We present an AI-assisted framework for predicting individual runs of complex quantum experiments, including contextuality and causality (adaptive measurements), within our long-term programme of discovering a local hidden-variable theory that extends quantum theory. In order to circumvent impossibility theorems, we replace the assumption of free choice (measurement independence and parameter independence) with a weaker, compatibilistic version called contingent free choice. Our framework is based on interpreting complex quantum experiments as a Chess-like game between observers and the universe, which is seen as an economic agent minimizing action. The game structures corresponding to generic experiments such as fixed-causal-order process matrices or causal contextuality scenarios, together with a deterministic non-Nashian resolution algorithm that abandons unilateral deviation assumptions (free choice) and assumes Perfect Prediction instead, were described in previous work. In this new research, we learn the reward functions of the game, which contain a hidden variable, using neural networks. The cost function is the Kullback-Leibler divergence between the frequency histograms obtained through many deterministic runs of the game and the predictions of the extended Born rule. Using our framework on the specific case of the EPR 2-2-2 experiment acts as a proof-of-concept and a toy local-realist hidden-variable model that non-Nashian quantum theory is a promising avenue towards a local hidden-variable theory. Our framework constitutes a solid foundation, which can be further expanded in order to fully discover a complete quantum theory.

翻译：我们提出了一种人工智能辅助框架，用于预测复杂量子实验（包括语境性与因果性（自适应测量））的个体运行结果，这是我们长期计划的一部分，旨在发现一种扩展量子理论的局域隐变量理论。为了规避不可能性定理，我们用一种更弱的、兼容论版本的"偶然自由选择"取代了自由选择假设（测量独立性与参数独立性）。我们的框架基于将复杂量子实验解释为观测者与宇宙之间类似国际象棋的博弈，其中宇宙被视为最小化作用量的经济主体。先前的研究已描述了对应一般性实验（如固定因果序过程矩阵或因果语境性场景）的博弈结构，以及一种确定性非纳什均衡求解算法，该算法摒弃了单边偏离假设（自由选择）并代之以完美预测假设。在这项新研究中，我们使用神经网络学习包含隐变量的博弈奖励函数。成本函数采用游戏多次确定性运行获得的频率直方图与扩展玻恩规则预测之间的Kullback-Leibler散度。将我们的框架应用于EPR 2-2-2实验的具体案例，既可作为概念验证，也可作为玩具局域实在论隐变量模型，表明非纳什均衡量子理论是通往局域隐变量理论的一条有前景的途径。我们的框架构成了坚实的研究基础，可通过进一步扩展以完整发现完备的量子理论。