Making a decision among numerous alternatives is a pervasive and central undertaking encountered by mammals in natural settings. While decision making for two-option tasks has been studied extensively both experimentally and theoretically, characterizing decision making in the face of a large set of alternatives remains challenging. We explore this issue by formulating a scalable mechanistic network model for decision making and analyzing the dynamics evoked given various potential network structures. In the case of a fully-connected network, we provide an analytical characterization of the model fixed points and their stability with respect to winner-take-all behavior for fair tasks. We compare several means of input integration, demonstrating a more gradual sigmoidal transfer function is likely evolutionarily advantageous relative to binary gain commonly utilized in engineered systems. We show via asymptotic analysis and numerical simulation that sigmoidal transfer functions with smaller steepness yield faster response times but depreciation in accuracy. However, in the presence of noise or degradation of connections, a sigmoidal transfer function garners significantly more robust and accurate decision-making dynamics. For fair tasks and sigmoidal gain, our model network also exhibits a stable parameter regime that produces high accuracy and persists across tasks with diverse numbers of alternatives and difficulties, satisfying physiological energetic constraints. In the case of more sparse and structured network topologies, including random, regular, and small-world connectivity, we show the high-accuracy parameter regime persists for biologically realistic connection densities. Our work shows how neural system architecture is potentially optimal in making economic, reliable, and advantageous decisions across tasks.

中文翻译：

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竞争性点火速率模型中的网络结构和输入集成，用于决策。

在众多替代方案中做出决定是哺乳动物在自然环境中所遇到的一项普遍而重要的任务。尽管在实验和理论上都对二选项任务的决策进行了广泛的研究，但面对大量备选方案时，表征决策仍然具有挑战性。我们通过制定用于决策的可扩展机械网络模型并分析给定各种潜在网络结构引起的动态来探索此问题。在完全连接的网络中，我们提供了模型定点及其相对于公平任务的赢家通吃行为的稳定性的分析表征。我们比较了几种输入集成方式，相对于工程系统中通常使用的二进制增益，证明更渐进的S型传递函数可能在进化上是有利的。我们通过渐近分析和数值模拟表明，具有较小陡度的S形传递函数会产生更快的响应时间，但精度会下降。但是，在存在噪音或连接质量下降的情况下，S形传递函数会明显提高鲁棒性和准确性。对于公平任务和S形增益，我们的模型网络还展现出稳定的参数体系，该参数体系可产生高精度，并在具有多种选择和难度的任务之间持续存在，满足了生理上的精力旺盛的约束。如果网络拓扑较为稀疏和结构化，包括随机，常规，和小世界的连通性，我们显示了对于生物现实的连接密度而言，高精度参数机制仍然存在。我们的工作表明，在跨任务做出经济，可靠和有利的决策时，神经系统体系结构可能是最佳的。