Knowledge-Driven Active Learning
Authors: Gabriele Ciravegna
Frederic Precioso
Marco Gori
Venue: Submitted to ICLR 2023 (2023)
Keywords: Active Learning
Knowledge-aided Learning
FOL
Human in the loop
Hybrid Model

Abstract: The deployment of Deep Learning (DL) models is still precluded in those contexts where the amount of supervised data is limited. To answer this issue, active learning strategies aim at minimizing the amount of labelled data required to train a DL model. Most active strategies are based on uncertain sample selection, and even often restricted to samples lying close to the decision boundary. These techniques are theoretically sound, but an understanding of the selected samples based on their content is not straightforward, further driving non-experts to consider DL as a black-box. For the first time, here we propose a different approach, taking into consideration common domain-knowledge and enabling non-expert users to train a model with fewer samples. In our Knowledge-driven Active Learning (KAL) framework, rule-based knowledge is converted into logic constraints and their violation is checked as a natural guide for sample selection. We show that even simple relationships among data and output classes offer a way to spot predictions for which the model need supervision. The proposed approach (i) outperforms many active learning strategies in terms of average F1 score, particularly in those contexts where domain knowledge is rich. Furthermore, we empirically demonstrate that (ii) KAL discovers data distribution lying far from the initial training data unlike uncertainty-based strategies, (iii) it ensures domain experts that the provided knowledge is respected by the model on test data, and (iv) it can be employed even when domain-knowledge is not available by coupling it with a XAI technique. Finally, we also show that KAL is also suitable for object recognition tasks and, its computational demand is low, unlike many recent active learning strategies.

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KNOWLEDGE-DRIVEN ACTIVE LEARNING
Anonymous authors Paper under double-blind review
ABSTRACT
The deployment of Deep Learning (DL) models is still precluded in those contexts where the amount of supervised data is limited. To answer this issue, active learning strategies aim at minimizing the amount of labelled data required to train a DL model. Most active strategies are based on uncertain sample selection, and even often restricted to samples lying close to the decision boundary. These techniques are theoretically sound, but an understanding of the selected samples based on their content is not straightforward, further driving non-experts to consider DL as a black-box. For the first time, here we propose different approach, taking into consideration common domain-knowledge and enabling non-expert users to train a model with fewer samples. In our Knowledge-driven Active Learning (KAL) framework, rule-based knowledge is converted into logic constraints and their violation is checked as a natural guide for sample selection. We show that even simple relationships among data and output classes offer way spot predictions for which the model need supervision. The proposed approach (i) outperforms many active learning strategies in terms of average Fl score, particularly in those contexts where domain knowledge is rich. Furthermore, we empirically demon- strate that (ii) KAL discovers data distribution lying far from the initial training data unlike uncertainty- based strategies, (iii) it ensures domain experts that the provided knowledge respected by the model on test data, and (iv) it can be employed even when domain-know knowledge is not available by coupling it with XAI technique. Finally, we also show that KAL is also suitable for object recognition tasks and, its computational demand is low, unlike many recent active learning strategies.
INTRODUCTION
Deep Learning (DL) methods have achieved impressive results over the past decade in fields ranging from computer vision text generation (LeCun et al.] 2015). However, most of these contributions relied on overly data-intensive models (e.g. Transformers), trained on huge amounts of data (Marcus 2018). With the advent Big Data, sample collection does not represent an issue any more, but, nonetheless, in some contexts the number of supervised data is limited, and manual labelling be expensive (Yu et al. 2013). Therefore, a common situation is the unlabelled pool scenario (McCal Jumzy & Nigamy 1998), where many data available, but only some are annotated. Historically, two strategies have been devised to tackle this situation: semi-supervised learning which exploit the unlabelled data to enrich feature representations (Zhu & Goldberg 2009), and active learning which select the smallest set of data to annotate to improve the most model performances (Settles) 2009).
The main assumption behind active learning strategies is that there exists a subset of samples that allows to train a model with a similar accuracy as when fed with all training data. Iteratively, the strategy indicates the optimal samples to be annotated from the unlabelled pool. This is generally done by ranking the unlabelled samples w.r.t. given measure, usually on the model predictions (Settles |009 Netzer et al., [201 1 Wang & Shang 2014). or on the input data distribution [Zhdanov] [2019] Santoro et al., (017)) ) and by selecting the samples associated to the highest rankings (Ren et al. 2021: Zhan et al. 2021). While being theoretically sound, an understanding of the selected samples based on their content is not straightforward, in particular to non-ML experts. This issue becomes particularly relevant when considering that Deep Neural Networks are already seen as black box models (Gilpin et al. 2018: Das & Rad 2020) On the contrary, we believe that neural models must be linked to Commonsense knowledge related to a given learning problem. Therefore, in this paper, propose for the first time exploit this symbolic knowledge in the selection process of active

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learning strategy. This not only lower the amount of supervised data, but it also enables domain experts to train a model leveraging their knowledge. More precisely, we propose to compare the predictions over the unsupervised data with the available knowledge and to exploit the inconsistencies as a criterion for selecting the data to be annotated. Domain knowledge, indeed, can be expressed as First-Ordel Logic (FOL. clauses and translated into real-valued logic constraints (among other choices) by means of T-Norms (Klement et al. 2013) to assess its satisfaction (Gnecco et al. 2015
Diligenti et al. 2017 Melacei et al. 2021).
In the experiments, we show that the proposed Knowledge-driven Active Learning (KAL) strategy (i) performs better (on average) than several standard active learning methods, particularly in those contexts where domain-knowledd knowledge is rich. We empirically demonstrate (ii) that this is mainly due to the fact that the proposed strategy allows discovering data distributions lying far from the initial training data, unlike uncertainty-hant -hased approaches. Furthermore, we show that (iii) the provided knowledge is acquired by the trained model and respected on unseen data, (iv) that KAL can also work on domains where no knowledge is available if we extract knowledge from the same model by means of a XAI technique, (v) that the KAL strategy can be easily employed also in the object-detection strategies
sot-strrgghhorwwaddd to apply (Haussmann ct al. 2020) and, finally, (vi) that is not computationally expensive, unlike many recent methods.
context, where standard uncertainty-basee
The paper is organized follows: in Section 2 the proposed method is explained in details, with first an example on inferring the XOR operation and then contextualized in more realistic active learning domains; the aforementioned experimental results on different datasets are reported in Section [ comparing the proposed technique with several active learning strategies; in Section 4 the related work about active learning and about integrating reasoning with machine learning is briefly resumed; finally, in Section we conclude the paper by considering possible future work.
2 KNOWLEDGE-DRIVEN ACTIVE LEARNING
In this paper, we focus on classification problems with classes, in which each input E X is associated to one or more classes and represents the input dimensionality. Let us consider the classification problem f: X + Y, where X Rd represents the feature space which may also comprehend non-structured data (c.g. input images) and Y S {0, is the output space composed of e 2 dimensions. More precisely, we consider vector function ʃ [J...... Se]. where each function Si predicts the probability that æ belongs to the i-th class. In the Active Learning context, also define X, X as the portion of input data already associated an annotation y Y, Y and n the dimensionality of the starting set of labelled data. At each iteration, a set of p samples X2 C X., X is selected by the active learning strategy to be annotated from X., the unlabelled data pool, and be added to X,, This process is repeated for iterations, after which the training terminates. The maximum budget of annotations b therefore amounts to b n + q * p. When considering an object-detection problem, for given class i and given image xy.. we consider as class membership probability, the maximum score value among all predicted bounding boxes around the objects belonging to the i-th class. Formally, fzz) max,es' (xx,)) s(x,) where Si (2,, is the set of the confidence scores of the bounding boxes predicting the i-th class for sample zz-
Let us also consider the case in which additional domain knowledge is available for the problem at hand, involving relationships between data and classes. By considering the logic predicate associated to each function f. First-Order Logic (FOL) becomes the natural way of describing these relationships. For example, Yz E X, (x) A x² + f(x), where X1 xx))) X2
x2(2)) (2) respectively
represent the logic predicates associated to the first and the second input features, and meaning that
when both predicates are true also the output function (xx) needs to be true. Also, we can consider
relations among classes, such as Vz E X, (x) (x) + fx)), meaning that the intersection between the v-th class and the z-th class is always included in the u-th one.
2.1 CONVERTING
INTO LOSS FUNCTIONS
The Learning from Constraints framework Gnecco et al. 2015 Diligenti et al. 2017) defines a way to convert domain knowledge into logic constraints and how to them the learning problem. Among a variety of other type of constraints (see, e.g., Table in (Gnecco et al. 2013),, it studies the process of handling FOL formulas that they can be either injected into the learning problem (in
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1 Iteration
5th Iteration
10 Iteration
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Previous
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Figure 1: A visual example of KAL working principles on the XOR-like problem. We depict network predictions with different colour degrees. Also, we depict in orange the samples selected by the active strategy in the current iteration and in blue those selected in previous iterations (or initially randomly annotated), Notice how the proposed method immediately discovers the data distribution not covered by the initial random sampling frghhtbbotoo quadrant).
semi- semi-supervised learning) or used as knowledge verification measure (as in (Melacci et al. 2021 and in the proposed method). Going into more details, the FOL formulas representing the domain knowledge are converted into numerical constraints using the Triangular Norms (T-Norms, (Klement al., 2013)). These binary functions generalize the conjunction operator and offer way to mathematically compute the satisfaction level of given rule. Based on this assumption, we can detect whether the predictions made by the model on unlabelled data are coherent with the domain knowledge, not, and possibly select these data to be annotated within an active learning strategy.
Following the previous example, X1 (x) A x2(xr) = f(x converted into a bilateral constraint ((f())) 1. By first rewriting the rule conjunction of terms -(x, A X2) A -f and by employing the product T-Norm which replace the A with the product operators and the -x with 1-x. the bilateral constraint become
Xx f)) 1. With p(f(=) 1 - of (x:) the loss function associated to the bilateral constraints, which measures the level of satisfaction of the given constraints and has its minimum value in zero. Again, recalling the previous example, the associated loss function would be (x(()) = X1 X1 f). which indeed is satisfied when either X1 or X2 is zero is approximately one. For further detail how convert FOL formulas into numerical constraints see Appendix A. and Marra et al. (2019) who also proposed an automatic computation of the loss function y associated to a rule. Finally, the loss function considering all the available FOL formulas K. for the given problem is computed to drive the active strategy, selecting the points x² which violate the most the constraints.
indicate
KAL:
arg max =xX,
Σ 9h (f())
(I)
kEK
At each iteration, the KAL strategy selects p samples x" to annotate from the unlabelled pool X...
2.2 AN INTUITIVE EXAMPLE: THE XOR-like PROBLEM
A well-known problem in machine learning is the inference of the eXclusive OR (XOR) operation. To show the working principles of the proposed approach, we propose variant of this experiment, in which neural network learns the XOR-like operation from distribution of non-boolean samples. Specifically, we sampled 10th points x E [0, 1)a. and we assigned a label yz)) as following:
1,
(x1 > 0.5 A 22 S 0.5) V (a1 I 0.5 > 0.5).
v(x) = (o. otherwise
(2)
Also, we express the XOR operation through FOL formula (x1 A -x2 V (-x1 A x2) seen before, through the T-Norm operation we can convert the logic rule into numerical constraint, and we can calculate its violation through the loss functions:
< f. As
Xx 0x2 ff (x1 X2 2x x2) )1 f),
fr-xx f(1 - (x1 + X2 2x1x2))
Practically, the predicate (x) is obtained applying steep logistic function over the input feature 2;:
Xj = (a.) = 1/(1 + e e-r(x,-h) where is temperature parameter and represents the midpoint of the logistic function itself. For predicates expressing incqualities, c.g., age(z) > 50 we simply need to set h = 50. For the sake of simplicity, here and in the following, we dropped the argument (Ir) of the logie predicates.
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each one representing the loss associated to one direction of the double implication.
In Fig. | we reported an example of the proposed strategy starting from n = 10 randomly selected labelled data and by selecting p 5 samples at each iteration violating the most Eq. B and for q = 100 iterations. We can appreciate how, as is often the case, the initial random sampling does not well represent the whole data distribution (no samples from the bottom-right quadrant). Nonetheless, the proposed method immediately discovers the data distribution not represented by the initial sampling (orange points-figure on the left), by selecting the samples violating X1 @ X2 f. After 5 iterations (figure at the centre) the network has mostly learnt the correct data distribution. Later, the proposed strategy refines network predictions by sampling along the decision boundaries (blue points figure on the right), allowing the network to almost already solve the learning problem (accuracy ~ 100%) in just 10 iterations. As it will be seen in the next section, standard random selection (but also uncertainty ones) will require many more iterations.
2.3 REAL-LIFE SCENARIO: PARTIAL KNOWLEDGE AND DIFFERENT TYPE OF RULES
is clear that, in the case of the XOR-like problem, the knowledge is complete: if we compute the predictions directly through the rule, we already solve the learning problem. However, the purpose of that simple experiment is to show the potentiality of the proposed approach in integrating the available symbolic knowledge into learning problem. In real-life scenarios, such a situation is unrealistic, but still we might have access to some partial useful knowledge that may allow solving more quickly a given learning problem. Also, it may promote an easier interaction of domain experts with DL model by asking them to provide their knowledge rather than just data annotations.
More precisely, when we consider structured data (c.g., tabular data), a domain expert may know some very simple relations taking into consideration few features and the output class. This knowledge may not be sufficient to solve the learning problem, but KAL strategy can still exploit it to drive the network to a fast convergence, as we will see in Section 33 On the opposite, when we consider unstructured data (e.g., images or audio signals) the employed knowledge cannot directly rely on the input features. Nonetheless, when considering multi-label learning problem, user may know in advance some relations between the output classes. Let us consider, as an example, a Dog-vs Ses-vs-Person classification: might know that main object (c.g., a dog) is composed of several parts (c.g.. muzzle, a body, a tail). A straightforward translation of this compositional property into a FOL rule is Dog- Muzzle V Body V Tail. Formulating the composition in the opposite way is correct as well (e.g.. Muzzle = Dog). Also, in all classification problems, at least one of the main classes needs to be predicted (e.g., Dog V Person). Finally, we can always incorporate an uncertainty-lik rule requiring each predicate to be either true or false, i.e., Dog O -Dog.
EXPERIMENTS
In this work, we considered four different learning scenarios, comparing the proposed technique with several standard active strategies. We evaluated the proposed method on two standard classification problems (Bishop 2006). the inference of the XOR-like problem and the classification of IRIS plants given their characteristics. We also considered two standard image-classification tasks: the ANIMALS dataset, extracted from ImageNet (Deng et al. 2009). and the Caltech-UCSDD Birds-200-200 dataset (CUB200, (Wah et al., 2011)). As a proof of concept, we analysed the performances of the KAL when employed in the simple DOGvsPERSON object recognition task. For more details regarding the latter, please refer to Appendix A.3 At last, in Appendix A.2 we report a case study showing how to apply KAL on regression task. For each dataset, n. P. q, as well as the number of training epochs and the network structure are fixed in advance according to the number of classes, the dataset size and the task complexity. Reported average results are computed on the test sets of a k-fold Cross Validation (with k = 10 in the tabular data problems and k 5 in the computer vision ones). More details regarding each experimental problem, as well as a table reporting all the employed rules, are available in Appendix A.4 The code will be published is provided in the supplementary material. A simple code example is also reported in Appendix B showing how to solve the XOR-like like problem with the KAL strategy. All experiments were on an Intel i7-9750H CPU machine with an NVIDIA 2080 RTX GPU and 64 GB of RAM.
a publicly available repository, and it
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Table 1: Comparison of the methods in terms of the mean Fl score AUBC and standard deviation when increasing the number of labelled points. On top, starting and ending labelling budget for each dataset. The three best results are reported in bold. NA indicates strategies too expensive compute.
Dataset
XOR
IRIS
Animals
CUB200
Strategy
Budget
10-400
10-70
100-2500
2000-7000
ADV
89.79 1:1.14
78.81 #21.02
53.93 10.42
50.82 10.36
ADV DEEPFOOL
87.56 #13.08
78.86 #21.04
NA
NA
BALD
83.94 #9.25
90.96 +6.88
53.74 +1.96
51.17 +0.62
KCENTER
96.79 =0.43
92. 62.65 13.90
43.37 13.29
48.86 20.52
KMEANS
83.73 2:440
88.55 15.10
52.87 11.18
49.96 =0.43
Entropy
90.11 :99661
82.11 +18.49
57.26 4:0.94
51.91 #0.12
Entropy P
87.80 11.00
81.91
56.56 1:095
51.92
LeastConf
89.97 10.55
84.35
113.89
12.12 53.33
50.20 20.43
LeastConf
89.98 12.05
84.83 +14.03
53.85 #0.84
50.07 =0.45
Margin
89.97 10.55
85.46 #14.8
57.26 +1.66
51.69 =0.41
Margin
$9.98 12.05
84.94
11432
57.03 1:042
51.54 #0.48
Random
96.18 20.55
92.04
15.14
52.62 10.49
50.29 =0.38
SupLoss
96. 77 #0.68
92.48
#3.34
54.97 +:210
49.53
+0.35
KAL
97.73 #0.83
93.60 60
43.87
56.15
#1104
51.98 #:0.5
KALp
97.96 #0.79
93.32
4:4.13
55.56 #1.21
52.10 1:0.44
Compared methods We compared KAL with 12 active learning strategies commonly considered in literature (Ren et al. 2021 Zhan et al. 2022). As representatives of uncertainty-basee strategies, considered Entropy (Settles 2009) selecting samples associated to predictions having maximum entropy, Margin (Netzer et al. 2011) predictions with minimum margin between the top-two classes, and LeastConf (Wang & Shang 2014) predictions with the lowest confidences, together with their Monte Carlo Dropout versions (Beluch et al.) (2018) (respectively Entropy D. Marginp. LeastConfp). which, by applying dropout test time, compare the predictions of Monte Carlo sampled networks to better asses uncertain predictions. As more recent uncertainty based strategies, we compared with Bayesian Active Learning by Disagreements BALD (Gal al. 2017). with two strategies computing the margin by means of adversarial attacks ADV DEEPFOOO (Ducoffe Precioso 2018). ADV BTM (Zhan et al.) 2022) and with SupLoss a simplified upper bound of the method proposed in (Yoo & Kweon 2019) employing the actual labels (available only on benchmarks). As Diversity-basee methods, we selected K.Maans (Zhdanov) 2019) and KCenter a greedy version of the CoreSet method (Sener & Savarese 2017). More details regarding each method
are reported in Appendix A..5 together with table resuming the associated losses.
3.1 KAL PROVIDES BETTER PERFORMANCE ON AVERAGE THAN ANY OTHER STRATEGY.
For quantitative comparison of the different methods, we evaluated the performances of the different active learning strategies. In Figure 2 we reported the average F1 scores budget curves when increasing the number of selected labelled data. In Table T we also report the Area Under the Budget Curves (AUBC), as defined in Zhan et al. (202)) In both the XOR-like and IRIS learning problems, we can observe how both the proposed methods KAL and KAL (the corresponding Monte-Carlo Dropout version) have the highest average AUC with a 7-12 % increment over standard uncertainty-bac based strategies in both cases. The only competitive method in both cases is the CoreSet- based approach KCenter. This behaviour will be better analysed in Section 3.3 Interestingly. when analysing the top plots in Fig. 2 we can appreciate how the proposed methods enable the network to learn more quickly the given tasks w.r.t. the other ones. While this was expected behaviour on the XOR-like task since the provided rules completely explain the learning problem, on the IRIS classification task it is surprising since only 3 simple rules considering maximum of 2 features each are given (e.g.. Long Petal = Setosa). A slightly-differen situation can be observed in the image classification tasks (bottom plots in Fig. (2). Here notice the importance of employing structurdd knowledge. In the ANIMALS task. indeed, only 17 rules are employed relating animal species and their characteristies (e.g., Fly = -Penguin). In this case, the results with KAL
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XOR
Animals
CUB200
1.0
1.0
0.8
0.7
0.9
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40 Parss
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Strategy
ACV BALD
KCENTER KMEANS
Entopy
KALp
Margin
Random Suplose
LeastConf LeastConty
ADV
KAL
Margin
Figure 2: Average test Fl score performance growth the four experiments when increasing the number of labelled samples. Confidence intervals have not been reported for better readability. Method variants (e.g., the Monte-Carlo Dropout versions) displayed with the same colour.
only on average w.r.t. uncertainty-basee approaches (better than LeastConf, BALD and ADV but worse than Margin and Entropy). On the contrary, KAL performs much better than KCENTER and KMEANS which are unable to correctly represents data distributions in complex scenarios. In the CUB200 task instead, where 311 rules are employed in the KAL strategy considering bird species and their attributes (c.g.. White Pelican = Black Eye Solid Belly Pattern Solid WWig__Pateet instead, provide low performances in the computer vision problems. Indeed, we believe that selecting samples with high supervision loss might not be an optimal active strategy in this scenario, mostly select outliers. These results prove that KAL is very effective active learning strategy when the provided knowledge sufficiently represents the given task, both in standard and computer vision classification problems, On the ANIMALS task, instead, where the provided knowledge is scarse, the KAL strategy is less effective than some uncertainty strategies.
the proposed approaches
again the best two strategies. SupLoss,
might
3.2 ABLATION STUDIES
The amount of knowledge is directly proportional to the performance improvement To further show the importance of having a diverse and rich set of rules as introduced in Section 3.T we performed here an ablation study. 2 reports the performance of the network when equipped with a KAL strategy considering only 0%. 25%, 50%, 75% or 100% of the available knowledge. The results show evidently that the amount of knowledge is directly proportional the performance improvement, up to +1.8%. In the 0% scenario, the only rule employed is the uncertainty- rule, which was always retained. Notice how 50.13 similar the LeastConf result (50.20), suggesting that KAL without any further knowledge results in an uncertainty-basee strategy. In Appendix A.6 we report the complete table showing this results is valid for all experimented scenarios.
Table 2: Ablation study the quantity of knowledge employed to support the KAL strategy on the CUB200 dataset. The amount of knowledge is directly proportional to the increase of performance.
Dataset
KAL 0%
KAL 25%
KAL 50%
KAL 75%
KAL 100%
CUB200
50.13 40.39
50.19 #0.42
50.22 +0.40
51.28 #0.29
51.98 +0.35
Selecting diverse constraint violations and uncertainty-like rule improve the performances Given a set of rules K., the proposed method might in theory select p samples all violating the same rule dh (x)). To avoid this issue, we select a maximum number r of samples violating a certain rule k, similarly to (Brinker 2003) introducing diversity in margin- based approaches. Specifically, we X,, according to the rule they violate the most, and we allow a maximum number of p/2 samples from each group (still following the ranking given by Eq. []. In Appendix A.7 we report a table showing how requiring samples violating diverse constraints improves the overall quality of the KAL selection process. Also, show the importance of adding the uncertainty- rule A f @ -f, introduced at the end of Section 2.3 Together, these two features allow improving the average performances of the network up to 2 %.
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KAL
BALD
Margin
KCENTER
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Figure 3: A comparison of the sample selection process on the XOR-like task at the 20th iteration (starting from the same points as in Figure Notice how both uncertainty-baat strategies (BALD and Margin) have not covered yet the novel data distribution (right-bottom quadrant).
3.3 KAL DISCOVERS NOVEL DATA DISTRIBUTIONS UNLIKE UNCERTAINTY STRATEGIES
To further analyse the results obtained, Figure we report the samples selected by some compared strategies after 20 iteration on the XOR- task (around ~ 100 labelled data), starting from the same randomly selected samples of Figure [ As introduced in Section 2.2 the KAL, strategy enables discovering data distribution lying far from the starting training data (lettmost figure). On the contrary, when the initial random sampling not well representative, uncertainty- based strategies (like Margin but also BALD, central figures) are unable to discover the whole data distribution. Indeed, they require all labelled data along the decision boundaries of already known distributions. For this reason they provide mediocre results in average XOR-like lokelike and IRIS and very high variance (> 15 20% on IRIS) ). The CoreSet representative strategy. instead, has covered the four quadrants. However, by only working on input features statistics and without notion the predictions, this strategy does not choose points along the decision boundaries, preventing the network from reaching high accuracy performances. More figures are reported in Appendix A.8
3.4 KAL ENSURES DOMAIN EXPERTS THAT THEIR KNOWLEDGE IS ACQUIRED BY THE MODEL
It may be the case that domain experts provided with small corpus of rules which is crucial be respected by the trained model, because, e.g., it has to be deployed in sensitive context. By always selecting the data that violate this corpus of rules, KAL ensures them that their knowledge is aquired by the model. To simulate this scenario, we computed the argument of Eq. I over a small part of the CUB knowledge KCUB-S (where- -5 stands for small) on the test data Xx for the fo model trained with all the budget: ((KCuR-SS s (T) = Σxex, EkEKCUB PPx (f)(). In Table 3 we report the increased percentage of the violation by models trained following few compared methods w.r.t. the violation of a model trained following the KAL strategy and equipped with the small corpus of rules (KALemat). The complete table together with more experimental detail is reported in appendix A.9. For the sake of completeness, this model reaches a lower test F1 AUBC (49.04). Nonetheless, ensures domain experts that the provided knowledge is respected significantly more than using Random selection, or, worse, than standard active learning strategies.
Table 3: Violation of the KCUR-S knowledge computed as the increased percentage over the violation of model trained to respect this knowledge (KAl-smal). The lower, the better. The proposed method ensures domain experts that their knowledge is acquired by the model.
KA KALamall
Random
ADV Brat + 591...0%
BALD
Entropy + +861.74%
KCENTER
LeastConf
+ +0.0%
+483.10%
+ +720.25
133..33%
+334.50%
3.5 KAL CAN BE EMPLOYED EVEN WHEN DOMAIN-KNOWLEHS IS NOT AVAILABLE
It might be argued that the proposed strategy can be employed only when domain knowledge is available. However, recent works in the eXplainable AI (XAI) field Guidotti et al. 2018 Ribeiro let al. 2018 Ciravegna et al.) 2020) have shown that we extract the same knowledge from trained model. In general, they achieve this by training a white-bor model (c.g. a decision tree) to globally explain the behaviour of neural network. Here, propose employ these FOL-bbased
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Table 4: Accuracy of the KAL strategy coupled with XAI method, extracting the knowledge from the same network. Notice how the AUCB reduction of performance is always smaller than %.
XOR
IRIS
Animals
CUB
KAL
97.73 40.83
93.60 33.87
56.15 11.04
51.98 10.35
KALXAr
97.11 10.60
92.97 44.48
55.71 11.24
51.38 10029
explanations (Ixx as the base knowledge of the proposed strategy when no other knowledge is available (KALxaI). More precisely, after each iteration, we employ a simple decision tree as proposed in Guidotti et al. (2018) extract the knowledge. More details on how we trained the XAI method are reported in Appendix [A However, the knowledge may be partial, particularly during the first iterations, since it is extracted on the training distribution only. Therefore, we use Eq. [ to select only 60% of the samples, with the remaining randomly selected. This allows to eventually recover the complete knowledge. In Table we report the performance of the network when equipped with this strategy (KALx AI), together with the performance of the standard strategy. Notice how the reduction of performance is limited to less than 1,, confirming the validity of the proposed approach even in this scenario. The amount of randomly chosen samples has not been cross-validated, therefore we expect to get even higher results by fine-tuning this parameter.
3.6 KAL CAN BE EMPLOYED IN OBJECT RECOGNITION TASKS
To test the proposed method in an object recognition context, as a proof of concept, we experimented on the simple nOGvsPERSON dataset. On this task, we compute the AUBC of the mean Average Precision curves. Also in this case, the network increases more its performances when equipped with the KAL strategy (55.90 =0.39) with respect to standard random sampling (51.41 +1.26) ) but also compared to the Supl.os method (55.30 20.54), proving the efficacy of the KAL strategy also in this context. A figure showing the three budget curves is reported in appendix [A.IT Reported results are averaged over 3 initialization seeds. We only compared with Random selection and the simplified version of Yoo & Kweon (2019), since uncertainty-based strategies are not straightforward to apply in this context (Haussmann et al. 2020). Finally, highlight again that the SupLoss performance reported is an upper bound of the performance of the method proposed in Yoo & Kweon (2019). Particularly in this context, we believe that the object recognition loss might not be easily learnt by an external model, reducing the performance of the SupLoss method.
3.7 KAL IS NOT COMPUTATIONALLY EXPENSIVE
When devising novel active learning techniques, of crucial importance is also the computational effort. Indeed, since re-training a deep neural network already requires a substantial amount of resources, the associated active strategy should be as light as possible. In Zhan et al. (2022), authors used as term of comparison the average time needed to randomly sample novel batch of data. In Table we report the increased computational time in percentage. The KAL strategy (in its vanilla version) does not increase it significantly (with an average + 2-23 %). On the contrary, BALD (+ 44-191%) and, more importantly, clustering (+ 8-742%), CoreSet (2-5446%) and ADV-based (162-2451%) strategies demand considerable amounts of computational resources, strongly reducing the usability of the same methods. Standard uncertainty-bret based techniques like Margin, instead, are not computationally demanding, with only the Dropout versions having an increase of 2-80% (similarly to KALD). The complete table with all methods is reported in Appendix A.12
RELATED WORK
Devising an active learning strategy is not an easy task. In the literature, two main approaches have been followed: uncertainty sampling which selects the data on which the model is the least confident; curriculum learning which instead focuses first on easy samples then extending the training set to incorporate more and more difficult ones while also targeting more diversity. Standard uncertain strategies consist in choosing samples associated to maximal prediction entropy (Houlsby et al. 2011) minimum distance from the hyperplane in SVM (Schohn & Cohn 2000) with
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Table 5: Computational demand computed as the percentage increase over the time required for random sampling as defined in (Zhan et al., 2022). The lower, the better. Notice how the proposed method is less computationally expensive than many recent methods (ADV, BALD, KCENTER).
XOR
IRIS
Animals
CUB
ADV BIM
+9400.8% #278.11
+162.41% 131.15
+1251 ..3% =39.03
+ 1355..6% #33.53
BALD
+191.44% 115.14
+72.08% 147.00
+44.48% 13.34
+112.47% 113.28
KCENTER
+321.06% 144..54
+2.01%
11.92
-606.94% 156.57
+5446.31% 159.38
KMEANS
+8.30% 112.39
+9.39%
13.16
+173. 20% 10.80
+742.47% 154.30
Margin
+0.66% +14.63
+1.55% #2.50
+1.26% +2.30
+0.65% #0.19
Margin,
+84.00% #13.94
-1.99% +3.90
+3.95% #3.93
+38.88% +2.49
KAL
+2.52% 113.60
+0.32%
12.56
+6.43%
#2.02
+23.42% 10.21
KALd
+88.28% 220.70
+5.441% 26.23
+8..8% 1.29
+62.98%% 12.37
the highest variation ratio in Query-by-committe with ensemble methods (Ducoffe & Precioso 2017; Beluch et al. 2018). Establishing prediction uncertainty more difficult with DL models. Indeed, they generally tend to be over-confident, particularly when employing softmax activation functions (Thulasidasan et al. 2019). Furthermore, there is no easy access to the distance to the decision boundary for SVM, so it needs be computed. This problem has been tackled by devising different uncertain strategies, such as employing Bayesian Neural Network with Monte Carlo Dropout (Gal et al. 2017). by calculating the minimum distance required to create an adversarial example (Ducoffe & Precioso 2018), or even predicting the loss associated to unlabelled sample YYo)) & Kweon 2019). As pointed out by (Pop & Fulop 2018), however, uncertain strategy may choose the same categories many times and create unbalanced datasets. To solve this, uncertain sample selection can be coupled with diversity sampling strategies. Diversity can be obtained by preferring batches of data maximizing the mutual information between model parameters and predictions (Kirsch et al. 2019), or selecting core-set points (Sener Savarese 2018), samples nearest to k-means cluster centroids (Zhdanov] 22019), even by learning sample dissimilarities in the latent space of VAE with an adversarial strategy (Sinha et al.) 2019) or by means of a GCN (Caramalau et al., 2021).
It has been pondered that human cognition mainly consists in two different tasks: perceiving the world and reasoning over it (Solso et al., 2005). While these two tasks in humans take place at the same times, in artificial intelligence they are separately conducted by machine learning and logic programming. It has been argued that joining these tasks (to create a so-called hybrid model) may overcome some of the most important limits of deep learning. among which the "data hungry" issue (Marcus 2018). In the literature, there exists a variety of proposals aiming at this objective, ranging from Statistical Relational Learning (SRL) (Koller et al. (007) and Probabilistic Logic Programming (De Raedt& & Kimmig 2013) which focuses on integrating learning with logic reasoning, to enhanced networks focusing on relations or with external memories (Santoro al., 2017 Graves et al. 2016). The learning from constraints framework Gnecco et al. (2015): Diligenti et al. (2017) (see survey Ginnchilia et al. (0222) for a complete list works in this domain), instead, computes and enforce the satisfaction of given domain knowledge within DL models. In this paper, we have shown that it can naturally leveraged to devise active learning strategies, providing the first example of integration of symbolic knowledge in this context.
5 CONCLUSIONS
In this paper, we proposed an active learning strategy driven by knowledge consistency principles. The performance of model equipped with such strategy outperforms standard uncertainty- bbsed approaches context where the domain knowledge is sufficiently rich, without being computationally demanding. Furthermore, we think that KAL could induce more trust in DL with respect to standard active learning techniques by enabling non-expert users to train models leveraging their domain knowledge and ensuring them that it will be acquired by the model. A main limitation of the proposed approach is in computer vision contexts, if no attributes about the main classes are known. A possible solution could be automatically extract such concepts from the latent space of the network, as recently proposed in Ghorbani et al. 2019): Chen et al. (2020). Also, if the domain knowledge is highly complex, FOL may not be able to fully express it and higher-order logic may be required.
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A EXPERIMENTAL DETAILS AND FURTHER RESULTS
A. CONVERTING LOGIC FORMULAS INTO NUMERICAL CONSTRAINTS
To better understand how the KAL framework works, in this section we will briefly go thorugh some basic principles on FOL and later we will focus on how to convert rules into numerical constraints by means of different T-Norms.
FOL Domains, Individuals, Functions, Predicates and Constraints In First Order Logic, Domain D is a data space representing Individuals x which share the same representation space X. As an example, domain can be composed of images representing birds, as in the CUB200 dataset. Each bird is an Individual, which is represented in a certain Domain by its features (e.g.. in this case, by its image). A Function is a mapping of individuals between input and output domain. In this paper, we only focus on unary-function, i.e., functions that take only one individual in input and transform it into an individual of an output domain. An example of function is Age(2)) which returns the age of a bird given its image representation. N-ary functions, taking more than z). returning the kind of relationship given two bird
one individual in input (e.g., Relationshipll images) are also supported by the framework but are not used in this case. The output domain can be the same or different domain w.r.t the input one. Predicate a special type of function returns as output a truth value 0, 1 if we consider boolean predicate, or in 0, 1 if also consider fuzzy values as in this work. An example of predicate is Il umminggirdd(z) which tells you whether the considered bird belongs to the Hummingbird species. Both predicates and functions can be parametrized and learnt. In our case, all considered predicates were modelled by means of a neural network. At last, we can provide our knowledge about certain domain by means of a set of Constraints. A constraint is a FOL. rule defined on functions and predicates (which are the atoms of the rule). An example of a constraint could be Va, H Humminghird(()) - Bird(a)). Finally, existential quantifier Fr X are also supported by the framework but we have not used them in this work.
Converting FOL rules into numerical constraints To convert a FOL formula into a numerical constraints we need way to convert connectives and quantifiers into numerical operators. To do so, we employ the fuzzy generalization of FOL that was first proposed by Novák et al. (1999). More precisely, T-norm fuzzy logic Hájek ( [1998) generalize Boolcan Logic to continuos values in [o, 1]. T-norm fuzzy logics are defined by the operator modelling the AND logic operator. All the other operators are generally derived from it. In Table (reported implementations of common connectives when using the Product (the one used in this paper), the Lukasiewicz and the Gödel Logics.
(reporrd from Marra al. (2019)) some possible
Table 6: Some of the most used example of T-Norm with their translation of some logic operators.
Table extracted from (Marra et al. 2019)
T-norm
Product
Lukasiewicz
Gödel
Op.
x A y
I. y
max(O, + 1)
min(r, 3)
x V y
X +
x y 1
y
min( I, x + y)
max(x, y)
1-
20
F +
1 (xr (1 y))
min(1 1, 1 - x + +)) S y?l y
Finally, to evaluate the violation of each numerical constraints, a loss function has to be chosen (also called generator). These functions need to be strictly decreasing 9 [0,1] + [0, + +inf] and such that g(1) O. Possible choices are g(z)
(as used in this paper), or g(x) (x)
A.2 KAL CAN ALSO BE EMPLOYED IN REGRESSION TASK
The proposed active learning strategy can also be applied in regression tasks. In the latter, we consider a learning function f : X + Y, where the output space Y E R now admits values also outside the unit interval. As previously, we model f with neural network but with single output neuron and no activation function. For what concerns the associated logic predicate, it now requires to be defined on open e.g., f > h or closed intervals e.g., hn f < hz. As when defining inequalities over an
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Table 7: Domain knowledge on the Insurance dataset.
Yr
Smoker Age 40 + Charge 7500
Yr
Smoker A Age > 40 + Charge > 7500 A Charge < 1,500
Yr Smoker A BMI < 30 + Charge > 15000
Charge < 30000
Vr Smoker BMI > 30 <> Charge > 30000
imput feature, also in this case model the logic predicate continuos function by means of sigmoid centered on h in the case of logic predicates defined over open intervals - or by means of the products of two sigmoid, the first centered on hı and the second one flipped and centered on hz in the case of closed intervals.
To asses the validity of the proposed method on regression tasks, experimented the Insurance dataset available from Kaggle The proposed task is to model insurance charges based on 6 features regarding the insured persons (Age. Sex, BMI, Number of Children, Smoker and Region). The knowledge employed in this case consists of 4 rules working on 3 features and defining 4 intervals over the output space, as reported in Table In Table and Figure 4 instead, reported the performance in terms of AUBC and R score when increasing the labelling budget, respectively. Also in this scenario KAL results a very effective active learning strategy. At last, uncertainty-bast strategies are not reported because they cannot be applied in this scenario unless using auxiliary models to estimate confidence this context as in (Corbiere et al. 2021).
Table 8: Comparison of the methods regression task in terms of R score mean AUBC and standard deviation. Budget starting ranging within 10-500 labelled points. Uncertainty hased-techniquss are not reported because they not be applied in regression tasks.
Dataset
Insurance (R)
Strategy
Budget
10-500
KCENTER
+99.9 1:4966
KMEANS
+58.40 16.85
Random
+66.23 #7.84
SupLoss
+53.33 +4.85
KAL
+70.63 #6.68
KAL
+71.11 46677
Insurance
0.8
0.6
0.4
0.2
200
400
# Points
Strategy KALp
KCENTER
KMEANS
KAL
Random
SupLoss
Figure 4: R Score curves when increasing the labelling budget on the Regression Insurance task.
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10a
10a
102
dog ear dog head dog leg
dog
dog muzzile dog neck
dog nase
dog paw
dog Torso
tail
person person amm person foot
person hair person hand person head person leg person neck person nose
person torso
dog
Figure 5: Class distribution in the DOGvSPERSON dataset.
A.3 THE DOGvSPERSON DATASET
The DOGvSPERSON dataset is publicly available dataset that we have created for showing the potentiality of the proposed method on simple object-recognition problem, where well-defined relations are present among the classes, and we can employ common-knowlede rule to easily relate them. It is extracted from the PASCAL-Part dataset by considering only the Dog and Person main classes and their corresponding parts. In the original PASCAL-Part dataset, labels are given in the form of segmentation masks. We extracted a bounding box from each mask by considering the leftmost and highest pixel as the first coordinate and the rightmost and lowest pixel as the second one. Very specific parts are merged into a single class, following the approach of [Serafini] & d' Avila Garcez (2016) (e.g.. Left Lower Arm, Left Upper Arm, Right Lower Arm, Right_ Upper Arm becomes Arm) Differently from the standard PASCAL-Part dataset, how- ever, the parts in common to different objects considered as different classes (head becomes Person _cad). Furthermore, we only consider masks having areas 2 1% of the whole image areas as valid label. At last, only classes appearing at least 100 times are retained. This lead to a total of 20 classes with 2 main classes (Dog and Person) and 18 parts (Dog Ear, Dog_Muzzle
Neck Nose, Dog_ Paw. Dog Dail, Dog Torso, Person Arm. Person Foot. Person Hair. Person Hand, Person Head, Person Leg, Person Neck, samples. Final classes are distributed in the samples as shown in Figure 5
Dog_Heas Dog_Leg
Neck. Person Nose. Person Torso) displayed a total of 4304
A.4 NETWORK ARCHITECTURES, HYPERPARAMETERS. AND DOMAIN KNOWLEDGES
XOR-like The problem of inferring the XOR-like operation has been already introduced in Sec- tion 2.2] an artificial dataset consisting of 100000 samples E X C R². mapped to the corresponding label y E Y [0, 1] as in Fq. 2 A Multi-Layer Perceptron (MLP) f: X + Y is used to solve the tast It is equipped with single hidden layer 100 neurons and Rectified Linear Unit (ReLU) activation, and a single output neuron with sigmoid activation. It has been trained with an AdamW optimizer Loshchilov & Hutter (017)) for 250 epochs at each iteration, with a learning rate 7 10-3, Standard cross-entropy loss has been used to enforce to learn the available supervisions. By starting from n = 10 samples, we added p = 5 labelled samples at each iteration for a total of q 78 iterations, resulting in total final budget of b 400 labelled samples. As anticipated, in the XOR problem, the rule employed for the KAL strategy is Vo X1 @ X2 <> f, as also reported in Table
For more real-life style problems, we have considered four more datasets where the domain- knowledge is partial only related to the class functions.
FFor all strategics requiring multi-class output, we considered the network output f= [f, fl.
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Table 9: Domain knowledge on the XOR-like dataset.
Vx
x1 ① x2 +
IRIS
The IRIS dataset is the standard iris-species classification problem. More precisely, the task consists in classifying
3 Iris species (Iris Setosa, Iris Versicolour, Iris Virginica) starting from 4 features (sepal length, sepal width, petal length, petal width). To solve the learning problem. an MLP f: X + Y is employed, with one hidden layer composed of 100 neurons equipped with ReLu activation functions. It has been trained again with A optimizer for 200 epochs at each iteration and learning rate supervisions. By starting from n = 5 points and by adding p = 5 labelled samples at each iteration total budget of b 75 labelled samples. The knowledge employed
3 * 10-3 3 A cross-entropy loss is employed to enforce the
for q 14 iterations, leading in this case consists of 3 very simple rules (one per class) based on the two predicates and Wide Petal (built on the 3rd and 4th features of the dataset, respectively, as explained in Section 2.2p. In addition, in this case, a mutually exclusive rule on the classes is also considered Vrr, Setosa Versicolour ( Virginica, as reported Table 10
Petal
Table 10: Domain knowledge on the IRIS dataset.
Vz
- Long Petal < Setosa
Yz
Lona_ Petal A- Wide_Petal <> Versicolour
Vz
Long Petal A Wide Wide_Petal <> Virginica
Yz
Setosa @ Versicolour e Virginica
ANIMALS The Animals' dataset is a collection of 8287 images of animals, taken from the ImageNet d The task consists in the classification of 7 main classes (Albatross, Giraffe, Cheetah, Ostrich, Penguin, Tiger. Zebra) and 26 animal attributes (e.g., Mammal, Fly or [ag_), for total of = 33 classes. In this case, a Resnet50 CNN has been employed to solve the task f: Xd + ye, Going into more details, a transfer learning strategy has been employed: the network f has been pretrained on the ImageNet dataset (Deng et al., 2009), and two fully connected layers (the first one equipped with 100 neurons) have been trained (from scratch) on the ANIMALS dataset. Again, an Adam optimizer is considered with a learning rate 17 10-3 employed for 250 epochs of training each iteration, with binary cross-entropy loss since we deal with a Iulti-label problem. We started with n = 100 labelled samples, and we added p 50 samples each time for q = 48 iterations, for final budget of b 2500 labelled samples. In the case of Animals, the employed knowledge is a simple collection of 16 FOL formulas, defined by Winston & Horn (1866) as a benchmark. They involve relationships between animals and their attributes, such as Fzy A Lay Eggs + Bird. To this collection of rules, we have also added a mutual exclusive disjunction among the animal classes (only one animal is present in each image) and standard disjunction over the animal attributes (each animal may be associated to many attributes). The complete list of rules employed reported in Table
CUB200 The Caltech-UCSD Birds-200-200 7 dataset Wah et al. 2011 is a collection of 11,788 images of birds. The task consists in the classification of 200 birds species (e.g.. Black_foooter [oooted_Albatross and birds attributes (e.g.. White_Throat, tribute annotation, however, is quite noisy. For this reason, attributes are denoised by considering class-level annotations similarly to Koh et al. (020)). A certain attribute is set as present only if is also present in at least 50 images of the same class. Furthermore, only considered attributes
(ediiummSizee) At-
$ Iris: Animals (Innggeeec//aattp///////.mgggggg http:://wwwwww.aaameeeeee vised" License
/iris released with BSD 3-Clause "New" or "Re-
200-20 released with MIT
License.
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Table 1I: Domain knowledge on the Animals dataset.
Vr
Hair Mammal
Vx
Milk + Mammal
Vr
Feather + Bird
Vr Fly A LayEggs = Bird
Vr Mammal A Meat Carnivore
Vr
Mamal PointedTeeth Claws A ForwardEyes = Carnivore
dx
Mammal A Hoofs Ungulate
Vr
Mammal A Cud + Ungulate
Vr
Mammal A Cud Eventoed
Vr
Carnivore A Tawny ^ DarkSpots = Cheetah
Vx
Carnivore A Tawny A BlackStripes
Tiger
Vx
Ungulate A Longlegs A LongNeck A Tawny A DarkSpots = Giraffe
Yr
Blackstripes A Ungulate A White + Zebra
Vr
Bird -Fly A LongLegs A LongNeck Black + Ostrich
Vr
Bird -Fly A Swim A WlackWhite > Penguin
Yx
Bird GoodFlier = Alhatross
Vr
Albatross a Giraffe & Cheetah @ Ostrich @ Penguin e Tiger @ Zebra)
Yx Mammal V Hair V Milk Feathers V Bird Fly V Meat v Carnivore V PointedTeeth
Claws ForwardEyes V Hoofs Ungulate V Cud v Eventoed Tawny BlackStripes
LongLegs v LongNeck DarkSpots White V Black V Swim BlackWhite GoodFlier
present in at least 10 classes after this refinement. In the end, 108 attributes have been retained, for total of c = 308 classes. Images have been resized to dimension d = 256 x 256 pixels. The same network as the ANIMALS case has been employed to solve the learning problem, with two fully connected layers trained from scratch (the first equipped with 620 neurons twice the dimension of the following layer). Again, an Adam W optimizer considered with a learning rate 7j = 10 for started with
100 epochs of training. Owing to the increased difficulty of the problem, labelled samples, and we added p = 200 samples for 25 iterations, for a final budget of b = 7000 labelled samples. The knowledge employed in this case consider the relation between the classes and their attributes, with logic implications both from the class to the attributes (e.g.. Black Eye Solid Belly Pattern Solid Wing Pattern). and the vice-versa (c.g.. Striped Breast Patterrttttttetee + Parakeet _ukeeett__ketttt. V Black throated t thermore, a disjunction on the main (Basse (Black_footed footed Albatross Laysan Albatross Sooty AlbatrossV...) and one on the attributes are considered (Dagger BillrrBilllllle B Hooked Billl All Purpose Bill Cone Bill V .... few examples of the rules employed are reported in
2000
Pelican +
Fur-
Table 12
DOGysPERSON
This dataset has already been introduced in Appendix A.3 Since we filtered out very small object masks in this dataset, we have been able employ a YOLOv3 model Redmon & Farhadi (2018) to solve the object-recognition problem. The model has been trained for 100 epochs at each iteration with AdamW optimizer, with learning rate v = 3 10 decreasing by 1/3 every 33 epochs. For both training and evaluation. the Input Over Union (IOU) threshold has been set to 0.5, the confidence threshold 0.01 and the -o--Maximum Suppression (NMS) threshold 0.5. We started training with 1000 labelled examples and by adding
500 samples for g = 4 iterations for a final budget of b 2000 labelled examples. In Section 3.6 we reported the AUBC of the mean Average Precision (mAP) of the model averaged 10 times with Intersection over Union (IoU) ranging from 0.5 to 0.95. On DOGysPERSON we considered set rules listing the parts belonging to the dog the person, (e.g.. Person = Person Arm V Person Foot V Person Hair Person Hand V .)., the opposite rules implying the presence of the main object given the part (e.g., Person Foot = Person). Also, considered disjunction of all the main classes and disjunction of all the object-parts, for a total of 22 rules employed, as reported in Table 13
In all experiments, we employed weight decay and low learning to avoid overfitting, rather than employing an early stopping strategy on a separate validation set. Indeed, we argue that it is not really
Duee to the dimensionality of the dataset, the mutual exclusion of the main classes computationally too expensive compute in this case.
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Table 12: Domain knowledge on the CUB200 dataset. Only a few rules for each type have been reported for the sake of clarity. Also, due to the length of the rules, rules with more than two terms implied have been truncated.
Black_footed, [loatr__llatrross has bill_ shape_hape___ swwpssaallppuueeeeeeaeeeaeesasee aul-ppr A has giss_uddeppart___ole cowtarttttsooooreoeeeeeeeooorree yellowwyellwww/eoooooo A...
Laysan Albatross = has bill shape hooked seabird A has_ breast_patterm, _att_pp_ttttttiiaeeae solid A...
va
= has bill _aal__saap____ wwapsphhooeeede seceeddddeeirdd has_wing, htt___ee_eatteerrrrr_t pattern_ solid A
fos__win__coooo color black_ A
vr
Groove_billed Ani = has jus_bill__ salll_sape___a__
hooeeedhhoeed__eee seaaddd__eerddeeee A has has_hreast
Va
has_ wingswwollllloo cacp__cooo_____aeeee has moss_pppeparts_comm color black A
Vi
has bill shape dagger = Green Kingfisher A Pied Kingfisher A...
Vi
has bill shape hooked seabird = Laysan Albatross A Sooty Albaiross A...
yr
mas_bill sis_bbillshhp_allll hill__sape_alllppppaaa purppos = Black_fore footed_ seteed__lattosss A Red_ Blackbird A...
has L____billl__pp_ paill_shape_eon_
Parakect_AAklet
Bartting_nntinggg/g A
bes_wing__oolr_brree brownr_broww-- =
American_Cret A...
Vr
Black footed_ Albatross v Laysan_At Albbatrsss V Sooty_Albatroe Albatross V...
Vr
has bill shape_dagger has_bill L_l__blll__aaa shall_shape__a shape_hooked seabird V has has_bill shape_alpe pallpppllp v
Table 13: Domain knowledge the DOGysPERSON dataset.
Væ
Dog Dog
Ve
Dog head Dog
Ve
Dog leg = Dog
Dog muzzle + Dog
Dog neck Dog
d
Dog_nos
Dog
Dog_pav paw = Dog
4
Dog_tail = Dog
Dog_tors torso = Dog
dx
Person
Person
de
Person foot Person
da
Person hair > Person
Z
Person_hand + Person
dz
Person_heard
Person
dx
Person_lcg Person
Nx
Person_nesdd neck + Person
Vx
Person nose + Person
Vz
Person_ torso = Person
Vz
Dog Dog_ooa_a _rr__ar_ Dog head V Dog_leg V Dog muzzle
Dog_neck neck V Dog__ooo nose Dog__aw V Dog tail Dog_ torso
Væ
Person > Person__aaae arm V Person_foor v Person hair V Person hand
Person_heat v Person__eg V Person_neck V Person__eae _ose V Person_torse torso
Yr
Dog V Person
Yz
Dog_ear Dog_head Dog_leg V Dog_muzzle Dog_neek Dog_nosc
Dog paw Dog v Dog torso Person arm V Person foot Person hair Person hand V Person head V Person leg V Person neck V Person nose V Person torso
realistic to rely sufficiently large validation sets in an active learning scenario, where the amount of labels is scarce, and we try to minimize it as much as possible. Also, rather than retraining the network from scratch at each iteration, choose keep training it to save computational time.
A.5 COMPARED METHOD DETAILS
In the experiments, several methods have been evaluated, comparing the performances both in terms of score improvement and terms of selection time. Compared techniques mostly follow two different active learning philosophies: uncertainty sample selection, which aim estimating
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Table 14: Resume of the active losses (a, x) maximized by each of the compared methods. Variants of the same methods (e.g., employing Monte Carlo Dropouts) have not been reported for the sake of brevity. We indicate with H the Entropy, with o the softmax activation, with py (3,, a) the probability of associated to the class i, with M the set of main classes, with the adversarial perturbation, g(-) the model used to learn the model loss, with ZCENTER the CoreSet points and with EMRANS the centroids of K-Means.
Entropy
L. [[]()]] = - (o(SM(z)) log(o([M(z)))
Margin
La (py(011z)- pr(02|z)), 21, D2 = arg max Ps Ps(yi,
LeastConf
L. 1 pr(() 1 arg max ()(
BALD
La H [[(x)|a||- ([H(f()))
ADV
L. ||<||= <: fa + # (M(
SupLoss
L. (((()),)) ~ rg((())
KCENTER
La || =x||:
2 = arg min s || - =||
KMEANS
L. - I 2x|1;
Z arg min gen || =||
KAL
La EKEK (f()))
prediction uncertainty in deep neural networks; and diversity selection, which aims at maximally covering the input data distribution. Several standard strategies like Entropy (Settles) 2009), Margin (Netzer et al. 2011) and LeastConf (Wang & Shang, 2014) belong to the first group, as well as some more recent methods like BALD (Gal et al. 7). ADV DEEPPOOL (Ducoffe Precioso 2018), ADV BIM (Zhan et al. (022) and SupLoss (Yoo & Kweon 2019). On the contrary, K.Means
(Zhdanov 2019) and KCenter (Sener& & Savarese 2017), aim at reaching the highest diversity among
selected samples.
In Table 14
we reported the loss (f used by each method to select active samples as following:
x² arg max La (J,
(4)
xxXc
As the name implies, the Entropy method aims at measuring the uncertainty of a prediction by means of its entropy. With a we indicate the softmax activation, that we applied on of of f'r to obtain a probability distribution - i.... ΣiEM (fs, x) = 1. as required to compute the Entropy. To adapt this method to the multi-label context, we restricted the computation the M main classes (mutually exclusive) of f. Similarly, in Margin and LeastConf we compute again the softmax over the main classes fM to obtain for each main class the probability py x) of being active. In the first case, the margin between the two classes associated to the highest probability is used to estimate the uncertainty of the prediction. In the second case, the inverse of the probability associated to the most probable class is used instead. BALD employs as acquisition function the mutual information between the model predictions and the model parameters. The first term of the loss is again the Entropy of the model predictions; the second term of the equation, instead, represents the expected value of the entropy over the posteriori of the model parameters. Basically, the overall value is high when the predictions differ lot, but the confidence of each prediction is rather high. Both ADV DEEPFOOL and ADV BrM use as a metric of uncertainty the norm of e, the minimum input alteration allowing to change the prediction of the network. The difference in the two methods relies on the way e is computed (i.c., on the adversarial attack employed). The stopping criterion to find e in both methods consists in finding perturbation that induce the network to predict a different class. To adapt these methods to the multi-label context, therefore, we restricted again the classes the main ones fM. The SupLoss strategy, instead, aims at approximating the supervision loss by means of a model (x))))). It receives in input the output of the f network (as well as the activation of the last hidden layers) and is trained to mimic the actual loss L( ((I(x),)) ~ g( (x)) on the supervised data. As Yoo & Kweon 2019) claim that [(f(x), y) is the actual upper bound of their method, for simplicity we employed the same L to select uncertain samples. However, as we have seen in Section 3.T] even in the best case scenario this strategy does not work very well in complex problem as it mostly end up selecting outliers and making network convergence more difficult. Both KCENTER and KMEANS, instead, base their selection criteria only on distance metric on the input
To avoid numerical issues, we applicd the logits of the output of the network log(f(>) (log))-oo111111111111)
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Strategy
XOR
IRIS
Animals
CUB200
KAL 00 %
93.54 20.83
81.45 18.88
53.42 1.66
50.13 20.36
KAL 25 %
91.72 15003
53.21
11.39
50.22 1:0.40
KAL 50 %
93.12 24.72
54.54
11.11
50.19 1:042
KAL 75 %
93.84 #3.94
54.61
#0.47
51.28 #0.29
KAL 100 %
97.73 +0.83
93.60 #3.87
56.15
#1.06
51.98 +0.31
Table 15: Complete version of Table 2 The amount of knowledge proportional to performance improvement. In the XOR dataset, since we only used the XOR rule, only reported
KCENTER aims covering much as possible the input data distribution, by selecting at each iteration the furthest sample to the current set of labelled samples (ZCENTER) On the contrary, KMEANS strategy selects the closest unlabelled sample to the set of centroids (Zmeans), following a curiculum-learming strategy.
data distribution TO
A.6 ABLATION STUDY: THE AMOUNT OF KNOWLEDGE IS PROPORTIONAL TO PERFORMANCE IMPROVEMENT
We here report the complete version of Table The result that we reported in the main paper for the CUB200 dataset is valid for all datasets: the amount of knowledge is proportional to the performance improvement. In the XOR dataset, since we only had the XOR rule, we only reported the performance with 0 % and 100 % knowledge. We recall that in the 0 % knowledge scenario (to still evaluate our method) we always retain the uncertainty-like rule.
A.7 ABLATION STUDY: SELECTING DIVERSE CONSTRAINT VIOLATIONS AND EMPLOYING UNCERTAINTY-LIKE RULE IMPROVES THE PERFORMANCES
In this section, we analyse the role of selecting samples violating a diverse set of rules and of employing the uncertainty-like rule introduced in Sec. 3.2 We recall that diversity sample selection achieved by requiring a maximum of r = p/2 samples violating certain rule k when selecting a new batch of p samples to be labelled. The uncertainty-likk rule, instead, consists in requiring each predicate f to be either true or false A; f @ -f. This way, in case many predicates for a certain sample have not well-defined value (e.g.. f((x)) 0.5). the violation of the constraint associated to this rule will be high.
We studied three different scenarios, employing the uncertainty-like rule (Unc), requiring set of sample violating different rules (Div) or both of them (Div Unc). We compared them with the plain versions both in the case of estimating predictions with a standard classifier (KAL) and when using Monte Carlo dropout (KALD), leading to total set of eight configurations. We report the results of these ablation study in Table [6] The results reported as KAL Section [.Tere, are, actually, the version with both features (KAL Div Unc). Indeed, KAL Div Une and KAL, Div Unc respectively increase the AUBC by 2.3% and 1.9% on the Animals dataset over KAL. and KALD; on the XOR-like and on the CUB200 dataset, the increase is well important, although smaller than in the latter case; only in the IRIS case, the performances get reduced when requiring samples violating a diverse set of rules. This can be most likely explained by considering the size of the Iris dataset and the fact that we employed only 3 rules, specific for each class. In this setting, it may be more convenient for the network gather samples related to specific class (i.e., violating specific rule) only. Indeed, labelling points related to a distribution already covered (i.e., where the knowledge is mostly respected) with very few examples available can slightly decrease the overall performances.
A.8 TRAINING EVOLUTIONS ON THE XOR-like PROBLEM
In Figure 6 we report further snapshots of the active selection process on the XOR- like dataset. They depict the model predictions similarly to Figure 3 but at different iterations and for all the
In the image recognition tasks, employed the latent distribution extracted by the convolutional features, commonly done (Ren al. 2021 Zhan al. 2022.
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XOR
Iris
Animals
CUB200
Strategy
KAL
97.38 00.0
94.01
1:406
53.86
1:179
51.94
40.43
KAL Une
97.46 00.40
93.97
43.61
54.12
10.97
51.98
10.35
KAL Div
97.62 =0.79
93.44
+4.50
54.56
+1.09
51.97
#0.39
KAL Div Une
97.73 =0.83
93.60
+3.87
+1.04 56.15
51.98
20.35
KALD
97.45 =0.49
94.11 24.23
53.67
11.64
51.93
20.47
KALp Div
97.96 10.79
93.32
14.14
53.74
#1.42
51.90
20.44
KALD Unc
97.57 =0.51
93.51
+3.80
53.92
+1.28
52.02
+0.33
KALD Div Unc
97.96 40079
93.32
444.33
55.56
+1.21
52.10
#0.24
Table 16: Ablation study on diverse rule selection (Div) and on the uncertainty-lice rule (Une), both on the standard KAL and Monte Carlo dropout version (KALp). In bold, the two best results. Notice how, the latter increase the AUBC by 2.3% and 1.9% respectively over KAL and KALp, on the Animals dataset.
compared methods. In this figure, it is even more clear that uncertainty-based strategy is capable of discovering novel data distributions. More precisely, nor Entropy, nor Margin, nor LeastConf, nor BALD, AdVBIM, nor Adv AdVDEEPFOOL angle (for which no samples have been drawn during the initial random sampling) even after 20 iterations. Diversity- bassd strategy, instead, cover all data distribution; however, both KCENTER and even more KMEANS cannot perfectly predict samples along the decision boundaries. Finally, interesting notice how the sampling selection performed by the SupLoss resemble the one made by KAL. However, even in the simplified upper case considered in this comparison, the selection process performed by SupLoss drives the network more slowly convergences with respect KAL. Indeed, as it can be noticed in the right-most plots, after 20th iterations the selection process in SupLoss has not covered very well yet the centre, differently from the selection process of KAL, which correctly covered this important zone.
cover the data distribution in the right-bottom
A.9 COMPARISON OF THE KNOWLEDGE VIOLATION
tested whether the proposed method allows the model to learn to respect the knowledge provided by domain experts. In Table 17 we reported an extended version of Table computing the increased percentage of violation of the KCUB-S knowledge by models trained following the compared active strategies w.r.t. a model trained following the proposed strategy (KALSM ALL). All the compared methods (including KALs when equipped with all the knowledge on CUB) violate the KCUB-s knowledge significantly more (4-13 times) than (KALSMALL).
As introduced in Section 3.4
10 EXTRACTING THE KNOWLEDGE WITH AN XAI METHOD
Explainable AI techniques more and more used in literature to mitigate the intrinsic opacity of deep neural networks. In Sec. 3.5 we employed Guidotti et al. (2018) to explain the f model at each iteration, and use the explanations (K AF)) This is a viable solution to employ when no other knowledge is available. More precisely, we trained decision tree h on the supervised training input data X, mimic the behaviour of the network f, i.e., we minimized the following loss Lx, (1(x), ((x) From the decision tree, we extracted global explanations of each class in the form of, e.g., Vz Setosa + - Long Petal. In computer vision tasks, however, decision trees are not suitable to be employed directly on the raw input data, For this reason, following Barbiero et al. (2022), we trained the decision tree to mimic the behaviour of the model If over the main classes when receiving in inputs the attribute ones. The extracted rules, in this case, are of the type footed Loooeed_llbabrrsseeeessseees Albatross + hal_bill_ halll_shae___a_ Seaape_lllpprposss A mos__nderparts. citerparts_cclor_____ wwwlroyyelloeeeyooeeeeeeeoooeooe A ... To also explain the attribute classes, we did the reverse, i.e. we trained the decision tree to mimic the behaviour of the model f over the attribute classes and receiving in input the main ones. The extracted rules in this are of the type has bill shape + Parakeet Auklet A Indigo Bunting A ..... Finally, we always added to this set of rule a mutual exclusion rule over the main classes and disjunction the attributes (where available). Indeed,
the base knowledge (K of the proposed method
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KAL
0.0
00-
0.0
0.5
1/ do
1.0 0.0
0.5
100 o
0.5
1.0
1,0-
Entropy
02.03
00
0.5
1.0 0.
0.5
1.0 0.0
0.5
1.0 0.0
0.5
X1
1.0-
Margin
60.55
00
0.5
0.0
0.5
1.0 0.0
0.5
1.0
0.5
X;
X:
X1
X1
1.0-
LeastConf
100 0.
1.0
1.0
X1
XL
1.0
BALD
0.0
0.0
0.0
1/c db
1.0 0.
0.5
1/0 no
10
ADV
055
0.0
0.
0.5
1. 0.0
0.5
1.0 0.o
0.5
1 do
0.5
10
Xs
X:
ADV DDDEEFFOOL
1.0
0.5
0.-
1.0 0.
1.0 doo
1/ do
1.0
Figure 6: An illustration of the selection process evolution for all the compared strategies the XOR-like like problem. We depict network predictions with different colour degrees (light colours negative predictions, dark colours positive prediction); in blue, samples selected in previous iterations, in orange those selected at the current iteration. Black lines at 21 = 0.5 and 22 = 0.5 are reported for visualization purposes only. From left to right, the state at the 1t 5th 10th and 20th iteration.
this notion must be always available as it conditions the choice of the training loss (e.g. binary vs standard cross entropy).
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Sup Loss
2.055
0.
0.5
10 00
0.5
1.0 0.0
1.0 0.0
0.5
KCENTER
0.5
00
0.5
100 0.0
05
1/0 0.0
0.5
1.0 0.
0.5
1.0
x:
X1
1.5-
KMEANS
0.5
0.0
0.5
100 0.0
1.0
0.5
0.6
1.0
X1
X1
X
Figure 6: A visual example on the XOR-lik like problem, showing how the training evolves in each of the compared strategy (continued from previous page).
Table 17:
Violation of the KCun-s knowledge computed as the increased percentage over the violation of a model trained to respect this knowledge (KALsmati). The proposed method ensures domain experts that their knowledge is acquired by the model on test data significantly more than using standard techniques.
Strategy
Increased Violation
KALSMALL
0.00
133.00
ADV ADV BIM
591.03 4532.47
BALD
720.25 1251.86
Entropy
861.74 1519.33 %
Entropy
812.35 1:359.23
KAL
863.53 1226.81
KAL
890.98 2290.79
KCENTER
530.13 188.74
KMEANS
555.23 1327..0 %
LeastConf
1334.50
%
LeastConfp
934.46 #300.21
Margin
846.05 #341.02 %
Margin
637.26 165,07 %
Random
483.10 1285.08
SupLoss
804.38 176.31
A.11 EMPLOYING ACTIVE STRATEGIES OBJECT RECOGNITION TASK
As introduced in Section 3.6 we tested the proposed method also in an object recognition context. As a proof of concept, we experimented on the simple DOGvsPERSON dataset, described in Appendix A.3 In Table 18] we report again the AUBC of the mean Average Precision curves when increasing the budget of labelled points. The same curves are reported in Figure The results in this case are averaged over three different seed initialization the network. The network increases its more performances when equipped with the KAL strategy (55.90) with respect to standard random sampling (51. 1,41) but also compared to the SupLoss method (55.30). Interestingly, by considering Figure 7 appreciate how also in this context the proposed strategy significantly improves the performance of the network already after the very first iterations. Finally, we highlight again that the LupLoss performance reported upper bound of the performance of the method proposed in (Yoo)
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Dataset
# Points
Random
SupLoss
KAL
Dog vs Person
1000-3000
51.27 11.41
55.30 20.54
55.90
20.39
Table 18: Comparison of the methods in terms of the mAP (%) AUBC (Zhan al. 2021 when increasing the number of labelled points on the object recognition task.
Dog vs Person
62
Strategy
KAL
Random
58
SupLoss
mAP
54
50
1000
1500
2000
2500
3000
# Points
Figure 7: Average test mAP performance growth on the object recognition task when increasing the number of labelled samples. Shadowed areas indicate the 95 % confidence interval.
& Kweon 2019). Particularly in this context, we believe that the object recognition supervision loss might not be easily learnt by the external model g. In this proof-of-concept, we only compared with Random and our implementation of the SupLoss method, since they were the most straightforwardly adaptable method to the object recognition context. In future work, we plan to compare with the adapted uncertainty-base strategy proposed in Haussmann et al. (2020).
A.12 EXPERIMENTAL TIME COMPARISON
In Table [9] we report the complete comparison of the time required by the different strategies. More precisely, reported the increased percentage computational time. We included both the time required to select the data and the time required to train the network. The KAL strategy does not come the cost of significantly increased time (with an average +0.3-23.4 %), comparably with standard uncertainty based strategies, Entropy (+0.0-32.9%) LeastConf (+0.0-2.01%% ()), and Margin (+0.6-1.8%% 1.8%.. Only the Monte Carlo Dropout versions, require higher computational time (KAL-p +5.4-88.3% Entropy p +0.0-89.22% LeastConf +0.3-36.6% Margin +1 +1.7-84.0 .7-84.0%% since they repeat several times a prediction with different switched-off neurons, to better assess uncertainty. On the contrary, BALD (+44.5-191.49) and, more importantly, KMeans (+8.3-74..5%) KCenter (+2.0- 5446.3%), ADV Fлы (+162.4-1353.6 remarkable computational resources, strongly reducing the usability of the same methods. In particular, ADV defpfool requires a huge amount of resource, since the DEEPFOOL attack is linearly dependent in both the selected samples and the predicted classes. For this reason, was computationally infeasible to experimented on the Animals and CUB datasets (respectively with 7 and 200 classes). At last, we reported SupLoss with since the computational time required to compute the cross-entie coosspy loss between the labels and the prediction (as simplified in this comparison), may be significantly different from the one required to predict the loss through the model g.
and ADV DEEPFOOL (+206.8-NA) strategies demand
24

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Under review as a conference paper at ICLR 2023
Table 19: Computational time required select the samples annotate by all the compared methods as percentage increase w.r.t the time required for random sampling as defined in (Zhan et al. (022). The lower, the better. NA indicates strategies computationally too expensive to compute on certain datasets. Notice how the proposed method is not computationally expensive, contrarily many recent active learning methods proposed in the literature.
XOR
IRIS
Animals
CUB
Strategy
ADV BTM
+910.38%
1162.11% #31.15
1251.36%
1333.64% #33.58
ADV DEEPFOOL
+2450.66% 11435.04
7906.79%
1110.24
NA
NA
BALD
4191.44% 115.14
+72.08% 147.00
+44.88% 13.34
+112.47% 113.28
KCENTER
+321.06% 148.54
+2.01% 11.92
+606.94% 156.57
+5446.31% 1:30.38
KMEANS
+8.30% 112.39
+9.39%
+173.20% 29.80
+742.477 #54.30
Entropy
+3.51% #15.95
+0.0%%
+2.85% #3.28
+32.93% #2.67
Entropy
+89.20% 114.58
+0.08% 24.24
+2.98% #2.31
+37.65% 22.81
LeastConf
+0.77% 14.70
+2.01% +33999
+0.06% +0.36
+0.68% +0.07
LeastConfo
+83.16% 14.50
+0.31% +4..88
+2.73% +3.08
+3659% #2.72
Margin
+0.66%
L.85%
+1.26%
+0.65%
Margin,
+84.00% 113.9
+1.69% 13.90
+3.95% 13:9
+38.88% 12.00
SupLoss
+3.04% 110.99
+1.54% 16
+1.6%% 11.80
+1.66% 11.34
KAL
+2.52% 113.89
+0.32% 1:2.8
+6.43% 12.02
+23.42% 20
KAL
+88.28%
#20.79
+5.41%
2..23
+8.18%
1:129
-2.98%
#2.37
25

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Under review as a conference paper at ICLR 2023
B SOFTWARE
Knowledge-drivg Active Learning Experiment the XOR problem
2 tot points 10000
first points
4 n. o_points =
iiiterations
seeds range (5)
7 x np nandom. uni (tot (totpppotttoooooooittt 2))
((x[:, 0] 0.5) (x[:, 0.5))
9 ((x:;, 1] 0.5) & (x[:, 0] < 0.5))
x_test, y y_train, y_test srain_test__pe split (x, y, rest_size=0.11
Defining constraints product t-norm of the FOL rule expressing the XoR loss tk__onninee, f):
def
discrate_x continue 0.5) .float()
discrete_x steep_sigmm sigmoid(x_coottaaiee 16
float ()
discrete_xie x(:,
18
x2 discrete x(:; 1]
cons lossl
((1 (x1 (1 x21)) (1
xi))))
cons_loss2
f) (1 (1 (x1 x2)) (1 (x2 (1 x1))))
return cons loss1 cons cons_loss2
23 Constrained Active learning strategy p idx
among available
selection (labelled idx, loss, a. c_loss (torch. sa__tesorrre (labelled_idk) =1
cal cal_idx idx = torch.argsore (c. loss, descendingsTrue) .ooliigsssruu)..ostttt.... tollist [:m_p]
100)
accuracies = []
used idx randint x trai.n. shape first_pointe tolist ()
available_idx [*range (tot_pointt]
for n in range (n. ittrations):
train_loop (net, x_train, y y_train, udxd_idx)
36
torch.no... no_ghd(())
38
preds_train train net (x (x_train)) squeazee(
preds test net test) squeezee
accuracy accuracy_scom (preds_tees) _eet, y_test)
cons_los loss calculate ponuulaat_constainttt loss (x trainnn, preds_ ardd_trrin)
list (set (available idxx)) set (used_ids) www.cceennnnncoooooooeooooooeeos (used idx, cons loss, n_poinnts) used idx +* active_idx _dx
available idx
active
Listing 1: KAL code Example on the XOR problem. For simplicity we do not consider in this case a train and test set.
The Python code and the scripts used for the experiments, including full documentation, is freely available under Apache 2.0 Public Licence in GitHub repository, and it is also provided in the supplementary material. The proposed approach only requires a few lines of code to train model following the KAL strategy, we sketch the code example reported in Listing
26


Reviews:
[{"review_id": "lUrneMfn7b", "reviewer": "Reviewer_fw63", "summary": "", "questions": "", "limitations": "", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "The paper introduces the idea of injecting human knowledge into the active learning process by First order logic using Triangle Norms. By formulating domain expert knowledge as loss functions (acquisition function), unlabeled points can be selected based on the number of violated knowledge. The paper tested on 4 different datasets and compared with a bunch of existing AL classification tasks and showed that KAL is surpassing average traditional AL methods.", "summary_of_the_review": "Given the concerns I have around the experimental setup, along with the presentation issue of the storyline for AL audiences, I recommend borderline reject for this manuscript.", "strength_and_weaknesses": "Strength:\n\nThis paper proposed an interesting idea: using domain knowledge to improve active learning performance. The benchmarked traditional AL methods are plentiful, and experimental results show the promise of KAL. The ablation study shows the amount of knowledge added to the AL progress. The graphic looks and clean.\n\nWeaknesses:\nApart from some clarity issue (below section), I would like to question the experimental design of this work, especially on the XOR illustration that serves the main purpose to conveying how this method work to the audience:\n\nThe initial batch of samples of the AL process is not random, or at least not representative of random. If we look at Figure 1, the first iteration where the blue points are previous samples (and therefore the initial samples that might be the same across experiments), they are heavily biased towards the top left corner. This is an important issue as the majority of the traditional AL algorithm relies on a randomly sampled initial set like BALD. If we then look at Figure 3, the BALD and Margin result, non of the queried points are in the bottom right corner, which indicates the model has not even seen any of those points. The only explanation that made sense to me is that their initialization is biased towards the top left corner, just like Fig 1 shows. This raises strong concerns with respect to the experimental setup. \n", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "2: Several of the paper’s claims are incorrect or not well-supported.", "technical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work.", "empirical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work."}, "extra_text": {}}, {"review_id": "_lESe5hY1sF", "reviewer": "Reviewer_JCBB", "summary": "", "questions": "", "limitations": "", "rating": 8, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "The paper proposed a new methodology for active learning. In particular, they propose to exploit the background knowledge available about a problem to better select the datapoints to be labelled. The background knowledge must be expressed as logical constraint as it is then mapped into the loss function via the usage of the t-norms. An extensive experimental analysis has been done to evaluate the strengths and weaknesses of the model.", "summary_of_the_review": "TL;DR I think this paper has all the potential to be a great paper. However, in the current form I have too many concerns. If all of them are addressed I would happily fully accept the paper", "strength_and_weaknesses": "**Strengths:**\n1. The proposed approached is very novel. As far as I know, nobody has proposed the usage of logical constraints for the task of active learning. \n2. The authors propose synthetic experiments that help in understanding the strengths of the work. \n3. The problem has been analysed from a variety of different angles. \n\n**Weaknesses**: \nEven though I really liked the paper, I found that at times it was written in an imprecise/misleading way. Please see the box below for more details.", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "4: All of the claims and statements are well-supported and correct.", "technical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work.", "empirical_novelty_and_significance": "4: The contributions are significant, and do not exist in prior works."}, "extra_text": {}}, {"review_id": "TZ6OozcDhZO", "reviewer": "Reviewer_KFBz", "summary": "", "questions": "", "limitations": "", "rating": 6, "confidence": 2, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "This paper presents an approach for active learning that selects examples using logic constraints specified as domain knowledge. The proposed approach is evaluated in a series of empirical experiments compared to traditional active learning baselines.", "summary_of_the_review": "An interesting approach for using domain knowledge in active learning. The proposed approach is extensively evaluated against active learning methods, however, in places where the best method is not abundantly clear, the paper could be improved to specify why one approach is preferred to another more succinctly. ", "strength_and_weaknesses": "**Strengths**\n\n* This paper presents an interesting and flexible framework for active learning. The proposed approach allows users to specify domain information in the form of FOL to determine selection criteria.\n* The authors demonstrate empirical effectiveness via a series of empirical experiments . The experiments are extensive and used to validate the approach.\n\n**Weaknesses**\n\n* I think that the paper could be improved if there was more succinct understanding as to where and when the proposed approach is more effective or efficient than baseline methods in active learning\n* Table 1 leads to a somewhat confusing landscape of empirical success, where baseline methods of kcenter and kmeans are highly effective. I think the presentation can be improved by highlighting reasons to select a particular method more.", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "3: Some of the paper’s claims have minor issues. A few statements are not well-supported, or require small changes to be made correct.", "technical_novelty_and_significance": "2: The contributions are only marginally significant or novel.", "empirical_novelty_and_significance": "2: The contributions are only marginally significant or novel."}, "extra_text": {}}, {"review_id": "PalxG0pj-oM", "reviewer": "Reviewer_r58Q", "summary": "", "questions": "", "limitations": "", "rating": 6, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "Summary: Authors propose an active learning pipeline that incorporates domain knowledge into the pipeline for more efficient active learning & yielding models more consistent with known domain rules. Specifically, the model employs first-order-logic (FOL) based encoding to employ domain rules to inform examples to be selected for active learning. Authors demonstrate the effectiveness of their generic FOL pipeline on variegated tasks like Object recognition, classification and compare their model to various state-of-the-art uncertainty based active learning approaches and other clustering based methods. Overall the proposed method yields good results. \n\n\n \n ", "summary_of_the_review": "The proposed model is somewhat novel and the core idea (i.e., encoding domain knowledge as FOL using T-Norms) is based on previously published paper.", "strength_and_weaknesses": "## Strengths: \n\nAuthors propose a light-weight model for active learning incorporating domain knowledge using the T-Norms based rules introduced in [1]. \n \n\nResults of the proposed model are convincing as a result of the multiple tasks and variegated baselines employed for state-of-the-art comparison. \n \n\nPaper is well written and well organized. \n\n \n\n## Weaknesses: \n\nThe proposed method is applied to classification problems and in somewhat balanced data contexts. It would be interesting to check the power of domain knowledge in data imbalanced contexts.  \n\n Proposed model is somewhat novel as the crux of the FOL encoding is based on the previously proposed T-Norm idea.\n\nThe discussion about contexts in which the proposed method would out-perform baselines would be especially insightful to readers.\n\nIncorporating a little more background regarding FOL might help readers fully comprehend the paper better.\n\n## References: \n\n1. Klement EP, Mesiar R, Pap E. Triangular norms. Springer Science & Business Media; 2013 Apr 17. ", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "3: Some of the paper’s claims have minor issues. A few statements are not well-supported, or require small changes to be made correct.", "technical_novelty_and_significance": "2: The contributions are only marginally significant or novel.", "empirical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work."}, "extra_text": {}}, {"review_id": "FtjLM3um8T", "reviewer": "Reviewer_NXVX", "summary": "", "questions": "", "limitations": "", "rating": 8, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "This paper presents a novel idea of incorporating domain knowledge into first-order logic  (FOL) for active learning. Consistency between the predictions made on unlabelled data and the quantified domain knowledge encoded in the form of FOL is assessed, and the examples defying make the candidate examples to query their label. Experiments are performed in multiple data sets and compared with a wide range of existing methods. \n", "summary_of_the_review": "I find the idea of injecting domain knowledge into active learning very interesting. Although the experiments are done on a small scale, they are convincing. ", "strength_and_weaknesses": "Active learning is a machine learning paradigm where a subset of examples is selected from a large pool of unlabelled data to query their labels. Most of the active learning literature works are based on either uncertainty or diversity, or both. I find the work novel because it introduces the idea of injecting domain knowledge. \n\nThe paper is well-motivated, and the previous works are discussed adequately. However, some of the recent works on model-based active learning are missing:\n\nSinha, Samarth, Sayna Ebrahimi, and Trevor Darrell. \"Variational adversarial active learning.\" Proceedings of the IEEE/CVF International Conference on Computer Vision. 2019.\n\nYoo, Donggeun, and In So Kweon. \"Learning loss for active learning.\" Proceedings of the IEEE/CVF conference on computer vision and pattern recognition. 2019.\n\nCaramalau, Razvan, Binod Bhattarai, and Tae-Kyun Kim. \"Sequential graph convolutional network for active learning.\" Proceedings of the IEEE/CVF conference on computer vision and pattern recognition. 2021.\n\nThe experiments are performed for both image classification and object recognition. The experimental results are either comparable to better than the existing method without incurring much computational cost.  Although the experiments are done on a small scale, I think this should not be considered a weakness. However, I wondered how domain knowledge could be applied to active learning for regression tasks. \n\n\nThe paper is well presented, and explaining with the toy example makes the idea easy to understand. \n", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "3: Some of the paper’s claims have minor issues. A few statements are not well-supported, or require small changes to be made correct.", "technical_novelty_and_significance": "4: The contributions are significant, and do not exist in prior works.", "empirical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work."}, "extra_text": {}}]

Author rebuttal:

Decision: Reject