This project introduces plug-and-play collaboration between Tsetlin machines (TMs), forming a TM Composite.
- The collaboration relies on a TM's ability to specialize during learning and to assess its competence during inference.
- When teaming up, the most confident TMs make the decisions, relieving the uncertain ones. In this manner, the TM Composite becomes more competent than its members, benefitting from their specializations.
- The members can be combined in any way, at any time, without fine-tuning (plug-and-play).
- The project implements four TM specializations as a demonstration:
- Histogram of Gradients;
- Adaptive Thresholding w/10x10 convolution;
- Color Thermometers w/3x3 convolution;
- Color Thermometers w/4x4 convolution.
The resulting TM Composite increases accuracy on Fashion-MNIST by two percentage points, CIFAR-10 by twelve points, and CIFAR-100 by nine points, yielding new state-of-the-art results for TMs.
The plug-and-play architecture is shown below.
In the normal case, a TM outputs the class
with the largest class sum (see Tsetlin machine):
.
When collaborating in a team, however, each TM team member outputs its class sums , with the class sum
signifying the confidence of TM
in class
:
.
In the ensuing normalization step, the class sums of each TM are divided by the difference
between the largest and smallest class sums in the data
:
.
The normalized class sums, in turn, are added together, forming the class sums of the team as a whole. The maximum value of these decides the class output in the final step.
Using Adaptive Thresholding on CIFAR-100 as an example, the above figure relates the accuracy of the TM to its confidence. Along the x-axis, we rank the 10000 test images from CIFAR-100 from lowest to highest class sum (confidence). The y-axis shows the test accuracy for the x-axis confidence level and upwards. When confidence is low, the TM operates at low accuracy. As confidence increases, accuracy increases as well, up to 100% accuracy at the highest confidence levels.
Now consider the confidence and accuracy of the Color Thermometers TM in the figure above. Notice how it specializes to get high confidence and accuracy in recognizing color texture. The weakness of the Adaptive Thresholding TM seems to be the strength of the Color Thermometers TM, and vice versa.
We are now ready to deploy our plug-and-play architecture for TM collaboration. The above table shows the accuracy of various team compositions for Fashion-MNIST, CIFAR-10, and CIFAR-100. Observe how adding team members improves accuracy. Indeed, the full team increased accuracy on Fashion-MNIST by two percentage points, CIFAR-10 by twelve points, and CIFAR-100 by nine points, yielding new state-of-the-art results for TMs.
Considering accuracy epoch-by-epoch for CIFAR-10, the team performance is superior already from the first epoch and stays ahead throughout the learning process.
The plug-and-play collaboration between TMs opens several research paths ahead:
- What other specializations (image processing techniques) can we add to the team?
- Can we design a light optimization layer that boosts the collaboration accuracy, e.g., by weighting the specialists based on their performance?
- Are there other ways to normalize and integrate the perspective of each TM?
- Can we find a way to fine-tune the TM specialists to enhance collaboration further?
- What is the best way to organize a library of composable pre-trained Tsetlin machines?
- How can we compose the most efficient team with a given size?
- Does this approach extend to speech?
Copyright (c) 2023 Ole-Christoffer Granmo
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