Fundamental performance bounds on time-series generation using reservoir computing
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909378846654464 |
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| author | Qian, Daoyuan Fiete, Ila |
| author_facet | Qian, Daoyuan Fiete, Ila |
| contents | Reservoir computing (RC) harnesses the intrinsic dynamics of a chaotic system, called the reservoir, to perform various time-varying functions. An important use-case of RC is the generation of target temporal sequences via a trainable output-to-reservoir feedback loop. Despite the promise of RC in various domains, we lack a theory of performance bounds on RC systems. Here, we formulate an existence condition for a feedback loop that produces the target sequence. We next demonstrate that, given a sufficiently chaotic neural network reservoir, two separate factors are needed for successful training: global network stability of the target orbit, and the ability of the training algorithm to drive the system close enough to the target, which we term `reach'. By computing the training phase diagram over a range of target output amplitudes and periods, we verify that reach-limited failures depend on the training algorithm while stability-limited failures are invariant across different algorithms. We leverage dynamical mean field theory (DMFT) to provide an analytical amplitude-period bound on achievable outputs by RC networks and propose a way of enhancing algorithm reach via forgetting. The resulting mechanistic understanding of RC performance can guide the future design and deployment of reservoir networks. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_20393 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fundamental performance bounds on time-series generation using reservoir computing Qian, Daoyuan Fiete, Ila Chaotic Dynamics Reservoir computing (RC) harnesses the intrinsic dynamics of a chaotic system, called the reservoir, to perform various time-varying functions. An important use-case of RC is the generation of target temporal sequences via a trainable output-to-reservoir feedback loop. Despite the promise of RC in various domains, we lack a theory of performance bounds on RC systems. Here, we formulate an existence condition for a feedback loop that produces the target sequence. We next demonstrate that, given a sufficiently chaotic neural network reservoir, two separate factors are needed for successful training: global network stability of the target orbit, and the ability of the training algorithm to drive the system close enough to the target, which we term `reach'. By computing the training phase diagram over a range of target output amplitudes and periods, we verify that reach-limited failures depend on the training algorithm while stability-limited failures are invariant across different algorithms. We leverage dynamical mean field theory (DMFT) to provide an analytical amplitude-period bound on achievable outputs by RC networks and propose a way of enhancing algorithm reach via forgetting. The resulting mechanistic understanding of RC performance can guide the future design and deployment of reservoir networks. |
| title | Fundamental performance bounds on time-series generation using reservoir computing |
| topic | Chaotic Dynamics |
| url | https://arxiv.org/abs/2410.20393 |