diff --git a/deep_learning4e.py b/deep_learning4e.py
index bea9c8d2c..64aa49e90 100644
--- a/deep_learning4e.py
+++ b/deep_learning4e.py
@@ -8,7 +8,7 @@
 from keras.layers import Embedding, SimpleRNN, Dense
 from keras.preprocessing import sequence
 
-from utils4e import (sigmoid, dot_product, softmax1D, conv1D, gaussian_kernel, element_wise_product, vector_add,
+from utils4e import (Sigmoid, dot_product, softmax1D, conv1D, gaussian_kernel, element_wise_product, vector_add,
                      random_weights, scalar_vector_product, matrix_multiplication, map_vector, mse_loss)
 
 
@@ -37,7 +37,7 @@ class NNUnit(Node):
     """
 
     def __init__(self, weights=None, value=None):
-        super(NNUnit, self).__init__(value)
+        super().__init__(value)
         self.weights = weights or []
 
 
@@ -59,7 +59,7 @@ class OutputLayer(Layer):
     """1D softmax output layer in 19.3.2"""
 
     def __init__(self, size=3):
-        super(OutputLayer, self).__init__(size)
+        super().__init__(size)
 
     def forward(self, inputs):
         assert len(self.nodes) == len(inputs)
@@ -73,7 +73,7 @@ class InputLayer(Layer):
     """1D input layer. Layer size is the same as input vector size."""
 
     def __init__(self, size=3):
-        super(InputLayer, self).__init__(size)
+        super().__init__(size)
 
     def forward(self, inputs):
         """Take each value of the inputs to each unit in the layer."""
@@ -92,10 +92,10 @@ class DenseLayer(Layer):
     """
 
     def __init__(self, in_size=3, out_size=3, activation=None):
-        super(DenseLayer, self).__init__(out_size)
+        super().__init__(out_size)
         self.out_size = out_size
         self.inputs = None
-        self.activation = sigmoid() if not activation else activation
+        self.activation = Sigmoid() if not activation else activation
         # initialize weights
         for node in self.nodes:
             node.weights = random_weights(-0.5, 0.5, in_size)
@@ -118,7 +118,7 @@ class ConvLayer1D(Layer):
     """
 
     def __init__(self, size=3, kernel_size=3):
-        super(ConvLayer1D, self).__init__(size)
+        super().__init__(size)
         # init convolution kernel as gaussian kernel
         for node in self.nodes:
             node.weights = gaussian_kernel(kernel_size)
@@ -142,7 +142,7 @@ class MaxPoolingLayer1D(Layer):
     """
 
     def __init__(self, size=3, kernel_size=3):
-        super(MaxPoolingLayer1D, self).__init__(size)
+        super().__init__(size)
         self.kernel_size = kernel_size
         self.inputs = None
 
@@ -326,7 +326,7 @@ class BatchNormalizationLayer(Layer):
     """Batch normalization layer."""
 
     def __init__(self, size, epsilon=0.001):
-        super(BatchNormalizationLayer, self).__init__(size)
+        super().__init__(size)
         self.epsilon = epsilon
         # self.weights = [beta, gamma]
         self.weights = [0, 0]
diff --git a/learning.py b/learning.py
index bcaf0961e..99ef8abc2 100644
--- a/learning.py
+++ b/learning.py
@@ -265,9 +265,9 @@ def cross_validation_wrapper(learner, dataset, k=10, trials=1):
     while True:
         errT, errV = cross_validation(learner, dataset, size, k, trials)
         # check for convergence provided err_val is not empty
-        if errT and not np.isclose(errT[-1], errT, rel_tol=1e-6):
+        if errT and not np.isclose(errT[-1], errT, rtol=1e-6):
             best_size = 0
-            min_val = inf
+            min_val = np.inf
             i = 0
             while i < size:
                 if errs[i] < min_val:
diff --git a/learning4e.py b/learning4e.py
index 01d9ea290..f581b9ec1 100644
--- a/learning4e.py
+++ b/learning4e.py
@@ -7,7 +7,6 @@
 from qpsolvers import solve_qp
 
 from probabilistic_learning import NaiveBayesLearner
-from utils import sigmoid, sigmoid_derivative
 from utils4e import *
 
 
@@ -265,9 +264,9 @@ def model_selection(learner, dataset, k=10, trials=1):
     while True:
         err = cross_validation(learner, dataset, size, k, trials)
         # check for convergence provided err_val is not empty
-        if err and not isclose(err[-1], err, rel_tol=1e-6):
+        if err and not np.isclose(err[-1], err, rtol=1e-6):
             best_size = 0
-            min_val = inf
+            min_val = np.inf
             i = 0
             while i < size:
                 if errs[i] < min_val:
@@ -569,8 +568,8 @@ def LogisticLinearLeaner(dataset, learning_rate=0.01, epochs=100):
         # pass over all examples
         for example in examples:
             x = [1] + example
-            y = sigmoid(dot_product(w, x))
-            h.append(sigmoid_derivative(y))
+            y = Sigmoid().f(dot_product(w, x))
+            h.append(Sigmoid().derivative(y))
             t = example[idx_t]
             err.append(t - y)
 
@@ -581,7 +580,7 @@ def LogisticLinearLeaner(dataset, learning_rate=0.01, epochs=100):
 
     def predict(example):
         x = [1] + example
-        return sigmoid(dot_product(w, x))
+        return Sigmoid().f(dot_product(w, x))
 
     return predict
 
diff --git a/tests/test_deep_learning4e.py b/tests/test_deep_learning4e.py
index 92d73e96e..ed8979a0a 100644
--- a/tests/test_deep_learning4e.py
+++ b/tests/test_deep_learning4e.py
@@ -1,4 +1,3 @@
-import numpy as np
 import pytest
 from keras.datasets import imdb
 
diff --git a/utils.py b/utils.py
index 1d7f1e4f5..4bf29a9a3 100644
--- a/utils.py
+++ b/utils.py
@@ -273,11 +273,6 @@ def normalize(dist):
     return [(n / total) for n in dist]
 
 
-def norm(x, ord=2):
-    """Return the n-norm of vector x."""
-    return np.linalg.norm(x, ord)
-
-
 def random_weights(min_value, max_value, num_weights):
     return [random.uniform(min_value, max_value) for _ in range(num_weights)]
 
diff --git a/utils4e.py b/utils4e.py
index 6ed4a7f79..1c376066e 100644
--- a/utils4e.py
+++ b/utils4e.py
@@ -92,6 +92,10 @@ def remove_all(item, seq):
     """Return a copy of seq (or string) with all occurrences of item removed."""
     if isinstance(seq, str):
         return seq.replace(item, '')
+    elif isinstance(seq, set):
+        rest = seq.copy()
+        rest.remove(item)
+        return rest
     else:
         return [x for x in seq if x != item]
 
@@ -368,11 +372,6 @@ def normalize(dist):
     return [(n / total) for n in dist]
 
 
-def norm(x, ord=2):
-    """Return the n-norm of vector x."""
-    return np.linalg.norm(x, ord)
-
-
 def random_weights(min_value, max_value, num_weights):
     return [random.uniform(min_value, max_value) for _ in range(num_weights)]
 
@@ -402,7 +401,10 @@ def gaussian_kernel_2D(size=3, sigma=0.5):
 
 class Activation:
 
-    def derivative(self, value):
+    def f(self, x):
+        pass
+
+    def derivative(self, x):
         pass
 
 
@@ -418,7 +420,7 @@ def softmax1D(x):
     return [exp / sum_exps for exp in exps]
 
 
-class sigmoid(Activation):
+class Sigmoid(Activation):
 
     def f(self, x):
         if x >= 100:
@@ -431,7 +433,7 @@ def derivative(self, value):
         return value * (1 - value)
 
 
-class relu(Activation):
+class Relu(Activation):
 
     def f(self, x):
         return max(0, x)
@@ -440,7 +442,7 @@ def derivative(self, value):
         return 1 if value > 0 else 0
 
 
-class elu(Activation):
+class Elu(Activation):
 
     def f(self, x, alpha=0.01):
         return x if x > 0 else alpha * (np.exp(x) - 1)
@@ -449,7 +451,7 @@ def derivative(self, value, alpha=0.01):
         return 1 if value > 0 else alpha * np.exp(value)
 
 
-class tanh(Activation):
+class Tanh(Activation):
 
     def f(self, x):
         return np.tanh(x)
@@ -458,7 +460,7 @@ def derivative(self, value):
         return 1 - (value ** 2)
 
 
-class leaky_relu(Activation):
+class LeakyRelu(Activation):
 
     def f(self, x, alpha=0.01):
         return x if x > 0 else alpha * x