=Paper=
{{Paper
|id=Vol-3644/p3
|storemode=property
|title=Active Learning in Neurosymbolic AI with Embed2Sym
|pdfUrl=https://ceur-ws.org/Vol-3644/IJCLR2023_paper_20_new.pdf
|volume=Vol-3644
|authors=Alexander Philipp Rader,Alessandra Russo
|dblpUrl=https://dblp.org/rec/conf/ijclr/RaderR23
}}
==Active Learning in Neurosymbolic AI with Embed2Sym==
https://ceur-ws.org/Vol-3644/IJCLR2023_paper_20_new.pdf
Active Learning in Neurosymbolic AI with
Embed2Sym
Alexander Philipp Rader1 , Alessandra Russo1
1
Imperial College London
Abstract
Neurosymbolic AI combines neural networks with symbolic reasoners in an effort to create robust and
logical machine learning frameworks. In one approach, a neural component processes raw data and
outputs latent concepts. A symbolic component then conducts logical reasoning with the concepts to
produce the final result. A major hurdle lies in the propagation of the end label signal to the latent space
when no latent labels are available. We investigate the use of active learning to alleviate this problem. In
particular, we consider the neurosymbolic framework Embed2Sym. We adapt the learning framework to
incorporate active learning by gaining a latent learning signal for misclassified examples. An oracle,
such as a human in the loop, provides latent labels, which are used to finetune the neural component.
Using the same benchmark datasets as the original paper, we empirically evaluate our method. We
demonstrate that even a small amount of labelled latent data leads to a sizeable increase in accuracy.
Keywords
Neurosymbolic AI, active learning, human-in-the-loop
1. Introduction
Neurosymbolic AI aims to combine the robustness of neural networks to real-world data with
the explainability and provable correctness of symbolic reasoners [1]. A particular stream is
known as ”[Neuro → Symbolic]” [2] and is reminiscent of the two-system model of the human
mind [3]. The neural network represents system 1 and processes raw inputs to produce latent
concepts. The symbolic component then logically reasons over the concepts, such as in system
2, to solve the given problem.
One such framework is Embed2Sym [4]. It consists of a neural network that transforms raw
inputs into embeddings, a clustering algorithm that assigns them categories, and a symbolic
optimiser based on answer set programming (ASP), that solves a logical task. One of the biggest
challenges for Embed2Sym, and [Neuro → Symbolic] architectures in general, is training the
neural component without labels for the intermediate representations.
In this paper, we propose to mitigate this problem by providing latent signals using active
learning, which allows the system to ask an oracle to annotate datapoints [5]. We extend
Embed2Sym to incorporate active learning for incorrectly classified examples. We investigate
the effect in three tasks: MNIST addition, CIFAR10 addition, and Member. Despite providing
only a small percentage of latent labels, we attain substantial accuracy improvements.
Cognitive AI 2023, 13th-15th November, 2023, Bari, Italy.
Envelope-Open apr20@ic.ac.uk (A. P. Rader); a.russo@ic.ac.uk (A. Russo)
© 2023 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
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2. Background
2.1. Task formulation
Each task contains raw and symbolic inputs and labels representing the result of a downstream
operation. For example, in MNIST Addition the input consists of images of two numbers and
the output equates to their sum. Crucially, no labels are provided for the intermediate, called
latent, representations. In our example, there are no labels for the numbers themselves, only
their sum.
2.2. Embed2Sym
The Embed2Sym framework contains a neural perception component and a symbolic reasoning
component. The system works in three stages: [4]
1. Fully neural model: A neural network is trained end-to-end on the downstream task.
It is a two-stage architecture containing a perception and a reasoning component, both
of which are neural. Each input is processed by the perception network which creates
embedding vectors. The reasoning network processes the concatenated embeddings to
output the predicted label.
2. Cluster discovery The k-means algorithm divides the embedding space created by the
perception network into clusters. The number of clusters is predetermined.
3. Cluster labelling An ASP algorithm assigns each cluster their symbolic meaning by
means of an optimisation task. It utilises a hard-coded symbolic component to compute
the downstream result from the latent concepts.
Perception Perception Perception Perception
network network network network
Finetuning
If y is incorrect
Cluster Cluster Dense Dense
label label layer layer
Latent
Latent cluster labels active argmax argmax
1 3 labels
P 1 3
P
y If y is correct
4
Figure 1: Embed2Sym framework on the left, active extension on the right, where additions are shown
as green dotted lines
At inference time, the algorithm works in three steps, as illustrated on the left side in Figure 1.
First, the neural perception network turns the inputs into embeddings 𝑣⃗𝑖 . Second, the clustering
assigns each embedding a symbolic label. Third, the hard-coded symbolic reasoning component
𝑃 calculates the end result.
3. Active Embed2Sym
The neural component in Embed2Sym generates embeddings of the latent concepts, for which
it has no labels. Instead, it uses downstream labels for training, which is a more difficult task.
The core idea of this paper is to finetune the neural network with latent labels after it has been
trained end-to-end. We acquire the latent labels from two sources, as shown in Figure 1:
1. For all examples with a correct end prediction, we assume that the predicted latent
concepts are correct as well. Therefore, we can use the cluster labels from the trained
perception networks. This represents the vast majority of examples.
2. For all examples with an incorrect end prediction, we ask an oracle for the corresponding
latent labels. We refer to these as active labels. For complex tasks, the oracle is typically
a human in the loop. In our case, we can use existing labels for MNIST and CIFAR10
images.
Since the last layer in the original framework uses k-means clustering, it is not differentiable.
Therefore, we replace the clustering layer with a multi-layer-perceptron, indicated by the green
boxes labelled ”dense layer”.
4. Results
We assess the effect of our extension by performing the tasks outlined in the original paper:
MNIST and CIFAR10 addition, as well as Member. In the first two tasks, the inputs consist of
images representing numbers and the output indicates their sum. In the member task, the input
consists of an MNIST image and a list of numbers. The output is a binary variable indicating
whether the number is a member of the list. [6]
We investigate two main questions:
1. What proportion of labels needs to be obtained by an oracle?
2. Does active learning improve the accuracy of the results?
We conducted each experiment for five independent runs and show the average scores and
their standard deviations.
4.1. Proportion of active labels
Even though the latent labels for these specific tasks are easy to come by, calls to oracles are
generally very expensive. Therefore, we need to evaluate our results in light of the percentage
of active labels utilised.
Table 1 presents the number of active labels used for each task, as well as their proportion
of the dataset. In each case, the percentages remain below 5%. We conclude that the number
Table 1
Active labels
Task Number of active labels Percentage of dataset
MNIST Addition 1 digit 526 0.9%
MNIST Addition 15 digits 2723 4.6%
CIFAR10 Addition 1 digit 1717 3.6%
Member 3 digits 269 0.9%
Member 20 digits 425 1.4%
Figure 2: MNIST Addition learning curves during finetuning
of necessary labels are feasible to obtain and the added effort is justifiable to achieve better
accuracies.
4.2. Experimental results
Figure 2 shows the learning curves while finetuning the neural component for MNIST addition
with 15 digits. The baseline is the accuracy achieved from the fully trained original framework.
The extended model surpasses the baseline within a few number of epochs. The test accuracies
are on average significantly higher than the baseline, with only one run being slightly below.
Similar results occur for MNIST additions with a lower number of digits, as well as CIFAR10
addition, albeit not as pronounced.
In Member, the accuracy already surpasses the baseline after only round of training (epoch 0),
as Figure 3 illustrates on the left. Interestingly, the accuracy starts to decline again after epoch
8. The graph on the right indicates that the model is overfitting, as the train and validation
curves diverge. Further investigation reveals that 5.9% of incorrect latent labels were missed
during the active labelling, because the downstream label was correct for them.
The nature of the member task facilitates correct end predictions despite wrong latent
predictions in two major ways: First, the label is binary, so a random guess can achieve an
accuracy of 50%. Second, most digits in each input list are irrelevant for the task. For example,
let the list be [0,8,5] and the digit be 2. It does not matter whether any numbers in the list are
misclassified, unless as a 2, the answer of ”No” is still correct.
Figure 3: Member learning curves during finetuning
Table 2
Test set accuracies on the downstream tasks
Task Embed2Sym Active Embed2Sym
MNIST Addition 1 digit 0.97 0.98±0.002
MNIST Addition 15 digits 0.67 0.73±0.036
CIFAR10 Addition 1 digit 0.83 0.88±0.004
Member 3 digits 0.96 0.98±0.003
Member 20 digits 0.96 0.97±0.002
Table 2 summarises the results. There are 3 main takeaways from this investigation:
1. Active learning improved the accuracy in every task while requiring only a small per-
centage of oracle-annotated labels.
2. Active learning is most effective when there is more room for improvement. The greatest
accuracy increase occurred on the dataset with the lowest baseline, MNIST 15.
3. False positives are an issue when the downstream labels are forgiving to mistakes in the
latent space. This was the case in the Member tasks, where incorrect digit classifications
often did not affect the outcome.
5. Conclusion
Active learning shows some promising results in our experiments. Providing a stronger signal
in the latent space helped achieve a better performance, especially when the baseline had room
for improvement. This work represents a first step towards investigating active learning in
neurosymbolic AI. Future work includes extending other frameworks, such as [7], and solving
more complex tasks. Using tasks that require human labelling will be able to demonstrate the
wider impact of our proposal. Furthermore, we aim to use active learning also for symbolic rule
learning. Embed2Sym hard-codes the rules, but for other frameworks we need to devise ways
of providing active labels for them.
Acknowledgments
This work was supported by UK Research and Innovation [grant number EP/S023356/1],
in the UKRI Centre for Doctoral Training in Safe and Trusted Artificial Intelligence (www.
safeandtrustedai.org).
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