Non-Markovian Momentum Computing: Universal and Efficient

Ray, Kyle J.; Wimsatt, Gregory W.; Boyd, Alexander B.; Crutchfield, James P.

doi:10.48550/arxiv.2010.01152

Cited by 2 publications

(5 citation statements)

References 32 publications

(50 reference statements)

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“…Such an efficient swap operation has been demonstrated in finite time [94]. The resulting joint distribution over the ancillary and primary system matches a flip of the desired computation:…”

Section: Appendix E Thermodynamically Efficient Markov Channelsmentioning

confidence: 88%

“…This is what we would expect in quasistatic computations, where the system energies E(z, t) are varied slowly enough that the system Z remains in equilibrium for the duration. We should note, though, that it is possible to implement efficient computations rapidly and out of equilibrium [94]. This also holds if we average over intermediate states of the SOI's state trajectory, yielding the work production of a computational map:…”

Section: A32 Input-output Machinesmentioning

confidence: 99%

“…This is described by detailed-balanced rate equations. However, if our physical state-space is limited to Z, then not all channels can be implemented with continuous-time rate equations [94]. Fortunately, this can be circumvented by additional ancillary or hidden states [94,98].…”

Section: Appendix E Thermodynamically Efficient Markov Channelsmentioning

confidence: 99%

“…However, if our physical state-space is limited to Z, then not all channels can be implemented with continuous-time rate equations [94]. Fortunately, this can be circumvented by additional ancillary or hidden states [94,98]. And so, to implement any possible channel, we add an ancillary copy of our original system Z , such that our entire physical system is Z total = Z × Z .…”

Section: Appendix E Thermodynamically Efficient Markov Channelsmentioning

confidence: 99%

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Thermodynamic machine learning through maximum work production

Boyd

Crutchfield

2022

New J. Phys.

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Adaptive systems---such as a biological organism gaining survival advantage, an autonomous robot executing a functional task, or a motor protein transporting intracellular nutrients---must model the regularities and stochasticity in their environments to take full advantage of thermodynamic resources. Analogously, but in a purely computational realm, machine learning algorithms estimate models to capture predictable structure and identify irrelevant noise in training data. This happens through optimization of performance metrics, such as model likelihood. If physically implemented, is there a sense in which computational models estimated through machine learning are physically preferred? We introduce the thermodynamic principle that work production is the most relevant performance metric for an adaptive physical agent and compare the results to the maximum-likelihood principle that guides machine learning. Within the class of physical agents that most efficiently harvest energy from their environment, we demonstrate that an efficient agent's model explicitly determines its architecture and how much useful work it harvests from the environment. We then show that selecting the maximum-work agent for given environmental data corresponds to finding the maximum-likelihood model. This establishes an equivalence between nonequilibrium thermodynamics and dynamic learning. In this way, work maximization emerges as an organizing principle that underlies learning in adaptive thermodynamic systems.

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Section: Appendix E Thermodynamically Efficient Markov Channelsmentioning

confidence: 88%

Section: A32 Input-output Machinesmentioning

confidence: 99%

Section: Appendix E Thermodynamically Efficient Markov Channelsmentioning

confidence: 99%

Section: Appendix E Thermodynamically Efficient Markov Channelsmentioning

confidence: 99%

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Thermodynamic machine learning through maximum work production

Boyd

Crutchfield

2022

New J. Phys.

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“…Moreover, the dissipation diverges with the effectiveness of the computation, elevating the importance of logical reversibility in designing efficient computations. This suggests that a transition to reversible universal logic gates, like the Fredkin gate [25,26], may provide considerable energetic benefits beyond Landauer's bound.…”

Section: Discussionmentioning

confidence: 99%

Time Symmetries of Memory Determine Thermodynamic Efficiency

Boyd

Riechers²,

Wimsatt

et al. 2021

Preprint

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While Landauer's Principle sets a lower bound for the work required for a computation, that work is recoverable for efficient computations. However, practical physical computers, such as modern digital computers or biochemical systems, are subject to constraints that make them inefficientirreversibly dissipating significant energy. Recent results show that the dissipation in such systems is bounded by the nonreciprocity of the embedded computation. We investigate the consequences of this bound for different types of memory, showing that different memory devices are better suited for different computations. This correspondence comes from the time-reversal symmetries of the memory, which depend on whether information is stored positionally or magnetically. This establishes that the time symmetries of the memory device play an essential roll in determining energetics. The energetic consequences of time symmetries are particularly pronounced in nearly deterministic computations, where the cost of computing diverges as minus log of the error rate. We identify the coefficient of that divergence as the dissipation divergence. We find that the dissipation divergence may be zero for a computation when implemented in one type of memory while it's maximal when implemented with another. Given flexibility in the type of memory, the dissipation divergence is bounded below by the average state compression of the computation. Moreover, we show how to explicitly construct the memory to achieve this minimal dissipation. As a result, we find that logically reversible computations are indeed thermodynamically efficient, but logical irreversibility comes at a much higher cost than previously anticipated.

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Non-Markovian Momentum Computing: Universal and Efficient

Cited by 2 publications

References 32 publications

Thermodynamic machine learning through maximum work production

Thermodynamic machine learning through maximum work production

Time Symmetries of Memory Determine Thermodynamic Efficiency

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