn
meaningful representations and how can the inference model transfer future
observations to the latent variables. PV-RNN does both by introducing adaptive
vectors mirroring the training data, whose values can then be adapted
differently during evaluation. Moreover, prediction errors during
backpropagation, rather than external inputs during the forward computation,
are used to convey information to the network about the external data. For
testing, we introduce error regression for predicting unseen sequences as
inspired by predictive coding that leverages those mechanisms. The model
introduces a weighting parameter, the meta-prior, to balance the optimization
pressure placed on two terms of a lower bound on the marginal likelihood of the
sequential data. We test the model on two datasets with probabilistic
structures and show that with high values of the meta-prior the network
develops deterministic chaos through which the data's randomness is imitated.
For low values, the model behaves as a random process. The network performs
best on intermediate values, and is able to capture the latent probabilistic
structure with good generalization. Analyzing the meta-prior's impact on the
network allows to precisely study the theoretical value and practical benefits
of incorporating stochastic dynamics in our model. We demonstrate better
prediction performance on a robot imitation task with our model using error
regression compared to a standard variational Bayes model lacking such a
procedure.Comment: The paper is accepted in Neural Computatio
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