Language learning with a bounded number of mind changes

This paper is concerned with the algorithmic learning where the learner is allowed to make finite but bounded number of mind changes. Briefly, in our learning paradigm, a learner is given examples from a recursive function, which the learner attempts to learn by producing programs to compute that function. We say that a team is successful if at least one member of the team learns the target function. The problem, given two teams with bounded number of learners and mind changes whether one team can provably learn more than the other team has been open for the last fifteen years. This paper makes significant progress toward a complete solution of this problem. In the case of error-free learning, this paper solves the open problem. Finally, in the case of EX learning our result shows that there is no team with a≥0 mind changes whose learning power is exactly equal to a single learner with bounded b(≠ a) number of mind changes. In the case of PEX learning we have a positive answer.

We consider the inductive inference model of Gold [15]. Suppose we are given a set of functions that are learnable with certain number of mind changes and errors. What can we consistently predict about those functions if we are allowed fewer mind changes or errors? In [20] we relaxed the notion of exact learning by considering some higher level properties of the input-output behavior of a given function. in this context, a learner produces a program that describes the property of a given function. Can we predict generic properties such as threshold or modality if we allow fewer number of mind changes or errors? These questions were completely answered in [20] when the learner is restricted to a single IIM. In this paper we allow a team of IIMs to collaborate in the learning process. The learning is considered to be successful if any one of the team member succeeds. A motivation for this extension is to understand and characterize properties that are learnable for a given set of functions in a team environment.

Freivalds defined an acceptable programming system independent criterion for learning programs for functions in which the final programs were required to be both correct and “nearly” minimal size. i.e.. within a computable function of being purely minimal size. Kinber showed that this parsimony requirement on final programs limits learning power. However, in scientific inference, parsimony is considered highly desirable. Alim-computable functionis (by definition) one calculable by a total procedure allowed to change its mind finitely many times about its output. Investigated is the possibility of assuaging somewhat the limitation on learning power resulting from requiring parsimonious final programs by use of criteria which require the final, correct programs to be “not-so-nearly” minimal size, e.g., to be within a lim-computable function of actual minimal size. It is shown that some parsimony in the final program is thereby retained, yet learning power strictly increases. Considered, then, are lim-computable functions as above but for whichnotations forconstructive ordinals are used to bound the number of mind changes allowed regarding the output. This is a variant of an idea introduced by Freivalds and Smith. For this ordinal notation complexity bounded version of lim-computability, the power of the resultant learning criteria form finely graded, infinitely ramifying, infinite hierarchies intermediate between the computable and the lim-computable cases. Some of these hierarchies, for the natural notations determining them, are shown to be optimally tight.

The present work investigates to which extent semantical knowledge can support the learning of basic mathematical concepts. The considered learning criteria are learning characteristic or enumerable indices for languages from positive data where the learner has to converge either syntactically (Ex) or semantically (BC). The considered classes are the classes of all monoids of a given group, all ideals of a given ring or all subspaces of a given vector space. The following is shown: (a) Learnability depends much on the amount of semantic knowledge given at the synthesis of the learner where this knowledge is represented by programs for the algebraic operations, codes for prominent elements of the algebraic structure (like 0 and 1 in fields) and certain parameters (like the dimension of finite dimensional vector spaces). For several natural examples good knowledge of the semantics may enable to keep ordinal mind change bounds while restricted knowledge may either allow only BC-convergence or even not permit learnability at all. (b) A recursive commutative ring is Noetherian iff the class of its ideals is BC-learnable. Such a BC-learner can be synthesized from programs for addition and multiplication. In many Noetherian rings, one can Ex-learn characteristic indices for the ideals with an ordinal bound on the number of mind changes. But there are also some Noetherian rings where it is impossible to Ex-learn the ideals or to learn characteristic indices for them.

Parametric logic is a framework that generalises classical first-order logic. A generalised notion of logical consequence—a form of preferential entailment based on a closed world assumption—is defined as a function of some parameters. A concept of possible knowledge base—the counterpart to the consistent theories of first-order logic—is introduced. The notion of compactness is weakened. The degree of weakening is quantified by a nonnull ordinal—the larger the ordinal, the more significant the weakening. For every possible knowledge base T, a hierarchy of sentences that are generalised logical consequences of T is built. The first layer of the hierarchies corresponds to sentences that can be obtained by a deductive inference, characterised by the compactness property. The second layer of the hierarchies corresponds to sentences that can be obtained by an inductive inference, characterised by the property of weak compactness quantified by 1. Weaker forms of compactness—quantified by nonnull ordinals—determine higher layers in the hierarchies, corresponding to more complex inferences. The naturalness of the hierarchies built over the possible knowledge bases is attested by fundamental connections with notions from Learning theory and from topology. The naturalness of the hierarchies built over the possible knowledge bases is attested by fundamental connections with notions from Learning theory—classification in the limit, with or without a bounded number of mind changes—and from topology—in reference to the Borel and the difference hierarchies. In this paper, we introduce the key model-theoretic aspects of Parametric logic, justify the concept of the knowledge base, define the hierarchies of generalised logical consequences and illustrate their relevance to Nonmonotonic reasoning. More specifically, we show that the degree of nonmonotonicity that is required to infer a sentence can be characterised by the least nonnull ordinal that quantifies the weakening of compactness used to locate the inferred sentence in the hierarchies.

Mind change efficient learning

We extend the line of research initiated by Fortnow and Klivans [6] that studies the relationship between efficient learning algorithms and circuit lower bounds. In [6], it was shown that if a Boolean circuit class \(\mathcal{C}\) has an efficient deterministic exact learning algorithm, (i.e. an algorithm that uses membership and equivalence queries) then \(\mathsf{EXP}^{\mathsf{NP}} \not \subseteq \mathsf{P/poly}[\mathcal{C}]\). Recently, in [14] EXP NP was replaced by DTIME(n ω(1)). Yet for the models of randomized exact learning or Valiant’s PAC learning, the best result so far is a lower bound against BPEXP (the exponential-time analogue of BPP). In this paper, we derive stronger lower bounds as well as some other consequences from randomized exact learning and PAC learning algorithms, answering an open question posed in [6] and [14]. In particular, we show that

Summary Mediation is a novel concept in language teaching and learning, and the needs and attitudes of language teachers towards it are largely unexplored. This article provides a brief overview of European language policy and discusses the action-oriented approach in the context of this paradigm shift in language learning and teaching. Finally, an exploratory study is presented that examined the needs and attitudes of language teachers from four European universities regarding mediation, as it has been formulated in the Common European Framework of Reference (CEFR) (Council of Europe, 2001) and redefined in the CEFR Companion Volume with New Descriptors (Council of Europe, 2018). The participating teachers were from the language centres of Charles University in the Czech Republic, Vytautas Magnus University in Lithuania, the University of Helsinki in Finland, and the University of Warsaw in Poland. The study survey measured the strength of (dis)agreement of the teachers with 12 statements concerning various aspects of mediation in the context of their teaching practice. These related to understanding what mediation is and its importance, mediating a text, mediating concepts, mediating communication, and mediation strategies. In addition, two open questions concerned the practice of promoting multilingual and intercultural education and the needs of teachers in the area of mediation. Although the vast majority of the 79 participating teachers (91%) agreed that mediation is vital in language learning and teaching, only a third of them claimed that they understood the concept. Furthermore, the findings indicate that some aspects of mediation are more challenging for the teachers to embrace than others and that some fundamental aspects of mediation do not seem to be part of the current teaching practice of all teachers. Overall, the present study confirmed some of the challenges with the implementation of the CEFR into teaching practice at the higher education level.

Many connections have been established between learning and logic, or learning and topology, or logic and topology. Still, the connections are not at the heart of these fields. Each of them is fairly independent of the others when attention is restricted to basic notions and main results. We show that connections can actually be made at a fundamental level, and result in a parametrized logic that needs topological notions for its early developments, and notions from learning theory for interpretation and applicability.One of the key properties of first-order logic is that the classical notion of logical consequence is compact. We generalize the notion of logical consequence, and we generalize compactness to β-weak compactness where β is an ordinal. The effect is to stratify the set of generalized logical consequences of a theory into levels, and levels into layers. Deduction corresponds to the lower layer of the first level above the underlying theory, learning with less than β mind changes to layer β of the first level, and learning in the limit to the first layer of the second level. Refinements of Borel-like hierarchies provide the topological tools needed to develop the framework.KeywordsTopological SpaceLogical ConsequenceCommon FrameworkInductive Logic ProgrammingDeductive LogicThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This chapter explores the transformative impact of artificial intelligence on English language teaching and learning, examining both theoretical frameworks and practical applications. Beginning with an analysis of the historical progression from Computer-Assisted Language Learning (CALL) to AI-Enhanced Language Learning (AIELL), the chapter investigates how machine learning algorithms, natural language processing, and adaptive learning systems are reshaping traditional pedagogical approaches. Through examination of empirical studies and case implementations across various educational contexts, the research reveals significant improvements in personalized learning experiences, assessment precision, and learner engagement. Particular attention is given to intelligent tutoring systems, automated feedback mechanisms, and AI-driven content creation tools that support both independent study and classroom instruction.

The impact of the pandemic of Covid 19 forces students to stay on top of online learning. Technology with reasonable sophistication can be used better by English education students than Indonesian Language Education students because, in addition to language acquisition, information and applications in digital are generally English-speaking and are more numerous and easily obtained. This study aims to describe digital literacy in language learning among Indonesian Language Education students and English Language Education students in the new normal era. This research is a quantitative descriptive study with qualitative data verified in the form of a percentage. The data was obtained using Google forms for each of 100 students (200 samples) in Java and Sumatra randomly and by purposive sampling. The instrument uses closed questions with a Likert scale (five options) and open questions. Research results show that digital literacy in language learning among Indonesian Language Education students and English Language students in the new normal era is not significantly different, at the same level. Digital literacy in language learning is at level 4, that is, students have been able to improve significantly (quantitatively stated) the performance of daily life activities through the use of information and technology with an average bind of 3.59 (71.8%) and bind 3.46 (69.2%). It shows that learning in networks has increased students' mastery and digital literacy abilities.

This paper presents some early results from the Machine Learning Toolbox (MLT) project. The MLT will be a system that recommends and implements one of several machine learning algorithms or systems for an application. The learning algorithms are being contributed by various members of the consortium, and as such have been developed with their own internal knowledge representation languages. In order for the user to supply application data in a form which can be understood by more than one algorithm, and in order for any algorithm to be capable of passing its results to any other algorithm, a Common Knowledge Representation Language (CKRL) has to be developed. The first stage in this task has been to investigate the different knowledge representation languages of the tools, with the aim of emphasising their commonalities and differences. The results of this comparison are currently being used as a basis for forming the first version of a CKRL We also discuss the possible roles for the CKRL within the MLT, and select that of an interface language between the different sub-components of the MLT as being the most flexible. The CKRL aims to solve the problem of mapping entities of the epistemic level into the logic level (and vice versa) in a pragmatic way, but it will not attempt to solve the problems of the different expressive powers of each of the current algorithm’s formalisms, or to evaluate the suitability of different languages for learning.

A team of learning machines is a multiset of learning machines. A team is said to successfully learn a concept just in case each member of some nonempty subset, of predetermined size, of the team learns the concept. Team learning of languages turns out to be a suitable theoretical model for studying computational limits on multi-agent machine learning. Team learning of recursively enumerable languages has been extensively studied. However, it may be argued that from a practical point of view all languages of interest are recursive.This paper gives theoretical results about team learnability of recursive languages. These results are mainly about two issues: redundancy and aggregation. The issue of redundancy deals with the impact of increasing the size of a team and increasing the number of machines required to be successful. The issue of aggregation deals with conditions under which a team may be replaced by a single machine without any loss in learning ability. The learning scenarios considered are:(a) Identification in the limit of accepting grammars for recursive languages. (b) Identification in the limit of decision procedures for recursive languages. (c) Identification in the limit of accepting grammars for indexed families of recursive languages. (d) Identification in the limit of accepting grammars for indexed families with enumerable class of grammars for the family as the hypothesis space. Scenarios which can be modeled by team learning are also presented.

- Smarter applications are making better use of the insights gleaned from data, having an impact on every industry and research discipline. At the core the revolution lies the tools and the methods that are driving it, from processing the massive piles of data generated each day to learning from and taking useful action. In this paper we first introduced you to the python programming characteristics and features. Python is one of the most preferred languages for scientific computing, data science, and machine learning, boosting both performance and productivity by enabling the use of low-level libraries. This paper offers insight into the field of machine learning with python, taking a tour through important topics and libraries of python which enables the development of machine learning model a easy process. Then we will look at different types of machine learning and various algorithms of machine leaning. And at last, we will look at the one of the most used models i.e., Linear Regression. Linear Regression is a Machine Learning algorithm based on supervised learning. It performs a regression task. It is used to predict the value of a variable based on the value of another variable. The variable you want to predict is called dependent variable. The variable you are using to predict the other variable’s value is called the independent variable. Hypothesis function for linear regression: Y = mx + c and at last, in this paper, we will be going to understand one of the linear 4 regression models for an ice-cream selling company which will predict the sales done by the business on different temperatures. Key words: Python; Machine Learning; Artificial Intelligence; Regression; Linear Regression.

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> With the current proliferation of high bandwidth and delay-sensitive multimedia applications and services, each wireless user will try to maximize its utility by acquiring as much spectrum resources as possible unless a preemptive mechanism exists in the network. Thus, emerging solutions for dynamic spectrum access in cognitive radio networks will need to adopt market-based approaches in order to effectively regulate the available resources. In this paper, we show how various centralized and decentralized spectrum access markets can be designed based on a stochastic game framework, where wireless users (also referred to as secondary users) can compete over time for the dynamically available transmission opportunities (spectrum “holes”). When operating in such spectrum access “markets,” wireless users become selfish, autonomous agents that strategically interact in order to acquire the necessary spectrum opportunities. We also show how wireless users can successfully compete with each other for the limited and time-varying spectrum opportunities, given the experienced dynamics in the wireless network, by optimizing both their external actions (e.g., the resource bids, power and channel used for transmission, etc.) and their internal actions (e.g., the modulation schemes, etc.). To determine their optimal actions in an informationally decentralized setting, users will need to learn and model directly or indirectly the other users' responses to their external actions. We studied the outcome of various dynamic interactions among self-interested wireless users possessing different knowledge and determine that the proposed framework can lead to multiuser communication systems that achieve new measures of efficiency, rationality and fairness. Lastly, our illustrative results show that the presented game-theoretic solution for wireless resource management enables users deploying enhanced (“smarter”) learning and communication algorithms and being able to make efficient use of the spectrum resources can derive higher utilities. This presents the designers of wireless devices and systems with important incentives to endow their next-generation products and services with enhanced capabilities to gather information, learn, and strategically compete for resources in the emerging spectrum resource markets made possible by the cognitive radio network technologies. </para>