Genewein Tim, Braun Daniel A
Max Planck Institute for Biological Cybernetics, Spemannstr. 38, 72076, Tübingen, Germany.
Max Planck Institute for Intelligent Systems, Tübingen, Germany.
Biol Cybern. 2016 Jun;110(2-3):135-50. doi: 10.1007/s00422-016-0684-8. Epub 2016 Mar 29.
Bayesian inference and bounded rational decision-making require the accumulation of evidence or utility, respectively, to transform a prior belief or strategy into a posterior probability distribution over hypotheses or actions. Crucially, this process cannot be simply realized by independent integrators, since the different hypotheses and actions also compete with each other. In continuous time, this competitive integration process can be described by a special case of the replicator equation. Here we investigate simple analog electric circuits that implement the underlying differential equation under the constraint that we only permit a limited set of building blocks that we regard as biologically interpretable, such as capacitors, resistors, voltage-dependent conductances and voltage- or current-controlled current and voltage sources. The appeal of these circuits is that they intrinsically perform normalization without requiring an explicit divisive normalization. However, even in idealized simulations, we find that these circuits are very sensitive to internal noise as they accumulate error over time. We discuss in how far neural circuits could implement these operations that might provide a generic competitive principle underlying both perception and action.
贝叶斯推理和有界理性决策分别需要积累证据或效用，以便将先验信念或策略转化为关于假设或行动的后验概率分布。至关重要的是，这个过程不能简单地由独立的积分器来实现，因为不同的假设和行动也会相互竞争。在连续时间里，这种竞争性整合过程可以用复制者方程的一个特殊情况来描述。在这里，我们研究了简单的模拟电路，这些电路在我们只允许一组有限的、我们认为具有生物学可解释性的构建模块（如电容器、电阻器、电压依赖性电导以及电压或电流控制的电流和电压源）的约束下实现基础微分方程。这些电路的吸引力在于它们内在地执行归一化，而无需显式的除法归一化。然而，即使在理想化模拟中，我们发现这些电路随着时间积累误差，对内部噪声非常敏感。我们讨论了神经回路在多大程度上可以实现这些操作，这些操作可能为感知和行动提供一个通用的竞争原则。
