Formal Learning Theory Research Articles

Both probability and rate of reinforcement can affect the acquisition and maintenance of conditioned responses.

In Pavlovian conditioning, the strength of a conditioned response is a function of the probability of reinforcement. However, manipulations of probability are often confounded with changes in the rate of reinforcement. Two between-group experiments in mice evaluated the effect of the probability of reinforcement, while controlling the rate of reinforcement, on appetitive conditioning and extinction. Experiment 1 equated the reinforcement rate by manipulating the number of reinforcements received in each reinforced trial in a critical group (one vs. two consecutive rewards). The results of this experiment showed that probability influenced the rate of responses in acquisition, even when controlling the reinforcement rate. Experiment 2 further assessed the role of probability on behavior while controlling the rate of reinforcement during the conditioned stimulus (CS) using a split-trial design, in which the total CS time was held constant but presented in different numbers of discrete trials (e.g., 50% reinforcement with two 12 s CS's vs. 100% reinforcement with a 24 s average CS duration). This experiment confirmed that probability influenced response rates, and both the probability and rate of reinforcement affected the proportion of trials with responses. Together, these results suggest that the probability of reinforcement, while having little effect on the speed at which responses emerged, affects responding even when the rate of reinforcement is held constant. The results challenge formal learning theories to account for the effects of both the probability and rate of reinforcement. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

Pavlovian safety learning: An integrative theoretical review.

Safety learning involves associating stimuli with the absence of threats, enabling the inhibition of fear and anxiety. Despite growing interest in psychology, psychiatry, and neuroscience, safety learning lacks a formal consensus definition, leading to inconsistent methodologies and varied results. Conceptualized as a form of inhibitory learning (conditioned inhibition), safety learning can be understood through formal learning theories, such as the Rescorla-Wagner and Pearce-Hall models. This review aims to establish a principled conceptualization of 'Pavlovian safety learning', identifying cognitive mechanisms that generate safety and the boundary conditions that constrain it. Based on these observations, we define Pavlovian safety learning as an active associative process, where surprising threat-omission (safety prediction error) acts as a salient reinforcing event. Instead of producing merely neutral or nonaversive states, safety learning endows stimuli with active positive associations to 'safety'. The resulting stimulus-safety memories counteract the influence of fear memories, promoting fear regulation, positive affect, and relief. We critically analyze traditional criteria of conditioned inhibition for their relevance to safety and propose areas for future innovation. A principled concept of Pavlovian safety learning may reduce methodological inconsistencies, stimulate translational research, and facilitate a comprehensive understanding of an indispensable psychological construct.

Many problems, different frameworks: classification of problems in computable analysis and algorithmic learning theory

AbstractIn this thesis, we study the complexity of some mathematical problems: in particular, those arising in computable analysis and algorithmic learning theory for algebraic structures. Our study is not limited to these two areas: indeed, in both cases, the results we obtain are tightly connected to ideas and tools coming from different areas of mathematical logic, including for example descriptive set theory and reverse mathematics.After giving the necessary preliminaries, we first study the uniform computational strength of the Cantor–Bendixson theorem in the Weihrauch lattice. This work falls into the program connecting reverse mathematics and computable analysis via the framework of Weihrauch reducibility. We concentrate on problems related to perfect subsets of Polish spaces, studying the perfect set theorem, the Cantor–Bendixson theorem, and various problems arising from them. As far as we know, this is the first systematic study of problems at the level of $\mathbf {\Pi }^1_1\mathsf {-CA}_0$ in the Weihrauch lattice. We show that the strength of some of the problems we study depends on the topological properties of the Polish space under consideration, while others have the same strength once the space is rich enough.We continue considering problems related to (induced) subgraphs. We provide results on the (effective) Wadge complexity of sets of graphs, that are also used to determine the Weihrauch degree of certain decision problems. The decision problems we consider are defined for a fixed graph G, and they take as input a graph H, answering whether G is an (induced) subgraph of H: we also consider the opposite problem (i.e., answering whether H is an induced subgraph of G). We conclude this part on (induced) subgraphs considering the Weihrauch degree of “search problems.”These problems are defined for a fixed graph G, and they take as input a graph H such that G is an (induced) subgraph H: the output is a copy of G in H. In both cases, we highlight differences and analogies between the subgraph and the induced subgraph relation.We then move our attention to algorithmic learning theory, and we present the framework we use to study the learnability of families of algebraic structures: here, given a countable family of pairwise nonisomorphic structures $\mathfrak {K}$ , a learner receives larger and larger pieces of an arbitrary copy of a structure in $\mathfrak {K}$ and, at each stage, is required to output a conjecture about the isomorphism type of such a structure. We say that $\mathfrak {K}$ is learnable if there exists a learner which eventually stabilizes to a correct guess. The framework was lacking a method for comparing the complexity of nonlearnable families, and so we propose a solution to this problem using tools coming from invariant descriptive set theory. To do so, we first prove that a family of structures is learnable if and only if its learning domain is continuously reducible to the relation $E_0$ of eventual agreement on infinite binary sequences and then, replacing $E_0$ with Borel equivalence relations of higher complexity, we obtain a new hierarchy of learning problems. This leads to the notion of E-learnability, where a family of structures $\mathfrak {K}$ is E-learnable, for a Borel equivalence relation E, if there is a continuous reduction from the isomorphism relation associated with $\mathfrak {K}$ to E. It is then natural to ask how the notion of E-learnability interacts with “classical” learning paradigms.Finally, we study the number of mind changes that a learner needs to learn a given family, both from a topological and a combinatorial point of view, and we consider how the complexity of a learner (in terms of Turing reducibility) affects the number of mind changes for learning a given family.Abstract prepared by Vittorio Cipriani.E-mail: vittorio.cipriani17@gmail.com.URL: https://air.uniud.it/handle/11390/1252226.

Use of digital e-learning technologies through the application of the SAM instructional design model in online medical education

Several instructional design behaviors are carried out by department operatives in higher teaching who lack formal learning theories and instructional science training. Teachers primarily use multimedia to deliver lectures in the form of power-point presentations. Even though there is a wealth of literature on using the program correctly, there are still some instances where the output is subpar. The application of digital technology in medical education is now regarded as a critical component of learning resources. The SAM method is defined as approximating an appropriate attention model successively. The first stage, evaluation, is divided into four sections: analysis, objectives, goals, and results. Design components are interaction, equivalence, technological options, appearance, and quality. The final stage is development, in which the objects and processes of design composition, development, and improvement are integrated.

On the Turing complexity of learning finite families of algebraic structures

Abstract In previous work, we have combined computable structure theory and algorithmic learning theory to study which families of algebraic structures are learnable in the limit (up to isomorphism). In this paper, we measure the computational power that is needed to learn finite families of structures. In particular, we prove that, if a family of structures is both finite and learnable, then any oracle which computes the Halting set is able to achieve such a learning. On the other hand, we construct a pair of structures which is learnable but no computable learner can learn it.

¿Cómo impacta el conocimiento que tiene un profesor acerca de la teoría APOE sobre su conocimiento especializado?

This article explores the influence of knowledge of formal learning theories on the rest of the math teacher's specialized knowledge. To this end, the MTSK model was chosen to explore specialized knowledge and APOS theory as a formal learning theory. The work was carried out with two top mid-level Mexican professors who had completed master's degrees and in whose final work they used the APOS theory. We analyzed his final work in the part related to the design of teaching sequences. In the results we present how the design of the activities of the informants shows evidence of the Pedagogical Content Knowledge, as there is a mobilization of knowledge corresponding to the different subdomains and categories framed in that domain.

A NOTE ON THE LEARNING-THEORETIC CHARACTERIZATIONS OF RANDOMNESS AND CONVERGENCE

AbstractRecently, a connection has been established between two branches of computability theory, namely between algorithmic randomness and algorithmic learning theory. Learning-theoretical characterizations of several notions of randomness were discovered. We study such characterizations based on the asymptotic density of positive answers. In particular, this note provides a new learning-theoretic definition of weak 2-randomness, solving the problem posed by (Zaffora Blando, Rev. Symb. Log. 2019). The note also highlights the close connection between these characterizations and the problem of convergence on random sequences.

Learning families of algebraic structures from informant

We combine computable structure theory and algorithmic learning theory to study learning of families of algebraic structures. Our main result is a model-theoretic characterization of the learning type InfEx≅, consisting of the structures whose isomorphism types can be learned in the limit. We show that a family of structures is InfEx≅-learnable if and only if the structures can be distinguished in terms of their Σ2inf-theories. We apply this characterization to familiar cases and we show the following: there is an infinite learnable family of distributive lattices; no pair of Boolean algebras is learnable; no infinite family of linear orders is learnable.

A LEARNING-THEORETIC CHARACTERISATION OF MARTIN-LÖF RANDOMNESS AND SCHNORR RANDOMNESS

AbstractNumerous learning tasks can be described as the process of extrapolating patterns from observed data. One of the driving intuitions behind the theory of algorithmic randomness is that randomness amounts to the absence of any effectively detectable patterns: it is thus natural to regard randomness as antithetical to inductive learning. Osherson and Weinstein [11] draw upon the identification of randomness with unlearnability to introduce a learning-theoretic framework (in the spirit of formal learning theory) for modelling algorithmic randomness. They define two success criteria—specifying under what conditions a pattern may be said to have been detected by a computable learning function—and prove that the collections of data sequences on which these criteria cannot be satisfied correspond to the set of weak 1-randoms and the set of weak 2-randoms, respectively. This learning-theoretic approach affords an intuitive perspective on algorithmic randomness, and it invites the question of whether restricting attention to learning-theoretic success criteria comes at an expressivity cost. In other words, is the framework expressive enough to capture most core algorithmic randomness notions and, in particular, Martin-Löf randomness—arguably, the most prominent algorithmic randomness notion in the literature? In this article, we answer the latter question in the affirmative by providing a learning-theoretic characterisation of Martin-Löf randomness. We then show that Schnorr randomness, another central algorithmic randomness notion, also admits a learning-theoretic characterisation in this setting.

Improving Teachers' Understanding of Theoretical Foundations of Technology Use

Situated in a theoretical foundations of educational technology course, this study explored how practicing teachers who had not previously taken any formal learning theories courses connected theories with the use of technology. It examined the mindset of teachers after their learning and exposure to learning theories and relevant school of thoughts for a sustained period of time. Results show that teachers showed an appreciation for theories and an awareness for the need of theories in guiding technology use. Teachers also connected theories with technology use. The learning of theories equipped teachers with theoretical guidance and justifications for the use of technology. The participating teachers were also able to evaluate pedagogical approaches toward the use of technology based on their learning. The study addressed the importance of theoretical understanding towards the use of technology and has implications for policies and practice regarding teacher education and professional development regarding the use of educational technology.

A dynamic logic for learning theory

Building on previous work [4,5] that bridged Formal Learning Theory and Dynamic Epistemic Logic in a topological setting, we introduce a Dynamic Logic for Learning Theory (DLLT), extending Subset Space Logics [18,10] with dynamic observation modalities[o]φ, as well as with a learning operatorL(o→), which encodes the learner's conjecture after observing a finite sequence of data o→. We completely axiomatise DLLT, study its expressivity and use it to characterise various notions of knowledge, belief, and learning.

How Theories of Induction Can Streamline Measurements of Scientific Performance

We argue that inductive analysis (based on formal learning theory and the use of suitable machine learning reconstructions) and operational (citation metrics-based) assessment of the scientific process can be justifiably and fruitfully brought together, whereby the citation metrics used in the operational analysis can effectively track the inductive dynamics and measure the research efficiency. We specify the conditions for the use of such inductive streamlining, demonstrate it in the cases of high energy physics experimentation and phylogenetic research, and propose a test of the method’s applicability.

Independence test and canonical correlation analysis based on the alignment between kernel matrices for multivariate functional data

In the case of vector data, Gretton et al. (Algorithmic learning theory. Springer, Berlin, pp 63–77, 2005) defined Hilbert–Schmidt independence criterion, and next Cortes et al. (J Mach Learn Res 13:795–828, 2012) introduced concept of the centered kernel target alignment (KTA). In this paper we generalize these measures of dependence to the case of multivariate functional data. In addition, based on these measures between two kernel matrices (we use the Gaussian kernel), we constructed independence test and nonlinear canonical variables for multivariate functional data. We show that it is enough to work only on the coefficients of a series expansion of the underlying processes. In order to provide a comprehensive comparison, we conducted a set of experiments, testing effectiveness on two real examples and artificial data. Our experiments show that using functional variants of the proposed measures, we obtain much better results in recognizing nonlinear dependence.

Equivalences between learning of data and probability distributions, and their applications

Algorithmic learning theory traditionally studies the learnability of effective infinite binary sequences (reals), while recent work by Vitányi and Chater has adapted this framework to the study of learnability of effective probability distributions from random data. We prove that for certain families of probability measures that are parametrized by reals, learnability of a subclass of probability measures is equivalent to learnability of the class of the corresponding real parameters. This equivalence allows to transfer results from classical algorithmic theory to learning theory of probability measures. We present a number of such applications, providing many new results regarding EX and BC learnability of classes of measures, thus drawing parallels between the two learning theories.

The Topology of Statistical Verifiability

Topological models of empirical and formal inquiry are increasingly prevalent. They have emerged in such diverse fields as domain theory [1, 16], formal learning theory [18], epistemology and philosophy of science [10, 15, 8, 9, 2], statistics [6, 7] and modal logic [17, 4]. In those applications, open sets are typically interpreted as hypotheses deductively verifiable by true propositional information that rules out relevant possibilities. However, in statistical data analysis, one routinely receives random samples logically compatible with every statistical hypothesis. We bridge the gap between propositional and statistical data by solving for the unique topology on probability measures in which the open sets are exactly the statistically verifiable hypotheses. Furthermore, we extend that result to a topological characterization of learnability in the limit from statistical data.

Explaining Delusions: Reducing Uncertainty Through Basic and Computational Neuroscience.

Delusions, the fixed false beliefs characteristic of psychotic illness, have long defied understanding despite their response to pharmacological treatments (e.g., D2 receptor antagonists). However, it can be challenging to discern what makes beliefs delusional compared with other unusual or erroneous beliefs. We suggest mapping the putative biology to clinical phenomenology with a cognitive psychology of belief, culminating in a teleological approach to beliefs and brain function supported by animal and computational models. We argue that organisms strive to minimize uncertainty about their future states by forming and maintaining a set of beliefs (about the organism and the world) that are robust, but flexible. If uncertainty is generated endogenously, beliefs begin to depart from consensual reality and can manifest into delusions. Central to this scheme is the notion that formal associative learning theory can provide an explanation for the development and persistence of delusions. Beliefs, in animals and humans, may be associations between representations (e.g., of cause and effect) that are formed by minimizing uncertainty via new learning and attentional allocation. Animal research has equipped us with a deep mechanistic basis of these processes, which is now being applied to delusions. This work offers the exciting possibility of completing revolutions of translation, from the bedside to the bench and back again. The more we learn about animal beliefs, the more we may be able to apply to human beliefs and their aberrations, enabling a deeper mechanistic understanding.

Inductive inference and reverse mathematics

The present work investigates inductive inference from the perspective of reverse mathematics. Reverse mathematics is a framework that allows gauging the proof strength of theorems and axioms in many areas of mathematics. The present work applies its methods to basic notions of algorithmic learning theory such as Angluin's tell-tale criterion and its variants for learning in the limit and for conservative learning, as well as to the more general scenario of partial learning. These notions are studied in the reverse mathematics context for uniformly and weakly represented families of languages. The results are stated in terms of axioms referring to induction strength and to domination of weakly represented families of functions.

Creating Activating Events for Transformative Learning in a Prison Classroom

In this article, we interpreted, in light of Mezirow’s theory of transformative learning, interviews with 13 educators regarding their work with marginalized adult learners in prisons in the northeastern United States. Transformative learning may have been aided by the educators’ response to unplanned activating events, humor, and respect, and being a role model, and counselor. Teachers presented activating events that they perceived as supporting resistant learners in altering their meaning schemes and revising their frames of reference. Administrators of educational programs for marginalized adult learners can help prison educators develop these pedagogical practices. Practitioners and researchers may wish to explore humor in restricted learning environments as well as the challenge mandatory prison classrooms present for the field of formal adult learning and transformative learning theory.

On Parity Check (0,1)-Matrix over $\mathbb{Z}_p$

We prove that for every prime $p$ there exists a (0,1)-matrix $M$ of size $t_p(n,m)\times n$, where $t_p(n,m)=O(m+\frac{m\log \frac{n}{m}}{\log \min({m,p})})$ such that every $m$ columns of $M$ are linearly independent over $\mathbb{Z}_p$, the field of integers modulo $p$ (and therefore over any field of characteristic $p$ and over the field of real numbers $\mathbb{R}$). In coding theory this matrix is a parity-check (0,1)-matrix over $\mathbb{Z}_p$ of a linear code of minimal distance m+1. Using the Hamming bound (for $p<m$) and the information theoretic argument (for $p\ge m$) it can be shown that the above bound is tight. This solves the following open problems: (1) Coin weighing problem: Suppose that $n$ coins are given among which there are at most $m$ counterfeit coins of arbitrary weights. There is a nonadaptive algorithm that finds the counterfeit coins and their weights in $t(n,m)=O((m\log n)/\log m)$ weighings. A previous result [S. S. Choi and J. H. Kim, in Proceedings of the 2008 ACM International Symposium on Theory of Computing, ACM, New York, 2008, pp. 749--758] proves the existence of a nonadaptive algorithm that solves the problem (with the same complexity) only for weights between $n^{-a}$ and $n^b$ for constants $a$ and $b$ and finds the counterfeit coins but not their weights. (2) Reconstructing graph from additive queries: Suppose that $G$ is an unknown weighted graph with $n$ vertices and at most $m$ edges. There exists a nonadaptive algorithm that finds the edges of $G$ and their weights in $O(t(n,m))$ additive queries. Previous results [S. S. Choi and J. H. Kim, in Proceedings of the 2008 ACM International Symposium on Theory of Computing, ACM, New York, 2008, pp. 749--758; N. H. Bshouty and H. Mazzawi, in Proceedings of the 20th International Conference on Algorithmic Learning Theory, Springer, Berlin, 2009, pp. 97--109] prove the existence of a nonadaptive algorithm that solves the problem only for weights between $n^{-a}$ and $n^b$ for constants $a$ and $b$ and finds the edges but not their weights. (3) Signature coding problem: Consider $n$ stations and at most $m$ of them want to send messages from $\mathbb{Z}_p$ through an adder channel, that is, a channel whose output is the sum of the messages. Then all messages can be sent (encoded and decoded) with $O(t(n,m))$ transmissions. Previous algorithms [E. Biglieri and L. Györfi, Multiple Access Channels: Theory and Practice, NATO Security through Sci. Ser. D: Inform. Commun. Security, IOS Press, Amsterdam, 2007] run with the same number of transmissions only for messages in $\{0,1\}$. Simple information theoretic arguments show that all the above bounds are tight.

Une « école de l’autodidaxie » ? L’enseignement des « musiques actuelles » au prisme de la forme scolaire

L’article se propose d’interroger la rupture avec l’approche scolaire revendiquee par l’enseignement institutionnel des « musiques actuelles ». Apres avoir presente les reflexions pedagogiques considerant mettre en œuvre une ecole de l’autodidaxie, nous entendons demontrer, a partir de l’exemple de deux pratiques d’enseignement, qu’en realite ces methodes ne remettent pas en question le rapport distancie a la musique et a sa pratique, caracteristique de la forme scolaire.