Symbolic Logic Meets Machine Learning: A Brief Survey in Infinite Domains SpringerLink

We have also evaluated CGBE on realistic examples of code generation tasks, to establish that it is effective for such tasks. One area where there have been particular problems for industrial users of MDE is in the definition and maintenance of code generators [32]. MDE code generation has potentially high benefits in reducing the cost of code production, and in improving code quality by ensuring that a systematic architectural approach is used in system implementations. However, the manual construction of such code generators can involve substantial effort and require specialised expertise in the transformation languages used. For example, several person-years of work were required for the construction of one UML to Java code generator [7]. One such project is the Neuro-Symbolic Concept Learner (NSCL), a hybrid AI system developed by the MIT-IBM Watson AI Lab.

Therefore, in this study, we employed interpretable machine learning to probe complex associations between 17 subjective art-attributes and creativity judgments across a diverse range of artworks. A cohort of 78 non-art expert participants assessed 54 artworks varying in styles and motifs. The applied Random Forests regressor models accounted for 30% of the variability in creativity judgments given our set of art-attributes. Our analyses revealed symbolism, emotionality, and imaginativeness as the primary attributes influencing creativity judgments. Abstractness, valence, and complexity also had an impact, albeit to a lesser degree. Notably, we observed non-linearity in the relationship between art-attribute scores and creativity judgments, indicating that changes in art-attributes did not consistently correspond to changes in creativity judgments.

Deep learning and neuro-symbolic AI 2011–now

It is about optimizing models that are capable of learning from huge amounts of data. Examples are computer vision algorithms for image recognition and general-purpose models like support vector machines and neural networks. Symbolic regression is an alternative to these methods that works by finding explicit formulas that connect the variables, allowing hidden nonlinear patterns to be uncovered.

Within my staging Google document for Substack posts I reached the end of the originally planned out posts for this series of content. Earlier this morning I expanded the staging shell post outlines to week 104 which as you can imagine is a significant point in the publication lifecycle. I have enough content in the backlog for this Substack series to get to week 120.

Computer Science > Symbolic Computation

The optimization procedures for the MLC variants in Table 1 are described below. However, M2M and M2T approaches require the definition of a source metamodel, which may not exist, for example, in the case of a DSL defined by a grammar. For these reasons, we decided to focus on learning T2T code generators, rather than M2M or M2T generators, as the goal of our research.

In our experiments, we found that the most common human responses were algebraic and systematic in exactly the ways that Fodor and Pylyshyn1 discuss. However, people also relied on inductive biases that sometimes support the algebraic solution and sometimes deviate from it; indeed, people are not purely algebraic machines3,6,7. We showed how MLC enables a standard neural network optimized for its compositional skills to mimic or exceed human systematic generalization in a side-by-side comparison. MLC shows much stronger systematicity than neural networks trained in standard ways, and shows more nuanced behaviour than pristine symbolic models. MLC also allows neural networks to tackle other existing challenges, including making systematic use of isolated primitives11,16 and using mutual exclusivity to infer meanings44.

There have been several efforts to create complicated symbolic AI systems that encompass the multitudes of rules of certain domains. Called expert systems, these symbolic AI models use hardcoded knowledge and rules to tackle complicated tasks such as medical diagnosis. But they require a huge amount of effort by domain experts and software engineers and only work in very narrow use cases. As soon as you generalize the problem, there will be an explosion of new rules to add (remember the cat detection problem?), which will require more human labor. This is particularly true for problems in a small number of dimensions — symbolic regression is unlikely to be useful for problems like image classification, which would require enormous formulas with millions of input parameters. A shift to explicit symbolic models could bring to light many hidden patterns in the sea of datasets that we have at our disposal today.

Set 2 has 10 examples, used as Query examples for most MLC variants (except copy only). Pseudocode for the bias-based transformation process is shown here for the instruction ‘tufa lug fep’. This transformation is applied to the query outputs before MLC and MLC (joint) process them. We chose UML to Java, Kotlin, and C translations as typical of the code generation tasks faced by practitioners. DSLs have been widely used for mobile app specification [5, 13, 31], and the synthesis of SwiftUI is a typical task in this domain.

Bayesian approaches enable a modeller to evaluate different representational forms and parameter settings for capturing human behaviour, as specified through the model’s prior45. These priors can also be tuned with behavioural data through hierarchical Bayesian modelling46, although the resulting set-up can be restrictive. MLC shows how meta-learning can be used like hierarchical Bayesian models for reverse-engineering inductive biases (see ref. 47 for a formal connection), although with the aid of neural networks for greater expressive power. Our research adds to a growing literature, reviewed previously48, on using meta-learning for understanding human49,50,51 or human-like behaviour52,53,54.

In our experiments, only MLC closely reproduced human behaviour with respect to both systematicity and biases, with the MLC (joint) model best navigating the trade-off between these two blueprints of human linguistic behaviour. Furthermore, MLC derives its abilities through meta-learning, where both systematic generalization and the human biases are not inherent properties of the neural network architecture but, instead, are induced from data. On SCAN, MLC solves three systematic generalization splits with an error rate of 0.22% or lower (99.78% accuracy or above), including the already mentioned ‘add jump’ split and ‘around right’ and ‘opposite right’, which examine novel combinations of known words. On COGS, MLC achieves an error rate of 0.87% across the 18 types of lexical generalization. Without the benefit of meta-learning, basic seq2seq has error rates at least seven times as high across the benchmarks, despite using the same transformer architecture.

Machine learning models, on the other hand, excels in handling such complexities. Its ability to model intricate patterns and interrelationships in high-dimensional space allows for a more nuanced understanding and prediction of non-linear human behavior, making it a powerful tool in art research. Precise sample size justification (power analysis) for complex machine learning-based data analysis methods is still an open matter, and to the best of our knowledge, no standards have been established. Therefore, we followed a series of available suggestions regarding a reasonable sample size. First, a commonly disputed suggestion is that 50 samples are required to start any meaningful machine learning-based data analysis (scikit-learn ). Second, a controversial suggestion is that 10 to 20 samples per degree of freedom (independent variable, art-attribute) is reasonable, particularly for logistic regression, which would result in a total of 170 to 340 samples needed for our study52.

NSCL uses both rule-based programs and neural networks to solve visual question-answering problems. As opposed to pure neural network–based models, the hybrid AI can learn new tasks with less data and is explainable. And unlike symbolic-only models, NSCL doesn’t struggle to analyze the content of images. Regarding the methods employed, our approach was a combination of RF ensemble regression39 with techniques from the field of interpretable machine learning to gain insights into the associations learned by the model46. With the prediction of creativity judgements ratings as a target of art-attributes, we introduce a comprehensive method and a newly established initial model for art judgment analysis. Other ways of handling more open-ended domains included probabilistic reasoning systems and machine learning to learn new concepts and rules.

We introduce the Deep Symbolic Network (DSN) model, which aims at becoming the white-box version of Deep Neural Networks (DNN). 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. The conjecture behind the DSN model is that any type of real world objects sharing enough common features are mapped into human brains as a symbol. Those symbols are connected by links, representing the composition, correlation, causality, or other relationships between them, forming a deep, hierarchical symbolic network structure. Powered by such a structure, the DSN model is expected to learn like humans, because of its unique characteristics.

• It is noticeable that the training time for C is significantly higher than for the Java or Kotlin code generators, due to the high complexity of the C grammar and the large structural difference between UML/OCL and C; however, the time remains practicable.
• Second, the participants responded to the query instructions all at once, on a single web page, allowing the participants to edit, go back and forth, and maintain consistency across responses.
• Indeed, as Immanuel Kant proposed, visual art is subject to the subjective perception of each viewer while simultaneously encapsulating universal aspects of human experience.
• MLC optimizes the transformers for systematic generalization through high-level behavioural guidance and/or direct human behavioural examples.
• Our research is intended to remove these obstacles by enabling general software practitioners to apply MDE techniques, via the use of simplified notations and by providing AI support for MDE processes.
• Because software languages are generally organised hierarchically into sublanguages, e.g., concerning types, expressions, statements, operations/functions, classes, etc., D will typically be divided into parts corresponding to the main source language divisions.

The four most frequent responses are shown, marked in parentheses with response rates (counts for people and the percentage of samples for MLC). The superscript notes indicate the algebraic answer (asterisks), a one-to-one error (1-to-1) or an iconic concatenation error (IC). The words and colours were randomized for each participant and a canonical assignment is therefore shown here. Optimisation of code generators so that they produce code satisfying various quality criteria is another important area of future work. CGBE strategies would need to be designed to favour the production of code generation rules which result in generated code satisfying the criteria. We used the proportion p of correct translations of an independent validation set to assess the accuracy of synthesised code generators.

A high correlation was found between imaginativeness and symbolism with a coefficient of 0.78, but no correlations above that. These finding still align with our initial hypothesis as the predictors were deliberately chosen to encapsulate the multifaceted and interrelated attributes of artistic creativity3,4,64. The influence of independent variables on the prediction can vary across the range of these variables due to the capacity of RF models to capture non-linear associations between independent and dependent variables.

A T2T approach to code generation specifies the translation from source to target languages in terms of the source and target language concrete syntax or grammars, and does not depend upon metamodels (abstract syntax) of the languages. A T2T author needs to know only the source language grammar and target language syntax, and the T2T language. To summarise our contribution, we have provided a new technique (CGBE) for automating the construction of code generators, via a novel application of symbolic machine learning.

However, the aforementioned models are hard to be used in practical engineering design, because the prediction process of pure data-driven approaches cannot be transformed into a useable mathematical equation for structural engineers. Therefore, data-driven approaches are often regarded as black-box models [30]. Fiber reinforced polymer (FRP)-reinforced concrete slabs, an extension of reinforced concrete (RC) slabs leveraged for resisting environment corrosion, are susceptible to punching shear failure due to the lower elasticity modulus of FRP reinforcement.

• Early work covered both applications of formal reasoning emphasizing first-order logic, along with attempts to handle common-sense reasoning in a less formal manner.
• The study and test items always differed from one another by more than one primitive substitution (except in the function 1 stage, where a single primitive was presented as a novel argument to function 1).
• Below each image, the attribute items and judgments were presented, and participants could scroll down using the mouse while keeping the artwork image fixed on the screen.
• In this study, a hybrid model (e.g., grey-box model) derived from modified compression field theory (MCFT) is proposed by this paper, in which the performance is improved by a machine-learning-aided approach (genetic programming).
• In our experiments, only MLC closely reproduced human behaviour with respect to both systematicity and biases, with the MLC (joint) model best navigating the trade-off between these two blueprints of human linguistic behaviour.

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