How Do Artificial Neural Networks Classify Musical Triads? A Case Study in Eluding Bonini's Paradox

How might artificial neural networks (ANNs) inform cognitive science? Often cognitive scientists use ANNs but do not examine their internal structures. In this paper, we use ANNs to explore how cognition might represent musical properties. We train ANNs to classify musical chords, and we interpret network structure to determine what representations ANNs discover and use. We find connection weights between input units and hidden units can be described using Fourier phase spaces, a representation studied in musical set theory. We find the total signal coming through these weighted connection weights is a measure of the similarity between two Fourier structures: the structure of the hidden unit's weights and the structure of the stimulus. This is surprising because neither of these Fourier structures is computed by the hidden unit. We then show how output units use such similarity measures to classify chords. However, we also find different types of units—units that use different activation functions—use this similarity measure very differently. This result, combined with other findings, indicates that while our networks are related to the Fourier analysis of musical sets, they do not perform Fourier analyses of the kind usually described in musical set theory. Our results show Fourier representations of music are not limited to musical set theory. Our results also suggest how cognitive psychologists might explore Fourier representations in musical cognition. Critically, such theoretical and empirical implications require researchers to understand how network structure converts stimuli into responses.     

Encoding Shape and Spatial Relations: The Role of Receptive Field Size in Coordinating Complementary Representations

An effective functional architecture facilitates interactions among subsystems that are often used together. Computer simulations showed that differences in receptive field sizes can promote such organization. When input was filtered through relatively small nonoverlapping receptive fields, artificial neural net-works learned to categorize shapes relatively quickly; in contrast, when input was filtered through relatively large overlapping receptive fields, networks learned to encode specific shape exemplars or metric spatial relations relatively quickly. Moreover, when the receptive field sizes were allowed to adapt during learning, networks developed smaller receptive fields when they were trained to categorize shapes or spatial relations, and developed larger receptive fields when they were trained to encode specific exemplars or metric distances. In addition, when pairs of networks were constrained to use input from the same type of receptive fields, networks learned a task faster when they were paired with networks that were trained to perform a compatible type of task. Finally, using a novel modular architecture, networks were not preassigned a task, but rather competed to perform the different tasks. Networks with small nonover-lapping receptive fields tended to win the competition for categorical tasks whereas networks with large overlapping receptive fields tended to win the competition for exemplar/metric tasks.     

Correlations Between Input and Output Units in Neural Networks

Correlation analyses of recent back-propagation neural networks show that network results are due to imbalances in stimulus input. Conclusions concerning the effects of receptive field size, hemispheric specialization, and other issues of relevance to psychology cannot therefore be drawn until the dominating effects of low-level correlations are removed. Statistical techniques for evaluating the stimulus materials for neural networks are introduced.     

Learning Continuous Probability Distributions with Symmetric Diffusion Networks

In this article we present symmetric diffusion networks, a family of networks that instantiate the principles of continuous, stochastic, adaptive and interactive propagation of information. Using methods of Markovion diffusion theory, we formalize the activation dynamics of these networks and then show that they can be trained to reproduce entire multivariate probability distributions on their outputs using the contrastive Hebbion learning rule (CHL). We show that CHL performs gradient descent on an error function that captures differences between desired and obtained continuous multivariate probability distributions. This allows the learning algorithm to go beyond expected values of output units and to approximate complete probability distributions on continuous multivariate activation spaces. We argue that learning continuous distributions is an important task underlying a variety of real-life situations that were beyond the scope of previous connectionist networks. Deterministic networks, like back propagation, cannot learn this task because they are limited to learning average values of independent output units. Previous stochastic connectionist networks could learn probability distributions but they were limited to discrete variables. Simulations show that symmetric diffusion networks can be trained with the CHL rule to approximate discrete and continuous probability distributions of various types.     

Nearest vertex attraction for actively reducing loss

In recent years the neural networks have received considerable success on classification tasks. The randomly initialized network is generally expected to adjust the weights for reducing the loss, which is also indicated as the total distance from the samples to the corresponding vertices. However, the output space of the conventional neural networks suffers from the fixed relation between the labels and vertices during learning. This case forces the mapped points around the unexpected vertex across the decision boundary into the neighborhood of the correct vertex, and simultaneously the boundary points cannot obtain the substantial rectification. Therefore, this study proposes a novel nearest vertex attraction (NVA) to actively adjust the relation between the categories and the output vertices for improving the neural network classifiers. The best relation allows that the data points can be attracted by the nearest vertices to minimize the total moving distances. In this way, the mapped points that are near to the vertices and the decision boundaries obtain the decent management. We evaluated the NVA with several conventional classification techniques and other neural network classifiers on 12 public UCI datasets. The numerical experiments demonstrate that the proposed method improves performance of the neural network classifiers on the involved benchmarks.     

Nicotinic modulation of tone-evoked responses in auditory cortex reflects the strength of prior auditory learning

Nicotinic acetylcholine receptors (nAChRs) contribute to sensory-cognitive function, as demonstrated by evidence that nAChR activation enhances, and nAChR blockade impairs, neural processing of sensory stimuli and sensory-cognitive behavior. To better understand the relationship between nAChR function and behavior, here we compare the strength of nAChR-mediated physiology in individual animals to their prior auditory behavioral performance. Adult rats were trained on an auditory-cued, active avoidance task over 4 days and classified as “good,” “intermediate” or “poor” performers based on their initial rate of learning and eventual level of performance. Animals were then anesthetized, and tone-evoked local field potentials (LFPs) recorded in layer 4 of auditory cortex (ACx) before and after a test dose of nicotine (0.7 mg/kg, s.c.) or saline. In “good” performers, nicotine enhanced LFP amplitude and decreased response threshold to characteristic frequency (CF) stimuli, yet had opposite effects (decreased amplitude, increased threshold) on responses to spectrally distant stimuli; i.e., cortical receptive fields became more selective for CF stimuli. In contrast, nicotine had little effect on LFP amplitude in “intermediate” or “poor” performing animals. Nicotine did, however, reduce LFP onset latency in all three groups, indicating that all received an effective dose of the drug. Our findings suggest that nicotinic regulation of cortical receptive fields may be a distinguishing feature of the best-performing animals, and may facilitate sensory-related learning by enhancing receptive field selectivity.     

Concurrent intramodal learning enhances multisensory responses of symmetric crossmodal learning in robotic audio-visual tracking

Tracking an audio-visual target involves integrating spatial cues about target position from both modalities. Such sensory cue integration is a developmental process in the brain involving learning, with neuroplasticity as its underlying mechanism. We present a Hebbian learning-based adaptive neural circuit for multi-modal cue integration. The circuit temporally correlates stimulus cues within each modality via intramodal learning as well as symmetrically across modalities via crossmodal learning to independently update modality-specific neural weights on a sample-by-sample basis. It is realised as a robotic agent that must orient towards a moving audio-visual target. It continuously learns the best possible weights required for a weighted combination of auditory and visual spatial target directional cues that is directly mapped to robot wheel velocities to elicit an orientation response. Visual directional cues are noise-free and continuous but arising from a relatively narrow receptive field while auditory directional cues are noisy and intermittent but arising from a relatively wider receptive field. Comparative trials in simulation demonstrate that concurrent intramodal learning improves both the overall accuracy and precision of the orientation responses of symmetric crossmodal learning. We also demonstrate that symmetric crossmodal learning improves multisensory responses as compared to asymmetric crossmodal learning. The neural circuit also exhibits multisensory effects such as sub-additivity, additivity and super-additivity.     

The influence of stimulus properties on multisensory processing in the awake primate superior colliculus.

Multisensory integration is a process whereby information converges from different sensory modalities to produce a response that is different from that elicited by the individual modalities presented alone. A neural basis for multisensory integration has been identified within a variety of brain regions, but the most thoroughly examined model has been that of the superior colliculus (SC). Multisensory processing in the SC of anaesthetized animals has been shown to be dependent on the physical parameters of the individual stimuli presented (e.g., intensity, direction, velocity) as well as their spatial relationship. However, it is unknown whether these stimulus features are important, or evident, in the awake behaving animal. To address this question, we evaluated the influence of physical properties of sensory stimuli (visual intensity, direction, and velocity; auditory intensity and location) on sensory activity and multisensory integration of SC neurons in awake, behaving primates. Monkeys were trained to fixate a central visual fixation point while visual and/or auditory stimuli were presented in the periphery. Visual stimuli were always presented within the contralateral receptive field of the neuron whereas auditory stimuli were presented at either ipsi- or contralateral locations. Many of the SC neurons responsive to these sensory stimuli (n = 66/84; 76%) had stronger responses when the visual and auditory stimuli were combined at contralateral locations than when the auditory stimulus was located on the ipsilateral side. This trend was significant across the population of auditory-responsive neurons. In addition, some SC neurons (n = 31) were presented a battery of tests in which the quality of one stimulus of a pair was systematically manipulated. A small proportion of these neurons (n = 8/31; 26%) showed preferential responses to stimuli with specific physical properties, and these preferences were not significantly altered when multisensory stimulus combinations were presented. These data demonstrate that multisensory processing in the awake behaving primate is influenced by the spatial congruency of the stimuli as well as their individual physical properties.     

Processing spatial relations with different apertures of attention

Neuropsychological studies suggest the existence of lateralized networks that represent categorical and coordinate types of spatial information. In addition, studies with neural networks have shown that they encode more effectively categorical spatial judgments or coordinate spatial judgments, if their input is based, respectively, on units with relatively small, nonoverlapping receptive fields, as opposed to units with relatively large, overlapping receptive fields. These findings leave open the question of whether interactive processes between spatial detectors and types of spatial relations can be modulated by spatial attention. We hypothesized that spreading the attention window to encompass an area that includes two objects promotes coordinate spatial relations, based on coarse coding by large, overlapping, receptive fields. In contrast, narrowing attention to encompass an area that includes only one of the objects benefits categorical spatial relations, by effectively parsing space. By use of a cueing procedure, the spatial attention window was manipulated to select regions of differing areas. As predicted, when the attention window was large, coordinate spatial transformations were noticed faster than categorical transformations; in contrast, when the attention window was relatively smaller, categorical spatial transformations were noticed faster than coordinate transformations. Another novel finding was that coordinate changes were noticed faster when cueing an area that included both objects as well as the empty space between them than when simultaneously cueing both areas including the objects while leaving the gap between them uncued.     

Direction- and velocity-specific responses from beyond the classical receptive field in the middle temporal visual area (MT)

The true receptive field of more than 90% of neurons in the middle temporal visual area (MT) extends well beyond the classical receptive field (crf), as mapped with conventional bar or spot stimuli, and includes a surrounding region that is 50 to 100 times the area of the crf. These extensive surrounds are demonstrated by simultaneously stimulating the crf and the surround with moving stimuli. The surrounds commonly have directional and velocity-selective influences that are antagonistic to the response from the crf. The crfs of MT neurons are organized in a topographic representation of the visual field. Thus MT neurons are embedded in an orderly visuotopic array, but are capable of integrating local stimulus conditions within a global context. The extensive surrounds of MT neurons may be involved in figure-ground discrimination, preattentive vision, perceptual constancies, and depth perception through motion cues.     

A distributed, developmental model of word recognition and naming

A parallel distributed processing model of visual word recognition and pronunciation is described. The model consists of sets of orthographic and phonological units and an interlevel of hidden units. Weights on connections between units were modified during a training phase using the back-propagation learning algorithm. The model simulates many aspects of human performance, including (a) differences between words in terms of processing difficulty, (b) pronunciation of novel items, (c) differences between readers in terms of word recognition skill, (d) transitions from beginning to skilled reading, and (e) differences in performance on lexical decision and naming tasks. The model's behavior early in the learning phase corresponds to that of children acquiring word recognition skills. Training with a smaller number of hidden units produces output characteristic of many dyslexic readers. Naming is simulated without pronunciation rules, and lexical decisions are simulated without accessing word-level representations. The performance of the model is largely determined by three factors: the nature of the input, a significant fragment of written English; the learning rule, which encodes the implicit structure of the orthography in the weights on connections; and the architecture of the system, which influences the scope of what can be learned.     

Categorical versus coordinate spatial relations: computational analyses and computer simulations.

Results of 4 sets of neural network simulations support the distinction between categorical and coordinate spatial relations representations: (a) Networks that were split so that different hidden units contributed to each type of judgment performed better than unsplit networks; the reverse was observed when they made 2 coordinate judgments. (b) Both computations were more difficult when finer discriminations were required; this result mirrored findings with human Ss. (c) Networks with large, overlapping "receptive fields" performed the coordinate task better than did networks with small, less overlapping receptive fields, but vice versa for the categorical task; this suggests a possible basis for observed cerebral lateralization of the 2 kinds of processing. (d) The previously observed effect of stimulus contrast on this hemispheric asymmetry could reflect contributions of more neuronal input in high-contrast conditions.     

A learning rule that explains how rewards teach attention

Many theories propose that top-down attentional signals control processing in sensory cortices by modulating neural activity. But who controls the controller? Here we investigate how a biologically plausible neural reinforcement learning scheme can create higher order representations and top-down attentional signals. The learning scheme trains neural networks using two factors that gate Hebbian plasticity: (1) an attentional feedback signal from the response-selection stage to earlier processing levels; and (2) a globally available neuromodulator that encodes the reward prediction error. We demonstrate how the neural network learns to direct attention to one of two coloured stimuli that are arranged in a rank-order. Like monkeys trained on this task, the network develops units that are tuned to the rank-order of the colours and it generalizes this newly learned rule to previously unseen colour combinations. These results provide new insight into how individuals can learn to control attention as a function of reward contingency.     

TRANSFER BETWEEN RECEPTIVE AND PRODUCTIVE LANGUAGE IN DEVELOPMENT ALLY DISABLED CHILDREN

The purpose of this study was to examine the relationship between receptive and productive language acquisition in developmentally disabled children. A single-subject operant methodology was employed to evaluate the effect of training in one mode on performance in the other mode. Noun labels for pictured objects were used as the unit of analysis. Six children with severe language deficits participated in the experiment. Each subject learning to identify a different set of five pictures in each of four successively administered training conditions. In the first condition, a set of pictures was trained in the productive mode. In the second condition, a different set was trained in the receptive mode. These training conditions were then repeated using two additional sets of pictures. Training was done using reinforcement for correct responses and prompting for incorrect responses. Nonreinforced probes were conducted throughout training to assess performance in the untrained mode. The pictures in each set were trained successively so that transfer across the language modes could be studied separately for each response trained. All subjects successfully met the criteria for learning each picture set in both the receptive and productive training conditions. The probe data showed that opposite-modality performance improved as a function of both types of training, although performance levels differed. After productive training, five of six subjects' performance was highly accurate on receptive probes. By contrast, receptive training resulted in limited correct productive performance. Transfer from receptive training was negatively related to subjects' use of extra-experimental labels on productive probe trials. In addition to these competing response errors, subjects frequently made articulation errors. The findings suggest that for retarded children similar to those studied here, productive training will be sufficient to establish accurate receptive performance on vocabulary tasks. However, receptive training does not appear to be either a necessary or a sufficient condition for productive performance. The results do not support the reception-then-production training sequence based on normal language development.     

Rule extraction using ensemble of neural network ensembles

Neural networks are well-known for their impressive classification performance, and the ensemble learning technique acts as a catalyst to improve this performance even further by integrating multiple networks.However, neural network ensembles, like neural networks, are regarded as a black box because they cannot explain their decision-making process. As a result, despite their high classification performance, neural networks and their ensembles are unsuitable for some applications that require explainable decisions. However, the rule extraction technique can overcome this drawback by representing the knowledge learned by a neural network in the guise of interpretable decision rules. A rule extraction algorithm provides neural networks the ability to justify their classification responses using explainable classification rules. There are several rule extraction algorithms for extracting classification rules from neural networks, but only a few of them use neural network ensembles to generate rules. As a result, this paper proposes a rule extraction algorithm called Rule Extraction Using Ensemble of Neural Network Ensembles (RE-E-NNES) to demonstrate the high performance of neural network ensembles.RE-E-NNES extracts classification rules by ensembling several neural network ensembles. The results demonstrate the efficacy of the proposed RE-E-NNES algorithm in comparison to other existing rule extraction algorithms.     

Feature extraction of event-related potentials using wavelets: an application to human performance monitoring

This report describes the development and evaluation of mathematical models for predicting human performance from discrete wavelet transforms (DWT) of event-related potentials (ERP) elicited by task-relevant stimuli. The DWT was compared to principal components analysis (PCA) for representation of ERPs in linear regression and neural network models developed to predict a composite measure of human signal detection performance. Linear regression models based on coefficients of the decimated DWT predicted signal detection performance with half as many free parameters as comparable models based on PCA scores. In addition, the DWT-based models were more resistant to model degradation due to over-fitting than PCA-based models. Feed-forward neural networks were trained using the backpropagation algorithm to predict signal detection performance based on raw ERPs, PCA scores, or high-power coefficients of the DWT. Neural networks based on high-power DWT coefficients trained with fewer iterations, generalized to new data better, and were more resistant to overfitting than networks based on raw ERPs. Networks based on PCA scores did not generalize to new data as well as either the DWT network or the raw ERP network. The results show that wavelet expansions represent the ERP efficiently and extract behaviorally important features for use in linear regression or neural network models of human performance. The efficiency of the DWT is discussed in terms of its decorrelation and energy compaction properties. In addition, the DWT models provided evidence that a pattern of low-frequency activity (1 to 3.5 Hz) occurring at specific times and scalp locations is a reliable correlate of human signal detection performance.     

The biological efficacy of the transfer function

The most popular neural network strategy is back propagation. This strategy initiated general interest in neural networks among researchers. While back propagation can solve nonlinear problems, it is considered to be a poor example of neuron functioning. Recently, Gardner (1993) has made a strong case for a back propagating phenomenon in networks of living neurons. In this paper, we present a few simple computational examples that investigate another component of the typical back propagation network. The effects of varying transfer functions are illustrated along with the resulting variations in possible synaptic weights. Graphic presentations in 3-D space of the relationship between transfer functions and synaptic weights suggest neural analogies of cell-firing rate and network control.     

Risk assessment of knowledge fusion in an innovation ecosystem based on a GA-BP neural network

The risk assessment of knowledge fusion in innovation ecosystems is directly related to these ecosystems’ success or failure. A back-propagation (BP) neural network optimized by a genetic algorithm (GA) is thus proposed to evaluate the risk of knowledge fusion in innovation ecosystems. First, an index system is constructed for evaluating the risk of knowledge fusion in innovation ecosystems, and data are collected by questionnaire for use as training data for the neural networks. To realize machine learning, 84 datasets were generated, of which 60 were used to train the network, and 24 were used to test the network in MATLAB (R2014b). Evaluation models were then constructed by the BP neural network and GA-BP neural network, and their accuracy was judged by comparing the evaluation value with the target value. The comparison shows that the GA-BP neural network has faster convergence speed and higher stability, can achieve the goal more often, and reduces the possibility of the BP neural network falling into a local optimum instead of reaching global optimization. The GA-BP neural network model for the knowledge fusion risk assessment of innovation ecosystems provides a new method for practice.     

基于联结主义的连续记分IRT模型的项目参数和被试能力估计

运用联结主义中的级连相关模型对于小样本条件下的连续记分项目反应理论 (IRT)模型的项目参数和被试能力进行了估计。一组被试对于一组项目的反应矩阵作为级连相关模型的输入 ,这组被试的能力θ或该组项目的参数a、b和c作为该模型的输出 ,对神经网络进行训练使之具备了估计θ,a ,b或c的能力。计算机模拟的实验表明 ,如果测验中有少量项目取自于题库 ,就可以运用联结主义方法对IRT参数和被试能力进行较好的估计     

Theory and scope of exact representation extraction from feed-forward networks

An algorithm to extract representations from feed-forward threshold networks is outlined. The representation is based on polytopic decision regions in the input space – and is exact not an approximation. Using this exact representation we explore scope questions, such as when and where do networks form artifacts, or what can we tell about network generalization from its representation. The exact nature of the algorithm also lends itself to theoretical questions about representation extraction in general, such as what is the relationship between factors such as input dimensionality, number of hidden units, number of hidden layers, and how the network output is interpreted to the potential complexity of the network’s function.