add more examples

examples/CategoryOfLenses.g

@@ -0,0 +1,330 @@
+#! @Chapter Examples and Tests
+
+#! @Section Category of Lenses
+
+LoadPackage( "MachineLearningForCAP" );
+
+#! @Example
+Smooth := CategoryOfSkeletalSmoothMaps( );
+#! SkeletalSmoothMaps
+Lenses := CategoryOfLenses( Smooth );
+#! CategoryOfLenses( SkeletalSmoothMaps )
+A := ObjectConstructor( Lenses, [ Smooth.( 1 ), Smooth.( 2 ) ] );
+#! (ℝ^1, ℝ^2)
+IsWellDefined( A );
+#! true
+CapCategory( A );
+#! CategoryOfLenses( SkeletalSmoothMaps )
+A_datum := ObjectDatum( A );
+#! [ ℝ^1, ℝ^2 ]
+CapCategory( A_datum[1] );
+#! SkeletalSmoothMaps
+B := ObjectConstructor( Lenses, [ Smooth.( 3 ), Smooth.( 4 ) ] );
+#! (ℝ^3, ℝ^4)
+get := RandomMorphism( Smooth.( 1 ), Smooth.( 3 ), 5 );
+#! ℝ^1 -> ℝ^3
+put := RandomMorphism( Smooth.( 1 + 4 ), Smooth.( 2 ), 5 );
+#! ℝ^5 -> ℝ^2
+f := MorphismConstructor( Lenses, A, [ get, put ], B );
+#! (ℝ^1, ℝ^2) -> (ℝ^3, ℝ^4) defined by:
+#!
+#! Get Morphism:
+#! ----------
+#! ℝ^1 -> ℝ^3
+#!
+#! Put Morphism:
+#! ----------
+#! ℝ^5 -> ℝ^2
+MorphismDatum( f );
+#! [ ℝ^1 -> ℝ^3, ℝ^5 -> ℝ^2 ]
+IsWellDefined( f );
+#! true
+Display( f );
+#! (ℝ^1, ℝ^2) -> (ℝ^3, ℝ^4) defined by:
+#!
+#! Get Morphism:
+#! ------------
+#! ℝ^1 -> ℝ^3
+#!
+#! ‣ 0.766 * x1 ^ 4 + 0.234
+#! ‣ 1. * x1 ^ 4 + 0.388
+#! ‣ 0.459 * x1 ^ 4 + 0.278
+#!
+#! Put Morphism:
+#! ------------
+#! ℝ^5 -> ℝ^2
+#!
+#! ‣ 0.677 * x1 ^ 5 + 0.19 * x2 ^ 4 + 0.659 * x3 ^ 4
+#! + 0.859 * x4 ^ 5 + 0.28 * x5 ^ 1 + 0.216
+#! ‣ 0.37 * x1 ^ 5 + 0.571 * x2 ^ 4 + 0.835 * x3 ^ 4
+#! + 0.773 * x4 ^ 5 + 0.469 * x5 ^ 1 + 0.159
+id_A := IdentityMorphism( Lenses, A );
+#! (ℝ^1, ℝ^2) -> (ℝ^1, ℝ^2) defined by:
+#!
+#! Get Morphism:
+#! ----------
+#! ℝ^1 -> ℝ^1
+#!
+#! Put Morphism:
+#! ----------
+#! ℝ^3 -> ℝ^2
+Display( id_A );
+#! (ℝ^1, ℝ^2) -> (ℝ^1, ℝ^2) defined by:
+#!
+#! Get Morphism:
+#! ------------
+#! ℝ^1 -> ℝ^1
+#!
+#! ‣ x1
+#!
+#! Put Morphism:
+#! ------------
+#! ℝ^3 -> ℝ^2
+#!
+#! ‣ x2
+#! ‣ x3
+IsCongruentForMorphisms( PreCompose( id_A, f ), f );
+#! true
+TensorUnit( Lenses );
+#! (ℝ^0, ℝ^0)
+TensorProductOnObjects( A, B );
+#! (ℝ^4, ℝ^6)
+f1 := RandomMorphism( A, B, 5 );
+#! (ℝ^1, ℝ^2) -> (ℝ^3, ℝ^4) defined by:
+#!
+#! Get Morphism:
+#! ----------
+#! ℝ^1 -> ℝ^3
+#!
+#! Put Morphism:
+#! ----------
+#! ℝ^5 -> ℝ^2
+f2 := RandomMorphism( A, B, 5 );
+#! (ℝ^1, ℝ^2) -> (ℝ^3, ℝ^4) defined by:
+#!
+#! Get Morphism:
+#! ----------
+#! ℝ^1 -> ℝ^3
+#!
+#! Put Morphism:
+#! ----------
+#! ℝ^5 -> ℝ^2
+f3 := RandomMorphism( A, B, 5 );
+#! (ℝ^1, ℝ^2) -> (ℝ^3, ℝ^4) defined by:
+#!
+#! Get Morphism:
+#! ----------
+#! ℝ^1 -> ℝ^3
+#!
+#! Put Morphism:
+#! ----------
+#! ℝ^5 -> ℝ^2
+f1_f2 := TensorProductOnMorphisms( Lenses, f1, f2 );
+#! (ℝ^2, ℝ^4) -> (ℝ^6, ℝ^8) defined by:
+#!
+#! Get Morphism:
+#! ----------
+#! ℝ^2 -> ℝ^6
+#!
+#! Put Morphism:
+#! ----------
+#! ℝ^10 -> ℝ^4
+f2_f3 := TensorProductOnMorphisms( Lenses, f2, f3 );
+#! (ℝ^2, ℝ^4) -> (ℝ^6, ℝ^8) defined by:
+#!
+#! Get Morphism:
+#! ----------
+#! ℝ^2 -> ℝ^6
+#!
+#! Put Morphism:
+#! ----------
+#! ℝ^10 -> ℝ^4
+t1 := TensorProductOnMorphisms( Lenses, f1_f2, f3 );
+#! (ℝ^3, ℝ^6) -> (ℝ^9, ℝ^12) defined by:
+#!
+#! Get Morphism:
+#! ----------
+#! ℝ^3 -> ℝ^9
+#!
+#! Put Morphism:
+#! ----------
+#! ℝ^15 -> ℝ^6
+t2 := TensorProductOnMorphisms( Lenses, f1, f2_f3 );
+#! (ℝ^3, ℝ^6) -> (ℝ^9, ℝ^12) defined by:
+#!
+#! Get Morphism:
+#! ----------
+#! ℝ^3 -> ℝ^9
+#!
+#! Put Morphism:
+#! ----------
+#! ℝ^15 -> ℝ^6
+IsCongruentForMorphisms( t1, t2 );
+#! true
+Display( Braiding( A, B ) );
+#! (ℝ^4, ℝ^6) -> (ℝ^4, ℝ^6) defined by:
+#!
+#! Get Morphism:
+#! ------------
+#! ℝ^4 -> ℝ^4
+#!
+#! ‣ x2
+#! ‣ x3
+#! ‣ x4
+#! ‣ x1
+#!
+#! Put Morphism:
+#! ------------
+#! ℝ^10 -> ℝ^6
+#!
+#! ‣ x9
+#! ‣ x10
+#! ‣ x5
+#! ‣ x6
+#! ‣ x7
+#! ‣ x8
+Display( PreCompose( Braiding( A, B ), BraidingInverse( A, B ) ) );
+#! (ℝ^4, ℝ^6) -> (ℝ^4, ℝ^6) defined by:
+#!
+#! Get Morphism:
+#! ------------
+#! ℝ^4 -> ℝ^4
+#!
+#! ‣ x1
+#! ‣ x2
+#! ‣ x3
+#! ‣ x4
+#!
+#! Put Morphism:
+#! ------------
+#! ℝ^10 -> ℝ^6
+#!
+#! ‣ x5
+#! ‣ x6
+#! ‣ x7
+#! ‣ x8
+#! ‣ x9
+#! ‣ x10
+R := EmbeddingIntoCategoryOfLenses( Smooth, Lenses );
+#! Embedding functor into category of lenses
+SourceOfFunctor( R );
+#! SkeletalSmoothMaps
+RangeOfFunctor( R );
+#! CategoryOfLenses( SkeletalSmoothMaps )
+f := Smooth.Softmax( 2 );
+#! ℝ^2 -> ℝ^2
+Display( f );
+#! ℝ^2 -> ℝ^2
+#!
+#! ‣ Exp( x1 ) / (Exp( x1 ) + Exp( x2 ))
+#! ‣ Exp( x2 ) / (Exp( x1 ) + Exp( x2 ))
+Rf := ApplyFunctor( R, f );
+#! (ℝ^2, ℝ^2) -> (ℝ^2, ℝ^2) defined by:
+#!
+#! Get Morphism:
+#! ----------
+#! ℝ^2 -> ℝ^2
+#!
+#! Put Morphism:
+#! ----------
+#! ℝ^4 -> ℝ^2
+Display( Rf );
+#! (ℝ^2, ℝ^2) -> (ℝ^2, ℝ^2) defined by:
+#!
+#! Get Morphism:
+#! ------------
+#! ℝ^2 -> ℝ^2
+#!
+#! ‣ Exp( x1 ) / (Exp( x1 ) + Exp( x2 ))
+#! ‣ Exp( x2 ) / (Exp( x1 ) + Exp( x2 ))
+#!
+#! Put Morphism:
+#! ------------
+#! ℝ^4 -> ℝ^2
+#!
+#! ‣ x3 *
+#!   ((Exp( x1 ) + Exp( x2 ) - Exp( x1 )) * (Exp( x1 ) / (Exp( x1 ) + Exp( x2 )) ^ 2))
+#!   + x4 * ((- Exp( x1 )) * (Exp( x2 ) / (Exp( x1 ) + Exp( x2 )) ^ 2))
+#! ‣ x3 * ((- Exp( x2 )) * (Exp( x1 ) / (Exp( x1 ) + Exp( x2 )) ^ 2)) +
+#!   x4 *
+#!   ((Exp( x1 ) + Exp( x2 ) - Exp( x2 )) * (Exp( x2 ) / (Exp( x1 ) + Exp( x2 )) ^ 2))
+Display( Lenses.GradientDescentOptimizer( :learning_rate := 0.01 )( 2 ) );
+#! (ℝ^2, ℝ^2) -> (ℝ^2, ℝ^2) defined by:
+#!
+#! Get Morphism:
+#! ------------
+#! ℝ^2 -> ℝ^2
+#!
+#! ‣ x1
+#! ‣ x2
+#!
+#! Put Morphism:
+#! ------------
+#! ℝ^4 -> ℝ^2
+#!
+#! ‣ x1 + 0.01 * x3
+#! ‣ x2 + 0.01 * x4
+Display( Lenses.GradientDescentWithMomentumOptimizer(
+            :learning_rate := 0.01, momentum := 0.9 )( 2 ) );
+#! (ℝ^4, ℝ^4) -> (ℝ^2, ℝ^2) defined by:
+#!
+#! Get Morphism:
+#! ------------
+#! ℝ^4 -> ℝ^2
+#!
+#! ‣ x3
+#! ‣ x4
+#!
+#! Put Morphism:
+#! ------------
+#! ℝ^6 -> ℝ^4
+#!
+#! ‣ 0.9 * x1 + 0.01 * x5
+#! ‣ 0.9 * x2 + 0.01 * x6
+#! ‣ x3 + (0.9 * x1 + 0.01 * x5)
+#! ‣ x4 + (0.9 * x2 + 0.01 * x6)
+Display( Lenses.AdagradOptimizer( :learning_rate := 0.01 )( 2 ) );
+#! (ℝ^4, ℝ^4) -> (ℝ^2, ℝ^2) defined by:
+#!
+#! Get Morphism:
+#! ------------
+#! ℝ^4 -> ℝ^2
+#!
+#! ‣ x3
+#! ‣ x4
+#!
+#! Put Morphism:
+#! ------------
+#! ℝ^6 -> ℝ^4
+#!
+#! ‣ x1 + x5 ^ 2
+#! ‣ x2 + x6 ^ 2
+#! ‣ x3 + 0.01 * x5 / (1.e-07 + Sqrt( (x1 + x5 ^ 2) ))
+#! ‣ x4 + 0.01 * x6 / (1.e-07 + Sqrt( (x2 + x6 ^ 2) ))
+Display( Lenses.AdamOptimizer(
+          :learning_rate := 0.01, beta_1 := 0.9, beta_2 := 0.999 )( 2 ) );
+#! (ℝ^7, ℝ^7) -> (ℝ^2, ℝ^2) defined by:
+#!
+#! Get Morphism:
+#! ------------
+#! ℝ^7 -> ℝ^2
+#!
+#! ‣ x6
+#! ‣ x7
+#!
+#! Put Morphism:
+#! ------------
+#! ℝ^9 -> ℝ^7
+#!
+#! ‣ x1 + 1
+#! ‣ 0.9 * x2 + 0.1 * x8
+#! ‣ 0.9 * x3 + 0.1 * x9
+#! ‣ 0.999 * x4 + 0.001 * x8 ^ 2
+#! ‣ 0.999 * x5 + 0.001 * x9 ^ 2
+#! ‣ x6 + 0.01 / (1 - 0.999 ^ x1)
+#!   * ((0.9 * x2 + 0.1 * x8) /
+#!      (1.e-07 + Sqrt( (0.999 * x4 + 0.001 * x8 ^ 2) / (1 - 0.999 ^ x1) )))
+#! ‣ x7 + 0.01 / (1 - 0.999 ^ x1)
+#!   * ((0.9 * x3 + 0.1 * x9) /
+#!      (1.e-07 + Sqrt( (0.999 * x5 + 0.001 * x9 ^ 2) / (1 - 0.999 ^ x1) )))
+#! @EndExample

examples/CategoryOfParametrisedMorphisms.g

@@ -137,27 +137,27 @@ Display( t );
 #!   + 0.88 * (Exp( x1 ) / (5.10727 + Exp( x1 ))) + 0.59
 #! ‣ 0.67 * (2.39116 / (5.10727 + Exp( x1 ))) + 0.05 * (2.71611 / (5.10727 + Exp( x1 )))
 #!   + 0.85 * (Exp( x1 ) / (5.10727 + Exp( x1 ))) + 0.31
-# gap> s := SimplifyMorphism( t, infinity );
-# ℝ^1 -> ℝ^2 defined by:
-#
-# Parameter Object:
-# -----------------
-# ℝ^0
-#
-# Parametrised Morphism:
-# ----------------------
-# ℝ^1 -> ℝ^2
-# gap> Display( s );
-# ℝ^1 -> ℝ^2 defined by:
-#
-# Parameter Object:
-# -----------------
-# ℝ^0
-#
-# Parametrised Morphism:
-# ----------------------
-# ℝ^1 -> ℝ^2
-#
-# ‣ (1.47 * Exp( x1 ) + 5.84111) / (Exp( x1 ) + 5.10727)
-# ‣ (1.16 * Exp( x1 ) + 3.32114) / (Exp( x1 ) + 5.10727)
+s := SimplifyMorphism( t, infinity );
+#! ℝ^1 -> ℝ^2 defined by:
+#!
+#! Parameter Object:
+#! -----------------
+#! ℝ^0
+#!
+#! Parametrised Morphism:
+#! ----------------------
+#! ℝ^1 -> ℝ^2
+#! gap> Display( s );
+#! ℝ^1 -> ℝ^2 defined by:
+#!
+#! Parameter Object:
+#! -----------------
+#! ℝ^0
+#!
+#! Parametrised Morphism:
+#! ----------------------
+#! ℝ^1 -> ℝ^2
+#!
+#! ‣ (1.47 * Exp( x1 ) + 5.84111) / (Exp( x1 ) + 5.10727)
+#! ‣ (1.16 * Exp( x1 ) + 3.32114) / (Exp( x1 ) + 5.10727)
 #! @EndExample

tst/neural-network-2.tst

@@ -18,9 +18,7 @@ gap> w2 := Concatenation( TransposedMat( w2 ) );;
 gap> w3 := [[-0.05885905, -0.81396204,  0.00370395, -0.42547446], [-0.39928403,  0.56314194,  0.6614479 ,  0.5060446 ], [ 0.6662301,  -0.2800727 ,  0.1187852 , -0.27065504], [ 0.15874296, -0.6039741 , -0.7533438 , -0.33242884], [ 0.26578736, -0.45036432, -0.61879224,  0.8060001 ], [ 0.,          0.,          0.,          0.,       ] ];;
 gap> w3 := Concatenation( TransposedMat( w3 ) );;
 gap> w := Concatenation( [ w3, w2, w1 ] );;
-gap> nr_epochs := 3;;
+gap> nr_epochs := 1;;
 gap> w := Fit( one_epoch_update, nr_epochs, w );;
-Epoch  0/3 - loss = 0.36090265698232782
-Epoch  1/3 - loss = 0.21968044680244986
-Epoch  2/3 - loss = 0.17883151112398918
-Epoch  3/3 - loss = 0.15935373922266871
+Epoch  0/1 - loss = 0.36090265698232782
+Epoch  1/1 - loss = 0.21968044680244986