Reliable quantification of uncertainty estimates in continuous-time (CT) representation learning remains nascent, particularly within CT attention architectures. We introduce the Neuronal Stochastic Attention Circuit (NSAC), a novel biologically-inspired CT attention architecture that reformulates attention logit computation as the solution of an Ornstein-Uhlenbeck stochastic differential equation modulated by input-dependent, nonlinear interlinked gates derived from repurposed C.elegans Neuronal Circuit Policies (NCPs) wiring mechanism. It induces Gaussian distribution over logits that propagates principled stochasticity through logistic-normal distribution over attention weights to yield probabilistic output. A two-term objective function combining Gaussian negative log-likelihood with an epistemic-separation regularizer enforces higher predictive variance and enables joint quantification of aleatoric and epistemic uncertainty. Empirically, we implement NSAC in a diverse set of learning tasks including: (i) irregular CT function approximation; (ii) multivariate regression; (iii) long-range forecasting; (iv) Industry 4.0; and (v) the lane-keeping of autonomous vehicles. We observe that the NSAC remains competitive against several baselines in terms of accuracy and produces reasonably well-calibrated uncertainty estimates while being interpretable at the neuronal cell level.

翻译：连续时间表征学习中不确定性估计的可靠量化仍处于起步阶段，尤其在连续时间注意力架构中。我们提出神经元随机注意力电路（NSAC），这是一种新颖的受生物启发的连续时间注意力架构，它将注意力对数计算重新表述为奥恩斯坦-乌伦贝克随机微分方程的解，该方程由基于输入的非线性互连门调控，这些门源于复用的秀丽隐杆线虫神经元回路策略（NCP）布线机制。该模型在对数上诱导高斯分布，通过注意力权重上的逻辑正态分布传播有原则的随机性，从而产生概率输出。一个结合高斯负对数似然与认知分离正则化项的双项目标函数，强制提高预测方差，并能够联合量化偶然不确定性和认知不确定性。实证中，我们将NSAC应用于多种学习任务，包括：（i）不规则连续时间函数逼近；（ii）多变量回归；（iii）长期预测；（iv）工业4.0；以及（v）自动驾驶车辆的车道保持。我们观察到，NSAC在准确性上与多种基线方法保持竞争力，同时产生合理校准的不确定性估计，并在神经细胞层面具有可解释性。