English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Higher order artificial neurons whose outputs are computed by applying anactivation function to a higher order multinomial function of the inputs havebeen considered in the past, but did not gain acceptance due to the extraparameters and computational cost. However, higher order neurons havesignificantly greater learning capabilities since the decision boundaries ofhigher order neurons can be complex surfaces instead of just hyperplanes. Theboundary of a single quadratic neuron can be a general hyper-quadric surfaceallowing it to learn many nonlinearly separable datasets. Since quadratic formscan be represented by symmetric matrices, only $\frac{n(n+1)}{2}$ additionalparameters are needed instead of $n^2$. A quadratic Logistic regression modelis first presented. Solutions to the XOR problem with a single quadratic neuronare considered. The complete vectorized equations for both forward and backwardpropagation in feedforward networks composed of quadratic neurons are derived.A reduced parameter quadratic neural network model with just $ n $ additionalparameters per neuron that provides a compromise between learning ability andcomputational cost is presented. Comparison on benchmark classificationdatasets are used to demonstrate that a final layer of quadratic neuronsenables networks to achieve higher accuracy with significantly fewer hiddenlayer neurons. In particular this paper shows that any dataset composed of$\mathcal{C}$ bounded clusters can be separated with only a single layer of$\mathcal{C}$ quadratic neurons.

Efficient Vectorized Backpropagation Algorithms for Training Feedforward Networks Composed of Quadratic Neurons