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A simple linear-threshold neural network, with an XOR neural net factory.
(ns user.neural-network
(:import [java.lang.reflect Array]))
;; So far, this handles linear threshold nodes, specifically examining
;; Minsky and Papert's XOR dilemma. The make-xor-network is a factory function
;; which produces such a network.
;;
;; It's fairly optimized, using deftypes and whatnot. One could add an
;; activation function for further generality, or add a logistic function
;; and add some training routines to further improve things.
(defn- sum
([coll] (reduce + coll))
([v coll] (reduce + v coll)))
(defn- unit-step [x]
(if (neg? x)
0
1))
(definterface ILayer
(getWeights [])
(setWeight [node-idx idx v])
(getOutputs [])
(setOutput [idx v])
(getBias [])
(setBias [b])
(netInput [node-idx inputs])
(propagate [inputs]))
(deftype Layer [outputs ; an array of M doubles
weights ; an array of M arrays of N+1 doubles
^:volatile-mutable bias
output-fn]
ILayer
(getWeights [_] weights)
(setWeight [this node-idx idx v] (. Array (set (aget weights node-idx)
idx v)))
(getOutputs [_] outputs)
(setOutput [this idx v] (. Array (set outputs idx v)))
(getBias [_] bias)
(setBias [this b] (set! bias b))
;; dot-product of weights and inputs
(netInput [_ node-idx inputs] (sum
(for [k (range (alength inputs))]
(* (aget inputs k)
(aget weights node-idx k)))))
;; set outputs based on array of N inputs
(propagate [this inputs]
(if (not= (alength (aget weights 0))
(inc (alength inputs)))
(throw (ArrayIndexOutOfBoundsException.))
(doseq [k (range (alength outputs))]
(.setOutput
this
k
(output-fn
(+ (* bias
(aget weights k (alength inputs)))
(.netInput this k inputs))))))))
(defn make-layer [number-output-nodes number-input-nodes output-fn]
(Layer. (make-array Double/TYPE number-output-nodes)
(make-array Double/TYPE number-output-nodes (inc number-input-nodes))
0.0
output-fn))
(defn make-xor-network []
(let [l1 (doto (make-layer 1 2 unit-step)
(.setBias 0.4)
(.setWeight 0 0 1)
(.setWeight 0 1 1)
(.setWeight 0 2 -1))
l2 (doto (make-layer 1 2 unit-step)
(.setBias 1.2)
(.setWeight 0 0 1)
(.setWeight 0 1 1)
(.setWeight 0 2 -1))
l3 (doto (make-layer 1 2 unit-step)
(.setBias 0.5)
(.setWeight 0 0 0.6)
(.setWeight 0 1 -0.2)
(.setWeight 0 2 -1))]
(fn [x1 x2]
(.propagate l1 (into-array Double/TYPE [x1 x2]))
(.propagate l2 (into-array Double/TYPE [x1 x2]))
(.propagate l3 (into-array Double/TYPE
[(aget (.getOutputs l1) 0)
(aget (.getOutputs l2) 0)]))
(aget (.getOutputs l3) 0))))
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