Example 3: Classification

Regression formulation

Let’s first treat the problem as a regression problem (output dimension = 1, MSE loss).

create the two moon dataset

from kan import KAN
import matplotlib.pyplot as plt
from sklearn.datasets import make_moons
import torch
import numpy as np

dataset = {}
train_input, train_label = make_moons(n_samples=1000, shuffle=True, noise=0.1, random_state=None)
test_input, test_label = make_moons(n_samples=1000, shuffle=True, noise=0.1, random_state=None)

dataset['train_input'] = torch.from_numpy(train_input)
dataset['test_input'] = torch.from_numpy(test_input)
dataset['train_label'] = torch.from_numpy(train_label[:,None])
dataset['test_label'] = torch.from_numpy(test_label[:,None])

X = dataset['train_input']
y = dataset['train_label']
plt.scatter(X[:,0], X[:,1], c=y[:,0])

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Train KAN

model = KAN(width=[2,1], grid=3, k=3)

def train_acc():
    return torch.mean((torch.round(model(dataset['train_input'])[:,0]) == dataset['train_label'][:,0]).float())

def test_acc():
    return torch.mean((torch.round(model(dataset['test_input'])[:,0]) == dataset['test_label'][:,0]).float())

results = model.train(dataset, opt="LBFGS", steps=20, metrics=(train_acc, test_acc));
results['train_acc'][-1], results['test_acc'][-1]

train loss: 1.56e-01 | test loss: 1.58e-01 | reg: 6.92e+00 : 100%|██| 20/20 [00:02<00:00,  9.97it/s]

(1.0, 1.0)

Automatic symbolic regression

lib = ['x','x^2','x^3','x^4','exp','log','sqrt','tanh','sin','tan','abs']
model.auto_symbolic(lib=lib)
formula = model.symbolic_formula()[0][0]
formula

fixing (0,0,0) with sin, r2=0.967966050300312
fixing (0,1,0) with tan, r2=0.9801151730516574

\[\displaystyle 0.39 \sin{\left(3.08 x_{1} + 1.56 \right)} - 0.79 \tan{\left(0.94 x_{2} - 3.37 \right)} + 0.51\]

How accurate is this formula?

# how accurate is this formula?
def acc(formula, X, y):
    batch = X.shape[0]
    correct = 0
    for i in range(batch):
        correct += np.round(np.array(formula.subs('x_1', X[i,0]).subs('x_2', X[i,1])).astype(np.float64)) == y[i,0]
    return correct/batch

print('train acc of the formula:', acc(formula, dataset['train_input'], dataset['train_label']))
print('test acc of the formula:', acc(formula, dataset['test_input'], dataset['test_label']))

train acc of the formula: tensor(1.)
test acc of the formula: tensor(1.)

Classification formulation

Let’s then treat the problem as a regression problem (output dimension = 2, CrossEntropy loss).

Create the two moon datatset

from kan import KAN
import matplotlib.pyplot as plt
from sklearn.datasets import make_moons
import torch
import numpy as np

dataset = {}
train_input, train_label = make_moons(n_samples=1000, shuffle=True, noise=0.1, random_state=None)
test_input, test_label = make_moons(n_samples=1000, shuffle=True, noise=0.1, random_state=None)

dataset['train_input'] = torch.from_numpy(train_input)
dataset['test_input'] = torch.from_numpy(test_input)
dataset['train_label'] = torch.from_numpy(train_label)
dataset['test_label'] = torch.from_numpy(test_label)

X = dataset['train_input']
y = dataset['train_label']
plt.scatter(X[:,0], X[:,1], c=y[:])

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Train KAN

model = KAN(width=[2,2], grid=3, k=3)

def train_acc():
    return torch.mean((torch.argmax(model(dataset['train_input']), dim=1) == dataset['train_label']).float())

def test_acc():
    return torch.mean((torch.argmax(model(dataset['test_input']), dim=1) == dataset['test_label']).float())

results = model.train(dataset, opt="LBFGS", steps=20, metrics=(train_acc, test_acc), loss_fn=torch.nn.CrossEntropyLoss());

train loss: 4.71e-10 | test loss: 6.99e-01 | reg: 1.10e+03 : 100%|██| 20/20 [00:02<00:00,  9.84it/s]

Automatic symbolic regression

lib = ['x','x^2','x^3','x^4','exp','log','sqrt','tanh','sin','abs']
model.auto_symbolic(lib=lib)

fixing (0,0,0) with sin, r2=0.8303828486153692
fixing (0,0,1) with sin, r2=0.7801497677237067
fixing (0,1,0) with x^3, r2=0.9535787267982471
fixing (0,1,1) with x^3, r2=0.9533594412300308

formula1, formula2 = model.symbolic_formula()[0]
formula1

\[\displaystyle - 3113.07 \left(0.21 - x_{2}\right)^{3} - 807.36 \sin{\left(3.13 x_{1} + 1.42 \right)} - 120.29\]

formula2

\[\displaystyle 3027.89 \left(0.21 - x_{2}\right)^{3} + 908.57 \sin{\left(3.19 x_{1} + 1.4 \right)} + 172.29\]

How accurate is this formula?

# how accurate is this formula?
def acc(formula1, formula2, X, y):
    batch = X.shape[0]
    correct = 0
    for i in range(batch):
        logit1 = np.array(formula1.subs('x_1', X[i,0]).subs('x_2', X[i,1])).astype(np.float64)
        logit2 = np.array(formula2.subs('x_1', X[i,0]).subs('x_2', X[i,1])).astype(np.float64)
        correct += (logit2 > logit1) == y[i]
    return correct/batch

print('train acc of the formula:', acc(formula1, formula2, dataset['train_input'], dataset['train_label']))
print('test acc of the formula:', acc(formula1, formula2, dataset['test_input'], dataset['test_label']))

train acc of the formula: tensor(0.9700)
test acc of the formula: tensor(0.9660)