Merge pull request #7 from kamalsaleh/master

change names of some attributes and include two examples in the readme file

Author: kamalsaleh

PackageInfo.g

@@ -10,7 +10,7 @@ SetPackageInfo( rec(
 
 PackageName := "MachineLearningForCAP",
 Subtitle := "Exploring categorical machine learning in CAP",
-Version := "2024.07-17",
+Version := "2024.07-20",
 Date := (function ( ) if IsBound( GAPInfo.SystemEnvironment.GAP_PKG_RELEASE_DATE ) then return GAPInfo.SystemEnvironment.GAP_PKG_RELEASE_DATE; else return Concatenation( ~.Version{[ 1 .. 4 ]}, "-", ~.Version{[ 6, 7 ]}, "-01" ); fi; end)( ),
 License := "GPL-2.0-or-later",
 

README.md

@@ -26,22 +26,22 @@ f := Smooth.Softmax( 3 );
 f := MorphismConstructor( Para, R1 / Para, [ R2, f ], R3 / Para );
 #! ℝ^1 -> ℝ^3 defined by:
 #!
-#! Parameter Object:
+#! Underlying Object:
 #! -----------------
 #! ℝ^2
 #!
-#! Parametrised Morphism:
-#! ----------------------
+#! Underlying Morphism:
+#! -------------------
 #! ℝ^3 -> ℝ^3
 Display( f );
 #! ℝ^1 -> ℝ^3 defined by:
 #!
-#! Parameter Object:
+#! Underlying Object:
 #! -----------------
 #! ℝ^2
 #!
-#! Parametrised Morphism:
-#! ----------------------
+#! Underlying Morphism:
+#! -------------------
 #! ℝ^3 -> ℝ^3
 #!
 #! ‣ Exp( x1 ) / (Exp( x1 ) + Exp( x2 ) + Exp( x3 ))
@@ -59,22 +59,22 @@ Display( r );
 g := ReparametriseMorphism( f, r );
 #! ℝ^1 -> ℝ^3 defined by:
 #!
-#! Parameter Object:
+#! Underlying Object:
 #! -----------------
 #! ℝ^2
 #!
-#! Parametrised Morphism:
-#! ----------------------
+#! Underlying Morphism:
+#! -------------------
 #! ℝ^3 -> ℝ^3
 Display( g );
 #! ℝ^1 -> ℝ^3 defined by:
 #!
-#! Parameter Object:
+#! Underlying Object:
 #! -----------------
 #! ℝ^2
 #!
-#! Parametrised Morphism:
-#! ----------------------
+#! Underlying Morphism:
+#! -------------------
 #! ℝ^3 -> ℝ^3
 #!
 #! ‣ Exp( Sqrt( x1 ) ) / (Exp( Sqrt( x1 ) ) + Exp( Cos( x2 ) ) + Exp( x3 ))
@@ -83,32 +83,32 @@ Display( g );
 l := Para.AffineTransformation( 3, 2 );
 #! ℝ^3 -> ℝ^2 defined by:
 #!
-#! Parameter Object:
+#! Underlying Object:
 #! -----------------
 #! ℝ^8
 #!
-#! Parametrised Morphism:
-#! ----------------------
+#! Underlying Morphism:
+#! -------------------
 #! ℝ^11 -> ℝ^2
 h := PreCompose( g, l );
 #! ℝ^1 -> ℝ^2 defined by:
 #!
-#! Parameter Object:
+#! Underlying Object:
 #! -----------------
 #! ℝ^10
 #!
-#! Parametrised Morphism:
-#! ----------------------
+#! Underlying Morphism:
+#! -------------------
 #! ℝ^11 -> ℝ^2
 Display( h );
 #! ℝ^1 -> ℝ^2 defined by:
 #!
-#! Parameter Object:
+#! Underlying Object:
 #! -----------------
 #! ℝ^10
 #!
-#! Parametrised Morphism:
-#! ----------------------
+#! Underlying Morphism:
+#! -------------------
 #! ℝ^11 -> ℝ^2
 #!
 #! ‣ x1 * (Exp( Sqrt( x9 ) ) / (Exp( Sqrt( x9 ) ) + Exp( Cos( x10 ) ) + Exp( x11 )))
@@ -123,22 +123,22 @@ r := Smooth.Constant( constants );
 t := ReparametriseMorphism( h, r );
 #! ℝ^1 -> ℝ^2 defined by:
 #!
-#! Parameter Object:
+#! Underlying Object:
 #! -----------------
 #! ℝ^0
 #!
-#! Parametrised Morphism:
-#! ----------------------
+#! Underlying Morphism:
+#! -------------------
 #! ℝ^1 -> ℝ^2
 Display( t );
 #! ℝ^1 -> ℝ^2 defined by:
 #!
-#! Parameter Object:
+#! Underlying Object:
 #! -----------------
 #! ℝ^0
 #!
-#! Parametrised Morphism:
-#! ----------------------
+#! Underlying Morphism:
+#! -------------------
 #! ℝ^1 -> ℝ^2
 #!
 #! ‣ 0.91 * (2.39116 / (5.10727 + Exp( x1 ))) + 0.24 * (2.71611 / (5.10727 + Exp( x1 )))
@@ -148,22 +148,22 @@ Display( t );
 s := SimplifyMorphism( t, infinity );
 #! ℝ^1 -> ℝ^2 defined by:
 #!
-#! Parameter Object:
+#! Underlying Object:
 #! -----------------
 #! ℝ^0
 #!
-#! Parametrised Morphism:
-#! ----------------------
+#! Underlying Morphism:
+#! -------------------
 #! ℝ^1 -> ℝ^2
 Display( s );
 #! ℝ^1 -> ℝ^2 defined by:
 #!
-#! Parameter Object:
+#! Underlying Object:
 #! -----------------
 #! ℝ^0
 #!
-#! Parametrised Morphism:
-#! ----------------------
+#! Underlying Morphism:
+#! -------------------
 #! ℝ^1 -> ℝ^2
 #!
 #! ‣ (1.47 * Exp( x1 ) + 5.84111) / (Exp( x1 ) + 5.10727)
@@ -175,22 +175,22 @@ ApplyFunctor( iota, Smooth.( 1 ) );
 psi := ApplyFunctor( iota, Smooth.Sum( 2 ) );
 #! ℝ^2 -> ℝ^1 defined by:
 #!
-#! Parameter Object:
+#! Underlying Object:
 #! -----------------
 #! ℝ^0
 #!
-#! Parametrised Morphism:
-#! ----------------------
+#! Underlying Morphism:
+#! -------------------
 #! ℝ^2 -> ℝ^1
 Print( DisplayString( psi ) );
 #! ℝ^2 -> ℝ^1 defined by:
 #!
-#! Parameter Object:
+#! Underlying Object:
 #! -----------------
 #! ℝ^0
 #!
-#! Parametrised Morphism:
-#! ----------------------
+#! Underlying Morphism:
+#! -------------------
 #! ℝ^2 -> ℝ^1
 #!
 #! ‣ x1 + x2

examples/CategoryOfParametrisedMorphisms.g

@@ -546,9 +546,9 @@ InstallMethod( ViewString,
         " -> ",
         ViewString( Target( f ) ),
         " defined by:",
-        "\n\nParameter Object:\n-----------------\n",
+        "\n\nUnderlying Object:\n-----------------\n",
         ViewString( UnderlyingObject( f ) ),
-        "\n\nParametrised Morphism:\n----------------------\n",
+        "\n\nUnderlying Morphism:\n-------------------\n",
         ViewString( UnderlyingMorphism( f ) ) );
 
 end );
@@ -565,9 +565,9 @@ InstallMethod( DisplayString,
         " -> ",
         ViewString( Target( f ) ),
         " defined by:",
-        "\n\nParameter Object:\n-----------------\n",
+        "\n\nUnderlying Object:\n-----------------\n",
         ViewString( UnderlyingObject( f ) ),
-        "\n\nParametrised Morphism:\n----------------------\n",
+        "\n\nUnderlying Morphism:\n-------------------\n",
         DisplayString( UnderlyingMorphism( f ) ) );
 
 end );
@@ -584,9 +584,9 @@ InstallMethod( Display,
         " -> ",
         ViewString( Target( f ) ),
         " defined by:",
-        "\n\nParameter Object:\n-----------------\n",
+        "\n\nUnderlying Object:\n-----------------\n",
         ViewString( UnderlyingObject( f ) ),
-        "\n\nParametrised Morphism:\n----------------------\n" ) );
+        "\n\nUnderlying Morphism:\n-------------------\n" ) );
 
     Display( UnderlyingMorphism( f ) );
 

gap/CategoryOfParametrisedMorphisms.gi

@@ -12,23 +12,23 @@ gap> Assert( 0, Para.AffineTransformation_( 3, 4 ) = Para.AffineTransformation(
 gap> l := Para.AffineTransformation( 3, 4 );
 ℝ^3 -> ℝ^4 defined by:
 
-Parameter Object:
+Underlying Object:
 -----------------
 ℝ^16
 
-Parametrised Morphism:
-----------------------
+Underlying Morphism:
+-------------------
 ℝ^19 -> ℝ^4
 gap> dummy_input := DummyInputForAffineTransformation( 3, 4, "w", "b", "x" );;
 gap> Display( l : dummy_input := dummy_input );
 ℝ^3 -> ℝ^4 defined by:
 
-Parameter Object:
+Underlying Object:
 -----------------
 ℝ^16
 
-Parametrised Morphism:
-----------------------
+Underlying Morphism:
+-------------------
 ℝ^19 -> ℝ^4
 
 ‣ w1_1 * x1 + w2_1 * x2 + w3_1 * x3 + b_1

pictures/linear_regression.gif

@@ -0,0 +1,113 @@
+gap> LoadPackage( "MachineLearningForCAP" );
+true
+
+gap> Para := CategoryOfParametrisedMorphisms( SkeletalSmoothMaps );
+CategoryOfParametrisedMorphisms( SkeletalSmoothMaps )
+
+gap> training_set := [ [ 1, 2.9 ], [ 2, 5.1 ], [ 3, 7.05 ] ];
+[ [ 1, 2.9 ], [ 2, 5.1 ], [ 3, 7.05 ] ]
+
+gap> input_dim := 1;; output_dim := 1;; hidden_dims := [ ];;
+
+gap> f := PredictionMorphismOfNeuralNetwork( Para, input_dim, hidden_dims, output_dim, "IdFunc" );;
+
+gap> Display( f );
+ℝ^1 -> ℝ^1 defined by:
+
+Underlying Object:
+-----------------
+ℝ^2
+
+Underlying Morphism:
+-------------------
+ℝ^3 -> ℝ^1
+
+‣ x1 * x3 + x2
+
+gap> parameters := [ 2, 1 ];; x := [ 2 ];;
+
+gap> Eval( f, [ parameters, x ] );
+[ 5 ]
+
+gap> ell := LossMorphismOfNeuralNetwork( Para, input_dim, hidden_dims, output_dim, "IdFunc" );;
+
+gap> Display( ell );
+ℝ^2 -> ℝ^1 defined by:
+
+Underlying Object:
+-----------------
+ℝ^2
+
+Underlying Morphism:
+-------------------
+ℝ^4 -> ℝ^1
+
+‣ (x1 * x3 + x2 - x4) ^ 2 / 1
+
+gap> Lenses := CategoryOfLenses( SkeletalSmoothMaps );
+CategoryOfLenses( SkeletalSmoothMaps )
+
+gap> optimizer := Lenses.GradientDescentOptimizer( : learning_rate := 0.01 );;
+
+gap> batch_size := 1;;
+
+gap> one_epoch_update := OneEpochUpdateLens( ell, optimizer, training_set, batch_size );;
+
+gap> parameters := [ 0.1, -0.1 ];;
+
+gap> nr_epochs := 15;;
+
+gap> parameters := Fit( one_epoch_update, nr_epochs, parameters );
+Epoch  0/15 - loss = 26.777499999999993
+Epoch  1/15 - loss = 13.002145872163197
+Epoch  2/15 - loss = 6.3171942035316935
+Epoch  3/15 - loss = 3.0722513061917534
+Epoch  4/15 - loss = 1.4965356389126505
+Epoch  5/15 - loss = 0.73097379078374358
+Epoch  6/15 - loss = 0.35874171019291579
+Epoch  7/15 - loss = 0.1775574969062125
+Epoch  8/15 - loss = 0.089228700384937534
+Epoch  9/15 - loss = 0.046072054531129378
+Epoch 10/15 - loss = 0.024919378473509772
+Epoch 11/15 - loss = 0.014504998499450883
+Epoch 12/15 - loss = 0.0093448161379050161
+Epoch 13/15 - loss = 0.0067649700132868147
+Epoch 14/15 - loss = 0.0054588596501628835
+Epoch 15/15 - loss = 0.0047859930295160499
+[ 2.08995, 0.802632 ]
+
+gap> theta := SkeletalSmoothMaps.Constant( parameters );
+ℝ^0 -> ℝ^2
+
+gap> Display( theta );
+ℝ^0 -> ℝ^2
+
+‣ 2.08995
+‣ 0.802632
+
+gap> f_theta := ReparametriseMorphism( f, theta );;
+
+gap> Display( f_theta );
+ℝ^1 -> ℝ^1 defined by:
+
+Underlying Object:
+-----------------
+ℝ^0
+
+Underlying Morphism:
+-------------------
+ℝ^1 -> ℝ^1
+
+‣ 2.08995 * x1 + 0.802632
+
+gap> f_theta := UnderlyingMorphism( f_theta );
+ℝ^1 -> ℝ^1
+
+gap> Eval( f_theta, [ 1 ] );
+[ 2.89259 ]
+
+gap> Eval( f_theta, [ 2 ] );
+[ 4.98254 ]
+
+gap> Eval( f_theta, [ 3 ] );
+[ 7.07249 ]