Data from: Probability matching in perceptrons: effects of conditional dependence and linear nonseparability

Probability matching occurs when the behavior of an agent matches the likelihood of occurrence of events in the agent's environment. For instance, when artificial neural networks match probability, the activity in their output unit equals the past probability of reward in the presence of a stimulus. Our previous research demonstrated that simple artificial neural networks (perceptrons, which consist of a set of input units directly connected to a single output unit) learn to match probability when presented different cues in isolation. The current paper extends this research by showing that perceptrons can match probabilities when presented simultaneous cues, with each cue signaling different reward likelihoods. In our first simulation, we presented up to four different cues simultaneously; the likelihood of reward signaled by the presence of one cue was independent of the likelihood of reward signaled by other cues. Perceptrons learned to match reward probabilities by treating each cue as an independent source of information about the likelihood of reward. In a second simulation, we violated the independence between cues by making some reward probabilities depend upon cue interactions. We did so by basing reward probabilities on a logical combination (AND or XOR) of two of the four possible cues. We also varied the size of the reward associated with the logical combination. We discovered that this latter manipulation was a much better predictor of perceptron performance than was the logical structure of the interaction between cues. This indicates that when perceptrons learn to match probabilities, they do so by assuming that each signal of a reward is independent of any other; the best predictor of perceptron performance is a quantitative measure of the independence of these input signals, and not the logical structure of the problem being learned.概率匹配（probability matching）指当智能体的行为与其所处环境中事件的发生概率相匹配时的现象。例如，当人工神经网络（artificial neural network）进行概率匹配时，其输出单元的激活值等于该刺激条件下过往的奖励发生概率。我们此前的研究表明，简单的人工神经网络——即感知机（perceptron），由一组直接连接至单个输出单元的输入单元构成——在单独呈现不同线索时，能够学会进行概率匹配。本研究将前述工作拓展至多线索同时呈现的场景，结果表明感知机仍可完成概率匹配，且每条线索各自对应不同的奖励发生概率。在第一项仿真实验中，我们同时呈现最多4条不同的线索，且单条线索所标记的奖励发生概率与其他线索所标记的奖励概率相互独立。感知机通过将每条线索视为奖励概率的独立信息来源，学会了匹配奖励概率。在第二项仿真实验中，我们通过让部分奖励概率依赖于线索间的交互作用，打破了线索间的概率独立性假设：具体方式为将奖励概率设定为4条可选线索中任意两条的逻辑组合（与（AND）或异或（XOR））。我们同时调整了与该逻辑组合绑定的奖励规模。研究发现，相较于线索间交互的逻辑结构，该后续调整能更好地预测感知机的表现。这表明，感知机在学习进行概率匹配时，会默认每条奖励信号之间相互独立；因此，能够更好预测感知机表现的指标是输入信号独立性的量化测度，而非待学习任务的逻辑结构。