Current state-of-the-art dynamical models, such as Mamba, assume the same level of noisiness for all elements of a given sequence, which limits their performance on noisy temporal data. In this paper, we introduce the $\alpha$-Alternator, a novel generative model for time-dependent data that dynamically adapts to the complexity introduced by varying noise levels in sequences. The $\alpha$-Alternator leverages the Vendi Score (VS), a flexible similarity-based diversity metric, to adjust, at each time step $t$, the influence of the sequence element at time $t$ and the latent representation of the dynamics up to that time step on the predicted future dynamics. This influence is captured by a parameter that is learned and shared across all sequences in a given dataset. The sign of this parameter determines the direction of influence. A negative value indicates a noisy dataset, where a sequence element that increases the VS is considered noisy, and the model relies more on the latent history when processing that element. Conversely, when the parameter is positive, a sequence element that increases the VS is considered informative, and the $\alpha$-Alternator relies more on this new input than on the latent history when updating its predicted latent dynamics. The $\alpha$-Alternator is trained using a combination of observation masking and Alternator loss minimization. Masking simulates varying noise levels in sequences, enabling the model to be more robust to these fluctuations and improving its performance in trajectory prediction, imputation, and forecasting. Our experimental results demonstrate that the $\alpha$-Alternator outperforms both Alternators and state-of-the-art state-space models across neural decoding and time-series forecasting benchmarks.

翻译：当前最先进的动态模型（如Mamba）假设给定序列的所有元素具有相同的噪声水平，这限制了其在含噪时序数据上的性能。本文提出α-交替器，这是一种面向时间依赖数据的新型生成模型，能够动态适应序列中变化噪声水平带来的复杂性。α-交替器利用Vendi分数（一种基于相似性的灵活多样性度量），在每一时间步t动态调整当前时刻序列元素与截至该时刻的动态潜表示对预测未来动态的影响权重。该影响权重由一个参数表征，该参数在给定数据集的所有序列中共享并通过学习获得。参数的正负决定了影响方向：当参数为负时，表明数据集噪声较高，此时增加VS的序列元素被视为噪声，模型在处理该元素时更依赖于潜历史信息；反之，当参数为正时，增加VS的序列元素被视为信息载体，α-交替器在更新其预测潜动态时会更依赖新输入而非潜历史。α-交替器通过结合观测掩码与交替器损失最小化进行训练。掩码操作模拟序列中变化的噪声水平，使模型对这些波动更具鲁棒性，从而提升其在轨迹预测、数据插补和时序预测任务中的性能。实验结果表明，在神经解码与时间序列预测基准测试中，α-交替器的性能均优于传统交替器模型及最先进的基于状态空间的模型。