Bach in a Box - Real-Time Harmony

We describe a system for learning J. S. Bach's rules of musical harmony. These rules are learned from examples and are expressed as rule-based neural networks. The rules are then applied in real-time to generate new accompanying harmony for a live performer. Real-time functionality imposes constraints on the learning and harmonizing processes, including limitations on the types of information the system can use as input and the amount of processing the system can perform. We demonstrate algorithms for generating and refining musical rules from examples which meet these constraints. We describe a method for including a priori knowledge into the rules which yields significant performance gains. We then describe techniques for applying these rules to generate new music in real-time. We conclude the paper with an analysis of experimental results

Transformers as Soft Reasoners over Language

Beginning with McCarthy's Advice Taker (1959), AI has pursued the goal of providing a system with explicit, general knowledge and having the system reason over that knowledge. However, expressing the knowledge in a formal (logical or probabilistic) representation has been a major obstacle to this research. This paper investigates a modern approach to this problem where the facts and rules are provided as natural language sentences, thus bypassing a formal representation. We train transformers to reason (or emulate reasoning) over these sentences using synthetically generated data. Our models, that we call RuleTakers, provide the first empirical demonstration that this kind of soft reasoning over language is learnable, can achieve high (99%) accuracy, and generalizes to test data requiring substantially deeper chaining than seen during training (95%+ scores). We also demonstrate that the models transfer well to two hand-authored rulebases, and to rulebases paraphrased into more natural language. These findings are significant as it suggests a new role for transformers, namely as limited "soft theorem provers" operating over explicit theories in language. This in turn suggests new possibilities for explainability, correctability, and counterfactual reasoning in question-answering.Comment: IJCAI 202

Fuzzy Rules from Ant-Inspired Computation

Centre for Intelligent Systems and their ApplicationsThis research identifies and investigates major issues in inducing accurate and comprehensible fuzzy rules from datasets.A review of the current literature on fuzzy rulebase induction uncovers two significant issues: A. There is a tradeoff between inducing accurate fuzzy rules and inducing comprehensible fuzzy rules; and, B. A common strategy for the induction of fuzzy rulebases, that of iterative rule learning where the rules are generated one by one and independently of each other, may not be an optimal one.FRANTIC, a system that provides a framework for exploring the claims above is developed. At the core lies a mechanism for creating individual fuzzy rules. This is based on a significantly modified social insect-inspired heuristic for combinatorial optimisation -- Ant Colony Optimisation. The rule discovery mechanism is utilised in two very different strategies for the induction of a complete fuzzy rulebase: 1. The first follows the common iterative rule learning approach for the induction of crisp and fuzzy rules; 2. The second has been designed during this research explicitly for the induction of a fuzzy rulebase, and generates all rules in parallel.Both strategies have been tested on a number of classification problems, including medical diagnosis and industrial plant fault detection, and compared against other crisp or fuzzy induction algorithms that use more well-established approaches. The results challenge statement A above, by presenting evidence to show that one criterion need not be met at the expense of the other. This research also uncovers the cost that is paid -- that of computational expenditure -- and makes concrete suggestions on how this may be resolved.With regards to statement B, until now little or no evidence has been put forward to support or disprove the claim. The results of this research indicate that definite advantages are offered by the second simultaneous strategy, that are not offered by the iterative one. These benefits include improved accuracy over a wide range of values for several key system parameters. However, both approaches also fare well when compared to other learning algorithms. This latter fact is due to the rule discovery mechanism itself -- the adapted Ant Colony Optimisation algorithm -- which affords several additional advantages. These include a simple mechanism within the rule construction process that enables it to cope with datasets that have an imbalanced distribution between the classes, and another for controlling the amount of fit to the training data.In addition, several system parameters have been designed to be semi-autonomous so as to avoid unnecessary user intervention, and in future work the social insect metaphor may be exploited and extended further to enable it to deal with industrial-strength data mining issues involving large volumes of data, and distributed and/or heterogeneous databases

Vulnerability and use of Ground and Surface Waters in the Southern Mississippi Valley Region

There is a concern in the Southern Mississippi River Valley of the United States over non-point source pollution of ground and surface waters resulting from activities associated with agricultural production. This agriculturally intensive region consists of two major land resource areas (MLRAs): Southern Mississippi Valley Silty Uplands (MLRA 134) and the Southern Mississippi Valley Alluvium (MLRA 131). Both MLRAs have level to undulating and rolling topography, relatively fertile soils and a climate particularly conducive for row crop production

Fuzzy Interpolation Systems and Applications

Fuzzy inference systems provide a simple yet effective solution to complex non-linear problems, which have been applied to numerous real-world applications with great success. However, conventional fuzzy inference systems may suffer from either too sparse, too complex or imbalanced rule bases, given that the data may be unevenly distributed in the problem space regardless of its volume. Fuzzy interpolation addresses this. It enables fuzzy inferences with sparse rule bases when the sparse rule base does not cover a given input, and it simplifies very dense rule bases by approximating certain rules with their neighbouring ones. This chapter systematically reviews different types of fuzzy interpolation approaches and their variations, in terms of both the interpolation mechanism (inference engine) and sparse rule base generation. Representative applications of fuzzy interpolation in the field of control are also revisited in this chapter, which not only validate fuzzy interpolation approaches but also demonstrate its efficacy and potential for wider applications

Using Xfuzzy environment for the whole design of fuzzy systems

Since 1992, Xfuzzy environment has been improving to ease the design of fuzzy systems. The current version, Xfuzzy 3, which is entirely programmed in Java, includes a wide set of new featured tools that allow automating the whole design process of a fuzzy logic based system: from its description (in the XFL3 language) to its synthesis in C, C++ or Java (to be included in software projects) or in VHDL (for hardware projects). The new features of the current version have been exploited in different application areas such as autonomous robot navigation and image processing.Comisión Interministerial de Ciencia y Tecnología DPI2005-02293 y TEC2005-04359Junta de Andalucía TIC2006-635 y TEP2006-37

Interval Type-2 TSK+ Fuzzy Inference System

Type-2 fuzzy sets and systems can better handle uncertainties compared to its type-1 counterpart, and the widely applied Mamdani and TSK fuzzy inference approaches have been both extended to support interval type-2 fuzzy sets. Fuzzy interpolation enhances the conventional Mamdani and TKS fuzzy inference systems, which not only enables inferences when inputs are not covered by an incomplete or sparse rule base but also helps in system simplification for very complex problems. This paper extends the recently proposed fuzzy interpolation approach TSK+ to allow the utilization of interval type-2 TSK fuzzy rule bases. One illustrative case based on an example problem from the literature demonstrates the working of the proposed system, and the application on the cart centering problem reveals the power of the proposed system. The experimental investigation confirmed that the proposed approach is able to perform fuzzy inferences using either dense or sparse interval type-2 TSK rule bases with promising results generated