What is SYMBOLIC LEARNING THEORY? definition of SYMBOLIC LEARNING THEORY Psychology Dictionary

For example, they require very large datasets to work effectively, entailing that they are slow to learn even when such datasets are available. Moreover, they lack the ability to reason on an abstract level, which makes it difficult to implement high-level cognitive functions such as transfer learning, analogical reasoning, and hypothesis-based reasoning. Finally, their operation is largely opaque to humans, rendering them unsuitable for domains in which verifiability is important. In this paper, we propose an end-to-end reinforcement learning architecture comprising a neural back end and a symbolic front end with the potential to overcome each of these shortcomings.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. ArXiv is committed to these values and only works with partners that adhere to them. McCarthy’s approach to fix the frame problem was circumscription, a kind of non-monotonic logic where deductions could be made from actions that need only specify what would change while not having to explicitly specify everything that would not change. Other non-monotonic logics provided truth maintenance systems that revised beliefs leading to contradictions. A similar problem, called the Qualification Problem, occurs in trying to enumerate the preconditions for an action to succeed.

For example, SRFC64 uses GA to verify the candidate solutions by the given structural constraints such as symmetry, monotonicity or convexity, or knowledge constraints such as logical range of the result, its slope, or boundary conditions. Our researchers are working to usher in a new era of AI where machines can learn more like the way humans do, by connecting words with images and mastering abstract concepts. However, the black-box nature of classic neural models, with most confirmations on their learning abilities being done empirically rather than analytically, renders some direct integration with the symbolic systems, possibly providing the missing capabilities, rather complicated. The key AI programming language in the US during the last symbolic AI boom period was LISP.

Meanwhile, with the progress in computing power and amounts of available data, another approach to AI has begun to gain momentum. Statistical machine learning, originally targeting “narrow” problems, such as regression and classification, has begun to penetrate the AI field. And while the current success and adoption of deep learning largely overshadowed the preceding techniques, these still have some interesting capabilities to offer. In this article, we will look into some of the original symbolic AI principles and how they can be combined with deep learning to leverage the benefits of both of these, seemingly unrelated (or even contradictory), approaches to learning and AI.

Marvin Minsky first proposed frames as a way of interpreting common visual situations, such as an office, and Roger Schank extended this idea to scripts for common routines, such as dining out. Cyc has attempted to capture useful common-sense knowledge and has “micro-theories” to handle particular kinds of domain-specific reasoning. The logic clauses that describe programs are directly interpreted to run the programs specified. No explicit series of actions is required, as is the case with imperative programming languages.

It dates all the way back to 1943 and the introduction of the first computational neuron [1]. Stacking these on top of each other into layers then became quite popular in the 1980s and ’90s already. However, at that time they were still mostly losing the competition against the more established, and better theoretically substantiated, learning models like SVMs.

The current state-of-the-art SR system in physics is the so-called AI Feynman system 66. AI Feynman combines neural network fitting with a recursive algorithm that decomposes the initial problem into simpler ones. Meaning that, suppose the problem is not directly solvable by polynomial fitting or brute-force search.

Advantages of multi-agent systems include the ability to divide work among the agents and to increase fault tolerance when agents are lost. Research problems include how agents reach consensus, distributed problem solving, multi-agent learning, multi-agent planning, and distributed constraint optimization. In contrast to the US, in Europe the key AI programming language during that same period was Prolog. Prolog provided a built-in store of facts and clauses that could be queried by a read-eval-print loop.

SciMED combines a wrapper selection method, that is based on a genetic algorithm, with automatic machine learning and two levels of SR methods. We test SciMED on five configurations of a settling sphere, with and without aerodynamic non-linear drag force, and with excessive noise in the measurements. We show that SciMED is sufficiently robust to discover the correct physically meaningful symbolic expressions from the data, and demonstrate how the integration of domain knowledge enhances its performance. Our results indicate better performance on these tasks than the state-of-the-art SR software packages , even in cases where no knowledge is integrated.

An infinite number of pathological conditions can be imagined, e.g., a banana in a tailpipe could prevent a car from operating correctly. The General Problem Solver (GPS) cast planning as problem-solving used means-ends analysis to create plans. Graphplan takes a least-commitment approach to planning, rather than sequentially choosing actions from an initial state, working forwards, or a goal state if working backwards. Satplan is an approach to planning where a planning problem is reduced to a Boolean satisfiability problem. Similarly, Allen’s temporal interval algebra is a simplification of reasoning about time and Region Connection Calculus is a simplification of reasoning about spatial relationships. A more flexible kind of problem-solving occurs when reasoning about what to do next occurs, rather than simply choosing one of the available actions.

SciMED’s design allows the user to integrate knowledge into the search and optimization process in five distinct but related places, as shown in Fig. 1, alongside a reach set of hyperparameters that can be customized to direct the search efforts and their computational resources. Here fundamental knowledge is expressed as simple mathematical or logical constraints that can be bounded to specific parameters or ranges. Opposed to the structure-related methods, the user gains the power to choose if and where to apply any function-structure assumption. Nonetheless, as opposed to the physical law’s methods, the user loses the ability to apply complex laws such as the first principles.

This perception persists mostly because of the general public’s fascination with deep learning and neural networks, which several people regard as the most cutting-edge deployments of modern AI. Neuro symbolic reasoning and learning is a topic that combines ideas from deep neural networks with symbolic reasoning and learning to overcome several significant technical hurdles such as explainability, modularity, verification, and the enforcement of constraints. While neuro symbolic ideas date back to the early 2000’s, there have been significant advances in the last 5 years.

The second AI summer: knowledge is power, 1978–1987

Second, we tested the ability of SciMED to find a linear equation from a vast dataset of tens of features (experiment B). This experiment aims to demonstrate the contribution of the a priori feature selection component by incorporating domain knowledge and reducing the search space. Third, we examined the ability of SciMED to find a non-linear equation from data with noise and a large number of features (compared to the average number of features in a benchmark set of 100 physical equations66).

Perhaps surprisingly, the correspondence between the neural and logical calculus has been well established throughout history, due to the discussed dominance of symbolic AI in the early days. Programs were themselves data structures that other programs could operate on, allowing the easy definition of higher-level languages. Our chemist was Carl Djerassi, inventor of the chemical behind the birth control pill, and also one of the world’s most respected mass spectrometrists. We began to add to their knowledge, inventing knowledge of engineering as we went along.

Rescuing Machine Learning with Symbolic AI for Language Understanding

1) Hinton, Yann LeCun and Andrew Ng have all suggested that work on unsupervised learning (learning from unlabeled data) will lead to our next breakthroughs. Symbolic artificial intelligence, also known as Good, Old-Fashioned AI (GOFAI), was the dominant paradigm in the AI community from the post-War era until the late 1980s. Buoyed by the demand for their offerings, the Foundation opened a new education center at the 27,000-acre El Sauz ranch in 2022. A large main pavilion serves as a receiving and congregation space, complementing the six smaller pavilions that serve as learning stations positioned along a walking trail winding around the education center. Each of the Foundation’s educators specialize in the Texas science curriculum, helping K-12 students understand the practical application of what they study in textbooks.

So how do we make the leap from narrow AI systems that leverage reinforcement learning to solve specific problems, to more general systems that can orient themselves in the world? Enter Tim Rocktäschel, a Research Scientist at Facebook AI Research London and a Lecturer in the Department of Computer Science at University College London. Much of Tim’s work has been focused on ways to make RL agents learn with relatively little data, using strategies known as sample efficient learning, in the hopes of improving their ability to solve more general problems. Similar to the problems in handling dynamic domains, common-sense reasoning is also difficult to capture in formal reasoning. Examples of common-sense reasoning include implicit reasoning about how people think or general knowledge of day-to-day events, objects, and living creatures. In contrast, a multi-agent system consists of multiple agents that communicate amongst themselves with some inter-agent communication language such as Knowledge Query and Manipulation Language (KQML).

• For instance, if you ask yourself, with the Symbolic AI paradigm in mind, “What is an apple?
• Meaning that, suppose the problem is not directly solvable by polynomial fitting or brute-force search.
• Stacking these on top of each other into layers then became quite popular in the 1980s and ’90s already.

Opposed to other physics-informed SR systems, this means that SciMED does not attempt to apply general rules for all physical SR tasks but instead allows the scientist to direct the search process with more precise information. This leads to more credible results and reduces the computational time and resources required by SciMED compared to other SR systems. It also aids in formulating an accurate symbolic expression even from data that contains high noise levels. Additionally, SciMED offers a novel a-priori feature selection process that enables scientists to test different hypotheses efficiently. Discovering a meaningful symbolic expression that explains experimental data is a fundamental challenge in many scientific fields. We present a novel, open-source computational framework called Scientist-Machine Equation Detector (SciMED), which integrates scientific discipline wisdom in a scientist-in-the-loop approach, with state-of-the-art symbolic regression (SR) methods.

The process of automating SR faces multiple challenges, such as an exponentially sizeable combinatorial space of symbolic expressions leading to a slow convergence speed in many real-world applications33 or increased sensitivity to overfitting stemming from unjustifiably long program length34. For instance, one prominent idea was to encode the (possibly infinite) interpretation structures of a logic program by (vectors of) real numbers and represent the relational inference as a (black-box) mapping between these, based on the universal approximation theorem. However, this assumes the unbound relational information to be hidden in the unbound decimal fractions of the underlying real numbers, which is naturally completely impractical for any gradient-based learning.

Combining Deep Neural Nets and Symbolic Reasoning

The Defense Advance Research Projects Agency (DARPA) launched programs to support AI research to use AI to solve problems of national security; in particular, to automate the translation of Russian to English for intelligence operations and to create autonomous tanks for the battlefield. By the mid-1960s neither useful natural language translation systems nor autonomous tanks had been created, and a dramatic backlash set in. Implementations of symbolic reasoning are called rules engines or expert systems or knowledge graphs.

This idea has also been later extended by providing corresponding algorithms for symbolic knowledge extraction back from the learned network, completing what is known in the NSI community as the “neural-symbolic learning cycle”. These old-school parallels between individual neurons and logical connectives might seem outlandish in the modern context of deep learning. However, given the aforementioned recent evolution of the neural/deep learning concept, the NSI field is now gaining more momentum than ever. When deep learning reemerged in 2012, it was with a kind of take-no-prisoners attitude that has characterized most of the last decade. He gave a talk at an AI workshop at Stanford comparing symbols to aether, one of science’s greatest mistakes. Constraint solvers perform a more limited kind of inference than first-order logic.

Imagine how Turbotax manages to reflect the US tax code – you tell it how much you earned and how many dependents you have and other contingencies, and it computes the tax you owe by law – that’s an expert system.

In this experiment, the prefactor is linked to a physical constant – the gravitational acceleration \(g\) (for an explanation, see Appendix). Therefore, SciMED’s identification of a prefactor within a 0.76% error means it could accurately learn the value of \(g\) used to construct the target from noisy data. For experiment D, the combination of good performance overall metrics by the AutoML component and poor performance overall metrics by the LV-SR component indicates that at least one dependent variable needs to be added to the dataset. This is because, on the one hand, the performance scores suggest that AutoML accurately learned the necessary information from the given variables. However, on the other hand, the robust SR component failed to find an equation that remotely describes the data (as seen by the zero-valued T-test’s \(p\) value). Hence no accurate equation can be formulated with the given variables, meaning at least one variable is missing from the equation.

We then apply our method to a non-trivial cosmology example-a detailed dark matter simulation-and discover a new analytic formula which can predict the concentration of dark matter from the mass distribution of nearby cosmic structures. The symbolic expressions extracted from the GNN using our technique also generalized to out-of-distribution data better than the GNN itself. Our approach offers alternative directions for interpreting neural networks and discovering novel physical principles from the representations they learn.

NSI has traditionally focused on emulating logic reasoning within neural networks, providing various perspectives into the correspondence between symbolic and sub-symbolic representations and computing. Historically, the community targeted mostly analysis of the correspondence and theoretical model expressiveness, rather than practical learning applications (which is probably why they have been marginalized by the mainstream research). Henry Kautz,[18] Francesca Rossi,[80] and Bart Selman[81] have also argued for a synthesis. Their arguments are based on a need to address the two kinds of thinking discussed in Daniel Kahneman’s book, Thinking, Fast and Slow.

For example, SR can adhere to a specific shape of the solution 49,50,51,52, or utilize probabilistic models to sample grammar of rules that determine how solutions are generated 53,54,55,56. It begins by building a population of naive random formulas representing a relationship between known independent variables (features) and targets (dependent variables) as tree-like structures. Then, in a stochastic optimization process, it performs replacement and recombination of the sub-trees, evaluating the fitness by executing the trees and assessing their output, and stochastic survival of the fittest. This method performs well on linear real-world problems37 and can be easily manipulated as a base for more complex systems. For other AI programming languages see this list of programming languages for artificial intelligence. Currently, Python, a multi-paradigm programming language, is the most popular programming language, partly due to its extensive package library that supports data science, natural language processing, and deep learning.

Furthermore, these systems tend to overfit given large and noisy data41, which is the case of typical empirical results in physics. Two main methods to overcome the computational expense are performed by42,43, where they apply a brute-force approach on a reduced search space rather than perform an incomplete search in the entire search space. In both methods, the search space is reduced by removing algebraically equivalent expressions, either through the recursive application of the grammar production rules42 or by preventing semantic duplicates using grammar restrictions and semantic hashing43. SR can be especially useful in physics35, frequently dealing with multivariate noisy empirical data from nonlinear systems with unknown laws36. Moreover, the SR’s output must retain dimensional homogeneity, meaning all terms in SR expression have to carry the same dimensional units.

We expect it to heat and possibly boil over, even though we may not know its temperature, its boiling point, or other details, such as atmospheric pressure. Cognitive architectures such as ACT-R may have additional capabilities, such as the ability to compile frequently used knowledge into higher-level chunks. Japan championed Prolog for its Fifth Generation Project, intending to build special hardware for high performance. Similarly, LISP machines were built to run LISP, but as the second AI boom turned to bust these companies could not compete with new workstations that could now run LISP or Prolog natively at comparable speeds. Time periods and titles are drawn from Henry Kautz’s 2020 AAAI Robert S. Engelmore Memorial Lecture[18] and the longer Wikipedia article on the History of AI, with dates and titles differing slightly for increased clarity.

Predictions acquired with the ML pipeline found in the AutoML component versus the true target value. Lines represent the regression, and the respective equation is shown in the legend. As a final experiment (experiment G), we performed robustness or noise analysis, demonstrating SciMED’s performance in the presence of three different types of noise and at various noise levels.

New deep learning approaches based on Transformer models have now eclipsed these earlier symbolic AI approaches and attained state-of-the-art performance in natural language processing. However, Transformer models are opaque and do not yet produce human-interpretable semantic representations for sentences and documents. Instead, they produce task-specific vectors where the meaning of the vector components is opaque.

An algorithm to optimize explainability using feature ensembles

Hence, it is expected that researchers could regularly use the SITL approach in their domain of expertise, or collaborate with others that can do so104. Finally, in experiment E, we highlight the competitiveness of the LV-based SR component by identifying a non-linear equation from a highly noisy dataset, that requires choosing 4 out of 12 features that range in similar values. In this task SciMED is the only system that accurately detects the correct features and their algebraic relation. In the next two cases (experiments C-D), we emphasized the contribution of the LV-based SR and AutoML components. In experiment C, SciMED significantly outperformed AI Feynman by finding the correct equation within a 0.76% error of the numerical prefactor, compared to AI Feynman that converged to a false equation (as summarized in Table 3).

Deep learning has its discontents, and many of them look to other branches of AI when they hope for the future. In support of the initiative, Enbridge recently awarded the Foundation a Fueling Futures grant of $15,000 to fund a learning station. The next covers the ranch’s watershed and the importance of protecting the health of nearby bays and estuaries. Another delves into the conservation of native plants and wildlife, such as the endangered ocelot, a spotted wild cat found near the Gulf of Mexico. Monarchs are projected to leave the Monarch Butterfly Biosphere Reserve over the next few weeks.

SR methods

In general, language model techniques are expensive and complicated because they were designed for different types of problems and generically assigned to the semantic space. Techniques like BERT, for instance, are based on an approach that works better for facial recognition or image recognition than on language and semantics. The SR results of SciMED are presented in Table 3 alongside those of AI Feynman and GP-GOMEA. In experiment A, all systems found the unknown equation despite the noise applied to the target.

In experiment F, we perform SR on experiment E, this time adding different types of domain knowledge. The information provided helps SciMED to increase its success rate from 65% percent of the time to 100%, while decreasing the computational time expense. 4 demonstrates that each type of domain knowledge affects the success rate to a different extent, but all kinds of information (even if they contain partially incorrect assumptions) improve it. In the first two cases (experiments A-B), we highlight the contribution of the GA-based SR and feature selection components.

Particularly, we will show how to make neural networks learn directly with relational logic representations (beyond graphs and GNNs), ultimately benefiting both the symbolic and deep learning approaches to ML and AI. Parsing, tokenizing, spelling correction, part-of-speech tagging, noun and verb phrase chunking are all aspects of natural language processing long handled by symbolic AI, but since improved by deep learning approaches. In symbolic AI, discourse representation theory and first-order logic have been used to represent sentence meanings. Latent semantic analysis (LSA) and explicit semantic analysis also provided vector representations of documents. In the latter case, vector components are interpretable as concepts named by Wikipedia articles.

This work presents SciMED, a novel SR system that combines the latest computational frameworks with a scientist-in-the-loop approach. This way, SciMED emphasizes knowledge specific to its current task to direct its SR efforts. It is constructed of four components that can be switched on or off independently to suit user needs. In addition, it allows users to easily introduce domain knowledge to improve accuracy and reduce computational time. To the best of our knowledge, allowing users to set distinct pairwise sets for the feature selection process is an unprecedented method of physical hypothesis evaluation that enables users to efficiently examine multiple hypotheses without increasing the SR search space. Thus, feature groups are a new and efficient way for researchers to explore several theories of the variables governing unknown dynamics that are otherwise unfeasible due to complex interactions between different feature groups.

In experiment B, all systems correctly identified the two out of the 33 variables appearing in the equation and their algebraic relation. However, SciMED found a numerical prefactor smaller by 0.02 than the actual value and added a constant term of 0.03, compared to AI Feynman and GP-GOMEA, which found a prefactor with an error of 0.33 and 0.05, and did not add a constant term. We evaluated SciMED on seven different experiments, testing its competitiveness against AI Feynman and GP-GOMEA on highly noisy data, demonstrating the contribution of knowledge integration, and evaluating its resistance to noise.

The second group of methods, the physical laws search space reduction, emphasizes the fundamental laws that any feasible solution should comply with. In contrast, the SR system LGGA62 reduces the search space with more specific physical knowledge formulated as mathematical constraints. Another example is the Multi-objective SR system for dynamic models63, which considers knowledge about steady-state characteristics or local behavior to direct the search efforts towards a logical result. You can foun additiona information about ai customer service and artificial intelligence and NLP. While the aforementioned correspondence between the propositional logic formulae and neural networks has been very direct, transferring the same principle to the relational setting was a major challenge NSI researchers have been traditionally struggling with.

Coupling may be through different methods, including the calling of deep learning systems within a symbolic algorithm, or the acquisition of symbolic rules during training. Neuro-symbolic AI has a long history; however, it remained a rather niche topic until recently, when landmark advances in machine learning—prompted by deep learning—caused a significant rise in interest and research activity in combining neural and symbolic methods. In this overview, we provide symbolic learning a rough guide to key research directions, and literature pointers for anybody interested in learning more about the field. The first five experiments are designed to highlight the importance of different components in SciMED. First, we assessed SciMED ability to detect linear relations between features from scarce and noisy data (experiment A). Here, we aim to highlight the contribution of the GA-based SR component and its ability to perform SR efficiently.

Neuro-symbolic artificial intelligence can be defined as the subfield of artificial intelligence (AI) that combines neural and symbolic approaches. By symbolic we mean approaches that rely on the explicit representation of knowledge using formal languages—including formal logic—and the manipulation of language items (‘symbols’) by algorithms to achieve a goal. Though these methods provide promising results, they do not consider valuable domain knowledge that their expert users (from now on referred to as scientists) can provide to help direct the regression efforts. The novelty of the proposed work lies in the straightforward integration of domain knowledge, specific to the current SR task, by using several input junctions throughout the system’s pipeline.

In supervised learning, those strings of characters are called labels, the categories by which we classify input data using a statistical model. The output of a classifier (let’s say we’re dealing with an image recognition algorithm that tells us whether we’re looking at a pedestrian, a stop sign, a traffic lane line or a moving semi-truck), can trigger business logic that reacts to each classification. As I indicated earlier, symbolic AI is the perfect solution to most machine learning shortcomings for language understanding. It enhances almost any application in this area of AI like natural language search, CPA, conversational AI, and several others. Not to mention the training data shortages and annotation issues that hamper pure supervised learning approaches make symbolic AI a good substitute for machine learning for natural language technologies. Sparse regression systems can substantially reduce the search space of all possible functions by identifying parsimonious models using sparsity-promoting optimization.