Agents acting in the natural world aim at selecting appropriate actions based on noisy and partial sensory observations. Many behaviors leading to decision mak- ing and action selection in a closed loop setting are naturally phrased within a control theoretic framework. Within the framework of optimal Control Theory, one is usually given a cost function which is minimized by selecting a control law based on the observations. While in standard control settings the sensors are assumed fixed, biological systems often gain from the extra flexibility of optimiz- ing the sensors themselves. However, this sensory adaptation is geared towards control rather than perception, as is often assumed. In this work we show that sen- sory adaptation for control differs from sensory adaptation for perception, even for simple control setups. This implies, consistently with recent experimental results, that when studying sensory adaptation, it is essential to account for the task being performed.

Restricted Boltzmann Machines (RBMs) are generative models which can learn useful representations from samples of a dataset in an unsupervised fashion. They have been widely employed as an unsupervised pre-training method in machine learning. RBMs have been modified to model time series in two main ways: The Temporal RBM stacks a number of RBMs laterally and introduces temporal dependencies between the hidden layer units; The Conditional RBM, on the other hand, considers past samples of the dataset as a conditional bias and learns a representation which takes these into account. Here we propose a new training method for both the TRBM and the CRBM, which enforces the dynamic structure of temporal datasets. We do so by treating the temporal models as denoising autoencoders, considering past frames of the dataset as corrupted versions of the present frame and minimizing the reconstruction error of the present data by the model. We call this approach Temporal Autoencoding. This leads to a significant improvement in the performance of both models in a filling-in-frames task across a number of datasets. The error reduction for motion capture data is 56\% for the CRBM and 80\% for the TRBM. Taking the posterior mean prediction instead of single samples further improves the model's estimates, decreasing the error by as much as 91\% for the CRBM on motion capture data. We also trained the model to perform forecasting on a large number of datasets and have found TA pretraining to consistently improve the performance of the forecasts. Furthermore, by looking at the prediction error across time, we can see that this improvement reflects a better representation of the dynamics of the data as opposed to a bias towards reconstructing the observed data on a short time scale.

Much work has been done refining and characterizing the receptive fields learned by deep learning algorithms. A lot of this work has focused on the development of Gabor-like filters learned when enforcing sparsity constraints on a natural image dataset. Little work however has investigated how these filters might expand to the temporal domain, namely through training on natural movies. Here we investigate exactly this problem in established temporal deep learning algorithms as well as a new learning paradigm suggested here, the Temporal Autoencoding Restricted Boltzmann Machine (TARBM).