To generate actions in the face of physiological delays, the brain must predict the future. Here we explore how prediction may lie at the core of brain function by considering a neuron predicting the future of a scalar time series input. Assuming that the dynamics of the lag vector (a vector composed of several consecutive elements of the time series) are locally linear, Normal Mode Decomposition decomposes the dynamics into independently evolving (eigen-)modes allowing for straightforward prediction. We propose that a neuron learns the top mode and projects its input onto the associated subspace. Under this interpretation, the temporal filter of a neuron corresponds to the left eigenvector of a generalized eigenvalue problem. We mathematically analyze the operation of such an algorithm on noisy observations of synthetic data generated by a linear system. Interestingly, the shape of the temporal filter varies with the signal-to-noise ratio (SNR): a noisy input yields a monophasic filter and a growing SNR leads to multiphasic filters with progressively greater number of phases. Such variation in the temporal filter with input SNR resembles that observed experimentally in biological neurons.

翻译：为了在生理延迟下产生行动，大脑必须预测未来。本文通过考虑神经元对标量时间序列输入的未来预测，探讨预测可能构成大脑功能核心的机制。假设滞后向量（由时间序列中若干连续元素构成的向量）的动态具有局部线性特征，正则模式分解将动态分解为独立演化的（特征）模态，从而实现直接预测。我们提出神经元学习主要模态并将其输入投影到关联子空间。在此解释框架下，神经元的时域滤波器对应于广义特征值问题的左特征向量。我们从数学角度分析了该算法在线性系统生成的含噪合成数据上的运行特性。有趣的是，时域滤波器的形状随信噪比变化：低信噪比输入产生单相滤波器，而信噪比升高则导致多相滤波器且相位数量逐步增加。这种时域滤波器随输入信噪比变化的特性与生物神经元实验中观察到的现象相似。