1,721,006 research outputs found
The Challenge of Modeling the Acquisition of Mathematical Concepts
Full text linkAs a full-blown research topic, numerical cognition is investigated by a variety of disciplines including cognitive science, developmental and educational psychology, linguistics, anthropology and, more recently, biology and neuroscience. However, despite the great progress achieved by such a broad and diversified scientific inquiry, we are still lacking a comprehensive theory that could explain how numerical concepts are learned by the human brain. In this perspective, I argue that computer simulation should have a primary role in filling this gap because it allows identifying the finer-grained computational mechanisms underlying complex behavior and cognition. Modeling efforts will be most effective if carried out at cross-disciplinary intersections, as attested by the recent success in simulating human cognition using techniques developed in the fields of artificial intelligence and machine learning. In this respect, deep learning models have provided valuable insights into our most basic quantification abilities, showing how numerosity perception could emerge in multi-layered neural networks that learn the statistical structure of their visual environment. Nevertheless, this modeling approach has not yet scaled to more sophisticated cognitive skills that are foundational to higher-level mathematical thinking, such as those involving the use of symbolic numbers and arithmetic principles. I will discuss promising directions to push deep learning into this uncharted territory. If successful, such endeavor would allow simulating the acquisition of numerical concepts in its full complexity, guiding empirical investigation on the richest soil and possibly offering far-reaching implications for educational practice
Underwater Acoustic Detection and Localization with a Convolutional Denoising Autoencoder
No full textDetecting and tracking moving targets is a challenging task, which becomes even harder in underwater scenarios due to the extremely low levels of signal-to-noise ratio associated with common acoustic measures. In the context of continuous marine monitoring, a further challenge is provided by the need to deploy computationally efficient methods that guarantee minimum use of power resources in off-shore monitoring platforms. Here we present a novel approach to accurately detect and track moving targets from the reflections of an active acoustic emitter. Our system is based on a computationally- and energy-efficient deep convolutional denoising autoencoder. System performance is evaluated both on simulated and emulated data, and benchmarked against a probabilistic tracking method based on the Viterbi algorithm
Learning representation hierarchies by sharing visual features: a computational investigation of Persian character recognition with unsupervised deep learning
No full textL'approccio moderno all'Intelligenza Artificiale e la rivoluzione del deep learning
No full textIn the past decade artificial intelligence research has achieved impressive results, mostly due to the creation of efficient machine learning algorithms. One of the most promising approaches is constituted by deep learning, which allows to build multi-layer artificial neural networks that can autonomously extract knowledge from large-scale data sets. In this review we will discuss the main theoretical and technological progresses underlying these achievements, also focusing on their relevance for psychology and cognitive neuroscience. We will also highlight some of the limits of deep learning models and possible research directions to overcome them
Transformers discover an elementary calculation system exploiting local attention and grid-like problem representation
Full text linkMathematical reasoning is one of the most impressive achievements of human intellect but remains a formidable challenge for artificial intelligence systems. In this work we explore whether modern deep learning architectures can learn to solve a symbolic addition task by discovering effective arithmetic procedures. Although the problem might seem trivial at first glance, generalizing arithmetic knowledge to operations involving a higher number of terms, possibly composed by longer sequences of digits, has proven extremely challenging for neural networks. Here we show that universal transformers equipped with local attention and adaptive halting mechanisms can learn to exploit an external, grid-like memory to carry out multi-digit addition. The proposed model achieves remarkable accuracy even when tested with problems requiring extrapolation outside the training distribution; most notably, it does so by discovering human-like calculation strategies such as place value alignment
Do estimates of numerosity really adhere to Weber’s law? A reexamination of two case studies
Full text linkBoth humans and nonhuman animals can exhibit sensitivity to the approximate number of items in a visual array or events in a sequence, and across various paradigms, uncertainty in numerosity judgments increases with the number estimated or produced. The pattern of increase is usually described as exhibiting approximate adherence to Weber’s law, such that uncertainty increases proportionally to the mean estimate, resulting in a constant coefficient of variation. Such a pattern has been proposed to be a signature characteristic of an innate “number sense.” We reexamine published behavioral data from two studies that have been cited as prototypical evidence of adherence to Weber’s law and observe that in both cases variability increases less than this account would predict, as indicated by a decreasing coefficient of variation with an increase in number. We also consider evidence from numerosity discrimination studies that show deviations from the constant coefficient of variation pattern. Though behavioral data can sometimes exhibit approximate adherence to Weber’s law, our findings suggest that such adherence is not a fixed characteristic of the mechanisms whereby humans and animals estimate numerosity. We suggest instead that the observed pattern of increase in variability with number depends on the circumstances of the task and stimuli, and reflects an adaptive ensemble of mechanisms composed to optimize performance under these circumstances
Can neural networks do arithmetic? A survey on the elementary numerical skills of state-of-the-art deep learning models
Full text linkCreating learning models that can exhibit sophisticated reasoning skills is
one of the greatest challenges in deep learning research, and mathematics is
rapidly becoming one of the target domains for assessing scientific progress in
this direction. In the past few years there has been an explosion of neural
network architectures, data sets, and benchmarks specifically designed to
tackle mathematical problems, reporting notable success in disparate fields
such as automated theorem proving, numerical integration, and discovery of new
conjectures or matrix multiplication algorithms. However, despite these
impressive achievements it is still unclear whether deep learning models
possess an elementary understanding of quantities and symbolic numbers. In this
survey we critically examine the recent literature, concluding that even
state-of-the-art architectures often fall short when probed with relatively
simple tasks designed to test basic numerical and arithmetic knowledge
Combining denoising autoencoders and dynamic programming for acoustic detection and tracking of underwater moving targets
Full text linkAccurate detection and tracking of moving targets in underwater environments pose significant challenges, because noise in acoustic measurements (e.g., SONAR) makes the signal highly stochastic. In continuous marine monitoring a further challenge is related to the computational complexity of the signal processing pipeline—due to energy constraints, in off-shore monitoring platforms algorithms should operate in real time with limited power consumption. In this paper, we present an innovative method that allows to accurately detect and track underwater moving targets from the reflections of an active acoustic emitter. Our system is based on a computationally-and energy-efficient pre-processing stage carried out using a deep convolutional denoising autoencoder (CDA), whose output is then fed to a probabilistic tracking method based on the Viterbi algorithm. The CDA is trained on a large database of more than 20,000 reflection patterns collected during 50 designated sea experiments. System performance is then evaluated on a controlled dataset, for which ground truth information is known, as well as on recordings collected during different sea experiments. Results show that, compared to the benchmark, our method achieves a favorable trade-off between detection and false alarm rate, as well as improved tracking accuracy
Investigating the Generative Dynamics of Energy-Based Neural Networks
Full text linkGenerative neural networks can produce data samples according to the statistical properties of their training distribution. This feature can be used to test modern computational neuroscience hypotheses suggesting that spontaneous brain activity is partially supported by top-down generative processing. A widely studied class of generative models is that of Restricted Boltzmann Machines (RBMs), which can be used as building blocks for unsupervised deep learning architectures. In this work, we systematically explore the generative dynamics of RBMs, characterizing the number of states visited during top-down sampling and investigating whether the heterogeneity of visited attractors could be increased by starting the generation process from biased hidden states. By considering an RBM trained on a classic dataset of handwritten digits, we show that the capacity to produce diverse data prototypes can be increased by initiating top-down sampling from chimera states, which encode high-level visual features of multiple digit classes. We also find that the model is not capable of transitioning between all possible digit states within a single generation trajectory, suggesting that the top-down dynamics is heavily constrained by the shape of the energy function. We also study the generative dynamics on a more challenging dataset containing pictures of faces, showing that the exploration of stable states also partially depends on complexity of the training data distribution
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