# Factored Conditional Restricted Boltzmann Machines

In this section we present a new model, based on the CRBM, that
explicitly captures contextual information. Our model preserves the
CRBM's most important computational properties and includes
multiplicative three-way interactions that allow the effective
interaction weight between two units to be modulated by the dynamic
state of a third unit. We factor the three-way weight tensor
implied by the multiplicative model, reducing the number of parameters
from O(N^{3}) to O(N^{2}). Again we demonstrate our model's
effectiveness by modeling human motion. The three-way interactions
greatly improve the model's ability to blend motion styles or to
transition smoothly among them.

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### 4.6.1 Modeling with discrete style labels

We use a factored CRBM with three-way, multiplicative interactions to
synthesize transitions and blends between two styles. Note that the
training data does not contain transitions nor blends.

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### 4.6.2 Modeling with real-valued style parameters

Here the architecture is identical to that in Section 4.6.1, except that instead of gating interactions by real-valued features connected to discrete labels, we gate directly by real-valued style variables. In our experiment, we use two style variables: stride length and speed. This video shows real-time online generation at 30fps (the video itself is only 10fps). We can manipulate the stride length and speed variables during generation, which changes the effective weights in the model. The hidden units and motion respond to the changing of these variables, producing smooth interpolation and extrapolation beyond the 9 discrete settings of the variables with which the model was trained.

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