What we learn from the learning rate

Abstract

The learning rate is an information-theoretical quantity for bipartite Markov chains describing two coupled subsystems. It is defined as the rate at which transitions in the downstream subsystem tend to increase the mutual information between the two subsystems, and is bounded by the dissipation arising from these transitions. Its physical interpretation, however, is unclear, although it has been used as a metric for the sensing performance of the downstream subsystem. In this paper, we explore the behaviour of the learning rate for a number of simple model systems, establishing when and how its behaviour is distinct from the instantaneous mutual information between subsystems. In the simplest case, the two are almost equivalent. In more complex steady-state systems, the mutual information and the learning rate behave qualitatively distinctly, with the learning rate clearly now reflecting the rate at which the downstream system must update its information in response to changes in the upstream system. It is not clear whether this quantity is the most natural measure for sensor performance, and, indeed, we provide an example in which optimising the learning rate over a region of parameter space of the downstream system yields an apparently sub-optimal sensor.

arXiv comment12 pages, 9 figures. Revised due to referees' comments. Extra comment on equation 7, terminology of 'information affinity' used, additional explanation in sections III.B. and IV., order of figures 5(a) and 5(b) reversed, typos corrected

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Cited by in corpus (11)

• Theory of nonequilibrium free energy transduction by molecular machines
• Energy and information flows in autonomous systems
• Role of sufficient statistics in stochastic thermodynamics and its implication to sensory adaptation
• The behaviour of information flow near criticality
• Internal energy and information flows mediate input and output power in bipartite molecular machines
• Free-energy transduction within autonomous systems
• Thermodynamics of collective enhancement of precision
• A universal lower bound on the free energy cost of molecular measurements
• Energy dissipation and information flow in coupled Markovian systems
• Dissipation in non-steady state regulatory circuits
• Information-thermodynamic characterization of stochastic Boolean networks