Next: 2.1. SELF-REFERENTIAL' DYNAMICS AND Up: selfref Previous: 1. INTRODUCTION

# 2. THE INTROSPECTIVE' NETWORK

Throughout the remainder of this paper, to save indices, I consider a single limited pre-specified time-interval of discrete time-steps during which our network interacts with its environment. An interaction sequence actually may be the concatenation of many conventional' training sequences for conventional recurrent networks. This will (in theory) help our self-referential' weight matrix to find regularities among solutions for different tasks. The network's output vector at time , , is computed from previous input vectors , by a discrete time recurrent network with input units and non-input units. A subset of the non-input units, the normal' output units, has a cardinality of .

is the -th unit in the network. is the -th non-input unit in the network. is the -th normal' input unit in the network. is the -th normal' output unit. If stands for a unit, then is its differentiable activation function and 's activation at time is denoted by . If stands for a vector, then is the -th component of .

Each input unit has a directed connection to each non-input unit. Each non-input unit has a directed connection to each non-input unit. There are connections in the network. The connection from unit to unit is denoted by . For instance, one of the names of the connection from the -th normal' input unit to the the -th normal' output unit is . 's real-valued weight at time is denoted by . Before training, all weights are randomly initialized.

The following features are needed to obtain self-reference'. Details of the network dynamics follow in the next section.

1. The network receives performance information through the eval units, which are special input units. is the -th eval unit (of such units) in the network.

2. Each connection of the net gets an address. One way of doing this is to introduce a binary address, , for each connection . This will help the network to do computations concerning its own weights in terms of activations, as will be seen later.

3. is the -th analyzing unit (of such units, where returns the first integer ). The analyzing units are special non-input units. They serve to indicate which connections the current algorithm of the network (defined by the current weight matrix plus the current activations) will access next (see next section). A special input unit for reading current weight values that is used in conjunction with the analyzing units is called .

4. The network may modify any of its weights. Some non-input units that are not normal' output units or analyzing units are called the modifying units. is the -th modifying unit (of such units). The modifying units serve to address connections to be modified. A special output unit for modifying weights (used in conjunction with the modifying units, see next section) is called . should allow both positive and negative activations .

Subsections

Next: 2.1. SELF-REFERENTIAL' DYNAMICS AND Up: selfref Previous: 1. INTRODUCTION
Juergen Schmidhuber 2003-02-21

Back to Metalearning page
Back to Recurrent Neural Networks page