3. The RFs of the hidden units are spatially located across the entire image patch with some distinct clustering along the borders (Fig. 3A). In 2D

Fourier space (Fig. 3B) one can see a good coverage of the space, representing frequency and direction selectivity, both these results being in agreeance with those found in similar studies (see Cadieu and Olshausen, 2012 and Bell and Sejnowski, 1997, for example). The filters also display Crenolanib price a preference for cardinal (horizontal and vertical) orientations (Fig. 3C), a phenomenon that has often been reported in electrophysiological experiments of primary visual cortex (e.g. Wang et al., 2003 and Coppola et al., 1998). We then analysed how the static filters are connected through the temporal weights learned during autoencoder training by visualizing their evolution over time. The filters discussed were learned by the aTRBM (see Eq. (1)) with our training algorithm described in Section 4.1.3. To visualize the dynamic RF of a hidden unit we clamped the activation

of that unit to 1 and set all other units to be inactive in the most delayed layer of the aTRBM. We then proceeded to sample from the distribution of all other hidden layers and chose the most active units in every delay. This is shown in Fig. 4. We have shown the most active units when a hidden unit is active for the 80 units with highest temporal variation among the subsequent filters. This, however, only gives us a superficial look into the dynamics of the RFs. One way to look Crizotinib nmr Y-27632 2HCl further is to consider the n   most active units at the second-furthest delay and then sequentially clamp each of these to an active

state and look at the resulting activations in the remaining layers. If one does this sequentially, we are left with a tree of active units, 1 at time t−Tt−T, n   at time t−(T−1)t−(T−1), and nT at time t. We can then look at what these units code for. We have performed this procedure with two hidden units, and to visualize what they code for we have plotted the center of mass of the filters in frequency and position space. This is shown in Fig. 5. Visualizing the temporal RFs learnt by the CRBM is simpler than for the aTRBM. We display the weight matrix WW and the temporal weights W1W1 to WdWd for each hidden unit directly as a projection into the visible layer (a 20×20 patch). This shows the temporal dependence of each hidden unit on the past visible layer activations and is plotted with time running from top to bottom in Fig. 4B. The aTRBM learns richer filter dynamics with a longer temporal dependency, whereas the CRBM only seems to care about the visible layers at times t   and t−1t−1, possibly because most of the variation is captured by the visible-to-visible weights.