Neural units with time-dependent functionality
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866913511229095936 |
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| author | Whitelam, Stephen |
| author_facet | Whitelam, Stephen |
| contents | We show that the time-resolved dynamics of an underdamped harmonic oscillator can be used to do multifunctional computation, performing distinct computations at distinct times within a single dynamical trajectory. We consider the amplitude of an oscillator whose inputs influence its frequency. The activity of the oscillator at fixed time is a nonmonotonic function of its inputs, and so it can solve problems such as XOR that are not linearly separable. The activity of the oscillator at fixed input is a nonmonotonic function of time, and so it is multifunctional in a temporal sense, able to carry out distinct nonlinear computations at distinct times within the same dynamical trajectory. We show that a single oscillator, observed at different times, can act as all of the elementary logic gates and can perform binary addition, the latter usually implemented in hardware using 5 logic gates. We show that a set of $n$ oscillators, observed at different times, can perform an arbitrary number of analog-to-$n$-bit digital conversions. We also show that oscillators can be trained by gradient descent to perform distinct classification tasks at distinct times. Computing with time-dependent functionality can be done in or out of equilibrium, and suggests a way of reducing the number of parameters or devices required to do nonlinear computations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_15545 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Neural units with time-dependent functionality Whitelam, Stephen Statistical Mechanics Neural and Evolutionary Computing We show that the time-resolved dynamics of an underdamped harmonic oscillator can be used to do multifunctional computation, performing distinct computations at distinct times within a single dynamical trajectory. We consider the amplitude of an oscillator whose inputs influence its frequency. The activity of the oscillator at fixed time is a nonmonotonic function of its inputs, and so it can solve problems such as XOR that are not linearly separable. The activity of the oscillator at fixed input is a nonmonotonic function of time, and so it is multifunctional in a temporal sense, able to carry out distinct nonlinear computations at distinct times within the same dynamical trajectory. We show that a single oscillator, observed at different times, can act as all of the elementary logic gates and can perform binary addition, the latter usually implemented in hardware using 5 logic gates. We show that a set of $n$ oscillators, observed at different times, can perform an arbitrary number of analog-to-$n$-bit digital conversions. We also show that oscillators can be trained by gradient descent to perform distinct classification tasks at distinct times. Computing with time-dependent functionality can be done in or out of equilibrium, and suggests a way of reducing the number of parameters or devices required to do nonlinear computations. |
| title | Neural units with time-dependent functionality |
| topic | Statistical Mechanics Neural and Evolutionary Computing |
| url | https://arxiv.org/abs/2404.15545 |