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The Neural Heat Exchanger

First consider a conventional, physical heat exchanger. See Figure 1 (C). There are two touching water pipes with opposite flow direction. Cold water enters the first pipe. Hot water enters the second pipe. But hot water exits the first pipe, and cold water exits the second pipe! At any given point where both pipes touch, their temperatures are the same (provided the water speed is low enough to allow for sufficient temperature exchange). Entirely local interaction can lead to a complete reversal of global, macroscopic properties such as temperature. Physical heat exchangers are common in technical applications (e.g., nuclear power plants) and animals, e.g., rodents (Geoff Hinton, personal communication, 1994).

Figure 1: (A) shows two water pipes that dont touch. Cold water enters and exits the first pipe. Hot water enters and exits the second pipe. (B) shows two touching water pipes with equal flow direction. Cold water enters the first pipe. Hot water enters the second pipe. Lukewarm water exits both. (C) shows two touching water pipes with opposite flow direction (a heat exchanger). Cold water enters the first pipe to become hot water. Hot water enters the second pipe to become cold water.

Basic idea. In analogy to the physical heat exchanger, I build a ``Neural Heat Exchanger. There are two multi-layer feedforward networks with opposite flow direction. They correspond to the pipes. Both nets have the same number of layers. They are aligned such that each nets input layer is ``next to the other nets output layer, and each hidden layer in the first net is ``next to exactly one hidden layer in the other net. Input patterns enter the first net and are propagated ``up. Desired outputs (targets) enter the ``opposite net and are propagated ``down. Using the local, simple delta rule, each layer in each net tries to be similar (in information content) to the preceding layer and to the corresponding layer in the other net. The input entering the first net slowly ``heats up to become the target. The target entering the opposite net slowly ``cools down to become the input. No global control mechanism is required. See Figure 2 and details below.

Figure: The Neural Heat Exchanger requires two multi-layer feedforward nets with opposite flow direction. Each nets input layer is next to the other nets output layer. Each hidden layer in the upper net is next to exactly one hidden layer in the lower net. Input patterns enter the upper net and are propagated to the right. Desired outputs (targets) enter the lower net and are propagated to the left. Each layer in each net tries to be similar to the preceding layer and to the corresponding layer in the other net. For example, consider the black unit: two dotted lines connect the black unit to those two units it tries to match using the simple delta rule. Inputs entering the upper net slowly ``heat up to become like the targets. Targets entering the lower net slowly ``cool down to become like the inputs. No global control mechanism is required.

Architecture. See Figure 2. The first pipe corresponds to a feedforward network with n layers , , ..., . Each unit in has directed connections to each unit in , . The second pipe corresponds to a feedforward network with n layers , , ..., . Each unit in has directed connections to each unit in , . For simplicity, let all layers have m units. The

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