The human brain is capable of diverse feats of intelligence. A particularly salient example is the ability to deduce structure from time-varying auditory and visual stimuli, enabling humans to master the rules of language and to build rich expectations of their physical environment. The broad relevance of this ability for human cognition motivates the need for a first-principles model explicating putative mechanisms. Here we propose a general framework for structural learningin the brain, composed of an evolving, high-dimensional dynamical system driven by external stimuli or internal processes. We operationalize the scenario in which humans learn the rules that generate a sequence of stimuli, rather than the exemplar stimuli themselves. We model external stimuli as seemingly disordered chaotic time series generated by complex dynamical systems; the underlying structure being deduced is then that of the corresponding chaotic attractor . This approach allows us to demonstrate and theoretically explain the emergence of five distinct phenomena reminiscent of cognitive functions: (i) learning the structure of a chaotic system purely from  time series, (ii) generating new streams of stimuli from a chaotic system, (iii) switching stream generation among multiple learned chaotic systems , either spontaneously or in response to external perturbations , (iv) inferring missing data from sparse observations of the chaotic system, and (v) deciphering superimposed input from different chaotic systems. Numerically, we show that these phenomena emerge naturally from a recurrent neural network of Erdos-Renyi topology in which the synaptic strengths adapt in a Hebbian-like manner. Broadly, our work blends chaotic theory and artificial neural networks to answer the long standing question of how neural systems can learn the structure underlying temporal sequences of stimuli .
Regardless of the marked differences between biological and artificial neural systems, one fundamental similarity is that they are essentially dynamical systems that can learn to imitate other dynamical systems, without knowing their governing equations. The brain is able to learn the dynamic nature of the physical world via experience; analogously, artificial neural systems can learn the long-term behavior of complex dynamical systems from data. Yet, precisely how this implicit learning occurs remains unknown. Here, we draw inspiration from human neuroscience and from reservoir computing to propose a first-principles framework explicating putative mechanisms of implicit learning. Specifically, we show that an arbitrary dynamical system implicitly learns other dynamical attractors by embedding them into its own phase space through invertible generalized synchronization. By sustaining the embedding through fine-tuned feedback loops, the arbitrary dynamical system can imitate the attractor dynamics it has learned. To evaluate the mechanism's relevance, we construct several distinct neural network models that adaptively learn and imitate multiple attractors. We observe and explain the emergence of 5 distinct phenomena reminiscent of cognitive functions: (i) imitating a dynamical system purely from learning the time series, (ii) learning multiple attractors by a single system, (iii) switching among the imitations of multiple attractors , either spontaneously or driven by external cues , (iv) filling-in missing variables from incomplete observations of a learned dynamical system, and (v) deciphering superimposed input from different dynamical systems. Collectively, our findings support the notion that artificial and biological neural networks can learn the dynamic nature of their environment, and systems within their environment, through the mechanism of invertible generalized synchronization .
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The human brain is capable of diverse feats of intelligence. A particularly salient example is the ability to deduce structure from time-varying auditory and visual stimuli, enabling humans to master the rules of language and to build rich expectations of their physical environment. The broad relevance of this ability for human cognition motivates the need for a first-principles model explicating putative mechanisms. Here we propose a general framework for structural learningin the brain, composed of an evolving, high-dimensional dynamical system driven by external stimuli or internal processes. We operationalize the scenario in which humans learn the rules that generate a sequence of stimuli, rather than the exemplar stimuli themselves. We model external stimuli as seemingly disordered chaotic time series generated by complex dynamical systems; the underlying structure being deduced is then that of the corresponding chaotic attractor . This approach allows us to demonstrate and theoretically
Regardless of the marked differences between biological and artificial neural systems, one fundamental similarity is that they are essentially dynamical systems that can learn to imitate other dynamical systems, without knowing their governing equations. The brain is able to learn the dynamic nature of the physical world via experience; analogously, artificial neural systems can learn the long-term behavior of complex dynamical systems from data. Yet, precisely how this implicit learning occurs remains unknown. Here, we draw inspiration from human neuroscience and from reservoir computing to propose a first-principles framework explicating putative mechanisms of implicit learning. Specifically, we show that an arbitrary dynamical system implicitly learns other dynamical attractors by embedding them into its own phase space through invertible generalized synchronization. By sustaining the embedding through fine-tuned feedback loops, the arbitrary dynamical system can imitate the attractor dynamics it has learned. To evaluate the mechanism's relevance, we construct several distinct neural network models that adaptively learn and imitate multiple attractors. We observe and
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five
5
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learning the structure of a chaotic
imitating a dynamical
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learning the
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generating new streams of stimuli from a chaotic
learning multiple attractors by a single
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stream generation among multiple learned chaotic systems
among the imitations of multiple attractors
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in response to external perturbations
driven by external cues
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inferring missing data from sparse observations of the chaotic
filling-in missing variables from incomplete observations of a learned dynamical
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chaotic systems. Numerically, we show that these phenomena emerge naturally from a recurrent neural network of Erdos-Renyi topology in which the synaptic strengths adapt in a Hebbian-like manner. Broadly, our work blends chaotic theory and artificial neural networks to answer the long standing question of how neural systems
dynamical systems. Collectively, our findings support the notion that artificial and biological neural networks
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structure underlying temporal sequences of stimuli
dynamic nature of their environment, and systems within their environment, through the mechanism of invertible generalized synchronization