Symbolic Deep Learning Explained

Meanwhile, the learned visual concepts facilitate learning new words and parsing new sentences. We use curriculum learning to guide searching over the large compositional space of images and language. Extensive experiments demonstrate the accuracy and efficiency of our model on learning visual concepts, word representations, and semantic parsing of sentences. Further, our method allows easy generalization to new object attributes, compositions, language concepts, scenes and questions, and even new program domains. It also empowers applications including visual question answering and bidirectional image-text retrieval. Combining symbolic reasoning with deep neural networks and deep reinforcement learning may help us address the fundamental challenges of reasoning, hierarchical representations, transfer learning, robustness in the face of adversarial examples, and interpretability (or explanatory power).

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. 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.

Symbolic Artificial Intelligence

Third, it is symbolic, with the capacity of performing causal deduction and generalization. Fourth, the symbols and the links between them are transparent to us, and thus we will know what it has learned or not – which is the key for the security of an AI system. We present the details of the model, the algorithm powering its automatic learning ability, and describe its usefulness in different use cases.

”, the answer will be that an apple is “a fruit,” “has red, yellow, or green color,” or “has a roundish shape.” These descriptions are symbolic because we utilize symbols (color, shape, kind) to describe an apple. 4 shows the percent of correct equations from 20 iterations of the same configuration, along with the normalized computational time for each case. The normalization was performed by dividing the time it took to complete each experiment by the time it took to complete the experiment with no added domain knowledge. As expected, the more knowledge added to guide the search, the more the success rate increases and the computational time decreases.

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.

Experimental design

To do so, GP-GOMEA prevents bloat by implementing a strict constraint on equation length. In addition, to maintain the accuracy of the equation, the system estimates what patterns to propagate. This is done by performing variation based on the linkage model, to capture genotypic interdependencies. Because a short yet accurate equation is needed in many physical use cases, GP-GOMEA has been adapted in several physical regression efforts75,76. This is despite the fact that it does not consider any domain knowledge or physical requirements aside from interoperability. And while these concepts are commonly instantiated by the computation of hidden neurons/layers in deep learning, such hierarchical abstractions are generally very common to human thinking and logical reasoning, too.

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.

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 symbolic learning 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.

In addition, several artificial intelligence companies, such as Teknowledge and Inference Corporation, were selling expert system shells, training, and consulting to corporations. One of the main stumbling blocks of symbolic AI, or GOFAI, was the difficulty of revising beliefs once they were encoded in a rules engine. Expert systems are monotonic; that is, the more rules you add, the more knowledge is encoded in the system, but additional rules can’t undo old knowledge. Monotonic basically means one direction; i.e. when one thing goes up, another thing goes up.

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.

This experiment (experiment C) is intended to demonstrate the contribution of the LV-based SR and its robustness to noise. This result means SciMED could correctly estimate the gravitational acceleration from noisy data, a difficult task by itself99. In experiment D, we demonstrate how the AutoML component may alert the user that a parameter of crucial importance is missing. To do so, we evaluated SciMED on a dataset with non-linear feature relations that is missing one essential feature. This experiment mimics a reasonable scenario in scientific research, where a researcher assumes to know all the parameters governing a phenomenon but neglects to consider (at least) one.

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.

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.

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.

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.

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.

Using symbolic knowledge bases and expressive metadata to improve deep learning systems. Metadata that augments network input is increasingly being used to improve deep learning system performances, e.g. for conversational agents. Metadata are a form of formally represented background knowledge, for example a knowledge base, a knowledge graph or other structured background knowledge, that adds further information or context to the data or system. You can foun additiona information about ai customer service and artificial intelligence and NLP. In its simplest form, metadata can consist just of keywords, but they can also take the form of sizeable logical background theories.

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.

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.

Google made a big one, too, which is what provides the information in the top box under your query when you search for something easy like the capital of Germany. These systems are essentially piles of nested if-then statements drawing conclusions about entities (human-readable concepts) and their relations (expressed in well understood semantics like X is-a man or X lives-in Acapulco). Symbolic AI is a sub-field of artificial intelligence that focuses on the high-level symbolic (human-readable) representation of problems, logic, and search. For instance, if you ask yourself, with the Symbolic AI paradigm in mind, “What is an apple?

They can simplify sets of spatiotemporal constraints, such as those for RCC or Temporal Algebra, along with solving other kinds of puzzle problems, such as Wordle, Sudoku, cryptarithmetic problems, and so on. Constraint logic programming can be used to solve scheduling problems, for example with constraint handling rules (CHR). Multiple different approaches to represent knowledge and then reason with those representations have been investigated. Below is a quick overview of approaches to knowledge representation and automated reasoning. Its history was also influenced by Carl Hewitt’s PLANNER, an assertional database with pattern-directed invocation of methods. Expert systems can operate in either a forward chaining – from evidence to conclusions – or backward chaining – from goals to needed data and prerequisites – manner.

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.

More advanced knowledge-based systems, such as Soar can also perform meta-level reasoning, that is reasoning about their own reasoning in terms of deciding how to solve problems and monitoring the success of problem-solving strategies. While we cannot give the whole neuro-symbolic AI field due recognition in a brief overview, we have attempted to identify the major current research directions based on our survey of recent literature, and we present them below. Literature references within this text are limited to general overview articles, but a supplementary online document referenced at the end contains references to concrete examples from the recent literature. Examples for historic overview works that provide a perspective on the field, including cognitive science aspects, prior to the recent acceleration in activity, are Refs [1,3]. This page includes some recent, notable research that attempts to combine deep learning with symbolic learning to answer those questions.

Furthermore, the deduction of an accurate prefactor, linked to the gravitational acceleration constant, from data with Gaussian noise poses a known challenge to SR99 that SciMED and GP-GOMEA succeeded at. Experiment D mimicked a scenario in which the user might fail to enter all the needed variables to explain the target. In such a case, an SR system should report its failure to converge to an equation of reasonable length rather than report a bloated equation of tens of variables that fails to generalize100.

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.

Symbolic artificial intelligence

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.

This component can be initialized several times with different initial populations. After all the runs are finished, the stability of the outcomes is tested in two ways. First, the standard deviation of a selected performance metric is evaluated to identify whether it’s converging. Second, equations from each run are compared to check whether a particular equation is repeated in a minimum \(\chi \in [0, 1]\)) percentage of the runs (\(\chi\) us user-defined). In addition, this component of SciMED sheds light on the feature groups selected by the user84,85,86, providing physical insight before obtaining symbolic expressions.

It is encouraged to provide SciMED with non-dimensional datasets, meaning that the user performed the dimensional analysis independently. This is because it guarantees that the units of the target variable agree with the units obtained by the solution. Additionally, during the independent analysis, the user can construct non-dimensional ratios known or suspected to be informative about the target that might not result from an automatic analysis. It is constructed from four components that each can be independently switched off or on. Theoretical knowledge or hypothesis can be entered at five input junctions, affecting the equation SciMED finds. We note that this was the state at the time and the situation has changed quite considerably in the recent years, with a number of modern NSI approaches dealing with the problem quite properly now.

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.

The purpose of this paper is to generate broad interest to develop it within an open source project centered on the Deep Symbolic Network (DSN) model towards the development of general AI. So, if you use unassisted machine learning techniques and spend three times the amount of money to train a statistical model than you otherwise would on language understanding, you may only get a five-percent improvement in your specific use cases. That’s usually when companies realize unassisted supervised learning techniques are far from ideal for this application. In the paper, we show that we find the correct known equations, including force laws and Hamiltonians, can be extracted from the neural network.

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.

• Statistical machine learning, originally targeting “narrow” problems, such as regression and classification, has begun to penetrate the AI field.
• Again, this stands in contrast to neural nets, which can link symbols to vectorized representations of the data, which are in turn just translations of raw sensory data.
• 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.
• The DSN model provides a simple, universal yet powerful structure, similar to DNN, to represent any knowledge of the world, which is transparent to humans.
• In experiment B, all systems correctly identified the two out of the 33 variables appearing in the equation and their algebraic relation.
• It dates all the way back to 1943 and the introduction of the first computational neuron [1].

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.

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.

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.