A Tutorial for Implementing Matrix Training in Practice.

Matrix training consists of arranging targets for instruction to promote fine-grained stimulus control resulting in the establishment of skills without direct training. Recent reviews of the matrix training literature (Curiel et al., 2020a, b.; Kemmerer et al., 2021) highlighted the efficacy and efficiency of the approach with learners with and without disabilities. These reviews noted substantial variations in procedures across studies, suggesting the approach may be flexibly deployed across content areas and teaching procedures. This outcome is positive for practitioners as they may customize matrix training to meet the unique needs of their clients. However, it also necessitates decision making to sort through the variations in the literature. This tutorial was developed to help practitioners weigh various considerations when using matrix training. Tools and resources are provided to illustrate and accelerate adoption into practice settings. Supplementary Information: The online version contains supplementary material available at 10.1007/s40617-022-00733-5.

Video Compressive Sensing Reconstruction Using Unfolded LSTM.

Video compression sensing can use a few measurements to obtain the original video by reconstruction algorithms. There is a natural correlation between video frames, and how to exploit this feature becomes the key to improving the reconstruction quality. More and more deep learning-based video compression sensing (VCS) methods are proposed. Some methods overlook interframe information, so they fail to achieve satisfactory reconstruction quality. Some use complex network structures to exploit the interframe information, but it increases the parameters and makes the training process more complicated. To overcome the limitations of existing VCS methods, we propose an efficient end-to-end VCS network, which integrates the measurement and reconstruction into one whole framework. In the measurement part, we train a measurement matrix rather than a pre-prepared random matrix, which fits the video reconstruction task better. An unfolded LSTM network is utilized in the reconstruction part, deeply fusing the intra- and interframe spatial-temporal information. The proposed method has higher reconstruction accuracy than existing video compression sensing networks and even performs well at measurement ratios as low as 0.01.

Comparing Matrix-Training Procedures with Children with Autism Spectrum Disorder.

Recombinative generalization is the production of responses in the presence of novel combinations of known components. For example, after learning "red triangle" and "blue square," recombinative generalization is observed when a child can tact "red square" and "blue triangle." Recombinative generalization can emerge from a history of matrix training, which involves carefully selecting and arranging stimuli and responses along at least two axes and training a subset of responses. With three children with autism spectrum disorder, we compared recombinative generalization of object-action or feature-object tacts when the component stimuli were trained before combination stimuli, trained along with combination stimuli, or untrained (i.e., combination only). For two participants, training the components along with some combinations led to the most untrained targets acquired without direct teaching. For the other participant, training the combinations only led to the greatest proportion of untrained targets acquired without direct teaching. We discuss stimulus control promoted by each teaching arrangement and suggestions for future research on recombinative generalization.

Promoting the emergence of tacting three-digit numerals through a chain prompt combined with matrix training.

Children with autism spectrum disorder (ASD) have difficulty generalizing from directly trained responses to untrained responses (i.e., emergent responding). In this study, we used a chain prompt combined with matrix training to teach 2 participants with ASD to tact 192 three-digit numerals. We used a multiple-baseline design across matrices to evaluate the treatment effects on trained and untrained tacts of numerals. Both participants mastered all numerals exposed to training and all numerals not exposed to training after 3 to 5 sixteen-trial sessions per matrix. One participant learned to tact 8 numerals for each 1 numeral exposed to direct training, and the other participant learned to tact 12 numerals for each 1 numeral exposed to direct training. We discuss these results relative to the effectiveness and efficiency of our chain prompt combined with matrix training for teaching tacting skills for targets with shared stimulus properties that facilitate generalization to untrained targets.

Estabelecendo recombinação generalizada de relações substantivo-verbo por meio de treino em matriz para crianças com Transtorno do Espectro Autista / Establishing recombinative generalization of noun-verb relations through matrix training for children with Autism Spectrum Disorder

O treino em matriz é um procedimento de ensino que implica na organização dos componentes do repertório a ser ensinado em dois eixos. Ele tem sido utilizado para favorecer a recombinação generalizada de repertórios verbais. No entanto, ainda que pessoas com Transtorno do Espectro Autista (TEA) apresentem geralmente dificuldades na linguagem, verifica-se que poucos estudos investigaram os efeitos do treino em matriz para o estabelecimento de repertórios verbais nessa população. O presente estudo avaliou, a partir de um delineamento de linha de base múltipla entre participantes, o efeito do treino em matriz na indução de recombinação generalizada de relações substantivo-verbo, em português, para duas crianças com TEA. As relações substantivo-verbo de nove figuras foram organizadas em uma matriz 3x3, sendo ensinadas diretamente três relações e testadas as outras seis. Outras nove relações substantivo-verbo foram organizadas em uma segunda matriz 3x3, sendo todas apenas testadas. O procedimento foi eficaz no estabelecimento das relações substantivo-verbo para um dos participantes e ocasionou aumento na emissão de respostas corretas das relações para o outro. Discutem-se a ampliação da validade externa do efeito do treino em matriz para crianças com TEA, questões relativas ao estabelecimento de controle de estímulos e quadros autoclíticos nesse procedimento de ensino.

Matrix training is a teaching procedure that involves the organizing the components of the repertoire to be taught in two axes. It has been used to promote the generalized recombination of verbal repertoires. However, even though people with Autism Spectrum Disorder (ASD) usually present language difficulties, few studies have investigated the effects of matrix training on the establishment of verbal repertoires in this population. The present study evaluated, from a multiple participant multiple baseline design, the effect of matrix training on the induction of generalized recombination of noun-verb relations, in Portuguese, for two children with ASD. The noun-verb relations of nine figures were organized in a 3x3 matrix, with three relations being directly taught and the other six tested. Another nine noun-verb relations were organized in a second 3x3 matrix, all of which were just tested. The procedure was effective in establishing noun-verb relations for one of the participants and produced an increase in the issuance of correct responses of the relations for the other. The expansion of the external validity of the effect of matrix training for children with ASD, issues related to the establishment of stimulus control and autoclitic frames in this teaching procedure are discussed.

Matrix training to teach tacts using speech generating devices: Replication and extension.

Research has shown that training diagonal targets in a matrix may result in correct responses to the nondiagonal targets within the same matrix and novel targets from a separate matrix. This study replicated prior research using matrix training to teach tact noun-verb combinations to 3 male participants with autism who use a speech generating device to communicate. Two matrices were constructed (Matrix 1 and Generalization Matrix), using mastered nouns and verbs. Following baseline, diagonal targets within Matrix 1 were trained. Posttests were conducted for the Generalization Matrix and Matrix 1. Two participants showed recombinative generalization within Matrix 1 and correct responding to all targets within the novel generalization matrix. For the 3rd participant, recombinative generalization was observed within Matrix 1. However, correct responding with the generalization matrix targets was only observed after training with 3 additional matrices. These results replicate and extend previous findings.

An evaluation of matrix training to teach college students piano notes and rhythms.

Twelve college students learned to tact the names of notes and rhythms and play them when presented with compound stimuli (visuals of notes and rhythms on a musical staff). In Experiment 1, we assessed generalization by presenting novel notes, rhythms, and compound stimuli not previously paired together. In the second experiment, we added a metronome that played at 60 beats per minute in all conditions for 3 out of 6 participants to ensure consistent tempo. Across both experiments, participants passed almost all posttests with the exception of tacting and playing in the presence of sound clips. Our data suggest that matrix training is an effective procedure to teach music skills to college students.

The Use of Matrix Training to Teach Color-Shape Tacts to Children with Autism.

Matrix training consists of preplanning instruction by arranging components of desired skills across a minimum of two axes. In the current study, three matrices were developed for each participant (e.g., Matrix 1, Generalization Matrix 1, and Generalization Matrix 2) with known color and shape components. Following baseline, nonoverlapping (i.e., diagonal) training was conducted with Matrix 1. Results of posttests were used to determine the extent of emergence of untrained color-shape combinations across all matrices. Results from all six participants indicated that mastery criteria were eventually met for Matrix 1. For five participants, mastery criteria were also eventually met for generalization matrices. Results replicate findings from prior studies and offer a simple approach for both testing emergence of untrained skills and remediating responding.

Matrix Training for Expanding the Communication of Toddlers and Preschoolers With Autism Spectrum Disorder.

Children diagnosed with autism spectrum disorder (ASD) typically exhibit a range of social communication deficits. Presequenced stimulus arrangements, such as matrix training, can be used to facilitate generative responding. Accordingly, training procedures can lead to the acquisition of a greater number of targets that are not taught explicitly, with fewer learning trials. Matrix training provides a useful framework for selecting teaching targets to promote the emergence of untaught skills. Participants were 3 young boys diagnosed with ASD, who were taught noun-verb combinations of play actions as tact and listener responses. All participants learned the taught noun-verb targets and showed varying degrees of recombinative generalization to untaught targets. Across subsequent matrices, the rate of acquisition of new targets and the number acquired without direct teaching increased (i.e., recombinative generalization). This suggests matrix training stimulus arrangements can facilitate the acquisition of novel targets by teaching young children with ASD to recombine language components appropriately.

The use of matrix training to promote generative language with children with autism.

Matrix training consists of planning instruction by arranging components of desired skills across 2 axes. After training with diagonal targets that each combine 2 unique skill components, responses to nondiagonal targets, consisting of novel combinations of the components, may emerge. A multiple-probe design across participants was used to evaluate matrix training with known nouns (e.g., cat) and verbs (e.g., jumping) with 5 children with autism spectrum disorders (ASD). Following baseline of Matrix 1 and a generalization matrix, diagonal targets within Matrix 1 were trained as noun-verb combinations (e.g., cat jumping). Posttests showed recombinative generalization within Matrix 1 and the generalization matrix for 4 participants. For 1 participant, diagonal training across multiple matrices was provided until correct responding was observed in the generalization matrix. Results support the use of matrix training to promote untrained responses for learners with ASD and offer a systematic way to evaluate the extent of generalization within and across matrices.

Sentence production after listener and echoic training by prelingual deaf children with cochlear implants.

Three children with neurosensory deafness who used cochlear implants were taught to match video clips to dictated sentences. We used matrix training with overlapping components and tested for recombinative generalization. Two 3 × 3 matrices generated 18 sentences. For each matrix, we taught 6 sentences and evaluated generalization with the remaining 3 sentences. We also tested for emergent tacting with all 18 video clips. After training, the participants were able to match untrained video clips to recombined dictated sentences. Tacts of both trained and untrained video clips increased for all participants.

Recombinative Generalization of Tacts Through Matrix Training with Individuals with Autism Spectrum Disorder.

Foss (Journal of Experimental Psychology, 76, 450-459, 1968a; Journal of Experimental Psychology, 77, 341-344, 1968b) compared overlap and non-overlap instruction to promote recombinative response generalization using a matrix training procedure. In the present study, we used a similar set of procedures to teach tacting of kitchen items and prepositions (i.e., relational autoclitics) to three females ages 13-20, diagnosed with autism spectrum disorder. We taught some kitchen items/prepositions as tacts (e.g., "the strainer is to the right of the box") according to a non-overlap instructional sequence. Subsequently, we taught more combinations in an overlap instructional sequence. Each training procedure was followed by probes of untrained relations. Two participants demonstrated recombinative generalization of untrained combinations following the first non-overlap phase, while the third participant demonstrated some response generalization of untrained relations after a few additional training sequences. All three participants demonstrated generalized tacting of object components while two participants showed generalized tacting of preposition components.

Matrix training of preliteracy skills with preschoolers with autism.

Matrix training is a generative approach to instruction in which words are arranged in a matrix so that some multiword phrases are taught and others emerge without direct teaching. We taught 4 preschoolers with autism to follow instructions to perform action-picture combinations (e.g., circle the pepper, underline the deer). Each matrix contained 6 actions on 1 axis and 6 pictures on the other axis. We used most-to-least prompting to train the instructions along the diagonal of each matrix and probed the untrained combinations. For 2 participants, untrained responding emerged after the minimum amount of training. The other 2 participants required further training before untrained combinations emerged. At the end of the study, 3 of the 4 participants performed the trained actions with previously known pictures, letters, and numbers. This study demonstrated that matrix training is an efficient approach to teaching language and literacy skills to children with autism.