AI 中文总结
研究线性高斯主动推理中认知价值缺失问题，提出状态依赖观测噪声方法，通过耦合协方差R(x)与潜在均值，使后验协方差和卡尔曼增益依赖行动，恢复认知驱动力，弥合对偶控制与主动推理差距。
AI 中文摘要
近期研究表明，在主动推理下，线性高斯状态空间模型在任何情况下都会失去认知驱动力。预期自由能的认知项变为常数，智能体退化为卡尔曼滤波器，其增益序列预先固定，与行动无关。恢复驱动力的最小偏离尚不清楚，唯一已知途径是控制以乘法形式进入动力学，而该边界的观测方面尚未探索。本文表明状态依赖观测噪声就是这样一种偏离：协方差R(x)随状态x变化，代表传感器精度随距离下降。智能体运行文献中的标准一阶高斯滤波器，在预测均值处评估R。将R(x)与可控潜在均值耦合，使后验协方差以及有效卡尔曼增益依赖于行动。因此，没有固定的线性高斯滤波器能重现智能体，在观测映射的温和秩条件和R(x)的非退化条件下，认知价值不再恒定；对于标量观测，仅需可达到的非恒定即可。这是智能体保持协方差中Bar-Shalom-Tse对偶效应的最小构造实例：行动现在影响未来估计的质量，而不仅仅是状态。我们的库cpomdp仅从模型规范中检测不兼容性，并引发类型化的IncompatibleLinearizationError。该定理附带一个可执行见证：展示任何能重现智能体信念的固定滤波器将同时反驳定理和见证。这共同为高斯智能体中的好奇心提供了精确的观测方面特征，弥合了对偶控制和主动推理之间的差距。
英文摘要
Recent work established that under active inference, linear-Gaussian state-space models lose their epistemic drive (any incentive to act so as to gain information) "under any circumstances". The epistemic term of the Expected Free Energy becomes constant: the agent flattens to a Kalman filter whose gain sequence is fixed in advance, regardless of action. The minimal departure that restores the drive is unknown; the only established route is control entering the dynamics multiplicatively; the observation side of this boundary is unexplored. We show that state-dependent observation noise is such a departure: a covariance R(x) that varies with the state x, representing a sensor's accuracy degrading with range. The agent runs the standard first-order Gaussian filter of this literature, R evaluated at the predicted mean. Coupling R(x) to a controllable latent mean makes the posterior covariance, and hence the effective Kalman gain, depend on the action. Consequently, no fixed linear-Gaussian filter reproduces the agent and, under a mild rank condition on the observation map and a non-degeneracy condition on R(x), epistemic value is no longer constant; for scalar observations, reachable non-constancy alone is needed. This is a minimal constructive instance of the Bar-Shalom-Tse dual effect in the agent's maintained covariance: actions now influence the quality of future estimates, not merely the state. Our library cpomdp detects the incompatibility from model specification alone and raises a typed IncompatibleLinearizationError. The theorem ships with an executable witness: exhibiting any fixed filter that reproduced the agent's beliefs would refute both theorem and witness at once. Together this offers a precise, observation-side characterisation of curiosity in a Gaussian agent, bridging dual control and active inference.
Comments44 pages, 2 figures. Companion software: cpomdp v0.4.2, archived at https://doi.org/10.5281/zenodo.21429863; development repository at https://github.com/inferogenesis/cpomdp
