pyTsetlinMachine

Implements the Tsetlin Machine, Convolutional Tsetlin Machine, Regression Tsetlin Machine, Weighted Tsetlin Machine, and Embedding Tsetlin Machine, with support for continuous features, multigranularity, and clause indexing

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pyTsetlinMachine

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Implementation of the Tsetlin Machine (https://arxiv.org/abs/1804.01508), Convolutional Tsetlin Machine (https://arxiv.org/abs/1905.09688), Regression Tsetlin Machine (https://arxiv.org/abs/1905.04206, https://royalsocietypublishing.org/doi/full/10.1098/rsta.2019.0165, https://link.springer.com/chapter/10.1007/978-3-030-30244-3_23), Weighted Tsetlin Machines (https://arxiv.org/abs/1911.12607, https://ieeexplore.ieee.org/document/9316190, https://arxiv.org/abs/2002.01245), and Embedding Tsetlin Machine, with support for continuous features (https://arxiv.org/abs/1905.04199, https://link.springer.com/chapter/10.1007%2F978-3-030-22999-3_49), multigranular clauses (https://arxiv.org/abs/1909.07310, https://link.springer.com/chapter/10.1007/978-3-030-34885-4_11), clause indexing (https://arxiv.org/abs/2004.03188, https://link.springer.com/chapter/10.1007/978-3-030-55789-8_60), drop clause (https://arxiv.org/abs/2105.14506), and drop literal.

Contents

Installation

pip install pyTsetlinMachine

Documentation

Documentation coming soon at https://pytsetlinmachine.readthedocs.io/en/latest/

Multi-threading

Multi-threaded implementation, https://github.com/cair/pyTsetlinMachineParallel

Tutorials

Convolutional Tsetlin Machine tutorial, https://github.com/cair/convolutional-tsetlin-machine-tutorial

Examples

Multiclass Demo

Code: NoisyXORDemo.py

from pyTsetlinMachine.tm import MultiClassTsetlinMachine
import numpy as np 

train_data = np.loadtxt("NoisyXORTrainingData.txt")
X_train = train_data[:,0:-1]
Y_train = train_data[:,-1]

test_data = np.loadtxt("NoisyXORTestData.txt")
X_test = test_data[:,0:-1]
Y_test = test_data[:,-1]

tm = MultiClassTsetlinMachine(10, 15, 3.9, boost_true_positive_feedback=0)

tm.fit(X_train, Y_train, epochs=200)

print("Accuracy:", 100*(tm.predict(X_test) == Y_test).mean())

print("Prediction: x1 = 1, x2 = 0, ... -> y = %d" % (tm.predict(np.array([[1,0,1,0,1,0,1,1,1,1,0,0]]))))
print("Prediction: x1 = 0, x2 = 1, ... -> y = %d" % (tm.predict(np.array([[0,1,1,0,1,0,1,1,1,1,0,0]]))))
print("Prediction: x1 = 0, x2 = 0, ... -> y = %d" % (tm.predict(np.array([[0,0,1,0,1,0,1,1,1,1,0,0]]))))
print("Prediction: x1 = 1, x2 = 1, ... -> y = %d" % (tm.predict(np.array([[1,1,1,0,1,0,1,1,1,1,0,0]]))))

Output

python3 ./NoisyXORDemo.py 

Accuracy: 100.00%

Prediction: x1 = 1, x2 = 0, ... -> y = 1
Prediction: x1 = 0, x2 = 1, ... -> y = 1
Prediction: x1 = 0, x2 = 0, ... -> y = 0
Prediction: x1 = 1, x2 = 1, ... -> y = 0

Interpretability Demo

Code: InterpretabilityDemo.py

from pyTsetlinMachine.tm import MultiClassTsetlinMachine
import numpy as np 

number_of_features = 20
noise = 0.1

X_train = np.random.randint(0, 2, size=(5000, number_of_features), dtype=np.uint32)
Y_train = np.logical_xor(X_train[:,0], X_train[:,1]).astype(dtype=np.uint32)
Y_train = np.where(np.random.rand(5000) <= noise, 1-Y_train, Y_train) # Adds noise

X_test = np.random.randint(0, 2, size=(5000, number_of_features), dtype=np.uint32)
Y_test = np.logical_xor(X_test[:,0], X_test[:,1]).astype(dtype=np.uint32)

tm = MultiClassTsetlinMachine(10, 15, 3.0, boost_true_positive_feedback=0)

tm.fit(X_train, Y_train, epochs=200)

print("Accuracy:", 100*(tm.predict(X_test) == Y_test).mean())

print("\nClass 0 Positive Clauses:\n")
for j in range(0, 10, 2):
    print("Clause #%d: " % (j), end=' ')
    l = []
    for k in range(number_of_features*2):
        if tm.ta_action(0, j, k) == 1:
            if k < number_of_features:
                l.append(" x%d" % (k))
            else:
                l.append("¬x%d" % (k-number_of_features))
    print(" ∧ ".join(l))

print("\nClass 0 Negative Clauses:\n")
for j in range(1, 10, 2):
    print("Clause #%d: " % (j), end=' ')
    l = []
    for k in range(number_of_features*2):
        if tm.ta_action(0, j, k) == 1:
            if k < number_of_features:
                l.append(" x%d" % (k))
            else:
                l.append("¬x%d" % (k-number_of_features))
    print(" ∧ ".join(l))

print("\nClass 1 Positive Clauses:\n")
for j in range(0, 10, 2):
    print("Clause #%d: " % (j), end=' ')
    l = []
    for k in range(number_of_features*2):
        if tm.ta_action(1, j, k) == 1:
            if k < number_of_features:
                l.append(" x%d" % (k))
            else:
                l.append("¬x%d" % (k-number_of_features))
    print(" ∧ ".join(l))

print("\nClass 1 Negative Clauses:\n")
for j in range(1, 10, 2):
    print("Clause #%d: " % (j), end=' ')
    l = []
    for k in range(number_of_features*2):
        if tm.ta_action(1, j, k) == 1:
            if k < number_of_features:
                l.append(" x%d" % (k))
            else:
                l.append("¬x%d" % (k-number_of_features))
    print(" ∧ ".join(l))

Output

python3 ./InterpretabilityDemo.py

Accuracy: 100.0

Class 0 Positive Clauses:

Clause #0:  ¬x0 ∧ ¬x1
Clause #2:   x0 ∧  x1
Clause #4:   x0 ∧  x1
Clause #6:  ¬x0 ∧ ¬x1
Clause #8:  ¬x0 ∧ ¬x1

Class 0 Negative Clauses:

Clause #1:   x0 ∧ ¬x1
Clause #3:   x0 ∧ ¬x1
Clause #5:   x1 ∧ ¬x0
Clause #7:   x1 ∧ ¬x0
Clause #9:   x0 ∧ ¬x1

Class 1 Positive Clauses:

Clause #0:   x1 ∧ ¬x0
Clause #2:   x1 ∧ ¬x0
Clause #4:   x0 ∧ ¬x1
Clause #6:   x0 ∧ ¬x1
Clause #8:   x0 ∧ ¬x1

Class 1 Negative Clauses:

Clause #1:   x0 ∧  x1
Clause #3:  ¬x0 ∧ ¬x1
Clause #5:  ¬x0 ∧ ¬x1
Clause #7:  ¬x0 ∧ ¬x1
Clause #9:   x0 ∧  x1

2D Convolution Demo

Code: 2DNoisyXORDemo.py

from pyTsetlinMachine.tm import MultiClassConvolutionalTsetlinMachine2D
import numpy as np 

train_data = np.loadtxt("2DNoisyXORTrainingData.txt")
X_train = train_data[:,0:-1].reshape(train_data.shape[0], 4, 4)
Y_train = train_data[:,-1]

test_data = np.loadtxt("2DNoisyXORTestData.txt")
X_test = test_data[:,0:-1].reshape(test_data.shape[0], 4, 4)
Y_test = test_data[:,-1]

ctm = MultiClassConvolutionalTsetlinMachine2D(40, 60, 3.9, (2, 2), boost_true_positive_feedback=0)

ctm.fit(X_train, Y_train, epochs=5000)

print("Accuracy:", 100*(ctm.predict(X_test) == Y_test).mean())

Xi = np.array([[[0,1,1,0],
        [1,1,0,1],
        [1,0,1,1],
        [0,0,0,1]]])

print("\nInput Image:\n")
print(Xi)
print("\nPrediction: %d" % (ctm.predict(Xi)))

Output

python3 ./2DNoisyXORDemo.py 

Accuracy: 99.97%

Input Image:

[[0 1 1 0]
 [1 1 0 1]
 [1 0 1 1]
 [0 0 0 1]]

Prediction: 1

Continuous Input Demo

Code: BreastCancerDemo.py

from pyTsetlinMachine.tm import MultiClassTsetlinMachine
from pyTsetlinMachine.tools import Binarizer
import numpy as np

from sklearn import datasets
from sklearn.model_selection import train_test_split

breast_cancer = datasets.load_breast_cancer()
X = breast_cancer.data
Y = breast_cancer.target

b = Binarizer(max_bits_per_feature = 10)
b.fit(X)
X_transformed = b.transform(X)

tm = MultiClassTsetlinMachine(800, 40, 5.0)

print("\nMean accuracy over 100 runs:\n")
tm_results = np.empty(0)
for i in range(100):
    X_train, X_test, Y_train, Y_test = train_test_split(X_transformed, Y, test_size=0.2)

    tm.fit(X_train, Y_train, epochs=25)
    tm_results = np.append(tm_results, np.array(100*(tm.predict(X_test) == Y_test).mean()))
    print("#%d Average Accuracy: %.2f%% +/- %.2f" % (i+1, tm_results.mean(), 1.96*tm_results.std()/np.sqrt(i+1)))

Output

python3 ./BreastCancerDemo.py 

Mean accuracy over 100 runs:

#1 Average Accuracy: 97.37% +/- 0.00
#2 Average Accuracy: 97.37% +/- 0.00
...
#99 Average Accuracy: 97.52% +/- 0.29
#100 Average Accuracy: 97.54% +/- 0.29

MNIST Demo

Code: MNISTDemo.py

from pyTsetlinMachine.tm import MultiClassTsetlinMachine
import numpy as np
from time import time

from keras.datasets import mnist

(X_train, Y_train), (X_test, Y_test) = mnist.load_data()

X_train = np.where(X_train.reshape((X_train.shape[0], 28*28)) > 75, 1, 0) 
X_test = np.where(X_test.reshape((X_test.shape[0], 28*28)) > 75, 1, 0) 

tm = MultiClassTsetlinMachine(2000, 50, 10.0)

print("\nAccuracy over 250 epochs:\n")
for i in range(250):
    start_training = time()
    tm.fit(X_train, Y_train, epochs=1, incremental=True)
    stop_training = time()

    start_testing = time()
    result = 100*(tm.predict(X_test) == Y_test).mean()
    stop_testing = time()

    print("#%d Accuracy: %.2f%% Training: %.2fs Testing: %.2fs" % (i+1, result, stop_training-start_training, stop_testing-start_testing))

Output

python3 ./MNISTDemo.py 

Accuracy over 250 epochs:

#1 Accuracy: 94.63% Training: 42.75s Testing: 3.06s
#2 Accuracy: 95.52% Training: 23.05s Testing: 3.12s
#3 Accuracy: 95.97% Training: 20.13s Testing: 3.07s
...

#248 Accuracy: 98.06% Training: 7.77s Testing: 3.09s
#249 Accuracy: 97.98% Training: 7.74s Testing: 3.10s
#250 Accuracy: 98.07% Training: 7.92s Testing: 3.12s

MNIST Demo w/Weighted Clauses

Code: MNISTDemoWeightedClauses.py

from pyTsetlinMachine.tm import MultiClassTsetlinMachine
import numpy as np
from time import time

from keras.datasets import mnist

(X_train, Y_train), (X_test, Y_test) = mnist.load_data()

X_train = np.where(X_train.reshape((X_train.shape[0], 28*28)) > 75, 1, 0) 
X_test = np.where(X_test.reshape((X_test.shape[0], 28*28)) > 75, 1, 0) 

tm = MultiClassTsetlinMachine(2000, 50*100, 10.0, weighted_clauses=True)

print("\nAccuracy over 60 epochs:\n")
for i in range(60):
        start_training = time()
        tm.fit(X_train, Y_train, epochs=1, incremental=True)
        stop_training = time()

        start_testing = time()
        result = 100*(tm.predict(X_test) == Y_test).mean()
        stop_testing = time()

        print("#%d Accuracy: %.2f%% Training: %.2fs Testing: %.2fs" % (i+1, result, stop_training-start_training, stop_testing-start_testing))

Output

python3 ./MNISTDemoWeightedClauses.py

Accuracy over 60 epochs:

#1 Accuracy: 93.65% Training: 60.98s Testing: 3.98s
#2 Accuracy: 95.33% Training: 26.84s Testing: 3.87s
#3 Accuracy: 96.08% Training: 22.41s Testing: 3.95s
...

#58 Accuracy: 98.14% Training: 8.54s Testing: 4.17s
#59 Accuracy: 98.08% Training: 8.49s Testing: 4.22s
#60 Accuracy: 98.19% Training: 8.80s Testing: 4.15s

MNIST 2D Convolution Demo w/Weighted Clauses

Code: MNISTDemo2DConvolutionWeightedClauses.py

from pyTsetlinMachine.tm import MultiClassConvolutionalTsetlinMachine2D
import numpy as np
from time import time

from keras.datasets import mnist

(X_train, Y_train), (X_test, Y_test) = mnist.load_data()

X_train = np.where(X_train >= 75, 1, 0) 
X_test = np.where(X_test >= 75, 1, 0) 

tm = MultiClassConvolutionalTsetlinMachine2D(2000, 50*100, 5.0, (10, 10), weighted_clauses=True)

print("\nAccuracy over 30 epochs:\n")
for i in range(30):
    start = time()
    tm.fit(X_train, Y_train, epochs=1, incremental=True)
    stop = time()
    
    result = 100*(tm.predict(X_test) == Y_test).mean()
    
    print("#%d Accuracy: %.2f%% (%.2fs)" % (i+1, result, stop-start))

Output

python3 ./MNISTDemo2DConvolutionWeightedClauses.py 

Accuracy over 30 epochs:

#1 Accuracy: 97.53% (403.06s)
#2 Accuracy: 98.07% (421.25s)
#3 Accuracy: 98.36% (430.48s)
...

#28 Accuracy: 99.14% (540.11s)
#29 Accuracy: 99.21% (546.38s)
#30 Accuracy: 99.16% (538.87s)

Fashion MNIST 2D Convolution Demo w/Weighted Clauses

Code: FashionMNISTDemo2DConvolutionWeightedClauses.py

from pyTsetlinMachine.tm import MultiClassConvolutionalTsetlinMachine2D
import numpy as np
from time import time
import cv2
from keras.datasets import fashion_mnist

(X_train, Y_train), (X_test, Y_test) = fashion_mnist.load_data()
X_train = np.copy(X_train)
X_test = np.copy(X_test)

for i in range(X_train.shape[0]):
    X_train[i,:] = cv2.adaptiveThreshold(X_train[i], 1, cv2.ADAPTIVE_THRESH_GAUSSIAN_C, cv2.THRESH_BINARY, 11, 2)

for i in range(X_test.shape[0]):
    X_test[i,:] = cv2.adaptiveThreshold(X_test[i], 1, cv2.ADAPTIVE_THRESH_GAUSSIAN_C, cv2.THRESH_BINARY, 11, 2)

tm = MultiClassConvolutionalTsetlinMachine2D(2000, 50*100, 5.0, (10, 10), weighted_clauses=True)

print("\nAccuracy over 30 epochs:\n")
for i in range(30):
    start = time()
    tm.fit(X_train, Y_train, epochs=1, incremental=True)
    stop = time()
    
    result = 100*(tm.predict(X_test) == Y_test).mean()
    
    print("#%d Accuracy: %.2f%% (%.2fs)" % (i+1, result, stop-start))

Output

python3 ./FashionMNISTDemo2DConvolutionWeightedClauses.py 

Accuracy over 30 epochs:

#1 Accuracy: 85.25% (615.68s)
#2 Accuracy: 86.60% (615.83s)
#3 Accuracy: 87.56% (607.37s)
...

#28 Accuracy: 90.14% (759.22s)
#29 Accuracy: 90.39% (564.35s)
#30 Accuracy: 90.06% (560.08s)

IMDb Text Categorization Demo

Code: IMDbTextCategorizationDemo.py

import numpy as np
import keras
from sklearn.feature_selection import SelectKBest
from sklearn.feature_selection import chi2
from keras.datasets import imdb
from pyTsetlinMachine.tm import MultiClassTsetlinMachine
from time import time

MAX_NGRAM = 2

NUM_WORDS=5000
INDEX_FROM=2 

FEATURES=5000

print("Downloading dataset...")

train,test = keras.datasets.imdb.load_data(num_words=NUM_WORDS, index_from=INDEX_FROM)

train_x,train_y = train
test_x,test_y = test

word_to_id = keras.datasets.imdb.get_word_index()
word_to_id = {k:(v+INDEX_FROM) for k,v in word_to_id.items()}
word_to_id["<PAD>"] = 0
word_to_id["<START>"] = 1
word_to_id["<UNK>"] = 2

print("Producing bit representation...")

# Produce N-grams

id_to_word = {value:key for key,value in word_to_id.items()}

vocabulary = {}
for i in range(train_y.shape[0]):
    terms = []
    for word_id in train_x[i]:
        terms.append(id_to_word[word_id])
    
    for N in range(1,MAX_NGRAM+1):
        grams = [terms[j:j+N] for j in range(len(terms)-N+1)]
        for gram in grams:
            phrase = " ".join(gram)
            
            if phrase in vocabulary:
                vocabulary[phrase] += 1
            else:
                vocabulary[phrase] = 1

# Assign a bit position to each N-gram (minimum frequency 10) 

phrase_bit_nr = {}
bit_nr_phrase = {}
bit_nr = 0
for phrase in vocabulary.keys():
    if vocabulary[phrase] < 10:
        continue

    phrase_bit_nr[phrase] = bit_nr
    bit_nr_phrase[bit_nr] = phrase
    bit_nr += 1

# Create bit representation

X_train = np.zeros((train_y.shape[0], len(phrase_bit_nr)), dtype=np.uint32)
Y_train = np.zeros(train_y.shape[0], dtype=np.uint32)
for i in range(train_y.shape[0]):
    terms = []
    for word_id in train_x[i]:
        terms.append(id_to_word[word_id])

    for N in range(1,MAX_NGRAM+1):
        grams = [terms[j:j+N] for j in range(len(terms)-N+1)]
        for gram in grams:
            phrase = " ".join(gram)
            if phrase in phrase_bit_nr:
                X_train[i,phrase_bit_nr[phrase]] = 1

    Y_train[i] = train_y[i]

X_test = np.zeros((test_y.shape[0], len(phrase_bit_nr)), dtype=np.uint32)
Y_test = np.zeros(test_y.shape[0], dtype=np.uint32)

for i in range(test_y.shape[0]):
    terms = []
    for word_id in test_x[i]:
        terms.append(id_to_word[word_id])

    for N in range(1,MAX_NGRAM+1):
        grams = [terms[j:j+N] for j in range(len(terms)-N+1)]
        for gram in grams:
            phrase = " ".join(gram)
            if phrase in phrase_bit_nr:
                X_test[i,phrase_bit_nr[phrase]] = 1             

    Y_test[i] = test_y[i]

print("Selecting features...")

SKB = SelectKBest(chi2, k=FEATURES)
SKB.fit(X_train, Y_train)

selected_features = SKB.get_support(indices=True)
X_train = SKB.transform(X_train)
X_test = SKB.transform(X_test)

tm = MultiClassTsetlinMachine(10000, 80, 5.0, weighted_clauses=True, clause_drop_p=0.75)

print("\nAccuracy over 40 epochs:\n")
for i in range(40):
    start_training = time()
    tm.fit(X_train, Y_train, epochs=1, incremental=True)
    stop_training = time()

    start_testing = time()
    result = 100*(tm.predict(X_test) == Y_test).mean()
    stop_testing = time()

    print("#%d Accuracy: %.2f%% Training: %.2fs Testing: %.2fs" % (i+1, result, stop_training-start_training, stop_testing-start_testing))

Output:

python ./IMDbTextCategorizationDemo.py

Downloading dataset...
Producing bit representation...
Selecting features...

Accuracy over 50 epochs:

#1 Accuracy: 85.42% Training: 761.58s Testing: 9.16s
#2 Accuracy: 86.56% Training: 667.68s Testing: 9.80s
#3 Accuracy: 87.01% Training: 612.66s Testing: 10.43s
...

#38 Accuracy: 89.81% Training: 286.38s Testing: 11.58s
#39 Accuracy: 89.75% Training: 282.54s Testing: 11.85s
#40 Accuracy: 89.76% Training: 278.88s Testing: 11.70s

Regression Demo

Code: RegressionDemo.py

from pyTsetlinMachine.tm import RegressionTsetlinMachine
from pyTsetlinMachine.tools import Binarizer
import numpy as np
from time import time

from sklearn import datasets
from sklearn.model_selection import train_test_split

california_housing = datasets.fetch_california_housing()
X = california_housing.data
Y = california_housing.target

b = Binarizer(max_bits_per_feature = 10)
b.fit(X)
X_transformed = b.transform(X)

tm = RegressionTsetlinMachine(1000, 500*10, 2.75, weighted_clauses=True)

print("\nRMSD over 25 runs:\n")
tm_results = np.empty(0)
for i in range(25):
    X_train, X_test, Y_train, Y_test = train_test_split(X_transformed, Y)

    start = time()
    tm.fit(X_train, Y_train, epochs=30)
    stop = time()
    tm_results = np.append(tm_results, np.sqrt(((tm.predict(X_test) - Y_test)**2).mean()))

    print("#%d RMSD: %.2f +/- %.2f (%.2fs)" % (i+1, tm_results.mean(), 1.96*tm_results.std()/np.sqrt(i+1), stop-start))

Output

python3 ./RegressionDemo.py 

RMSD over 25 runs:

#1 RMSD: 0.62 +/- 0.00 (13.17s)
#2 RMSD: 0.61 +/- 0.01 (13.19s)
...

#24 RMSD: 0.61 +/- 0.00 (13.65s)
#25 RMSD: 0.61 +/- 0.00 (13.73s)

Further Work

  • Multilayer Tsetlin Machine
  • Recurrent Tsetlin Machine
  • GPU support
  • Optimize convolution code
  • More extensive hyper-parameter search for the demos

Requirements

Acknowledgements

I thank my colleagues from the Centre for Artificial Intelligence Research (CAIR), Lei Jiao, Xuan Zhang, Geir Thore Berge, Darshana Abeyrathna, Saeed Rahimi Gorji, Sondre Glimsdal, Rupsa Saha, Bimal Bhattarai, Rohan K. Yadav, Bernt Viggo Matheussen, Morten Goodwin, Christian Omlin, Vladimir Zadorozhny (University of Pittsburgh), Jivitesh Sharma, and Ahmed Abouzeid, for their contributions to the development of the Tsetlin machine family of techniques. I would also like to thank our House of CAIR partners, Alex Yakovlev, Rishad Shafik, Adrian Wheeldon, Jie Lei, Tousif Rahman (Newcastle University), Jonny Edwards (Temporal Computing), Marco Wiering (University of Groningen), Christian D. Blakely (PwC Switzerland), Adrian Phoulady, Anders Refsdal Olsen, Halvor Smørvik, and Erik Mathisen for their many contributions.

Tsetlin Machine Papers

@InProceedings{wheeldon2021self,
  title="{Self-Timed Reinforcement Learning using Tsetlin Machine}",
  author={Adrian Wheeldon and Alex Yakovlev and Rishad Shafik},
  booktitle={27th IEEE International Symposium on Asynchronous Circuits and Systems (ASYNC 2021)},
  year={2021},
  organization={IEEE},
  url={https://arxiv.org/abs/2109.00846}
}
@article{glimsdal2021coalesced,
  title={Coalesced Multi-Output Tsetlin Machines with Clause Sharing},
  author={Sondre Glimsdal and Ole-Christoffer Granmo},
  journal = {arXiv preprint arXiv:2108.07594}, year = {2021},
  url = {https://arxiv.org/abs/2108.07594}
}
@article{Abeyrathna2021adaptivesparse,
  title="{Adaptive Sparse Representation of Continuous Input for Tsetlin Machines Based on Stochastic Searching on the Line}",
  volume={10},
  ISSN={2079-9292},
  url={http://dx.doi.org/10.3390/electronics10172107},
  DOI={10.3390/electronics10172107},
  number={17},
  journal={Electronics},
  publisher={MDPI AG},
  author={Abeyrathna, Kuruge Darshana and Granmo, Ole-Christoffer and Goodwin, Morten},
  year={2021},
  month={Aug},
  pages={2107}}
@article{zhang2021convergence,
  title = {On the {{Convergence}} of {{Tsetlin Machines}} for the {{IDENTITY}}- and {{NOT Operators}}},
  author = {Zhang, Xuan and Jiao, Lei and Granmo, Ole-Christoffer and Goodwin, Morten},
  year = {2021},
  journal = {IEEE Transactions on Pattern Analysis and Machine Intelligence}
}
@InProceedings{abeyrathna2021parallel,
  title="{Massively Parallel and Asynchronous Tsetlin Machine Architecture Supporting Almost Constant-Time Scaling}",
  author={K. Darshana Abeyrathna and Bimal Bhattarai and Morten Goodwin and Saeed Gorji and Ole-Christoffer Granmo and Lei Jiao and Rupsa Saha and Rohan K. Yadav},
  booktitle={The Thirty-eighth International Conference on Machine Learning (ICML 2021)},
  year={2021},
  organization={ICML}
}
@article{sharma2021dropclause,
  title="{Human Interpretable AI: Enhancing Tsetlin Machine Stochasticity with Drop Clause}",
  author={Jivitesh Sharma and Rohan Yadav and Ole-Christoffer Granmo and Lei Jiao},
  journal = {arXiv preprint arXiv:2105.14506}, year = {2021},
  url = {https://arxiv.org/abs/2105.14506}
}
@article{bhattarai2021fakenews,
  title="{Explainable Tsetlin Machine framework for fake news detection with credibility score assessment}",
  author={Bimal Bhattarai and Ole-Christoffer Granmo and Lei Jiao},
  journal = {arXiv preprint arXiv:2105.09114}, year = {2021},
  url = {https://arxiv.org/abs/2105.09114}
}
@article{bhattarai2021wordlevel,
  title="{Word-level Human Interpretable Scoring Mechanism for Novel Text Detection Using Tsetlin Machines}",
  author={Bimal Bhattarai and Ole-Christoffer Granmo and Lei Jiao},
  journal = {arXiv preprint arXiv:2105.04708}, year = {2021},
  url = {https://arxiv.org/abs/2105.04708}
}
@article{yadav2021dwr,
  title="{Distributed Word Representation in Tsetlin Machine}",
  author={Rohan Kumar Yadav and Lei Jiao and Ole-Christoffer Granmo and Morten Goodwin},
  journal = {arXiv preprint arXiv:2104.06901}, year = {2021},
  url = {https://arxiv.org/abs/2104.06901}
}
@article{lei2021kws,
  title="{Low-Power Audio Keyword Spotting Using Tsetlin Machines}",
  author={Jie Lei and Tousif Rahman and Rishad Shafik and Adrian Wheeldon and Alex Yakovlev and Ole-Christoffer Granmo and Fahim Kawsar and Akhil Mathur},
  journal = {Journal of Low Power Electronics and Applications}, year = {2021},
  volume=11,
  issue=18,
  url = {https://www.mdpi.com/2079-9268/11/2/18},
  organization={MDPI}
}
@InProceedings{blakely2021closed,
  title="{Closed-Form Expressions for Global and Local Interpretation of Tsetlin Machines}",
  author={Christian D. {Blakely} and Ole-Christoffer {Granmo}},
  booktitle={34th International Conference on Industrial, Engineering and Other Applications of Applied Intelligent Systems (IEA/AIE 2021)},
  year={2021},
  organization={Springer}
}
@InProceedings{gorji2021rl,
  title="{Explainable Reinforcement Learning with the Tsetlin Machine}",
  author={Saeed {Gorji} and Ole Christoffer {Granmo} and Marco {Wiering}},
  booktitle={34th International Conference on Industrial, Engineering and Other Applications of Applied Intelligent Systems (IEA/AIE 2021)},
  year={2021},
  organization={Springer}
}
@InProceedings{yadav2021sentiment,
  title="{Human-Level Interpretable Learning for Aspect-Based Sentiment Analysis}",
  author={Rohan Kumar {Yadav} and Lei {Jiao} and Ole-Christoffer {Granmo} and Morten {Goodwin}},
  booktitle={The Thirty-Fifth AAAI Conference on Artificial Intelligence (AAAI-21)},
  year={2021},
  organization={AAAI}
}
@InProceedings{nicolae2021question,
  title="{Question Classification using Interpretable Tsetlin Machine}",
  author={Dragos Constantin {Nicolae}},
  booktitle={The 1st International Workshop on Machine Reasoning (MRC 2021)},
  year={2021}
}
@article{saha2021relational,
  title="{A Relational Tsetlin Machine with Applications to Natural Language Understanding}",
  author={Rupsa Saha and Ole-Christoffer Granmo and Vladimir I. Zadorozhny and Morten Goodwin},
  journal = {arXiv preprint arXiv:2102.10952}, year = {2021},
  url = {https://arxiv.org/abs/2102.10952}
}
@InProceedings{yadav2021wordsense,
  title="{Interpretability in Word Sense Disambiguation using Tsetlin Machine}",
  author={Rohan Kumar {Yadav} and Lei {Jiao} and Ole-Christoffer {Granmo} and Morten {Goodwin}},
  booktitle={13th International Conference on Agents and Artificial Intelligence (ICAART 2021)},
  year={2021},
  organization={INSTICC}
}
@InProceedings{bhattarai2021novelty,
  title="{Measuring the Novelty of Natural Language Text Using the Conjunctive Clauses of a Tsetlin Machine Text Classifier}",
  author={Bimal Bhattarai and Lei Jiao and Ole-Christoffer Granmo},
  booktitle={13th International Conference on Agents and Artificial Intelligence (ICAART 2021)},
  year={2021},
  organization={INSTICC}
}
@InProceedings{abeyrathna2021convreg,
  title="{Convolutional Regression Tsetlin Machine}",
  author={Abeyrathna, Kuruge Darshana and Granmo, Ole-Christoffer and Goodwin, Morten},
  booktitle={6th International Conference on Machine Learning Technologies (ICMLT 2021)},
  year={2021},
  organization={ACM}
}
@article{abeyrathna2021integer,
  author = {Abeyrathna, Kuruge Darshana and Granmo, Ole-Christoffer and Goodwin, Morten},
  title = "{Extending the Tsetlin Machine With Integer-Weighted Clauses for Increased Interpretability}",
  journal = {IEEE Access},
  volume = 9,
  year = {2021}
}
@article{jiao2021xor,
  title="{On the Convergence of Tsetlin Machines for the XOR Operator}",
  author={Lei Jiao and Xuan Zhang and Ole-Christoffer Granmo and K. Darshana Abeyrathna},
  journal = {arXiv preprint arXiv:2101.02547}, year = {2021},
  url = {https://arxiv.org/abs/2101.02547}
}
@InProceedings{wheeldon2021low,
  title="{Low-Latency Asynchronous Logic Design for Inference at the Edge}",
  author={Adrian Wheeldon and Alex Yakovlev and Rishad Shafik and Jordan Morris},
  booktitle={2021 Design, Automation and Test in Europe Conference (DATE21)},
  year={2021},
  pages="370-373"
}
@InProceedings{lei2020arithmetic,
  title="{From Arithmetic to Logic Based AI: A Comparative Analysis of Neural Networks and Tsetlin Machine}",
  author={Jie {Lei} and Adrian {Wheeldon} and Rishad {Shafik} and Alex {Yakovlev} and Ole-Christoffer {Granmo}},
  booktitle={27th IEEE International Conference on Electronics Circuits and Systems (ICECS2020)},
  year={2020},
  organization={IEEE}
}
@InProceedings{abeyrathna2020auc,
  title="{On Obtaining Classification Confidence, Ranked Predictions and AUC with Tsetlin Machines}",
  author={K. Darshana Abeyrathna and Ole-Christoffer Granmo and Morten Goodwin},
  booktitle={2020 IEEE Symposium Series on Computational Intelligence (SSCI)},
  year={2020},
  organization={IEEE}
}
@InProceedings{abeyrathna2020intrusion,
  title="{Intrusion Detection with Interpretable Rules Generated Using the Tsetlin Machine}",
  author={K. Darshana Abeyrathna and Harsha S. Gardiyawasam Pussewalage and Sasanka N. Ranasinghea and Vladimir A. Oleshchuk and Ole-Christoffer Granmo},
  booktitle={2020 IEEE Symposium Series on Computational Intelligence (SSCI)},
  year={2020},
  organization={IEEE}
}
@InProceedings{abeyrathna2020adaptive,
  title="{Adaptive Continuous Feature Binarization for Tsetlin Machines Applied to Forecasting Dengue Incidences in the Philippines}",
  author={K. Darshana Abeyrathna and Ole-Christoffer Granmo and Xuan Zhang and Morten Goodwin},
  booktitle={2020 IEEE Symposium Series on Computational Intelligence (SSCI)},
  year={2020},
  organization={IEEE}
}
@InProceedings{saha2020causal,
  author = {Rupsa {Saha} and Ole-Christoffer {Granmo} and Morten {Goodwin}},
  title = "{Mining Interpretable Rules for Sentiment and Semantic Relation Analysis using Tsetlin Machines}",
  booktitle="Lecture Notes in Computer Science: Proceedings of the 40th International Conference on Innovative Techniques and Applications of Artificial Intelligence (SGAI-2020)", year="2020",
  publisher="Springer International Publishing"
}
@InProceedings{abeyrathna2020deterministic,
  title="{A Novel Multi-Step Finite-State Automaton for Arbitrarily Deterministic Tsetlin Machine Learning}",
  author={K. Darshana Abeyrathna and Ole-Christoffer Granmo and Rishad Shafik and Alex Yakovlev and Adrian Wheeldon and Jie Lei and Morten Goodwin},
  booktitle="Lecture Notes in Computer Science: Proceedings of the 40th International Conference on Innovative Techniques and Applications of Artificial Intelligence (SGAI-2020)", year="2020",
  publisher="Springer International Publishing"
}
@article{wheeldon2020learning, 
  author={Adrian {Wheeldon} and Rishad {Shafik} and Tousif {Rahman} and Jie {Lei} and Alex {Yakovlev} and Ole-Christoffer {Granmo}}, 
  journal={Philosophical Transactions of the Royal Society A},
  title="{Learning Automata based Energy-efficient AI Hardware Design for IoT}",
  year={2020}
}
@InProceedings{shafik2020explainability,
  title="{Explainability and Dependability Analysis of Learning Automata based AI Hardware}",
  author={Rishad {Shafik} and Adrian {Wheeldon} and Alex {Yakovlev}},
  booktitle={IEEE 26th International Symposium on On-Line Testing and Robust System Design (IOLTS)},
  year={2020},
  organization={IEEE}
}
@article{lavrova2020,
  author = {D. S. {Lavrova} and N. N. {Eliseev}},
  title = "{Network Attacks Detection based on Tsetlin Machine}",
  pages = {17-23},
  journal = {Information Security Problems. Computer Systems.}, year = {2020}
}
@InProceedings{gorji2020indexing,
  title="{Increasing the Inference and Learning Speed of Tsetlin Machines with Clause Indexing}",
  author={Saeed {Gorji} and Ole Christoffer {Granmo} and Sondre {Glimsdal} and Jonathan {Edwards} and Morten {Goodwin}},
  booktitle={33rd International Conference on Industrial, Engineering and Other Applications of Applied Intelligent Systems (IEA/AIE 2020)},
  year={2020},
  organization={Springer}
}
@InProceedings{abeyrathna2020integerregression,
  title="{A Regression Tsetlin Machine with Integer Weighted Clauses for Compact Pattern Representation}",
  author={Abeyrathna, Kuruge Darshana and Granmo, Ole-Christoffer and Goodwin, Morten},
  booktitle={33rd International Conference on Industrial, Engineering and Other Applications of Applied Intelligent Systems (IEA/AIE 2020)},
  year={2020},
  organization={Springer}
}
@InProceedings{phoulady2020weighted, 
  author={Adrian {Phoulady} and Ole-Christoffer {Granmo} and Saeed Rahimi {Gorji} and Hady Ahmady {Phoulady}}, 
  booktitle={Proceedings of the Ninth International Workshop on Statistical Relational AI (StarAI 2020)}, 
  title="{The Weighted Tsetlin Machine: Compressed Representations with Clause Weighting}",
  year={2020}
}
@InProceedings{wheeldon2020pervasive, 
  author={Adrian {Wheeldon} and Rishad {Shafik} and Alex {Yakovlev} and Jonathan {Edwards} and Ibrahim {Haddadi} and Ole-Christoffer {Granmo}}, 
  booktitle={SCONA Workshop at Design, Automation and Test in Europe (DATE 2020)}, 
  title="{Tsetlin Machine: A New Paradigm for Pervasive AI}",
  year={2020}
}
@article{abeyrathna2020nonlinear, 
  author={K. Darshana {Abeyrathna} and Ole-Christoffer {Granmo} and Xuan {Zhang} and Lei {Jiao} and Morten {Goodwin}}, 
  journal={Philosophical Transactions of the Royal Society A},
  title="{The Regression Tsetlin Machine - A Novel Approach to Interpretable Non-Linear Regression}",
  volume={378}, issue={2164},
  year={2020}
}
@InProceedings{gorji2019multigranular,
  author = {Saeed Rahimi {Gorji} and Ole-Christoffer {Granmo} and Adrian {Phoulady} and Morten {Goodwin}},
  title = "{A Tsetlin Machine with Multigranular Clauses}",
  booktitle="Lecture Notes in Computer Science: Proceedings of the Thirty-ninth International Conference on Innovative Techniques and Applications of Artificial Intelligence (SGAI-2019)", year="2019",
  volume = {11927},
  publisher="Springer International Publishing"
}
@article{berge2019text, 
  author={Geir Thore {Berge} and Ole-Christoffer {Granmo} and Tor Oddbjørn {Tveit} and Morten {Goodwin} and Lei {Jiao} and Bernt Viggo {Matheussen}}, 
  journal={IEEE Access}, 
  title="{Using the Tsetlin Machine to Learn Human-Interpretable Rules for High-Accuracy Text Categorization with Medical Applications}",
  volume={7},
  pages={115134-115146}, 
  year={2019}, 
  doi={10.1109/ACCESS.2019.2935416}, 
  ISSN={2169-3536}
}
@article{granmo2019convtsetlin,
  author = {{Granmo}, Ole-Christoffer and {Glimsdal}, Sondre and {Jiao}, Lei and {Goodwin}, Morten and {Omlin}, Christian W. and {Berge}, Geir Thore},
  title = "{The Convolutional Tsetlin Machine}",
  journal = {arXiv preprint arXiv:1905.09688}, year = {2019},
  url={https://arxiv.org/abs/1905.09688}
}
@InProceedings{abeyrathna2019regressiontsetlin,
  author = {{Abeyrathna}, Kuruge Darshana and {Granmo}, Ole-Christoffer and {Jiao}, Lei and {Goodwin}, Morten},
  title = "{The Regression Tsetlin Machine: A Tsetlin Machine for Continuous Output Problems}",
  editor="Moura Oliveira, Paulo and Novais, Paulo and Reis, Lu{\'i}s Paulo ",
  booktitle="Progress in Artificial Intelligence", year="2019",
  publisher="Springer International Publishing",
  pages="268--280"
}
@InProceedings{abeyrathna2019continuousinput,
  author = {{Abeyrathna}, Kuruge Darshana and {Granmo}, Ole-Christoffer and {Zhang}, Xuan and {Goodwin}, Morten},
  title = "{A Scheme for Continuous Input to the Tsetlin Machine with Applications to Forecasting Disease Outbreaks}",
  booktitle = "{Advances and Trends in Artificial Intelligence. From Theory to Practice}", year = "2019",
  editor = "Wotawa, Franz and Friedrich, Gerhard and Pill, Ingo and Koitz-Hristov, Roxane and Ali, Moonis",
  publisher = "Springer International Publishing",
  pages = "564--578"
}
@article{granmo2018tsetlin,
  author = {{Granmo}, Ole-Christoffer},
  title = "{The Tsetlin Machine - A Game Theoretic Bandit Driven Approach to Optimal Pattern Recognition with Propositional Logic}",
  journal = {arXiv preprint arXiv:1804.01508}, year = {2018},
  url={https://arxiv.org/abs/1804.01508}
}

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Copyright (c) 2021 Ole-Christoffer Granmo

Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.

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