Cooperation and knowledge sharing are of paramount importance in the evolution of an intelligent species. Knowledge sharing requires a set of symbols with a shared interpretation, enabling efective communication supporting cooperation. The engineering of intelligent systems may then benefit from the distribution of knowledge among multiple components capable of cooperation and symbolic knowledge sharing. Accordingly, in this paper, we propose a roadmap for the exploitation of knowledge representation and sharing to foster higher degrees of artificial intelligence. We do so by envisioning intelligent systems as composed by multiple agents, capable of cooperative (transfer) learning-Co(T)L for short. In CoL, agents can improve their local (sub-symbolic) knowledge by exchanging (symbolic) information among each others. In CoTL, agents can also learn new tasks autonomously by sharing information about similar tasks. Along this line, we motivate the introduction of Co(T)L and discuss benefits and feasibility.
Human beings can perform a huge number of diferent tasks: if a human needs to learn a new
task, it can typically manage to do so easily. Broadly speaking, humans may learn new skills
in two ways: by generalising experience – e.g., via inductive reasoning –, or, by deductively
infer new knowledge from that they already hold or can get from others—e.g., talking (direct
communication) or reading (indirect communication) [
When learners are computational agents (rather than humans), algorithms are available to mimic basic cognitive capabilities such as induction, communication, knowledge representation, and reasoning. These have been developed under the umbrella of symbolic artificial intelligence (AI) and machine learning (ML). However, unlike the human case, symbolic AI and ML algorithms are commonly tailored to solving one or few tasks at a time, and they are not meant to take advantage from interaction, cooperation, nor knowledge exchange.
This paper stems from the idea that ML-based intelligent systems could and should take
advantage from the exchange of symbolic knowledge to improve their learning capabilities
[
Along this line, we envision two sorts kind of intelligent systems: Cooperative Learning (CoL) and Cooperative Transfer Learning (CoTL). CoL systems are multi-agent systems (MAS) whose agents can retrieve / provide knowledge about a specific task from / to other agents, so as to exploit that knowledge during learning and possibly at inference time. CoTL systems are CoL systems whose agents can acquire, exploit, and combine knowledge about diferent related tasks so as to learn to execute novel tasks they were not designed for. Both kinds of systems are able to mimic the learning process of human societies, despite to diferent extents. In other words, agents help each others by sharing (predominantly) symbolic and (possibly) sub-symbolic knowledge about the tasks they need to do—similarly to what humans do.
Accordingly, in this paper we propose a roadmap for the exploitation of knowledge representation and sharing to foster higher degrees of artificial intelligence, via CoL and CoTL. In particular, we analyse the requirements of both CoL and CoTL w.r.t. the state of the art, and discuss how they could be realised in principle. Along this line, the paper is organised as follows. Section 2 provides definitions for symbolic and sub-symbolic knowledge representations along with techniques to manipulate knowledge. Section 3 introduces the definition of CoL and CoTL systems providing general agent architectures. Finally, Section 4 discuses the main advantages of CoL and CoTL, it draw conclusions, and provides insights about future works.
Symbols are carriers of meaning that people may exploit in communication, e.g., words, trafic signs, flags, etc. They are commonly used to represent knowledge in a way that is interpretable for humans. Furthermore, symbols can be automatically processed by algorithms, and, therefore, by computational agents.
Following the definition given in [
Formal logics allow for both intensional and extensional knowledge representation. In
particular, an intensional definition means represent data indirectly by describing the elements
of relations or set via other relations or sets. Because of intensional representation (a.k.a.
compactness), domain independence, and versatility, logic can be used as lingua franca for
knowledge representation [
Conversely, sub-symbolic representations violate the definition provided in [
Sub-symbolic functions are widely used in ML tasks, such as neural networks (NN). The vast
majority of NN consist in a direct acyclic graph of neurons, which are composed by several
connection weights plus a bias value and an activation function. NN (and in general any
subsymbolic predictor) cannot be conventiently interpreted by humans: even small NN would
require a significant cognitive to be partially understood by the human mind. Therefore, NN
are used as black-boxes [
Symbolic Knowledge Extraction (SKE) is the set of methods accepting trained sub-symbolic
predictors as input and producing symbolic knowledge as output, in such a way that the
extracted knowledge reflects the behaviour of the predictor with fidelity [
Despite SKE is usually used as a way to post-hoc explain black-box predictors to humans, it may serve other purposes. For instance, knowledge extracted via SKE could be exploited to help ML during training. In this case, representing knowledge symbolically brings several benefits: the extracted knowledge is agnostic w.r.t. the original predictor, and it is compact due to intensionality.
Dually to SKE, Symbolic Knowledge Injection (SKI) is the set of algorithms afecting how
sub-symbolic predictors draw their inferences by making them consistent with some prior
symbolic knowledge [
Generally speaking, SKI improves the eficiency or efectiveness of the sub-symbolic predictors it is applied to (e.g., accuracy, training time, data greediness, etc.). The common SKI workflow requires a human expert providing domain-specific knowledge to be injected. However, this is not a strict requirement. In fact, symbolic knowledge may be provided not only by humans, but by other computational agents as well. For instance, the knowledge to be injected may be the result of some prior SKE process.
Let us denote as ‘task’ any kind of supervised ML task. Accordingly, Transfer Learning (TL) is the set of techniques aimed at letting a predictor , targetting task , take advantage from the knowledge acquired by some prior predictor ′, trained on some other task ′. Of course, tasks and ′ are assumed to be similar to some extent. The main objectives of TL are to: (i) reduce the amount of data required to train , (ii) speed up its training, and (iii) improve its predictive performance.
TL algorithms from literature difer w.r.t. two major dimensions: what to transfer and how to transfer [26]. Of course, another relevant aspect is when to transfer (cf. Sections 2.3 and 3.1). Finally, similarity among tasks is yet another fundamental aspect—which is often devoted to the experience of practitioners.
Notably, TL has been most successfully applied to convolutional NN – in particular, ImageNet [27] – for biomedical image processing [28]. However, despite their variety, most TL techniques only support the transfer of sub-symbolic knowledge. In fact, the transferred knowledge commonly consist of the shallowest layers of a NN, which are transplanted into another NN, of which only the deeper layers are then re-trained. Hence, to the best of our knowledge, there are no TL algorithms explicitly leveraging upon symbolic knowledge transfer.
Multi-task Learning (MTL) is a set of mechanisms aimed to improve the performance of a predictor via transfer learning [29]. More precisely, given a set of similar tasks {1, . . . , } – according to some notion of task similarity –, MTL aims at learning the tasks altogether, by training as many predictors 1, . . . , . In doing so, MTL attempts to improve the performance of each , by taking advantage of the knowledge while training the other predictors [30].
Diferently from TL techniques where there is one task that receives the knowledge from the others, in MTL all tasks receive knowledge from the others, simultaneously. Similarly to TL, virtually all MTL techniques rely on sub-symbolic knowledge transfer.
MTL techniques may be classiefid w.r.t. whether they target either homogeneous or heterogeneous tasks. Two tasks 1, 2 are homogeneous when they share the same input and output attributes (names and type). What may be diferent is data sampling, and its distribution. Conversely, heterogeneous tasks have diferent attributes, with possibly no overlapping [31].
In MTL the question “where to transfer” is not avoided like in TL. Especially for heterogeneous tasks, the problem of computing a ‘degree of similarity’ is still open. Empirically, one could test if two or more tasks are related by applying MTL itself: if the overall performance increases using MTL, then the tasks can be considered as similar.
A CoL system is a MAS where agents can retrieve knowledge about a task from other agents
and provide knowledge to others when requested. Explicit knowledge sharing – especially
symbolic – is of paramount importance for the MAS as a whole, as it enables agent-to-agent
knowledge transfer [
To support CoL, agents should be endowed with some fundamental capabilities, namely: (a) Agent’s architecture for CoL.
As the reader may notice, capabilities 2 and 3 are complementary. When combined with capability 4, these may pave the way to cooperation among agents, aimed at learning by interaction. Finally, capability 1 is necessary to let some agents learn novel behaviours independently of others.
When actually building CoL systems, capability 1 is likely supported by sub-symbolic ML. In particular, each agent is assumed to be endowed with some ML predictor, supporting learning from local data. However, since MAS are commonly composed by heterogeneous agents serving disparate purposes, many predictors of diverse sorts are likely to be exploited within the same system.
To support capability 4 in spite of heterogeneity, agents should agree on common, shared symbolic representation means by which behavioural specifications could be described—and later exchanged. Along this line, SKE and SKI may serve the purposes of capabilities 2 and 3, respectively
Figure 1a shows the general design of CoL agents. Each CoL agent must be equipped with (possibly multiple) SKE and SKI algorithms, in order to support symbolic knowledge I/O. When queried, an agent may extract symbolic knowledge from its inner ML predictor (via some SKE technique) and send it to the querying agent. The recipient may then update its local predictor by injecting the received knowledge into it. Knowledge pre- and post-processing steps (e.g., pruning / merging / selecting formulae) may occur before SKI or after SKE, to regulate which particular chunks of knowledge are actually transferred.
Crucial choices to be addressed during the design of a CoL system are: (i) the supported formalisms for knowledge representation, and (ii) an appropriate SKE/SKI toolkit w.r.t. the undergoing predictor(s) knowledge representation (almost straightforward for pedagogical SKE techniques). About (i), one could choose FOL over PL or KG for its expressiveness. However, the more one formalism is expressive the less are the available techniques: it is therefore reasonable to consider also less expressive logics for (ii).
It is worth mentioning that a single agent can be initially trained even in lack of prior knowledge. At some point in the training process, the agent may extract knowledge, combine it with other knowledge received from other agents, inject it back, and continue training. In this way, the agent performs several train-extract-fix-inject cycles, in order to boost its performance w.r.t. the target task. In principle, at every new cycle, the extracted knowledge is more and more accurate in describing how to approach the task, because the predictor itself is more and more accurate in its prediction due to better new prior knowledge.
A CoTL system is a MAS where agents can retrieve knowledge about several tasks from other agents and provide knowledge to others when requested. Unlike simple CoL systems, agents in CoTL systems may exploit knowledge (either their own, or other agents’ one) about related tasks to learn novel tasks they were not originally designed for. In other words, the ultimate goal of CoTL systems is to make agents able to “learning to learn”.
Learning to learn [novel tasks] is an extension of the well known definition of ML [ 32] introduced in [33]. More precisely, given: • a set of task = {1, . . . , }, • trainable experience for each task {1, . . . , } = ℰ (e.g., ML predictors or symbolic knowledge bases), and • a performance measure for each task {1, . . . , } s.t. : × ℰ → R, a computational agent is capable of learning to learn when each increases as a function of all items in ℰ , and well as .
Relevant practical aspects about CoTL concern when and how to transfer experience. Concerning the ‘when’, humans should not intervene in the process and arbitrary choose which tasks is correlated with the others—as it would be infeasible. Therefore, agents must also be endowed with the ability of computing similarity among diferent tasks. The choice of which one(s) use is up to the designer (e.g., similarity based, distance based, etc.) or it could be also be treated as a task to learn. The interested reader may find useful insights in [29].
Let us now focus on ‘how’ to transfer experience. If an agent is dealing with homogeneous tasks (that is, tasks with the same input and output space but diferent data distributions), it can easily use the knowledge of one task while addressing the other. Instead, heterogeneous tasks are diferent beasts: they can difer in both input and output features—and there may also be no overlap at all. Consider for instance the case of two heterogeneous classification tasks 1 and 2, for which an agent owns experience in the form of logic knowledge bases 1 and 2 composed by Horn clauses. That agent may then transfer knowledge from one task to the other via the following procedure: 1. if there exist some rule ∈ 1 ∪ 2 s.t. both the head and the body of only refer to input features shared and classes which are shared among 1 and 2, then the rule can be used as-is; 2. if the body of refers to shared input features and the head targets to classes which are either 1- or 2-specific, then the rule could be used anyway by some SKI algorithm (e.g., [34]) otherwise it is necessary to find a mapping between the specific classes of the two tasks if it exists (e.g., just renaming, linear dependencies with other labels, etc.); 3. finally, if both shared and task-specific features are referred in , one could: a) relax the rule (e.g., considering only terms involving shared features) then go to step 1; b) find a mapping between task-specific features of the two tasks [ 31], then go to step 1; c) if none of the previous step are possible (e.g., resulting in empty body), then ignore the rule.
A similar procedure can be applied for other sorts of task (e.g., regression) and adapted to deal with other form of knowledge representations.
Figure 1b shows a general design for a CoTL agent. In the same way as for CoL systems, multiple SKE and SKI algorithms must be available for each agent in order to exploit symbolic knowledge.
In addition to CoL, the core component of a CoTL agent is the task similarity score. Accordingly, we assume designers provide a function : 2 → R≥ 0, where is the task space, to evaluate the degree of similarity between two tasks.
Another relevant design aspect of CoTL is the criterion for selecting knowledge for related tasks. For instance, designers may leverage threshold-based approach selecting the knowledge of all the tasks having a score greater than the threshold. Alternatively, one can use the knowledge of the most related tasks.
The joint exploitation of symbolic and sub-symbolic knowledge representation means, as well as knowledge manipulation tools, to build MAS that miminc humans’ knowledge sharing capabilities is a promising research direction. It has the potential to overcome current limitation from the state of the art, such as: (i) TL considers sub-symbolic knowledge representation but not symbolic one therefore it is not human interpretable; (ii) MTL has to train a predictor on related tasks at the same time implying intrinsic dificulties to scale, moreover (iii) it is currently tailored on sub-symbolic knowledge alone.
CoL and CoTL systems can bring a great impulse in the study and developing of intelligent systems. A non-exhaustive list of advantages of CoL and CoTL are: (i) they could provide more and more accurate human-interpretable explanation for a task; (ii) they may increase the performance of an agent/predictor in solving a single task; (iii) the improvement of one agent in solving a task should lead other agents to improve; (iv) the improvement on one task could lead towards the improvement of other tasks; (v) learning is a continuous and automated process that does not require human intervention.
However, there are a number of challenges to be addressed for research on CoL and CoTL to proceed. First, in spite of the many algorithms proposed into the literature so far, running implementation of SKE and SKI algorithms are rare. Second, the choice of how to deal with task similarity in CoTL is not trivial and can afect the performance of the whole system. Third, trust should be taken into account, eventually. How good is the knowledge that an agent is receiving? What is the reputation of an agent? Finally, there is still the need for datasets – probably smaller ones w.r.t. not using CoL and CoTL – to successfully train predictors on new tasks. Indeed, humans can perform new tasks quite well even with just an explanation of how to do it and without explicit training (e.g., play a new game). Achieving such ability would be a big jump towards artificial general intelligent systems.
Summarising, this paper introduces novel concepts of Cooperative Learning and Cooperative Transfer Learning within the scope of MAS. These systems integrate both symbolic and subsymbolic knowledge representation and manipulation tools to mimic the learning process of the human society. The paper proposes a general agent architecture for both CoL and CoTL and discusses about advantages and limits.
This preliminary work is a forerunner for empirical future works on CoL and CoTL. Proceeding by crescent complexity, the first works will address CoL: starting from a train-extract-fix-inject local workflow and then perform tests on a whole MAS. The next step will be investigating CoTL systems and a new kind of CoTL MAS capable of learn a new task without the explicit need of a dataset.
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